Explain scoring matrices (BLOSUM, PAM) — Hinglish notes

6.4.5 · Biology › Bioinformatics & Computational Biology

SCORING MATRIX ki zaroorat KYUN hai?

Score ko KISI CHEEZ ko represent karna chahiye? Sahi quantity yeh hai: kya yeh pairing zyada likely hai kyunki dono residues truly homologous hain (common ancestor se related), ya yeh sirf random coincidence hai? Yeh ek likelihood ratio hai.

Log-odds score ko first principles se KAISE derive karein

Formula Log-odds score derive karna

Ek trusted alignment mein ek column consider karo jisme residues $a$ aur $b$ paired hain.

Do competing hypotheses:

$H_{1}$ (homology): woh isliye paired hain kyunki woh ek common ancestor se aaye hain. Is pair ko observe karne ki probability = $q_{ab}$ (trusted alignments mein observed joint frequency).
$H_{0}$ (random): woh chance se saath aaye. Probability = $p_{a} p_{b}$ , jahan $p_{a}$ amino acid $a$ ki background frequency hai.

Is pairing ke real hone ke odds hain $odds = \frac{q _{ab}}{p _{a} p _{b}} .$

Log kyun lete hain? Alignment scores ko columns ke across additive hona chahiye (total score = column scores ka sum). Lekin independent columns ki probabilities multiply hoti hain. Log lene se multiplication, addition mein convert ho jaata hai: $lo g (\prod_{i} \frac{q _{i}}{p _{i}}) = \sum_{i} lo g \frac{q _{i}}{p _{i}} .$ Toh hum substitution score define karte hain $s (a, b) = \frac{1}{λ} lo g_{2} \frac{q _{ab}}{p _{a} p _{b}}$ Ek scaling constant se multiply karo aur integers mein round karo (isliye BLOSUM entries chhote whole numbers hote hain). BLOSUM base-2 logs (bits) use karta hai, $λ = 1/2$ se scale karke (yaani half-bits).

Yeh step kyun? Kyunki log-odds $H_{1}$ vs $H_{0}$ test karne ke liye statistically optimal score hai (Neyman–Pearson lemma ka consequence). Sign ka matlab:

$s (a, b) > 0$ : substitution chance se zyada dekhi gayi → conserved/favorable.
$s (a, b) < 0$ : chance se kam dekhi gayi → disruptive.
$s (a, b) = 0$ : bilkul chance se expected jaisi.

BLOSUM — BLOcks SUbstitution Matrix

Number KAISE kaam karta hai (yahan sabse zyada confuse hote hain log):

PAM — Point Accepted Mutation

Higher-PAM matrices KAISE bante hain — extrapolation:

Closely-related sequences se directly ek $20 \times 20$ mutation probability matrix $M$ banao 1 PAM ke liye.
Zyada distant sequences model karne ke liye, matrix ko khud se multiply karo: $M^{(n)} = M^{n} \Rightarrow PAM250 = M^{250} .$ Yeh assume karta hai ki mutations ek Markov process ki tarah accumulate hoti hain (har step past se independent).
$M^{n}$ ko upar wale formula se log-odds mein convert karo.

Figure — Explain scoring matrices (BLOSUM, PAM)

Worked Examples

Active Recall

Recall Positive vs negative matrix entry ka kya matlab hota hai?

Positive → substitution chance se zyada hoti hai (conserved/favorable). Negative → chance se kam (disruptive). Zero → chance se expected jaisi.

Recall PAM aur BLOSUM ke liye "distant" kis direction mein hai?

PAM high = distant (zyada mutations). BLOSUM high = close (higher identity clustering). Woh opposite direction mein chalte hain.

Recall Odds ratio ka logarithm kyun lete hain?

Taaki per-column scores add up ho sakein multiply karne ki jagah — yeh match karta hai is baat se ki alignment algorithms scores sum karte hain aur independent probabilities combine hoti hain.

Recall Feynman: ek 12-saal ke baache ko explain karo

Trading cards imagine karo. Kuch swaps fair hain ("main tujhe ek common card deta hoon ek common card ke badle") aur kuch unfair. Ek scoring matrix ek cheat sheet hai jo batata hai ki har swap kitna fair hai. Yeh real card-trading history (real proteins jo evolve hue) dekhta hai aur plus points deta hai un swaps ko jo log actually bahut karte hain (kyunki woh cards basically interchangeable hain) aur minus points un swaps ko jo almost koi nahi karta (kyunki woh cards bilkul alag hain). Hum points add karte hain yeh decide karne ke liye ki do poore decks (proteins) cousins hain ya nahi.

Flashcards

Scoring-matrix entry

s (a, b)

kis quantity ko represent karta hai?

Ek scaled log-odds ratio:

\frac{1}{λ} lo g_{2} \frac{q _{ab}}{p _{a} p _{b}}

— pair (a,b) real alignments mein kitni baar occur karta hai vs chance se.

Log-odds score mein log kyun liya jaata hai?

Per-column scores additive banane ke liye (logs independent column probabilities ke product ko sum mein convert karte hain).

BLOSUM62 mein "62" ka kya matlab hai?

Clustering threshold: ek block ke andar ≥62% identical sequences ko substitutions count karne se pehle merge/ek maana jaata hai.

Higher BLOSUM number kin sequences ke liye hai?

Zyada closely related (higher identity) sequences ke liye.

1 PAM unit ka kya matlab hai?

Ek evolutionary distance jahan 1 accepted point mutation per 100 residues hua ho (1% change).

High-PAM matrices kaise generate kiye jaate hain?

1-PAM mutation matrix ko khud se multiply karke: PAM250 = M^250 (Markov extrapolation).

Higher PAM number kin sequences ke liye hai?

Zyada distantly related (zyada accumulated mutations wali) sequences ke liye.

BLOSUM vs PAM: unke numbers directionally kaise relate karte hain?

Opposite — high BLOSUM = close; high PAM = distant. (e.g. BLOSUM62 ≈ PAM160–200 behavior.)

W↔W +11 score karta hai lekin L↔L sirf +4 BLOSUM62 mein kyun?

Trp rare hai, toh Trp match statistically surprising hai (high info), bada log-odds deta hai; Leu common hai, toh uska match kam informative hai.

~25% identity distant homolog search ke liye kaun sa matrix?

BLOSUM45 ya PAM250.

Kaun sa statistical principle log-odds ko optimal score banata hai?

Neyman–Pearson lemma (homology H1 vs random H0 ke liye likelihood-ratio test).

BLOSUM kin data se bana hai?

BLOCKS database ke ungapped, conserved local protein alignments se (directly observed).

PAM kin model se bana hai?

Closely related proteins par fit kiye gaye point mutations ke ek Markov evolutionary model se (Dayhoff).

Mnemonic

Connections

Sequence Alignment — scoring matrices Needleman-Wunsch Algorithm & Smith-Waterman Algorithm mein feed hoti hain.
BLAST — default matrix BLOSUM62 hai; choice sensitivity affect karti hai.
Log-odds and Likelihood Ratios — statistical backbone (Neyman–Pearson).
Markov Chains — PAM extrapolation matrix powers $M^{n}$ ke zariye.
Amino Acid Properties — hydrophobicity/charge explain karta hai kyun kuch substitutions high score karti hain.
Gap Penalties — alignment score ka doosra aadha hissa.