Lecture 3: Protein sequences and protein similarity

class: center, middle, inverse, title-slide

.title[
# Lecture 3: Protein sequences and protein similarity
]
.subtitle[
## BE_22 Bioinformatics SS 21
]
.author[
### January Weiner
]
.date[
### 2024-04-22
]

---

# Why do we need sequence similarity, phylogeny and structure prediction?

---

## We lack information!

![:scale 80%](images/genes_citations.png)

*Huss et al. “The Gene Wiki: community intelligence applied to human gene
annotation”. 2010. Nucleic Acids Res. 38:D633-D639. doi:10.1093/nar/gkp760*

---

## We lack information and we will lack information

.pull-left[
![:scale 75%](images/genes_grants.jpg)
]

.pull-right[
* top: literature
* bottom: grant funding
]

*Su and Hogenesch. “Power-law-like distributions in biomedical publications
and research funding”. 2007. Genome Biol. 8(4):404.  doi:10.1186/gb-2007-8-4-404*

---

## How bioinformatics can help

* Evolutionary relationships allow to find orthologous proteins with
   conserved functions
    * we need phylogeny 
    * we need sequence similarity
 * Structural bioinformatics allows to predict protein structures and
   protein-protein interactions
    * we need structure prediction from sequences
 * Modern deep learning structure prediction methods use both (evolutionary
   relationships + structural predictions) to accurately predict protein
   structures.

In any case, we need to understand AA sequences!

---

## The genetic code ✪

<table class="table" style="font-size: 12px; margin-left: auto; margin-right: auto;">
 <thead>
<tr>
<th style="empty-cells: hide;border-bottom:hidden;" colspan="1"></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="4"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Second position in a codon</div></th>
</tr>
  <tr>
   <th style="text-align:left;"> First position </th>
   <th style="text-align:left;"> T </th>
   <th style="text-align:left;"> C </th>
   <th style="text-align:left;"> A </th>
   <th style="text-align:left;"> G </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> T </td>
   <td style="text-align:left;color: #000000 !important;"> TTT F (Phe) </td>
   <td style="text-align:left;color: #000000 !important;"> TCT S (Ser) </td>
   <td style="text-align:left;color: #000000 !important;"> TAT Y (Tyr) </td>
   <td style="text-align:left;color: #000000 !important;"> TGT C (Cys) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> TTC F (Phe) </td>
   <td style="text-align:left;color: #000000 !important;"> TCC S (Ser) </td>
   <td style="text-align:left;color: #000000 !important;"> TAC Y (Tyr) </td>
   <td style="text-align:left;color: #000000 !important;"> TGC C (Cys) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> TTA L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;"> TCA S (Ser) </td>
   <td style="text-align:left;color: #BB0000 !important;"> TAA * (STP) </td>
   <td style="text-align:left;color: #BB0000 !important;"> TGA * (STP) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> TTG L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;"> TCG S (Ser) </td>
   <td style="text-align:left;color: #BB0000 !important;"> TAG * (STP) </td>
   <td style="text-align:left;color: #000000 !important;"> TGG W (Trp) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> C </td>
   <td style="text-align:left;color: #000000 !important;"> CTT L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;"> CCT P (Pro) </td>
   <td style="text-align:left;color: #000000 !important;"> CAT H (His) </td>
   <td style="text-align:left;color: #000000 !important;"> CGT R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> CTC L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;"> CCC P (Pro) </td>
   <td style="text-align:left;color: #000000 !important;"> CAC H (His) </td>
   <td style="text-align:left;color: #000000 !important;"> CGC R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> CTA L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;"> CCA P (Pro) </td>
   <td style="text-align:left;color: #000000 !important;"> CAA Q (Gln) </td>
   <td style="text-align:left;color: #000000 !important;"> CGA R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> CTG L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;"> CCG P (Pro) </td>
   <td style="text-align:left;color: #000000 !important;"> CAG Q (Gln) </td>
   <td style="text-align:left;color: #000000 !important;"> CGG R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> A </td>
   <td style="text-align:left;color: #000000 !important;"> ATT I (Ile) </td>
   <td style="text-align:left;color: #000000 !important;"> ACT T (Thr) </td>
   <td style="text-align:left;color: #000000 !important;"> AAT N (Asn) </td>
   <td style="text-align:left;color: #000000 !important;"> AGT S (Ser) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> ATC I (Ile) </td>
   <td style="text-align:left;color: #000000 !important;"> ACC T (Thr) </td>
   <td style="text-align:left;color: #000000 !important;"> AAC N (Asn) </td>
   <td style="text-align:left;color: #000000 !important;"> AGC S (Ser) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> ATA I (Ile) </td>
   <td style="text-align:left;color: #000000 !important;"> ACA T (Thr) </td>
   <td style="text-align:left;color: #000000 !important;"> AAA K (Lys) </td>
   <td style="text-align:left;color: #000000 !important;"> AGA R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> ATG M (Met) </td>
   <td style="text-align:left;color: #000000 !important;"> ACG T (Thr) </td>
   <td style="text-align:left;color: #000000 !important;"> AAG K (Lys) </td>
   <td style="text-align:left;color: #000000 !important;"> AGG R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> G </td>
   <td style="text-align:left;color: #000000 !important;"> GTT V (Val) </td>
   <td style="text-align:left;color: #000000 !important;"> GCT A (Ala) </td>
   <td style="text-align:left;color: #000000 !important;"> GAT D (Asp) </td>
   <td style="text-align:left;color: #000000 !important;"> GGT G (Gly) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> GTC V (Val) </td>
   <td style="text-align:left;color: #000000 !important;"> GCC A (Ala) </td>
   <td style="text-align:left;color: #000000 !important;"> GAC D (Asp) </td>
   <td style="text-align:left;color: #000000 !important;"> GGC G (Gly) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> GTA V (Val) </td>
   <td style="text-align:left;color: #000000 !important;"> GCA A (Ala) </td>
   <td style="text-align:left;color: #000000 !important;"> GAA E (Glu) </td>
   <td style="text-align:left;color: #000000 !important;"> GGA G (Gly) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> GTG V (Val) </td>
   <td style="text-align:left;color: #000000 !important;"> GCG A (Ala) </td>
   <td style="text-align:left;color: #000000 !important;"> GAG E (Glu) </td>
   <td style="text-align:left;color: #000000 !important;"> GGG G (Gly) </td>
  </tr>
</tbody>
</table>

---

## The genetic code: variants ✪

```
Standard SGC0
Vertebrate Mitochondrial SGC1
Yeast Mitochondrial SGC2
Mold Mitochondrial; Protozoan Mitochondrial; Coelenterate Mitochondrial; Mycoplasma; Spiroplasma SGC3
Invertebrate Mitochondrial SGC4
Ciliate Nuclear; Dasycladacean Nuclear; Hexamita Nuclear SGC5
Echinoderm Mitochondrial; Flatworm Mitochondrial SGC8
Euplotid Nuclear SGC9
Bacterial and Plant Plastid
Alternative Yeast Nuclear
Ascidian Mitochondrial
Alternative Flatworm Mitochondrial
Blepharisma Macronuclear
Chlorophycean Mitochondrial
Trematode Mitochondrial
Scenedesmus obliquus Mitochondrial
Thraustochytrium Mitochondrial
```

---

## The genetic code: Protozoan mitochondrial, Mycoplasma

.pull-left[

<table class="table" style="font-size: 11px; margin-left: auto; margin-right: auto;">
 <thead>
<tr>
<th style="empty-cells: hide;border-bottom:hidden;" colspan="1"></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="4"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Second position in a codon</div></th>
</tr>
  <tr>
   <th style="text-align:left;"> First position </th>
   <th style="text-align:left;"> T </th>
   <th style="text-align:left;"> C </th>
   <th style="text-align:left;"> A </th>
   <th style="text-align:left;"> G </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> T </td>
   <td style="text-align:left;color: #000000 !important;"> TTT F (Phe) </td>
   <td style="text-align:left;color: #000000 !important;"> TCT S (Ser) </td>
   <td style="text-align:left;color: #000000 !important;"> TAT Y (Tyr) </td>
   <td style="text-align:left;color: #000000 !important;"> TGT C (Cys) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> TTC F (Phe) </td>
   <td style="text-align:left;color: #000000 !important;"> TCC S (Ser) </td>
   <td style="text-align:left;color: #000000 !important;"> TAC Y (Tyr) </td>
   <td style="text-align:left;color: #000000 !important;"> TGC C (Cys) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> TTA L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;"> TCA S (Ser) </td>
   <td style="text-align:left;color: #BB0000 !important;"> TAA * (STP) </td>
   <td style="text-align:left;color: #BB0000 !important;"> TGA * (STP) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> TTG L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;"> TCG S (Ser) </td>
   <td style="text-align:left;color: #BB0000 !important;"> TAG * (STP) </td>
   <td style="text-align:left;color: #000000 !important;"> TGG W (Trp) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> C </td>
   <td style="text-align:left;color: #000000 !important;"> CTT L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;"> CCT P (Pro) </td>
   <td style="text-align:left;color: #000000 !important;"> CAT H (His) </td>
   <td style="text-align:left;color: #000000 !important;"> CGT R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> CTC L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;"> CCC P (Pro) </td>
   <td style="text-align:left;color: #000000 !important;"> CAC H (His) </td>
   <td style="text-align:left;color: #000000 !important;"> CGC R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> CTA L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;"> CCA P (Pro) </td>
   <td style="text-align:left;color: #000000 !important;"> CAA Q (Gln) </td>
   <td style="text-align:left;color: #000000 !important;"> CGA R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> CTG L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;"> CCG P (Pro) </td>
   <td style="text-align:left;color: #000000 !important;"> CAG Q (Gln) </td>
   <td style="text-align:left;color: #000000 !important;"> CGG R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> A </td>
   <td style="text-align:left;color: #000000 !important;"> ATT I (Ile) </td>
   <td style="text-align:left;color: #000000 !important;"> ACT T (Thr) </td>
   <td style="text-align:left;color: #000000 !important;"> AAT N (Asn) </td>
   <td style="text-align:left;color: #000000 !important;"> AGT S (Ser) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> ATC I (Ile) </td>
   <td style="text-align:left;color: #000000 !important;"> ACC T (Thr) </td>
   <td style="text-align:left;color: #000000 !important;"> AAC N (Asn) </td>
   <td style="text-align:left;color: #000000 !important;"> AGC S (Ser) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> ATA I (Ile) </td>
   <td style="text-align:left;color: #000000 !important;"> ACA T (Thr) </td>
   <td style="text-align:left;color: #000000 !important;"> AAA K (Lys) </td>
   <td style="text-align:left;color: #000000 !important;"> AGA R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> ATG M (Met) </td>
   <td style="text-align:left;color: #000000 !important;"> ACG T (Thr) </td>
   <td style="text-align:left;color: #000000 !important;"> AAG K (Lys) </td>
   <td style="text-align:left;color: #000000 !important;"> AGG R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> G </td>
   <td style="text-align:left;color: #000000 !important;"> GTT V (Val) </td>
   <td style="text-align:left;color: #000000 !important;"> GCT A (Ala) </td>
   <td style="text-align:left;color: #000000 !important;"> GAT D (Asp) </td>
   <td style="text-align:left;color: #000000 !important;"> GGT G (Gly) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> GTC V (Val) </td>
   <td style="text-align:left;color: #000000 !important;"> GCC A (Ala) </td>
   <td style="text-align:left;color: #000000 !important;"> GAC D (Asp) </td>
   <td style="text-align:left;color: #000000 !important;"> GGC G (Gly) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> GTA V (Val) </td>
   <td style="text-align:left;color: #000000 !important;"> GCA A (Ala) </td>
   <td style="text-align:left;color: #000000 !important;"> GAA E (Glu) </td>
   <td style="text-align:left;color: #000000 !important;"> GGA G (Gly) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;"> GTG V (Val) </td>
   <td style="text-align:left;color: #000000 !important;"> GCG A (Ala) </td>
   <td style="text-align:left;color: #000000 !important;"> GAG E (Glu) </td>
   <td style="text-align:left;color: #000000 !important;"> GGG G (Gly) </td>
  </tr>
</tbody>
</table>

Standard SGC0

]

.pull-right[

<table class="table" style="font-size: 11px; margin-left: auto; margin-right: auto;">
 <thead>
<tr>
<th style="empty-cells: hide;border-bottom:hidden;" colspan="1"></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="4"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Second position in a codon</div></th>
</tr>
  <tr>
   <th style="text-align:left;"> First position </th>
   <th style="text-align:left;"> T </th>
   <th style="text-align:left;"> C </th>
   <th style="text-align:left;"> A </th>
   <th style="text-align:left;"> G </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> T </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TTT F (Phe) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TCT S (Ser) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TAT Y (Tyr) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TGT C (Cys) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TTC F (Phe) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TCC S (Ser) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TAC Y (Tyr) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TGC C (Cys) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TTA L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TCA S (Ser) </td>
   <td style="text-align:left;color: #BB0000 !important;background-color: #FFFFFF !important;"> TAA * (STP) </td>
   <td style="text-align:left;color: #FFFFFF !important;background-color: #CC0000 !important;"> TGA W (Trp) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TTG L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TCG S (Ser) </td>
   <td style="text-align:left;color: #BB0000 !important;background-color: #FFFFFF !important;"> TAG * (STP) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TGG W (Trp) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> C </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CTT L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CCT P (Pro) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CAT H (His) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CGT R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CTC L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CCC P (Pro) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CAC H (His) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CGC R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CTA L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CCA P (Pro) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CAA Q (Gln) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CGA R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CTG L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CCG P (Pro) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CAG Q (Gln) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CGG R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> A </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> ATT I (Ile) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> ACT T (Thr) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> AAT N (Asn) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> AGT S (Ser) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> ATC I (Ile) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> ACC T (Thr) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> AAC N (Asn) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> AGC S (Ser) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> ATA I (Ile) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> ACA T (Thr) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> AAA K (Lys) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> AGA R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> ATG M (Met) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> ACG T (Thr) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> AAG K (Lys) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> AGG R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> G </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GTT V (Val) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GCT A (Ala) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GAT D (Asp) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GGT G (Gly) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GTC V (Val) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GCC A (Ala) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GAC D (Asp) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GGC G (Gly) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GTA V (Val) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GCA A (Ala) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GAA E (Glu) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GGA G (Gly) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GTG V (Val) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GCG A (Ala) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GAG E (Glu) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GGG G (Gly) </td>
  </tr>
</tbody>
</table>

Mold Mitochondrial; Protozoan Mitochondrial; Coelenterate Mitochondrial; Mycoplasma; Spiroplasma SGC3

]

---

## The genetic code: Vertebrate Mitochondrial SGC1

.pull-left[

Standard SGC0

]

.pull-right[

<table class="table" style="font-size: 11px; margin-left: auto; margin-right: auto;">
 <thead>
<tr>
<th style="empty-cells: hide;border-bottom:hidden;" colspan="1"></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="4"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Second position in a codon</div></th>
</tr>
  <tr>
   <th style="text-align:left;"> First position </th>
   <th style="text-align:left;"> T </th>
   <th style="text-align:left;"> C </th>
   <th style="text-align:left;"> A </th>
   <th style="text-align:left;"> G </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> T </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TTT F (Phe) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TCT S (Ser) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TAT Y (Tyr) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TGT C (Cys) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TTC F (Phe) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TCC S (Ser) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TAC Y (Tyr) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TGC C (Cys) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TTA L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TCA S (Ser) </td>
   <td style="text-align:left;color: #BB0000 !important;background-color: #FFFFFF !important;"> TAA * (STP) </td>
   <td style="text-align:left;color: #FFFFFF !important;background-color: #CC0000 !important;"> TGA W (Trp) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TTG L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TCG S (Ser) </td>
   <td style="text-align:left;color: #BB0000 !important;background-color: #FFFFFF !important;"> TAG * (STP) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> TGG W (Trp) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> C </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CTT L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CCT P (Pro) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CAT H (His) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CGT R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CTC L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CCC P (Pro) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CAC H (His) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CGC R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CTA L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CCA P (Pro) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CAA Q (Gln) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CGA R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CTG L (Leu) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CCG P (Pro) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CAG Q (Gln) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> CGG R (Arg) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> A </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> ATT I (Ile) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> ACT T (Thr) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> AAT N (Asn) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> AGT S (Ser) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> ATC I (Ile) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> ACC T (Thr) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> AAC N (Asn) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> AGC S (Ser) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #FFFFFF !important;background-color: #CC0000 !important;"> ATA M (Met) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> ACA T (Thr) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> AAA K (Lys) </td>
   <td style="text-align:left;color: #FFFFFF !important;background-color: #CC0000 !important;"> AGA * (STP) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> ATG M (Met) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> ACG T (Thr) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> AAG K (Lys) </td>
   <td style="text-align:left;color: #FFFFFF !important;background-color: #CC0000 !important;"> AGG * (STP) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> G </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GTT V (Val) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GCT A (Ala) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GAT D (Asp) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GGT G (Gly) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GTC V (Val) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GCC A (Ala) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GAC D (Asp) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GGC G (Gly) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GTA V (Val) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GCA A (Ala) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GAA E (Glu) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GGA G (Gly) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ,, </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GTG V (Val) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GCG A (Ala) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GAG E (Glu) </td>
   <td style="text-align:left;color: #000000 !important;background-color: #FFFFFF !important;"> GGG G (Gly) </td>
  </tr>
</tbody>
</table>

Vertebrate Mitochondrial SGC1

]

---

## Reading frames ✪

```
A A T G G T G C T G T C T C C T G C C G A C A A G A C C A A C G T C A A G G T A  
```

```
A A T|G G T|G C T|G T C|T C C|T G C|C G A|C A A|G A C|C A A|C G T|C A A|G G T|A  
```

```
  N     
```

---

## Reading frames

```
A A T G G T G C T G T C T C C T G C C G A C A A G A C C A A C G T C A A G G T A  
```

```
A A T|G G T|G C T|G T C|T C C|T G C|C G A|C A A|G A C|C A A|C G T|C A A|G G T|A  
```

```
  N     G     
```

---

## Reading frames

```
A A T G G T G C T G T C T C C T G C C G A C A A G A C C A A C G T C A A G G T A  
```

```
A A T|G G T|G C T|G T C|T C C|T G C|C G A|C A A|G A C|C A A|C G T|C A A|G G T|A  
```

```
  N     G     A     V     S     C     R     Q     D     Q     R     Q     G   
```

```
A|A T G|G T G|C T G|T C T|C C T|G C C|G A C|A A G|A C C|A A C|G T C|A A G|G T A|

```

```
    M     V     L     S     P     A     D     K     T     N     V     K     V   
```

```
A A|T G G|T G C|T G T|C T C|C T G|C C G|A C A|A G A|C C A|A C G|T C A|A G G|T A  
```

```
      W     C     C     L     L     P     T     R     P     T     S     R   
```

---

## Reading frames: reverse complement

```
5'- A A T G G T G C T G T C T C C T G C C G A C A A G A C C A A C G T C A A G G T A -3'
```

```
3'- T T A C C A C G A C A G A G G A C G G C T G T T C T G G T T G C A G T T C C A T -5'
```

--
(in normal direction)

```
5'- T A C C T T G A C G T T G G T C T T G T C G G C A G G A G A C A G C A C C A T T -3'
```

```
      Y     L     D     V     G     L     V     G     R     R     Q     H     H

T     L     T     L     V     L     S     A     G     D     S     T     I

P     *     R     W     S     C     R     Q     E     T     A     P   
```

---

## Open reading frames

* By definition, an ORF is a protein sequence in a reading frame that ends with a stop codon ✪ 
 * However, sometimes any peptide sequence is referred to as an ORF (not
   correctly)
 * There are six possible reading frames, 3 on the forward strand and 3 on
   the reverse complement strand ✪

Why do we need them?

* Gene prediction

---
class:empty-slide,myinverse
background-image:url(images/aa_overview.png)

---

## AA properties ✪

![](images/aa_properties_0.png)

---

## AA properties ✪

![:scale 70%](images/aa_properties.jpg)

---

## AA properties ✪

Non-synonymous mutations (which change amino acids) can change the
structure and / or function of a protein.

They are more likely to change the function if the result is less similar:

<table>
<tbody>
  <tr>
   <td style="text-align:left;"> TTT (Phe) </td>
   <td style="text-align:left;"> Phenylalanine: a large, hydrophobic, aromatic AA </td>
  </tr>
  <tr>
   <td style="text-align:left;"> TTT (Phe) -&gt; TTC (Ser) </td>
   <td style="text-align:left;"> a tiny, polar AA </td>
  </tr>
  <tr>
   <td style="text-align:left;"> TTT (Phe) -&gt; TAC (Tyr) </td>
   <td style="text-align:left;"> another large, hydrophobic/polar, aromatic AA </td>
  </tr>
  <tr>
   <td style="text-align:left;"> GCT (Ala) </td>
   <td style="text-align:left;"> Alanine – small, alpha helix-forming AA </td>
  </tr>
  <tr>
   <td style="text-align:left;"> GCT (Ala) -&gt; CTC (Leu) </td>
   <td style="text-align:left;"> very similar, also alpha helix forming </td>
  </tr>
  <tr>
   <td style="text-align:left;"> GCT (Ala) -&gt; ACT (Thr) </td>
   <td style="text-align:left;"> threonine is beta-sheet forming </td>
  </tr>
  <tr>
   <td style="text-align:left;"> GCT (Ala) -&gt; CCT (Pro) </td>
   <td style="text-align:left;"> proline is a helix breaker! </td>
  </tr>
</tbody>
</table>

✪ Replacing an AA by a similar AA is less likely to lead to a loss of
function, therefore such substitutions happen more often in the course of
evolution.

---

## Aligning protein sequences

Basic idea: instead of using a score "match / mismatch", use a score which

* reflects the similarity between amino acids, or
 * reflects the frequency of given substitutions during evolution

---

???

Horizontal: original AA
Vertical: replacement AA

---

---

.pull-left[
<table class="table" style="font-size: 7px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> A </th>
   <th style="text-align:right;"> R </th>
   <th style="text-align:right;"> N </th>
   <th style="text-align:right;"> D </th>
   <th style="text-align:right;"> C </th>
   <th style="text-align:right;"> Q </th>
   <th style="text-align:right;"> E </th>
   <th style="text-align:right;"> G </th>
   <th style="text-align:right;"> H </th>
   <th style="text-align:right;"> I </th>
   <th style="text-align:right;"> L </th>
   <th style="text-align:right;"> K </th>
   <th style="text-align:right;"> M </th>
   <th style="text-align:right;"> F </th>
   <th style="text-align:right;"> P </th>
   <th style="text-align:right;"> S </th>
   <th style="text-align:right;"> T </th>
   <th style="text-align:right;"> W </th>
   <th style="text-align:right;"> Y </th>
   <th style="text-align:right;"> V </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> A </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(181, 222, 43, 1) !important;background-color: rgba(72, 40, 120, 1) !important;"> 624 </td>
   <td style="text-align:right;color: rgba(200, 224, 32, 1) !important;background-color: rgba(72, 31, 112, 1) !important;"> 434 </td>
   <td style="text-align:right;color: rgba(197, 224, 33, 1) !important;background-color: rgba(72, 32, 113, 1) !important;"> 368 </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 660 </td>
   <td style="text-align:right;color: rgba(119, 209, 83, 1) !important;background-color: rgba(64, 69, 136, 1) !important;"> 846 </td>
   <td style="text-align:right;color: rgba(117, 208, 84, 1) !important;background-color: rgba(64, 70, 136, 1) !important;"> 769 </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 1251 </td>
   <td style="text-align:right;color: rgba(160, 218, 57, 1) !important;background-color: rgba(70, 50, 126, 1) !important;"> 412 </td>
   <td style="text-align:right;color: rgba(213, 226, 26, 1) !important;background-color: rgba(72, 24, 106, 1) !important;"> 473 </td>
   <td style="text-align:right;color: rgba(189, 223, 38, 1) !important;background-color: rgba(72, 36, 117, 1) !important;"> 604 </td>
   <td style="text-align:right;color: rgba(160, 218, 57, 1) !important;background-color: rgba(70, 50, 126, 1) !important;"> 734 </td>
   <td style="text-align:right;color: rgba(72, 193, 110, 1) !important;background-color: rgba(54, 93, 141, 1) !important;"> 1309 </td>
   <td style="text-align:right;color: rgba(218, 227, 25, 1) !important;background-color: rgba(72, 22, 104, 1) !important;"> 396 </td>
   <td style="text-align:right;color: rgba(68, 57, 131, 1) !important;background-color: rgba(144, 215, 67, 1) !important;"> 903 </td>
   <td style="text-align:right;color: rgba(45, 112, 142, 1) !important;background-color: rgba(42, 176, 127, 1) !important;"> 2432 </td>
   <td style="text-align:right;color: rgba(127, 211, 78, 1) !important;background-color: rgba(66, 65, 134, 1) !important;"> 16 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 215 </td>
   <td style="text-align:right;color: rgba(223, 227, 24, 1) !important;background-color: rgba(71, 19, 101, 1) !important;"> 441 </td>
   <td style="text-align:right;color: rgba(88, 199, 101, 1) !important;background-color: rgba(58, 84, 140, 1) !important;"> 1585 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> R </td>
   <td style="text-align:right;color: rgba(92, 200, 99, 1) !important;background-color: rgba(59, 82, 139, 1) !important;"> 444 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(42, 176, 127, 1) !important;background-color: rgba(45, 112, 142, 1) !important;"> 757 </td>
   <td style="text-align:right;color: rgba(157, 217, 59, 1) !important;background-color: rgba(70, 51, 127, 1) !important;"> 374 </td>
   <td style="text-align:right;color: rgba(137, 213, 72, 1) !important;background-color: rgba(67, 61, 132, 1) !important;"> 158 </td>
   <td style="text-align:right;color: rgba(55, 91, 141, 1) !important;background-color: rgba(76, 194, 108, 1) !important;"> 1670 </td>
   <td style="text-align:right;color: rgba(50, 182, 122, 1) !important;background-color: rgba(48, 106, 142, 1) !important;"> 835 </td>
   <td style="text-align:right;color: rgba(82, 197, 105, 1) !important;background-color: rgba(56, 88, 140, 1) !important;"> 311 </td>
   <td style="text-align:right;color: rgba(31, 149, 139, 1) !important;background-color: rgba(34, 139, 141, 1) !important;"> 639 </td>
   <td style="text-align:right;color: rgba(234, 229, 26, 1) !important;background-color: rgba(71, 13, 96, 1) !important;"> 224 </td>
   <td style="text-align:right;color: rgba(218, 227, 25, 1) !important;background-color: rgba(72, 22, 104, 1) !important;"> 314 </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 2766 </td>
   <td style="text-align:right;color: rgba(162, 218, 55, 1) !important;background-color: rgba(70, 48, 126, 1) !important;"> 494 </td>
   <td style="text-align:right;color: rgba(248, 230, 33, 1) !important;background-color: rgba(69, 4, 87, 1) !important;"> 161 </td>
   <td style="text-align:right;color: rgba(49, 181, 123, 1) !important;background-color: rgba(47, 107, 142, 1) !important;"> 350 </td>
   <td style="text-align:right;color: rgba(147, 215, 65, 1) !important;background-color: rgba(69, 56, 130, 1) !important;"> 578 </td>
   <td style="text-align:right;color: rgba(160, 218, 57, 1) !important;background-color: rgba(70, 50, 126, 1) !important;"> 608 </td>
   <td style="text-align:right;color: rgba(168, 219, 52, 1) !important;background-color: rgba(71, 46, 124, 1) !important;"> 404 </td>
   <td style="text-align:right;color: rgba(202, 225, 31, 1) !important;background-color: rgba(72, 29, 111, 1) !important;"> 394 </td>
   <td style="text-align:right;color: rgba(234, 229, 26, 1) !important;background-color: rgba(71, 13, 96, 1) !important;"> 267 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> N </td>
   <td style="text-align:right;color: rgba(139, 214, 70, 1) !important;background-color: rgba(68, 59, 132, 1) !important;"> 216 </td>
   <td style="text-align:right;color: rgba(103, 204, 92, 1) !important;background-color: rgba(61, 77, 138, 1) !important;"> 530 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(72, 32, 113, 1) !important;background-color: rgba(197, 224, 33, 1) !important;"> 1237 </td>
   <td style="text-align:right;color: rgba(39, 173, 129, 1) !important;background-color: rgba(44, 114, 142, 1) !important;"> 164 </td>
   <td style="text-align:right;color: rgba(31, 152, 139, 1) !important;background-color: rgba(35, 136, 142, 1) !important;"> 807 </td>
   <td style="text-align:right;color: rgba(68, 191, 112, 1) !important;background-color: rgba(53, 95, 141, 1) !important;"> 518 </td>
   <td style="text-align:right;color: rgba(68, 59, 132, 1) !important;background-color: rgba(139, 214, 70, 1) !important;"> 527 </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 823 </td>
   <td style="text-align:right;color: rgba(231, 228, 25, 1) !important;background-color: rgba(71, 14, 97, 1) !important;"> 167 </td>
   <td style="text-align:right;color: rgba(246, 230, 32, 1) !important;background-color: rgba(69, 5, 89, 1) !important;"> 132 </td>
   <td style="text-align:right;color: rgba(58, 186, 118, 1) !important;background-color: rgba(50, 101, 142, 1) !important;"> 697 </td>
   <td style="text-align:right;color: rgba(176, 221, 47, 1) !important;background-color: rgba(71, 42, 122, 1) !important;"> 306 </td>
   <td style="text-align:right;color: rgba(226, 228, 24, 1) !important;background-color: rgba(71, 17, 100, 1) !important;"> 177 </td>
   <td style="text-align:right;color: rgba(32, 146, 140, 1) !important;background-color: rgba(33, 143, 141, 1) !important;"> 307 </td>
   <td style="text-align:right;color: rgba(31, 161, 136, 1) !important;background-color: rgba(39, 128, 142, 1) !important;"> 868 </td>
   <td style="text-align:right;color: rgba(84, 197, 104, 1) !important;background-color: rgba(57, 86, 140, 1) !important;"> 632 </td>
   <td style="text-align:right;color: rgba(246, 230, 32, 1) !important;background-color: rgba(69, 5, 89, 1) !important;"> 123 </td>
   <td style="text-align:right;color: rgba(189, 223, 38, 1) !important;background-color: rgba(72, 36, 117, 1) !important;"> 311 </td>
   <td style="text-align:right;color: rgba(226, 228, 24, 1) !important;background-color: rgba(71, 17, 100, 1) !important;"> 221 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> D </td>
   <td style="text-align:right;color: rgba(157, 217, 59, 1) !important;background-color: rgba(70, 51, 127, 1) !important;"> 218 </td>
   <td style="text-align:right;color: rgba(200, 224, 32, 1) !important;background-color: rgba(72, 31, 112, 1) !important;"> 311 </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 1468 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(129, 211, 77, 1) !important;background-color: rgba(66, 64, 134, 1) !important;"> 136 </td>
   <td style="text-align:right;color: rgba(55, 184, 120, 1) !important;background-color: rgba(49, 103, 142, 1) !important;"> 718 </td>
   <td style="text-align:right;color: rgba(69, 55, 129, 1) !important;background-color: rgba(149, 216, 64, 1) !important;"> 1600 </td>
   <td style="text-align:right;color: rgba(34, 140, 141, 1) !important;background-color: rgba(31, 148, 140, 1) !important;"> 422 </td>
   <td style="text-align:right;color: rgba(88, 199, 101, 1) !important;background-color: rgba(58, 84, 140, 1) !important;"> 343 </td>
   <td style="text-align:right;color: rgba(251, 231, 35, 1) !important;background-color: rgba(68, 2, 86, 1) !important;"> 97 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 129 </td>
   <td style="text-align:right;color: rgba(142, 214, 69, 1) !important;background-color: rgba(68, 58, 131, 1) !important;"> 493 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 89 </td>
   <td style="text-align:right;color: rgba(248, 230, 33, 1) !important;background-color: rgba(69, 4, 87, 1) !important;"> 131 </td>
   <td style="text-align:right;color: rgba(31, 162, 135, 1) !important;background-color: rgba(39, 126, 142, 1) !important;"> 329 </td>
   <td style="text-align:right;color: rgba(96, 202, 96, 1) !important;background-color: rgba(60, 80, 139, 1) !important;"> 650 </td>
   <td style="text-align:right;color: rgba(200, 224, 32, 1) !important;background-color: rgba(72, 31, 112, 1) !important;"> 393 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 131 </td>
   <td style="text-align:right;color: rgba(239, 229, 28, 1) !important;background-color: rgba(70, 10, 93, 1) !important;"> 207 </td>
   <td style="text-align:right;color: rgba(251, 231, 35, 1) !important;background-color: rgba(68, 2, 86, 1) !important;"> 143 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> C </td>
   <td style="text-align:right;color: rgba(84, 197, 104, 1) !important;background-color: rgba(57, 86, 140, 1) !important;"> 249 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 84 </td>
   <td style="text-align:right;color: rgba(231, 228, 25, 1) !important;background-color: rgba(71, 14, 97, 1) !important;"> 124 </td>
   <td style="text-align:right;color: rgba(234, 229, 26, 1) !important;background-color: rgba(71, 13, 96, 1) !important;"> 87 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 92 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 49 </td>
   <td style="text-align:right;color: rgba(173, 220, 48, 1) !important;background-color: rgba(71, 44, 122, 1) !important;"> 104 </td>
   <td style="text-align:right;color: rgba(176, 221, 47, 1) !important;background-color: rgba(71, 42, 122, 1) !important;"> 142 </td>
   <td style="text-align:right;color: rgba(226, 228, 24, 1) !important;background-color: rgba(71, 17, 100, 1) !important;"> 141 </td>
   <td style="text-align:right;color: rgba(229, 228, 25, 1) !important;background-color: rgba(71, 16, 99, 1) !important;"> 142 </td>
   <td style="text-align:right;color: rgba(248, 230, 33, 1) !important;background-color: rgba(69, 4, 87, 1) !important;"> 92 </td>
   <td style="text-align:right;color: rgba(202, 225, 31, 1) !important;background-color: rgba(72, 29, 111, 1) !important;"> 172 </td>
   <td style="text-align:right;color: rgba(197, 224, 33, 1) !important;background-color: rgba(72, 32, 113, 1) !important;"> 194 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 76 </td>
   <td style="text-align:right;color: rgba(189, 223, 38, 1) !important;background-color: rgba(72, 36, 117, 1) !important;"> 228 </td>
   <td style="text-align:right;color: rgba(234, 229, 26, 1) !important;background-color: rgba(71, 13, 96, 1) !important;"> 185 </td>
   <td style="text-align:right;color: rgba(251, 231, 35, 1) !important;background-color: rgba(68, 2, 86, 1) !important;"> 87 </td>
   <td style="text-align:right;color: rgba(231, 228, 25, 1) !important;background-color: rgba(71, 14, 97, 1) !important;"> 146 </td>
   <td style="text-align:right;color: rgba(210, 226, 27, 1) !important;background-color: rgba(72, 26, 108, 1) !important;"> 215 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Q </td>
   <td style="text-align:right;color: rgba(49, 181, 123, 1) !important;background-color: rgba(47, 107, 142, 1) !important;"> 380 </td>
   <td style="text-align:right;color: rgba(40, 125, 142, 1) !important;background-color: rgba(32, 163, 134, 1) !important;"> 1053 </td>
   <td style="text-align:right;color: rgba(43, 116, 142, 1) !important;background-color: rgba(37, 172, 130, 1) !important;"> 726 </td>
   <td style="text-align:right;color: rgba(32, 164, 134, 1) !important;background-color: rgba(40, 124, 142, 1) !important;"> 545 </td>
   <td style="text-align:right;color: rgba(112, 207, 87, 1) !important;background-color: rgba(63, 72, 137, 1) !important;"> 110 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 1426 </td>
   <td style="text-align:right;color: rgba(31, 153, 138, 1) !important;background-color: rgba(36, 135, 142, 1) !important;"> 293 </td>
   <td style="text-align:right;color: rgba(58, 84, 140, 1) !important;background-color: rgba(88, 199, 101, 1) !important;"> 573 </td>
   <td style="text-align:right;color: rgba(239, 229, 28, 1) !important;background-color: rgba(70, 10, 93, 1) !important;"> 120 </td>
   <td style="text-align:right;color: rgba(192, 223, 37, 1) !important;background-color: rgba(72, 35, 116, 1) !important;"> 261 </td>
   <td style="text-align:right;color: rgba(46, 109, 142, 1) !important;background-color: rgba(46, 179, 124, 1) !important;"> 1162 </td>
   <td style="text-align:right;color: rgba(34, 167, 133, 1) !important;background-color: rgba(41, 121, 142, 1) !important;"> 797 </td>
   <td style="text-align:right;color: rgba(234, 229, 26, 1) !important;background-color: rgba(71, 13, 96, 1) !important;"> 138 </td>
   <td style="text-align:right;color: rgba(41, 121, 142, 1) !important;background-color: rgba(34, 167, 133, 1) !important;"> 316 </td>
   <td style="text-align:right;color: rgba(68, 191, 112, 1) !important;background-color: rgba(53, 95, 141, 1) !important;"> 574 </td>
   <td style="text-align:right;color: rgba(90, 200, 100, 1) !important;background-color: rgba(58, 83, 139, 1) !important;"> 549 </td>
   <td style="text-align:right;color: rgba(147, 215, 65, 1) !important;background-color: rgba(69, 56, 130, 1) !important;"> 292 </td>
   <td style="text-align:right;color: rgba(173, 220, 48, 1) !important;background-color: rgba(71, 44, 122, 1) !important;"> 316 </td>
   <td style="text-align:right;color: rgba(213, 226, 26, 1) !important;background-color: rgba(72, 24, 106, 1) !important;"> 240 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> E </td>
   <td style="text-align:right;color: rgba(63, 188, 115, 1) !important;background-color: rgba(51, 98, 141, 1) !important;"> 544 </td>
   <td style="text-align:right;color: rgba(88, 199, 101, 1) !important;background-color: rgba(58, 84, 140, 1) !important;"> 831 </td>
   <td style="text-align:right;color: rgba(46, 179, 124, 1) !important;background-color: rgba(46, 109, 142, 1) !important;"> 735 </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 1914 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 92 </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 2250 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(90, 200, 100, 1) !important;background-color: rgba(58, 83, 139, 1) !important;"> 296 </td>
   <td style="text-align:right;color: rgba(34, 168, 132, 1) !important;background-color: rgba(42, 120, 142, 1) !important;"> 555 </td>
   <td style="text-align:right;color: rgba(234, 229, 26, 1) !important;background-color: rgba(71, 13, 96, 1) !important;"> 212 </td>
   <td style="text-align:right;color: rgba(239, 229, 28, 1) !important;background-color: rgba(70, 10, 93, 1) !important;"> 222 </td>
   <td style="text-align:right;color: rgba(31, 162, 135, 1) !important;background-color: rgba(39, 126, 142, 1) !important;"> 1257 </td>
   <td style="text-align:right;color: rgba(205, 225, 29, 1) !important;background-color: rgba(72, 28, 110, 1) !important;"> 317 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 139 </td>
   <td style="text-align:right;color: rgba(72, 41, 121, 1) !important;background-color: rgba(178, 221, 45, 1) !important;"> 667 </td>
   <td style="text-align:right;color: rgba(134, 213, 73, 1) !important;background-color: rgba(67, 62, 133, 1) !important;"> 626 </td>
   <td style="text-align:right;color: rgba(157, 217, 59, 1) !important;background-color: rgba(70, 51, 127, 1) !important;"> 616 </td>
   <td style="text-align:right;color: rgba(223, 227, 24, 1) !important;background-color: rgba(71, 19, 101, 1) !important;"> 243 </td>
   <td style="text-align:right;color: rgba(231, 228, 25, 1) !important;background-color: rgba(71, 14, 97, 1) !important;"> 282 </td>
   <td style="text-align:right;color: rgba(221, 227, 24, 1) !important;background-color: rgba(72, 20, 103, 1) !important;"> 335 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> G </td>
   <td style="text-align:right;color: rgba(33, 142, 141, 1) !important;background-color: rgba(32, 146, 140, 1) !important;"> 1292 </td>
   <td style="text-align:right;color: rgba(216, 226, 25, 1) !important;background-color: rgba(72, 23, 105, 1) !important;"> 452 </td>
   <td style="text-align:right;color: rgba(44, 177, 126, 1) !important;background-color: rgba(46, 111, 142, 1) !important;"> 1092 </td>
   <td style="text-align:right;color: rgba(110, 206, 88, 1) !important;background-color: rgba(62, 73, 137, 1) !important;"> 737 </td>
   <td style="text-align:right;color: rgba(80, 196, 106, 1) !important;background-color: rgba(56, 89, 140, 1) !important;"> 284 </td>
   <td style="text-align:right;color: rgba(162, 218, 55, 1) !important;background-color: rgba(70, 48, 126, 1) !important;"> 673 </td>
   <td style="text-align:right;color: rgba(192, 223, 37, 1) !important;background-color: rgba(72, 35, 116, 1) !important;"> 433 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(162, 218, 55, 1) !important;background-color: rgba(70, 48, 126, 1) !important;"> 418 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 142 </td>
   <td style="text-align:right;color: rgba(251, 231, 35, 1) !important;background-color: rgba(68, 2, 86, 1) !important;"> 237 </td>
   <td style="text-align:right;color: rgba(210, 226, 27, 1) !important;background-color: rgba(72, 26, 108, 1) !important;"> 488 </td>
   <td style="text-align:right;color: rgba(229, 228, 25, 1) !important;background-color: rgba(71, 16, 99, 1) !important;"> 317 </td>
   <td style="text-align:right;color: rgba(234, 229, 26, 1) !important;background-color: rgba(71, 13, 96, 1) !important;"> 327 </td>
   <td style="text-align:right;color: rgba(59, 187, 117, 1) !important;background-color: rgba(50, 100, 142, 1) !important;"> 485 </td>
   <td style="text-align:right;color: rgba(117, 208, 84, 1) !important;background-color: rgba(64, 70, 136, 1) !important;"> 1013 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 402 </td>
   <td style="text-align:right;color: rgba(241, 229, 29, 1) !important;background-color: rgba(70, 8, 92, 1) !important;"> 272 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 274 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 220 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> H </td>
   <td style="text-align:right;color: rgba(144, 215, 67, 1) !important;background-color: rgba(68, 57, 131, 1) !important;"> 164 </td>
   <td style="text-align:right;color: rgba(132, 212, 75, 1) !important;background-color: rgba(66, 63, 133, 1) !important;"> 357 </td>
   <td style="text-align:right;color: rgba(44, 113, 142, 1) !important;background-color: rgba(40, 174, 128, 1) !important;"> 656 </td>
   <td style="text-align:right;color: rgba(142, 214, 69, 1) !important;background-color: rgba(68, 58, 131, 1) !important;"> 230 </td>
   <td style="text-align:right;color: rgba(31, 152, 139, 1) !important;background-color: rgba(35, 136, 142, 1) !important;"> 150 </td>
   <td style="text-align:right;color: rgba(46, 179, 124, 1) !important;background-color: rgba(46, 109, 142, 1) !important;"> 508 </td>
   <td style="text-align:right;color: rgba(112, 207, 87, 1) !important;background-color: rgba(63, 72, 137, 1) !important;"> 312 </td>
   <td style="text-align:right;color: rgba(99, 203, 95, 1) !important;background-color: rgba(60, 79, 138, 1) !important;"> 161 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(246, 230, 32, 1) !important;background-color: rgba(69, 5, 89, 1) !important;"> 82 </td>
   <td style="text-align:right;color: rgba(246, 230, 32, 1) !important;background-color: rgba(69, 5, 89, 1) !important;"> 106 </td>
   <td style="text-align:right;color: rgba(149, 216, 64, 1) !important;background-color: rgba(69, 55, 129, 1) !important;"> 319 </td>
   <td style="text-align:right;color: rgba(216, 226, 25, 1) !important;background-color: rgba(72, 23, 105, 1) !important;"> 154 </td>
   <td style="text-align:right;color: rgba(218, 227, 25, 1) !important;background-color: rgba(72, 22, 104, 1) !important;"> 160 </td>
   <td style="text-align:right;color: rgba(152, 216, 62, 1) !important;background-color: rgba(69, 53, 129, 1) !important;"> 131 </td>
   <td style="text-align:right;color: rgba(173, 220, 48, 1) !important;background-color: rgba(71, 44, 122, 1) !important;"> 271 </td>
   <td style="text-align:right;color: rgba(165, 219, 54, 1) !important;background-color: rgba(71, 47, 125, 1) !important;"> 329 </td>
   <td style="text-align:right;color: rgba(197, 224, 33, 1) !important;background-color: rgba(72, 32, 113, 1) !important;"> 177 </td>
   <td style="text-align:right;color: rgba(53, 183, 121, 1) !important;background-color: rgba(49, 104, 142, 1) !important;"> 587 </td>
   <td style="text-align:right;color: rgba(244, 230, 30, 1) !important;background-color: rgba(70, 7, 90, 1) !important;"> 114 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> I </td>
   <td style="text-align:right;color: rgba(129, 211, 77, 1) !important;background-color: rgba(66, 64, 134, 1) !important;"> 375 </td>
   <td style="text-align:right;color: rgba(239, 229, 28, 1) !important;background-color: rgba(70, 10, 93, 1) !important;"> 250 </td>
   <td style="text-align:right;color: rgba(229, 228, 25, 1) !important;background-color: rgba(71, 16, 99, 1) !important;"> 266 </td>
   <td style="text-align:right;color: rgba(251, 231, 35, 1) !important;background-color: rgba(68, 2, 86, 1) !important;"> 130 </td>
   <td style="text-align:right;color: rgba(31, 154, 138, 1) !important;background-color: rgba(36, 134, 142, 1) !important;"> 297 </td>
   <td style="text-align:right;color: rgba(248, 230, 33, 1) !important;background-color: rgba(69, 4, 87, 1) !important;"> 211 </td>
   <td style="text-align:right;color: rgba(218, 227, 25, 1) !important;background-color: rgba(72, 22, 104, 1) !important;"> 237 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 109 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 164 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(45, 113, 142, 1) !important;background-color: rgba(41, 175, 127, 1) !important;"> 2145 </td>
   <td style="text-align:right;color: rgba(226, 228, 24, 1) !important;background-color: rgba(71, 17, 100, 1) !important;"> 298 </td>
   <td style="text-align:right;color: rgba(47, 107, 142, 1) !important;background-color: rgba(49, 181, 123, 1) !important;"> 2197 </td>
   <td style="text-align:right;color: rgba(108, 205, 90, 1) !important;background-color: rgba(62, 74, 137, 1) !important;"> 810 </td>
   <td style="text-align:right;color: rgba(210, 226, 27, 1) !important;background-color: rgba(72, 26, 108, 1) !important;"> 203 </td>
   <td style="text-align:right;color: rgba(244, 230, 30, 1) !important;background-color: rgba(70, 7, 90, 1) !important;"> 253 </td>
   <td style="text-align:right;color: rgba(173, 220, 48, 1) !important;background-color: rgba(71, 44, 122, 1) !important;"> 626 </td>
   <td style="text-align:right;color: rgba(226, 228, 24, 1) !important;background-color: rgba(71, 17, 100, 1) !important;"> 263 </td>
   <td style="text-align:right;color: rgba(210, 226, 27, 1) !important;background-color: rgba(72, 26, 108, 1) !important;"> 398 </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 4345 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> L </td>
   <td style="text-align:right;color: rgba(96, 202, 96, 1) !important;background-color: rgba(60, 80, 139, 1) !important;"> 766 </td>
   <td style="text-align:right;color: rgba(216, 226, 25, 1) !important;background-color: rgba(72, 23, 105, 1) !important;"> 559 </td>
   <td style="text-align:right;color: rgba(248, 230, 33, 1) !important;background-color: rgba(69, 4, 87, 1) !important;"> 336 </td>
   <td style="text-align:right;color: rgba(236, 229, 27, 1) !important;background-color: rgba(70, 11, 94, 1) !important;"> 276 </td>
   <td style="text-align:right;color: rgba(31, 152, 139, 1) !important;background-color: rgba(35, 136, 142, 1) !important;"> 476 </td>
   <td style="text-align:right;color: rgba(178, 221, 45, 1) !important;background-color: rgba(72, 41, 121, 1) !important;"> 739 </td>
   <td style="text-align:right;color: rgba(216, 226, 25, 1) !important;background-color: rgba(72, 23, 105, 1) !important;"> 398 </td>
   <td style="text-align:right;color: rgba(200, 224, 32, 1) !important;background-color: rgba(72, 31, 112, 1) !important;"> 291 </td>
   <td style="text-align:right;color: rgba(226, 228, 24, 1) !important;background-color: rgba(71, 17, 100, 1) !important;"> 337 </td>
   <td style="text-align:right;color: rgba(31, 148, 140, 1) !important;background-color: rgba(34, 140, 141, 1) !important;"> 3432 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(226, 228, 24, 1) !important;background-color: rgba(71, 17, 100, 1) !important;"> 473 </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 5271 </td>
   <td style="text-align:right;color: rgba(33, 166, 133, 1) !important;background-color: rgba(41, 122, 142, 1) !important;"> 2160 </td>
   <td style="text-align:right;color: rgba(152, 216, 62, 1) !important;background-color: rgba(69, 53, 129, 1) !important;"> 419 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 340 </td>
   <td style="text-align:right;color: rgba(221, 227, 24, 1) !important;background-color: rgba(72, 20, 103, 1) !important;"> 710 </td>
   <td style="text-align:right;color: rgba(86, 198, 103, 1) !important;background-color: rgba(57, 85, 140, 1) !important;"> 1167 </td>
   <td style="text-align:right;color: rgba(200, 224, 32, 1) !important;background-color: rgba(72, 31, 112, 1) !important;"> 722 </td>
   <td style="text-align:right;color: rgba(99, 203, 95, 1) !important;background-color: rgba(60, 79, 138, 1) !important;"> 1881 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> K </td>
   <td style="text-align:right;color: rgba(68, 191, 112, 1) !important;background-color: rgba(53, 95, 141, 1) !important;"> 505 </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 2675 </td>
   <td style="text-align:right;color: rgba(34, 141, 141, 1) !important;background-color: rgba(32, 147, 140, 1) !important;"> 961 </td>
   <td style="text-align:right;color: rgba(84, 197, 104, 1) !important;background-color: rgba(57, 86, 140, 1) !important;"> 574 </td>
   <td style="text-align:right;color: rgba(112, 207, 87, 1) !important;background-color: rgba(63, 72, 137, 1) !important;"> 168 </td>
   <td style="text-align:right;color: rgba(65, 68, 135, 1) !important;background-color: rgba(122, 209, 81, 1) !important;"> 1782 </td>
   <td style="text-align:right;color: rgba(36, 134, 142, 1) !important;background-color: rgba(31, 154, 138, 1) !important;"> 1222 </td>
   <td style="text-align:right;color: rgba(66, 190, 113, 1) !important;background-color: rgba(52, 96, 141, 1) !important;"> 325 </td>
   <td style="text-align:right;color: rgba(33, 165, 133, 1) !important;background-color: rgba(41, 123, 142, 1) !important;"> 551 </td>
   <td style="text-align:right;color: rgba(226, 228, 24, 1) !important;background-color: rgba(71, 17, 100, 1) !important;"> 258 </td>
   <td style="text-align:right;color: rgba(229, 228, 25, 1) !important;background-color: rgba(71, 16, 99, 1) !important;"> 257 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(155, 217, 60, 1) !important;background-color: rgba(70, 52, 128, 1) !important;"> 518 </td>
   <td style="text-align:right;color: rgba(248, 230, 33, 1) !important;background-color: rgba(69, 4, 87, 1) !important;"> 153 </td>
   <td style="text-align:right;color: rgba(49, 104, 142, 1) !important;background-color: rgba(53, 183, 121, 1) !important;"> 525 </td>
   <td style="text-align:right;color: rgba(124, 210, 80, 1) !important;background-color: rgba(65, 66, 135, 1) !important;"> 645 </td>
   <td style="text-align:right;color: rgba(137, 213, 72, 1) !important;background-color: rgba(67, 61, 132, 1) !important;"> 667 </td>
   <td style="text-align:right;color: rgba(216, 226, 25, 1) !important;background-color: rgba(72, 23, 105, 1) !important;"> 256 </td>
   <td style="text-align:right;color: rgba(213, 226, 26, 1) !important;background-color: rgba(72, 24, 106, 1) !important;"> 336 </td>
   <td style="text-align:right;color: rgba(229, 228, 25, 1) !important;background-color: rgba(71, 16, 99, 1) !important;"> 282 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> M </td>
   <td style="text-align:right;color: rgba(35, 136, 142, 1) !important;background-color: rgba(31, 152, 139, 1) !important;"> 380 </td>
   <td style="text-align:right;color: rgba(168, 219, 52, 1) !important;background-color: rgba(71, 46, 124, 1) !important;"> 201 </td>
   <td style="text-align:right;color: rgba(144, 215, 67, 1) !important;background-color: rgba(68, 57, 131, 1) !important;"> 178 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 43 </td>
   <td style="text-align:right;color: rgba(43, 116, 142, 1) !important;background-color: rgba(37, 172, 130, 1) !important;"> 132 </td>
   <td style="text-align:right;color: rgba(34, 139, 141, 1) !important;background-color: rgba(31, 149, 139, 1) !important;"> 515 </td>
   <td style="text-align:right;color: rgba(184, 222, 41, 1) !important;background-color: rgba(72, 38, 119, 1) !important;"> 130 </td>
   <td style="text-align:right;color: rgba(152, 216, 62, 1) !important;background-color: rgba(69, 53, 129, 1) !important;"> 89 </td>
   <td style="text-align:right;color: rgba(170, 220, 50, 1) !important;background-color: rgba(71, 45, 123, 1) !important;"> 112 </td>
   <td style="text-align:right;color: rgba(32, 146, 140, 1) !important;background-color: rgba(33, 143, 141, 1) !important;"> 804 </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 1206 </td>
   <td style="text-align:right;color: rgba(157, 217, 59, 1) !important;background-color: rgba(70, 51, 127, 1) !important;"> 218 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(40, 174, 128, 1) !important;background-color: rgba(44, 113, 142, 1) !important;"> 458 </td>
   <td style="text-align:right;color: rgba(137, 213, 72, 1) !important;background-color: rgba(67, 61, 132, 1) !important;"> 101 </td>
   <td style="text-align:right;color: rgba(178, 221, 45, 1) !important;background-color: rgba(72, 41, 121, 1) !important;"> 191 </td>
   <td style="text-align:right;color: rgba(105, 205, 91, 1) !important;background-color: rgba(62, 76, 138, 1) !important;"> 331 </td>
   <td style="text-align:right;color: rgba(157, 217, 59, 1) !important;background-color: rgba(70, 51, 127, 1) !important;"> 177 </td>
   <td style="text-align:right;color: rgba(162, 218, 55, 1) !important;background-color: rgba(70, 48, 126, 1) !important;"> 223 </td>
   <td style="text-align:right;color: rgba(86, 198, 103, 1) !important;background-color: rgba(57, 85, 140, 1) !important;"> 463 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> F </td>
   <td style="text-align:right;color: rgba(149, 216, 64, 1) !important;background-color: rgba(69, 55, 129, 1) !important;"> 236 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 135 </td>
   <td style="text-align:right;color: rgba(223, 227, 24, 1) !important;background-color: rgba(71, 19, 101, 1) !important;"> 211 </td>
   <td style="text-align:right;color: rgba(236, 229, 27, 1) !important;background-color: rgba(70, 11, 94, 1) !important;"> 132 </td>
   <td style="text-align:right;color: rgba(56, 89, 140, 1) !important;background-color: rgba(80, 196, 106, 1) !important;"> 307 </td>
   <td style="text-align:right;color: rgba(241, 229, 29, 1) !important;background-color: rgba(70, 8, 92, 1) !important;"> 183 </td>
   <td style="text-align:right;color: rgba(239, 229, 28, 1) !important;background-color: rgba(70, 10, 93, 1) !important;"> 117 </td>
   <td style="text-align:right;color: rgba(147, 215, 65, 1) !important;background-color: rgba(69, 56, 130, 1) !important;"> 189 </td>
   <td style="text-align:right;color: rgba(162, 218, 55, 1) !important;background-color: rgba(70, 48, 126, 1) !important;"> 240 </td>
   <td style="text-align:right;color: rgba(144, 215, 67, 1) !important;background-color: rgba(68, 57, 131, 1) !important;"> 609 </td>
   <td style="text-align:right;color: rgba(39, 173, 129, 1) !important;background-color: rgba(44, 114, 142, 1) !important;"> 1015 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 133 </td>
   <td style="text-align:right;color: rgba(45, 178, 125, 1) !important;background-color: rgba(46, 110, 142, 1) !important;"> 941 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(110, 206, 88, 1) !important;background-color: rgba(62, 73, 137, 1) !important;"> 229 </td>
   <td style="text-align:right;color: rgba(210, 226, 27, 1) !important;background-color: rgba(72, 26, 108, 1) !important;"> 295 </td>
   <td style="text-align:right;color: rgba(244, 230, 30, 1) !important;background-color: rgba(70, 7, 90, 1) !important;"> 261 </td>
   <td style="text-align:right;color: rgba(37, 131, 142, 1) !important;background-color: rgba(30, 157, 137, 1) !important;"> 1012 </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 2326 </td>
   <td style="text-align:right;color: rgba(194, 223, 35, 1) !important;background-color: rgba(72, 33, 115, 1) !important;"> 415 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> P </td>
   <td style="text-align:right;color: rgba(41, 175, 127, 1) !important;background-color: rgba(45, 113, 142, 1) !important;"> 502 </td>
   <td style="text-align:right;color: rgba(205, 225, 29, 1) !important;background-color: rgba(72, 28, 110, 1) !important;"> 274 </td>
   <td style="text-align:right;color: rgba(144, 215, 67, 1) !important;background-color: rgba(68, 57, 131, 1) !important;"> 342 </td>
   <td style="text-align:right;color: rgba(147, 215, 65, 1) !important;background-color: rgba(69, 56, 130, 1) !important;"> 310 </td>
   <td style="text-align:right;color: rgba(165, 219, 54, 1) !important;background-color: rgba(71, 47, 125, 1) !important;"> 112 </td>
   <td style="text-align:right;color: rgba(149, 216, 64, 1) !important;background-color: rgba(69, 55, 129, 1) !important;"> 391 </td>
   <td style="text-align:right;color: rgba(84, 197, 104, 1) !important;background-color: rgba(57, 86, 140, 1) !important;"> 525 </td>
   <td style="text-align:right;color: rgba(68, 191, 112, 1) !important;background-color: rgba(53, 95, 141, 1) !important;"> 261 </td>
   <td style="text-align:right;color: rgba(197, 224, 33, 1) !important;background-color: rgba(72, 32, 113, 1) !important;"> 184 </td>
   <td style="text-align:right;color: rgba(239, 229, 28, 1) !important;background-color: rgba(70, 10, 93, 1) !important;"> 143 </td>
   <td style="text-align:right;color: rgba(236, 229, 27, 1) !important;background-color: rgba(70, 11, 94, 1) !important;"> 184 </td>
   <td style="text-align:right;color: rgba(155, 217, 60, 1) !important;background-color: rgba(70, 52, 128, 1) !important;"> 424 </td>
   <td style="text-align:right;color: rgba(221, 227, 24, 1) !important;background-color: rgba(72, 20, 103, 1) !important;"> 195 </td>
   <td style="text-align:right;color: rgba(221, 227, 24, 1) !important;background-color: rgba(72, 20, 103, 1) !important;"> 214 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(105, 205, 91, 1) !important;background-color: rgba(62, 76, 138, 1) !important;"> 579 </td>
   <td style="text-align:right;color: rgba(173, 220, 48, 1) !important;background-color: rgba(71, 44, 122, 1) !important;"> 439 </td>
   <td style="text-align:right;color: rgba(205, 225, 29, 1) !important;background-color: rgba(72, 28, 110, 1) !important;"> 233 </td>
   <td style="text-align:right;color: rgba(229, 228, 25, 1) !important;background-color: rgba(71, 16, 99, 1) !important;"> 226 </td>
   <td style="text-align:right;color: rgba(216, 226, 25, 1) !important;background-color: rgba(72, 23, 105, 1) !important;"> 287 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> S </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 2196 </td>
   <td style="text-align:right;color: rgba(147, 215, 65, 1) !important;background-color: rgba(69, 56, 130, 1) !important;"> 733 </td>
   <td style="text-align:right;color: rgba(49, 103, 142, 1) !important;background-color: rgba(55, 184, 120, 1) !important;"> 1570 </td>
   <td style="text-align:right;color: rgba(40, 174, 128, 1) !important;background-color: rgba(44, 113, 142, 1) !important;"> 992 </td>
   <td style="text-align:right;color: rgba(72, 38, 119, 1) !important;background-color: rgba(184, 222, 41, 1) !important;"> 545 </td>
   <td style="text-align:right;color: rgba(46, 179, 124, 1) !important;background-color: rgba(46, 109, 142, 1) !important;"> 1155 </td>
   <td style="text-align:right;color: rgba(94, 201, 98, 1) !important;background-color: rgba(59, 81, 139, 1) !important;"> 799 </td>
   <td style="text-align:right;color: rgba(60, 80, 139, 1) !important;background-color: rgba(96, 202, 96, 1) !important;"> 886 </td>
   <td style="text-align:right;color: rgba(55, 184, 120, 1) !important;background-color: rgba(49, 103, 142, 1) !important;"> 614 </td>
   <td style="text-align:right;color: rgba(231, 228, 25, 1) !important;background-color: rgba(71, 14, 97, 1) !important;"> 288 </td>
   <td style="text-align:right;color: rgba(246, 230, 32, 1) !important;background-color: rgba(69, 5, 89, 1) !important;"> 242 </td>
   <td style="text-align:right;color: rgba(124, 210, 80, 1) !important;background-color: rgba(65, 66, 135, 1) !important;"> 846 </td>
   <td style="text-align:right;color: rgba(170, 220, 50, 1) !important;background-color: rgba(71, 45, 123, 1) !important;"> 593 </td>
   <td style="text-align:right;color: rgba(200, 224, 32, 1) !important;background-color: rgba(72, 31, 112, 1) !important;"> 447 </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 940 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 3325 </td>
   <td style="text-align:right;color: rgba(189, 223, 38, 1) !important;background-color: rgba(72, 36, 117, 1) !important;"> 430 </td>
   <td style="text-align:right;color: rgba(205, 225, 29, 1) !important;background-color: rgba(72, 28, 110, 1) !important;"> 479 </td>
   <td style="text-align:right;color: rgba(221, 227, 24, 1) !important;background-color: rgba(72, 20, 103, 1) !important;"> 441 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> T </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 759 </td>
   <td style="text-align:right;color: rgba(139, 214, 70, 1) !important;background-color: rgba(68, 59, 132, 1) !important;"> 637 </td>
   <td style="text-align:right;color: rgba(31, 154, 138, 1) !important;background-color: rgba(36, 134, 142, 1) !important;"> 946 </td>
   <td style="text-align:right;color: rgba(122, 209, 81, 1) !important;background-color: rgba(65, 68, 135, 1) !important;"> 496 </td>
   <td style="text-align:right;color: rgba(50, 101, 142, 1) !important;background-color: rgba(58, 186, 118, 1) !important;"> 366 </td>
   <td style="text-align:right;color: rgba(53, 183, 121, 1) !important;background-color: rgba(49, 104, 142, 1) !important;"> 914 </td>
   <td style="text-align:right;color: rgba(96, 202, 96, 1) !important;background-color: rgba(60, 80, 139, 1) !important;"> 650 </td>
   <td style="text-align:right;color: rgba(105, 205, 91, 1) !important;background-color: rgba(62, 76, 138, 1) !important;"> 291 </td>
   <td style="text-align:right;color: rgba(31, 161, 136, 1) !important;background-color: rgba(39, 128, 142, 1) !important;"> 618 </td>
   <td style="text-align:right;color: rgba(173, 220, 48, 1) !important;background-color: rgba(71, 44, 122, 1) !important;"> 590 </td>
   <td style="text-align:right;color: rgba(197, 224, 33, 1) !important;background-color: rgba(72, 32, 113, 1) !important;"> 418 </td>
   <td style="text-align:right;color: rgba(119, 209, 83, 1) !important;background-color: rgba(64, 69, 136, 1) !important;"> 724 </td>
   <td style="text-align:right;color: rgba(94, 201, 98, 1) !important;background-color: rgba(59, 81, 139, 1) !important;"> 852 </td>
   <td style="text-align:right;color: rgba(210, 226, 27, 1) !important;background-color: rgba(72, 26, 108, 1) !important;"> 327 </td>
   <td style="text-align:right;color: rgba(53, 95, 141, 1) !important;background-color: rgba(68, 191, 112, 1) !important;"> 589 </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 2750 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(144, 215, 67, 1) !important;background-color: rgba(68, 57, 131, 1) !important;"> 490 </td>
   <td style="text-align:right;color: rgba(213, 226, 26, 1) !important;background-color: rgba(72, 24, 106, 1) !important;"> 373 </td>
   <td style="text-align:right;color: rgba(96, 202, 96, 1) !important;background-color: rgba(60, 80, 139, 1) !important;"> 1118 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W </td>
   <td style="text-align:right;color: rgba(200, 224, 32, 1) !important;background-color: rgba(72, 31, 112, 1) !important;"> 45 </td>
   <td style="text-align:right;color: rgba(192, 223, 37, 1) !important;background-color: rgba(72, 35, 116, 1) !important;"> 118 </td>
   <td style="text-align:right;color: rgba(253, 231, 37, 1) !important;background-color: rgba(68, 1, 84, 1) !important;"> 51 </td>
   <td style="text-align:right;color: rgba(236, 229, 27, 1) !important;background-color: rgba(70, 11, 94, 1) !important;"> 46 </td>
   <td style="text-align:right;color: rgba(129, 211, 77, 1) !important;background-color: rgba(66, 64, 134, 1) !important;"> 48 </td>
   <td style="text-align:right;color: rgba(162, 218, 55, 1) !important;background-color: rgba(70, 48, 126, 1) !important;"> 135 </td>
   <td style="text-align:right;color: rgba(208, 225, 28, 1) !important;background-color: rgba(72, 27, 109, 1) !important;"> 72 </td>
   <td style="text-align:right;color: rgba(178, 221, 45, 1) !important;background-color: rgba(72, 41, 121, 1) !important;"> 55 </td>
   <td style="text-align:right;color: rgba(144, 215, 67, 1) !important;background-color: rgba(68, 57, 131, 1) !important;"> 93 </td>
   <td style="text-align:right;color: rgba(231, 228, 25, 1) !important;background-color: rgba(71, 14, 97, 1) !important;"> 69 </td>
   <td style="text-align:right;color: rgba(137, 213, 72, 1) !important;background-color: rgba(67, 61, 132, 1) !important;"> 192 </td>
   <td style="text-align:right;color: rgba(229, 228, 25, 1) !important;background-color: rgba(71, 16, 99, 1) !important;"> 77 </td>
   <td style="text-align:right;color: rgba(178, 221, 45, 1) !important;background-color: rgba(72, 41, 121, 1) !important;"> 127 </td>
   <td style="text-align:right;color: rgba(34, 167, 133, 1) !important;background-color: rgba(41, 121, 142, 1) !important;"> 354 </td>
   <td style="text-align:right;color: rgba(88, 199, 101, 1) !important;background-color: rgba(58, 84, 140, 1) !important;"> 87 </td>
   <td style="text-align:right;color: rgba(213, 226, 26, 1) !important;background-color: rgba(72, 24, 106, 1) !important;"> 99 </td>
   <td style="text-align:right;color: rgba(200, 224, 32, 1) !important;background-color: rgba(72, 31, 112, 1) !important;"> 137 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(56, 89, 140, 1) !important;background-color: rgba(80, 196, 106, 1) !important;"> 604 </td>
   <td style="text-align:right;color: rgba(223, 227, 24, 1) !important;background-color: rgba(71, 19, 101, 1) !important;"> 98 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Y </td>
   <td style="text-align:right;color: rgba(137, 213, 72, 1) !important;background-color: rgba(67, 61, 132, 1) !important;"> 210 </td>
   <td style="text-align:right;color: rgba(194, 223, 35, 1) !important;background-color: rgba(72, 33, 115, 1) !important;"> 264 </td>
   <td style="text-align:right;color: rgba(142, 214, 69, 1) !important;background-color: rgba(68, 58, 131, 1) !important;"> 296 </td>
   <td style="text-align:right;color: rgba(202, 225, 31, 1) !important;background-color: rgba(72, 29, 111, 1) !important;"> 166 </td>
   <td style="text-align:right;color: rgba(32, 147, 140, 1) !important;background-color: rgba(34, 141, 141, 1) !important;"> 184 </td>
   <td style="text-align:right;color: rgba(149, 216, 64, 1) !important;background-color: rgba(69, 55, 129, 1) !important;"> 335 </td>
   <td style="text-align:right;color: rgba(197, 224, 33, 1) !important;background-color: rgba(72, 32, 113, 1) !important;"> 190 </td>
   <td style="text-align:right;color: rgba(178, 221, 45, 1) !important;background-color: rgba(72, 41, 121, 1) !important;"> 126 </td>
   <td style="text-align:right;color: rgba(71, 44, 122, 1) !important;background-color: rgba(173, 220, 48, 1) !important;"> 703 </td>
   <td style="text-align:right;color: rgba(210, 226, 27, 1) !important;background-color: rgba(72, 26, 108, 1) !important;"> 239 </td>
   <td style="text-align:right;color: rgba(194, 223, 35, 1) !important;background-color: rgba(72, 33, 115, 1) !important;"> 271 </td>
   <td style="text-align:right;color: rgba(205, 225, 29, 1) !important;background-color: rgba(72, 28, 110, 1) !important;"> 232 </td>
   <td style="text-align:right;color: rgba(152, 216, 62, 1) !important;background-color: rgba(69, 53, 129, 1) !important;"> 366 </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 1859 </td>
   <td style="text-align:right;color: rgba(96, 202, 96, 1) !important;background-color: rgba(60, 80, 139, 1) !important;"> 193 </td>
   <td style="text-align:right;color: rgba(202, 225, 31, 1) !important;background-color: rgba(72, 29, 111, 1) !important;"> 253 </td>
   <td style="text-align:right;color: rgba(231, 228, 25, 1) !important;background-color: rgba(71, 14, 97, 1) !important;"> 238 </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 1381 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
   <td style="text-align:right;color: rgba(223, 227, 24, 1) !important;background-color: rgba(71, 19, 101, 1) !important;"> 219 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> V </td>
   <td style="text-align:right;color: rgba(47, 108, 142, 1) !important;background-color: rgba(47, 180, 124, 1) !important;"> 1499 </td>
   <td style="text-align:right;color: rgba(226, 228, 24, 1) !important;background-color: rgba(71, 17, 100, 1) !important;"> 354 </td>
   <td style="text-align:right;color: rgba(197, 224, 33, 1) !important;background-color: rgba(72, 32, 113, 1) !important;"> 418 </td>
   <td style="text-align:right;color: rgba(231, 228, 25, 1) !important;background-color: rgba(71, 14, 97, 1) !important;"> 228 </td>
   <td style="text-align:right;color: rgba(68, 58, 131, 1) !important;background-color: rgba(142, 214, 69, 1) !important;"> 540 </td>
   <td style="text-align:right;color: rgba(189, 223, 38, 1) !important;background-color: rgba(72, 36, 117, 1) !important;"> 505 </td>
   <td style="text-align:right;color: rgba(178, 221, 45, 1) !important;background-color: rgba(72, 41, 121, 1) !important;"> 448 </td>
   <td style="text-align:right;color: rgba(210, 226, 27, 1) !important;background-color: rgba(72, 26, 108, 1) !important;"> 201 </td>
   <td style="text-align:right;color: rgba(218, 227, 25, 1) !important;background-color: rgba(72, 22, 104, 1) !important;"> 272 </td>
   <td style="text-align:right;color: rgba(68, 1, 84, 1) !important;background-color: rgba(253, 231, 37, 1) !important;"> 5186 </td>
   <td style="text-align:right;color: rgba(58, 186, 118, 1) !important;background-color: rgba(50, 101, 142, 1) !important;"> 1403 </td>
   <td style="text-align:right;color: rgba(221, 227, 24, 1) !important;background-color: rgba(72, 20, 103, 1) !important;"> 388 </td>
   <td style="text-align:right;color: rgba(44, 177, 126, 1) !important;background-color: rgba(46, 111, 142, 1) !important;"> 1509 </td>
   <td style="text-align:right;color: rgba(165, 219, 54, 1) !important;background-color: rgba(71, 47, 125, 1) !important;"> 658 </td>
   <td style="text-align:right;color: rgba(39, 173, 129, 1) !important;background-color: rgba(44, 114, 142, 1) !important;"> 489 </td>
   <td style="text-align:right;color: rgba(213, 226, 26, 1) !important;background-color: rgba(72, 24, 106, 1) !important;"> 462 </td>
   <td style="text-align:right;color: rgba(52, 182, 121, 1) !important;background-color: rgba(48, 105, 142, 1) !important;"> 1416 </td>
   <td style="text-align:right;color: rgba(192, 223, 37, 1) !important;background-color: rgba(72, 35, 116, 1) !important;"> 445 </td>
   <td style="text-align:right;color: rgba(218, 227, 25, 1) !important;background-color: rgba(72, 22, 104, 1) !important;"> 435 </td>
   <td style="text-align:right;color: #BBBBBB !important;background-color: #BBBBBB !important;"> – </td>
  </tr>
</tbody>
</table>
]

.pull-right[

![](images/aa_properties_0.png)

]

---

## What do these numbers depend on? ✪

* Frequency of the original AA: if an amino acid is more frequent, you
   will find more substitutions of that amino acid
 * Number of codons that code for a given amino acid: mutations happen on
   DNA level, not on AA level. Synonymous mutations are more likely if the
   AA is encoded by multiple codons
 * Random chance: mutations are random
 * Natural selection and genetic drift: 
   * some mutations are do not change the structure of the protein - they are neutral
   * some mutations change the structure of the protein: these can be
     beneficial or detrimental

---

## The problem: multiple substitutions ✪

This makes sense when you think of *one* mutation only.

```
A -> V
```

However, in the millions of years of evolution each amino acid has multiple
"chances" to be mutated, so there is a chain of substitutions. Say, in one
species we find at a given site a leucine. This might have happened, with
the ancestral sequence having alanine:

```
A -> V -> I -> M -> L
```

Moreover, this chain (Markov chain!) occurs independently in another species:

```
   -> V -> I -> M -> L
 /
A
 \
   -> S -> T
```

However, we only see the mismatch `T <-> L`.

Long evolutionary time means that the observed mutation frequencies will
change

---

## Margaret Dayhoff

.pull-left[

![:scale 70%](images/dayhoff.png)

]

.pull-right[

Margaret Dayhoff (1925-1983)

* Pioneer of bioinformatics
 * Started by calculating resonance energies of polycyclic organic
   molecules using a punch-card computer
 * First computer program to predict protein structure (together with
   Robert Ledley)
 * Worked with Carl Sagan on planetary prebiotic atmospheric models
 * Pioneered molecular phylogeny methods
 * Developed the PAM matrices for protein sequence comparison
 * Worked for years on IBM 7094 (100 Kflops/s! for comparison: a graphic
   card may have several teraflops)

![:scale 50%](images/ibm7094.jpg)

]

---

## PAM matrices ✪

PAM - point accepted mutations

Basic idea: estimate the mutation frequency from closely related sequences,
then use a Markov-chain model to estimate the expected frequencies of
mutations for longer evolutionary times.

---

## Constructing the mutation matrix `$M_1$`

We assume that for closely related sequences, at most one mutation may have
occured. We calculate the entries in the `$PAM_1$` matrix simply by looking
at the frequencies of `$AA_i \leftrightarrow AA_j$` substitutions (mismatches
in an alignment).

`$$M_1(i, j) = \lambda \frac{A(i, j)}{N\cdot f(j)}$$`

Where `$i$`, `$j$` are amino acids, `$A(i, j)$` is the number of occurences of
mismatches of `$i$` with `$j$` amino acids, `$N$` is the total number of amino
acids in the alignment(s) and `$f(j)$` is the frequency of amino acid `$j$`.

Clearly, `$$\N\cdot f(j)$$` is simply the number of occurences of amino acid
`$j$`.

`$\lambda$` is simply a scaling factor which ensures that the sum of all elements in
the matrix is 1.

---

## Constructing the mutation matrix `$M_1$`

`$$M_1(i, j) = \lambda \frac{A(i, j)}{N\cdot f(j)}$$`

---

## Constructing PAM matrices for longer evolutionary times

Using a Markov chain model of AA substitutions:

`$$M_n = M_1^n$$`

<table>
 <thead>
  <tr>
   <th style="text-align:left;"> PAM </th>
   <th style="text-align:left;"> Sequence.identity </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> PAM1 </td>
   <td style="text-align:left;"> 99% </td>
  </tr>
  <tr>
   <td style="text-align:left;"> PAM30 </td>
   <td style="text-align:left;"> 75% </td>
  </tr>
  <tr>
   <td style="text-align:left;"> PAM80 </td>
   <td style="text-align:left;"> 50% </td>
  </tr>
  <tr>
   <td style="text-align:left;"> PAM200 </td>
   <td style="text-align:left;"> 25% </td>
  </tr>
</tbody>
</table>

---

.pull-left[

PAM10 (similar sequences)

]

.pull-right[

PAM400 (distant sequences)

]

---

## BLOSUM matrices ✪

BLOSUM - Blocks Substitution Matrix, a set of substitution matrices
first created by Steven Henikoff and Jorja Henikoff in 1992.

---

## BLOSUM matrices ✪

Idea: instead of extrapolating, use different sets of sequences with
different average similarity (50%, 60%, 90%, 99%).

For each set, calculate scores as log-odds ratios

`$$S_{i,j}=\frac{1}{\lambda}\frac{f_O(i,j)}{f_E(i,j)}=\frac{1}{\lambda}\log\frac{p_{i,j}}{q_{i} q_{j}}$$`

Where `$f_O$` is the observed frequency, `$f_E$` is the expected frequency
(based on frequencies of both amino acids), `$p_{i,j}$` is the frequency of
observed mismatches, `$q_{i}$` and `$q_{j}$` are the observed frequencies of
the amino acids (independent of each other).

So if there were 20 `$A \leftrightarrow L$` mismatches out of 1000 observed
mismatches, and `$A$` frequency was `$0.01$`, `$L$` frequency was `$0.005$`, then
`$f_O = p_{L,A} = \frac{20}{1000} = 0.02$` and

`$$\frac{f_O}{f_E}=\frac{0.02}{0.01 \cdot 0.005} = 400$$`

`$$\log\frac{f_O}{f_E} = 6$$`

---

.pull-left[
```
                🠗
                WLL
                WLI
                WIL
                WIL
                YIW
                YIL
```
]

.pull-right[
Number of pairs in the first column:

`$$c_{i,i} = \frac{N(N-1)}{2}$$`

`$$c_{i,j} = n_i \cdot n_j$$`

```
W-W: 6
Y-Y: 1
W-Y: 8
```
]

---

.pull-left[
```
                 🠗
                WLL
                WLI
                WIL
                WIL
                YIW
                YIL
```
]

.pull-right[
Number of pairs in the second column:

```
L-L: 1
I-I: 6
L-I: 8
```
]

---

.pull-left[
```
                  🠗
                WLL
                WLI
                WIL
                WIL
                YIW
                YIL
```
]

.pull-right[
Number of pairs in the third column:

```
L-L: 6
I-I: 0
L-W: 4
L-I: 4
I-W: 1
```
]

---

.pull-left[
```
                  
                WLL
                WLI
                WIL
                WIL
                YIW
                YIL
```
]

.pull-right[
Number of pairs in all columns:

```
W-W: 6
Y-Y: 1
W-Y: 8
L-L: 7
L-W: 4
L-I: 12
I-I: 6
I-W: 1
```
]

---

.pull-left[
```
                  
                WLL
                WLI
                WIL
                WIL
                YIW
                YIL
```
]

.pull-right[
Number of pairs in all columns:

```
    I    L    W    Y
I   6    12   1    ?
L        7    4    ?
W             6    8
Y                  1
```
]

---

.pull-left[
```
                  
                WLL
                WLI
                WIL
                WIL
                YIW
                YIL
```
]

.pull-right[
To get frequencies, divide by total number of pairs:

`$$N_c \cdot \frac{N_s\cdot(N_s - 1)}{2} = 3 \cdot \frac{6\cdot 5}{2} = 45$$`

where

`$N_c$` – number of columns, `$N_s$` – number of sequences

Matrix of observed frequencies, `$f_O$`

```
    I      L       W      Y
I 0.133  0.267   0.022 ?
L        0.156   0.089 ?
W                0.133 0.178
Y                      0.022
```

]

---

.pull-left[
```
                  
                WLL
                WLI
                WIL
                WIL
                YIW
                YIL
```
]

.pull-right[
To get expected frequencies, we need to calculate the frequencies of amino acids

```
f(W) = (4+1)/(3 * 6) = 5/18 = 0.28
f(Y) = 2/18 = 0.11
p(W, W) = f(W) * f(W) = 0.28^2 = 0.08
p(Y, W) = 2 * f(W) * f(Y) = 2 * 0.28 * 0.11 = 0.062
```

etc.

]

---

.pull-left[
```
                  
                WLL
                WLI
                WIL
                WIL
                YIW
                YIL
```
]

.pull-right[
To get expected frequencies, we need to calculate the frequencies of amino acids

```
f(W) = (4+1)/(3 * 6) = 5/18 = 0.28
f(Y) = 2/18 = 0.11
p(W, W) = f(W) * f(W) = 0.28^2 = 0.08
p(Y, W) = 2 * f(W) * f(Y) = 2 * 0.28 * 0.11 = 0.062
```

```
    I      L       W      Y
I 0.077  0.186   0.155 0.062
L        0.112   0.186 0.074
W                0.077 0.062
Y                      0.012
```

etc.

]

---

Now we have to divide one matrix by another
and logarithmize them

.pull-left[
Observed frequencies:
```
    I      L       W      Y
I 0.133  0.267   0.022 ?
L        0.156   0.089 ?
W                0.133 0.178
Y                      0.022
```
]

.pull-right[
Expected frequencies:
```
    I      L       W      Y
I 0.077  0.186   0.155 0.062
L        0.112   0.186 0.074
W                0.077 0.062
Y                      0.012
```
]

e.g.

`$$\log\frac{f_O(W, Y)}{f_E(W, Y)} = \log\frac{0.178}{0.062} = 1.05$$`

---

Now we have to divide one matrix by another
and logarithmize them

.pull-left[
Observed frequencies:
```
    I      L       W      Y
I 0.133  0.267   0.022 ?
L        0.156   0.089 ?
W                0.133 0.178
Y                      0.022
```

Result:

```
    I      L       W      Y
I 0.55   0.36    -1.95    ?
L        0.33    -0.74    ?
W                0.55   1.05
Y                       0.61
```

]

.pull-right[
Expected frequencies:
```
    I      L       W      Y
I 0.077  0.186   0.155 0.062
L        0.112   0.186 0.074
W                0.077 0.062
Y                      0.012
```
]

---

To get the scores, we multiply by 10 and round the numbers

.pull-left[
Observed frequencies:
```
    I      L       W      Y
I 0.133  0.267   0.022 ?
L        0.156   0.089 ?
W                0.133 0.178
Y                      0.022
```

Result:

```
    I      L       W      Y
I 0.55   0.36    -1.95    ?
L        0.33    -0.74    ?
W                0.55   1.05
Y                       0.61
```

]

.pull-right[
Expected frequencies:
```
    I      L       W      Y
I 0.077  0.186   0.155 0.062
L        0.112   0.186 0.074
W                0.077 0.062
Y                      0.012
```

After rounding:

```
    I      L       W      Y
I   6      4      -20     ?
L          3       -7     ?
W                   6    11
Y                         6
```

]

---

To get the scores, we multiply by 10 and round the numbers

.pull-left[
Our matrix:

```
    I      L       W      Y
I   6      4      -20     ?
L          3       -7     ?
W                   6    11
Y                         6
```

]

.pull-right[

Real BLOSUM62:

```
    I      L       W      Y
I   4      2       -3    -1
L          3       -2    -1
W                  11     2
Y                         7
```
]

---

.pull-left[

BLOSUM100 (very similar sequences, almost 100%)

]

.pull-right[

BLOSUM35 (distant sequences)

]

---

## Short vs long evolutionary distances

.pull-left[

![](weiner_BE_22_lecture_03_files/figure-html/unnamed-chunk-20-1.png)

]

.pull-right[

![](weiner_BE_22_lecture_03_files/figure-html/unnamed-chunk-21-1.png)

]

---

## BLOSUM vs PAM

.pull-left[

![](weiner_BE_22_lecture_03_files/figure-html/unnamed-chunk-22-1.png)

]

.pull-right[

![](weiner_BE_22_lecture_03_files/figure-html/unnamed-chunk-23-1.png)

]

---

## PAM vs BLOSUM ✪

Remember:

* PAM[number]: the lower the number, the shorter the evolutionary
   distance, the more similar the sequences
 * BLOSUM[number]: the higher the number, the higher the similarity, the
   shorter the evolutionary distance
 * PAM1 = BLOSUM100; PAM400 = BLOSUM30

---

## Protein structures ✪

.pull-left[
![:scale 70%](images/protein_structures.jpeg)
]

.pull-right[

Predicting secondary structures (alpha helices / beta sheets) is easier
than predicting the tertiary structure.

]

---

## Alpha helices and beta sheets

.pull-left[

Alpha helices:

![:scale 50%](images/leucine_zipper.jpg)

A leucine zipper

]

.pull-right[

Beta sheets:

![:scale 70%](images/barrel_fold.png)

Beta sheets in a barrel fold

]

---

## Sequence prediction ✪

![:scale 70%](images/sequence_pred.png)

*Torrisi, Mirko, Gianluca Pollastri, and Quan Le. "Deep learning methods in
protein structure prediction." Computational and Structural Biotechnology
Journal (2020).*

---

## Secondary structures

✪ Helix-forming amino acids: "MALEK" (methionine, alanine, leucine,
glutamate, uncharged lysine)

✪ Beta-sheet forming amino acids: large aromatic, or branching: tyrosine,
phenylalanine, tryptophan, threonine, valine, isoleucine

✪ Helix breakers: proline (P) and glycine (G)

---

## Chou-Fasman algorithm

* Assign a "potential" score to each amino acid based on known structures
   (15 at the time): 
   * separately potential for forming alpha-helices and beta-sheets
   * scores are log-odds plus 1 (so `$0+1=1$` means that observed frequency is
     equal to expected frequency)
 * For a given structure (a-helix or b-sheet):
    * Find "seed" regions where there are several of high scoring residues
    * Try to extend the region in both direction, as long as the number of
      high scoring residues does not fall below a threshold

---

.pull-left[

<table class="table" style="font-size: 12px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;"> Abbr </th>
   <th style="text-align:left;"> Name </th>
   <th style="text-align:right;"> P(a) </th>
   <th style="text-align:left;"> A? </th>
   <th style="text-align:left;"> Abbr </th>
   <th style="text-align:left;"> Name </th>
   <th style="text-align:right;"> P(b) </th>
   <th style="text-align:left;"> B? </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> M </td>
   <td style="text-align:left;"> Methionine </td>
   <td style="text-align:right;"> 1.45 </td>
   <td style="text-align:left;"> +A </td>
   <td style="text-align:left;"> V </td>
   <td style="text-align:left;"> Valine </td>
   <td style="text-align:right;"> 1.70 </td>
   <td style="text-align:left;"> +B </td>
  </tr>
  <tr>
   <td style="text-align:left;"> A </td>
   <td style="text-align:left;"> Alanine </td>
   <td style="text-align:right;"> 1.42 </td>
   <td style="text-align:left;"> +A </td>
   <td style="text-align:left;"> I </td>
   <td style="text-align:left;"> Isoleucine </td>
   <td style="text-align:right;"> 1.60 </td>
   <td style="text-align:left;"> +B </td>
  </tr>
  <tr>
   <td style="text-align:left;"> L </td>
   <td style="text-align:left;"> Leucine </td>
   <td style="text-align:right;"> 1.41 </td>
   <td style="text-align:left;"> +A </td>
   <td style="text-align:left;"> Y </td>
   <td style="text-align:left;"> Tyrosine </td>
   <td style="text-align:right;"> 1.47 </td>
   <td style="text-align:left;"> +B </td>
  </tr>
  <tr>
   <td style="text-align:left;"> E </td>
   <td style="text-align:left;"> Glutamic Acid </td>
   <td style="text-align:right;"> 1.39 </td>
   <td style="text-align:left;"> +A </td>
   <td style="text-align:left;"> F </td>
   <td style="text-align:left;"> Phenylalanine </td>
   <td style="text-align:right;"> 1.38 </td>
   <td style="text-align:left;"> +b </td>
  </tr>
  <tr>
   <td style="text-align:left;"> K </td>
   <td style="text-align:left;"> Lysine </td>
   <td style="text-align:right;"> 1.14 </td>
   <td style="text-align:left;"> +a </td>
   <td style="text-align:left;"> W </td>
   <td style="text-align:left;"> Tryptophan </td>
   <td style="text-align:right;"> 1.37 </td>
   <td style="text-align:left;"> +b </td>
  </tr>
  <tr>
   <td style="text-align:left;"> F </td>
   <td style="text-align:left;"> Phenylalanine </td>
   <td style="text-align:right;"> 1.13 </td>
   <td style="text-align:left;"> +a </td>
   <td style="text-align:left;"> L </td>
   <td style="text-align:left;"> Leucine </td>
   <td style="text-align:right;"> 1.30 </td>
   <td style="text-align:left;"> +b </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Q </td>
   <td style="text-align:left;"> Glutamine </td>
   <td style="text-align:right;"> 1.11 </td>
   <td style="text-align:left;"> +a </td>
   <td style="text-align:left;"> C </td>
   <td style="text-align:left;"> Cysteine </td>
   <td style="text-align:right;"> 1.19 </td>
   <td style="text-align:left;"> +b </td>
  </tr>
  <tr>
   <td style="text-align:left;"> I </td>
   <td style="text-align:left;"> Isoleucine </td>
   <td style="text-align:right;"> 1.08 </td>
   <td style="text-align:left;"> +a </td>
   <td style="text-align:left;"> T </td>
   <td style="text-align:left;"> Threonine </td>
   <td style="text-align:right;"> 1.19 </td>
   <td style="text-align:left;"> +b </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W </td>
   <td style="text-align:left;"> Tryptophan </td>
   <td style="text-align:right;"> 1.08 </td>
   <td style="text-align:left;"> +a </td>
   <td style="text-align:left;"> E </td>
   <td style="text-align:left;"> Glutamic Acid </td>
   <td style="text-align:right;"> 1.17 </td>
   <td style="text-align:left;"> +b </td>
  </tr>
  <tr>
   <td style="text-align:left;"> V </td>
   <td style="text-align:left;"> Valine </td>
   <td style="text-align:right;"> 1.06 </td>
   <td style="text-align:left;"> +a </td>
   <td style="text-align:left;"> Q </td>
   <td style="text-align:left;"> Glutamine </td>
   <td style="text-align:right;"> 1.10 </td>
   <td style="text-align:left;"> +b </td>
  </tr>
  <tr>
   <td style="text-align:left;"> D </td>
   <td style="text-align:left;"> Aspartic Acid </td>
   <td style="text-align:right;"> 1.01 </td>
   <td style="text-align:left;"> 0 </td>
   <td style="text-align:left;"> M </td>
   <td style="text-align:left;"> Methionine </td>
   <td style="text-align:right;"> 1.05 </td>
   <td style="text-align:left;"> +b </td>
  </tr>
  <tr>
   <td style="text-align:left;"> H </td>
   <td style="text-align:left;"> Histidine </td>
   <td style="text-align:right;"> 1.00 </td>
   <td style="text-align:left;"> 0 </td>
   <td style="text-align:left;"> R </td>
   <td style="text-align:left;"> Arginine </td>
   <td style="text-align:right;"> 0.93 </td>
   <td style="text-align:left;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> R </td>
   <td style="text-align:left;"> Arginine </td>
   <td style="text-align:right;"> 0.98 </td>
   <td style="text-align:left;"> -a </td>
   <td style="text-align:left;"> N </td>
   <td style="text-align:left;"> Asparagine </td>
   <td style="text-align:right;"> 0.89 </td>
   <td style="text-align:left;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> T </td>
   <td style="text-align:left;"> Threonine </td>
   <td style="text-align:right;"> 0.83 </td>
   <td style="text-align:left;"> -a </td>
   <td style="text-align:left;"> H </td>
   <td style="text-align:left;"> Histidine </td>
   <td style="text-align:right;"> 0.87 </td>
   <td style="text-align:left;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> S </td>
   <td style="text-align:left;"> Serine </td>
   <td style="text-align:right;"> 0.77 </td>
   <td style="text-align:left;"> -a </td>
   <td style="text-align:left;"> A </td>
   <td style="text-align:left;"> Alanine </td>
   <td style="text-align:right;"> 0.83 </td>
   <td style="text-align:left;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> C </td>
   <td style="text-align:left;"> Cysteine </td>
   <td style="text-align:right;"> 0.70 </td>
   <td style="text-align:left;"> -a </td>
   <td style="text-align:left;"> G </td>
   <td style="text-align:left;"> Glycine </td>
   <td style="text-align:right;"> 0.75 </td>
   <td style="text-align:left;"> -b </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Y </td>
   <td style="text-align:left;"> Tyrosine </td>
   <td style="text-align:right;"> 0.69 </td>
   <td style="text-align:left;"> -a </td>
   <td style="text-align:left;"> S </td>
   <td style="text-align:left;"> Serine </td>
   <td style="text-align:right;"> 0.75 </td>
   <td style="text-align:left;"> -b </td>
  </tr>
  <tr>
   <td style="text-align:left;"> N </td>
   <td style="text-align:left;"> Asparagine </td>
   <td style="text-align:right;"> 0.67 </td>
   <td style="text-align:left;"> -a </td>
   <td style="text-align:left;"> K </td>
   <td style="text-align:left;"> Lysine </td>
   <td style="text-align:right;"> 0.74 </td>
   <td style="text-align:left;"> -b </td>
  </tr>
  <tr>
   <td style="text-align:left;"> G </td>
   <td style="text-align:left;"> Glycine </td>
   <td style="text-align:right;"> 0.57 </td>
   <td style="text-align:left;"> -A </td>
   <td style="text-align:left;"> P </td>
   <td style="text-align:left;"> Proline </td>
   <td style="text-align:right;"> 0.55 </td>
   <td style="text-align:left;"> -B </td>
  </tr>
  <tr>
   <td style="text-align:left;"> P </td>
   <td style="text-align:left;"> Proline </td>
   <td style="text-align:right;"> 0.57 </td>
   <td style="text-align:left;"> -A </td>
   <td style="text-align:left;"> D </td>
   <td style="text-align:left;"> Aspartic Acid </td>
   <td style="text-align:right;"> 0.54 </td>
   <td style="text-align:left;"> -B </td>
  </tr>
</tbody>
</table>

]

.pull-right[

![](images/aa_properties.jpg)

]

---

Given this sequence...

```

Gly– His – Glu – Val - Glu – Ala – Glu – Gly – Val – Tyr – Val – Tyr –Gly

```

---

Assign alpha-helix scores from the table

```

Gly– His – Glu – Val - Glu – Ala – Glu – Gly – Val – Tyr – Val – Tyr –Gly

0.57 1.00  1.51  1.06  1.51  1.42  1.51  0.57  1.06  0.69  1.06  0.69 0.57

```

---

(we show the alpha-helix forming property)

```

Gly– His – Glu – Val - Glu – Ala – Glu – Gly – Val – Tyr – Val – Tyr –Gly

0.57 1.00  1.51  1.06  1.51  1.42  1.51  0.57  1.06  0.69  1.06  0.69 0.57
 -A    0     +A    +a    +A    +A    +A    -A    +a    -a    +a    -a   -A

```

---

Find a nucleation site where 5/6 are a+ or A+

```
 [---  nucleation site  --------]

Gly– His – Glu – Val - Glu – Ala – Glu – Gly – Val – Tyr – Val – Tyr –Gly

0.57 1.00  1.51  1.06  1.51  1.42  1.51  0.57  1.06  0.69  1.06  0.69 0.57
 -A    0     +A    +a    +A    +A    +A    -A    +a    -a    +a    -a   -A
  H     H     H     H     H     H

```

Nucleation site gets to be a helix.

---

Use a sliding window to extend the helix. Abort if score falls below 1.03

```
 [---  nucleation site  --------]
                  [--- window of 4 -->]
 Gly– His – Glu – Val - Glu – Ala – Glu – Gly – Val – Tyr – Val – Tyr –Gly

0.57 1.00  1.51  1.06  1.51  1.42  1.51  0.57  1.06  0.69  1.06  0.69 0.57
 -A    0     +A    +a    +A    +A    +A    -A    +a    -a    +a    -a   -A
  H     H     H     H     H     H     H

```

Score: `(1.06 + 1.51 + 1.42 + 1.51)/4 = 1.38 > 1.03`

---

Extend...

```
 [---  nucleation site  --------]
                        [--- window of 4 -->]
 Gly– His – Glu – Val - Glu – Ala – Glu – Gly – Val – Tyr – Val – Tyr –Gly

0.57 1.00  1.51  1.06  1.51  1.42  1.51  0.57  1.06  0.69  1.06  0.69 0.57
 -A    0     +A    +a    +A    +A    +A    -A    +a    -a    +a    -a   -A
  H     H     H     H     H     H     H     H

```

Score: `(1.51 + 1.42 + 1.51 + 0.57 )/4 = 1.25 > 1.03`

---

Extend...

```
 [---  nucleation site  --------]
                              [--- window of 4 -->]
 Gly– His – Glu – Val - Glu – Ala – Glu – Gly – Val – Tyr – Val – Tyr –Gly

0.57 1.00  1.51  1.06  1.51  1.42  1.51  0.57  1.06  0.69  1.06  0.69 0.57
 -A    0     +A    +a    +A    +A    +A    -A    +a    -a    +a    -a   -A
  H     H     H     H     H     H     H     H     H

```

Score: `(1.42 + 1.51 + 0.57 + 1.06)/4 = 1.14 > 1.03`

---

Abort when the score drops off.

```
 [---  nucleation site  --------]
                                    [--- window of 4 -->]
 Gly– His – Glu – Val - Glu – Ala – Glu – Gly – Val – Tyr – Val – Tyr –Gly

```

Score: `(1.51 + 0.57 + 1.06 + 0.69 )/4 = 0.96 < 1.03` `$\rightarrow$` ABORT!

---

Now, the same for amino acids: nucleation = 3 out of 5 are +b/+B

```
                                                 [-- nucleation site ----]

Gly– His – Glu – Val - Glu – Ala – Glu – Gly – Val – Tyr – Val – Tyr –Gly

0.75 0.87  0.37  1.70  0.37  0.83  0.37  0.75  1.70  1.47  1.70  1.47 0.75
 -b    0     -B    +B    -B     0    -B    -b    +B    +B    +B    +B   -b
                                                  E     E     E     E    E
```

---

Sliding window goes in both directions.

```
                                                 [-- nucleation site ----]
                                          [<- window ---------]
 Gly– His – Glu – Val - Glu – Ala – Glu – Gly – Val – Tyr – Val – Tyr –Gly

0.75 0.87  0.37  1.70  0.37  0.83  0.37  0.75  1.70  1.47  1.70  1.47 0.75
 -b    0     -B    +B    -B     0    -B    -b    +B    +B    +B    +B   -b
                                            E     E     E     E     E    E
```

---

Extend...

```
                                                 [-- nucleation site ----]
                                    [<- window ---------]
 Gly– His – Glu – Val - Glu – Ala – Glu – Gly – Val – Tyr – Val – Tyr –Gly

0.75 0.87  0.37  1.70  0.37  0.83  0.37  0.75  1.70  1.47  1.70  1.47 0.75
 -b    0     -B    +B    -B     0    -B    -b    +B    +B    +B    +B   -b
                                      E     E     E     E     E     E    E
```

---

Abort!

```
                                                 [-- nucleation site ----]
                              [<- window ---------]
 Gly– His – Glu – Val - Glu – Ala – Glu – Gly – Val – Tyr – Val – Tyr –Gly

Score: `(0.83 + 0.37 + 0.75 + 1.70)/4 = 0.91 < 1.0`

(threshold for extended strands: 1.0)

---

Conflicts resolved by higher average

```

Gly– His – Glu – Val - Glu – Ala – Glu – Gly – Val – Tyr – Val – Tyr –Gly

0.57 1.00  1.51  1.06  1.51  1.42  1.51  0.57  1.06  0.69  1.06  0.69 0.57
 -A    0     +A    +a    +A    +A    +A    -A    +a    -a    +a    -a   -A
  H     H     H     H     H     H     H     H     H
 0.75 0.87  0.37  1.70  0.37  0.83  0.37  0.75  1.70  1.47  1.70  1.47 0.75
 -b    0     -B    +B    -B     0    -B    -b    +B    +B    +B    +B   -b
                                      E     E     E     E     E     E    E
```

Average for a-helices: `(1.51 + 0.57 + 1.06 )/3 = 1.05`

Average for b-sheets:  `(0.37 + 0.75 + 1.70 )/3 = 0.94`

---

Choose H over E (because of averages)

```

Gly– His – Glu – Val - Glu – Ala – Glu – Gly – Val – Tyr – Val – Tyr –Gly

---

Final result

```

Gly– His – Glu – Val - Glu – Ala – Glu – Gly – Val – Tyr – Val – Tyr –Gly

H     H     H     H     H     H     H     H     H    E     E     E    E
```

---
class:empty-slide,myinverse
background-image:url(images/quokka.png)

---

![](images/consensus_stru.png)

---

## Sequence structure gap

![](images/growth_sequences.png)

It appears that structural information grows linearly, while amount of
sequence information grows exponentially.

*Torrisi, Mirko, Gianluca Pollastri, and Quan Le. "Deep learning methods in
protein structure prediction." Computational and Structural Biotechnology
Journal (2020).*

---

## Improvements in structure prediction

![:scale 70%](images/performance_increase.png)

(2D structure prediction)

"stat" are statistical models (like Chou-Fasman)

---

## AlphaFold

![:scale 70%](images/Nature-AlphaFold-Google-CASP13-500w@72ppi.webp)

---

## AlphaFold

![:scale 70%](images/alphafold.webp)

* 1st main input: evolutionary information (multiple sequence alignment)
  * Also: structures of closest homologs
 * 2nd main input: predicted secondary structures

The prediction is done iteratively, as you can see
[here](https://static-content.springer.com/esm/art%3A10.1038%2Fs41586-021-03819-2/MediaObjects/41586_2021_3819_MOESM5_ESM.mp4).

Read more [here](https://www.blopig.com/blog/2021/07/alphafold-2-is-here-whats-behind-the-structure-prediction-miracle/).