Doug RaifordLesson 19

Framework model Secondary structure

first Assemble secondary

structure segments Hydrophobic

collapse Molten: compact but

denatured Formation of

secondary structure after: settles in

van der Waals forces and hydrogen bonds require close proximity

04/21/23 2Protein Conformation Prediction (Part III)

Two main approaches

Focus this lesson: De novo

04/21/23 Protein Conformation Prediction (Part III) 3

Did a quick look at threading (homology based)

Chou-Fasman (frequency of occurrence of aa’s at specific locations in structure)

Looked at HMM’s (HMMR and Protein Families—PFAM)

Looked at ROSETTA (De Novo, knowledge based)

04/21/23 4Protein Conformation Prediction (Part III)

Name P(a) P(b) P(turn)Alanine 142 83 66Arginine 98 93 95Aspartic Acid 101 54 146• • • Valine 106 170 50

Lattice Approach Abstraction: take a problem of

extreme complexity and simplify Levinthal’s paradox (Physicist,

Berkely, MIT, Columbia) Protein with 100 amino acids => 3100

possible structures Even if really fast (10-13 seconds to sample

each structure) 1.6*1027 years to go through all structures

04/21/23 5Protein Conformation Prediction (Part III)

Premise: proteins fold into lowest energy conformation Reduce complexity by

restricting amino acid locations to evenly spaced lattice points

Generate all possible conformations (within certain constraints)

Lowest energy models should be representative

04/21/23 6Protein Conformation Prediction (Part III)

Only occupy nodes of a lattice

Globular limit number of nodes to

50 Ellipsoidal bounding

volume No nodes without at least

2 connecting edges (no dead-ends)

Fewer nodes than aa’s in sequence (n/2) Must align after the fact From 0 to 3 residues

between nodes

04/21/23 7Protein Conformation Prediction (Part III)

Limit to sequence length of 100 (n)

Energy function statistically derived (verses computationally expensive energy calculations)

Minimal edge lattice – diamond lattice

Between 105 and 107 enumerated conformations

04/21/23 Protein Conformation Prediction (Part III) 8

“We are able to do exhaustive searches of compact, bounded lattice structures with up to approximately 40 vertices. These searches take on the order of a few hours on a fast workstation, and can easily be executed in parallel over several machines.”

04/21/23 9Protein Conformation Prediction (Part III)

At most 3 choices at each node

Self avoiding therefore much pruning

Constrained to small volume (ellipse)

Probably recursive enumeration with self avoidance

Filter Symmetry check: remove

conformations that differ only in their orientation

26 already Remember, total of 50

04/21/23 10Protein Conformation Prediction (Part III)

How to align sequence Remember there are more aa’s than

nodes (from 0 to 3 residues between nodes)

How to score overall energy of a conformation

How to judge similarity to known protein (native) conformation

04/21/23 11Protein Conformation Prediction (Part III)

Iterative/Dynamic Start out evenly spaced For each node determine

the seven possible residues

Choose lowest energy not taken previously

Rinse and repeat Converges in 3 to 5

iterations

04/21/23 12Protein Conformation Prediction (Part III)

6

21111 nmnmnmnmnm rrrrrrrrrr

mn

eeeeeE

m m+1m-1

n n+1n-1

Energy associated with m,n contact average of 5 adjacent energies

m and n given double weight

Rest given single weight

Average of all energies (divide by 6)

04/21/23 13Protein Conformation Prediction (Part III)

But from where did erm,rn come

Statistically derived

puvp

p

p

puvp

vu

TT

C

C

kTe ln,

04/21/23 14Protein Conformation Prediction (Part III)

Given a database of proteins the energy of any given combination of two amino acids is given by:

How contacty is a given proteinExpected number of u,v contacts

Across all proteins, number of v’s next to u’s

•If 1 then across all proteins there are about as many u,v’s as expected.•If >1 then more •If <1 then fewer

04/21/23 15Protein Conformation Prediction (Part III)

Instead of limiting residues to regularly spaced lattice nodes in space…

Limit phi and psi angles to a reduced set of discrete angles

04/21/23 Protein Conformation Prediction (Part III) 16

Off lattice models often attempt to minimize total energy

04/21/23 Protein Conformation Prediction (Part III) 17

G : Free energyH : EnthalpyS : Entropy

G : Free energyH : EnthalpyS : Entropy

ΔE=q-wΔE=q-w

ΔH=ΔE+Δ(PV)ΔH=ΔE+Δ(PV)

S=klnΩS=klnΩ

ΔG = ΔGvan der Waals+ ΔGH-bonds+ ΔGsolvent+ ΔGCoulombΔG = ΔGvan der Waals+ ΔGH-bonds+ ΔGsolvent+ ΔGCoulomb

Backbone RMSD Root mean square deviation

Usually choose top 100 or so predictions and show that actual resides in the set

04/21/23 Protein Conformation Prediction (Part III) 18

Ni

iiN

RMSD1

21

Top 100 conformations--------------------------------!!Actual!!----------------------------------------------

Top 100 conformations--------------------------------!!Actual!!----------------------------------------------

04/21/23 19Protein Conformation Prediction (Part III)

04/21/23 20Protein Conformation Prediction (Part III)

X Y Z Occu Temp ElementATOM 1 N THR A 5 23.200 72.500 13.648 1.00 51.07 N ATOM 2 CA THR A 5 23.930 72.550 12.350 1.00 51.27 C ATOM 3 C THR A 5 23.034 72.048 11.220 1.00 50.34 C ATOM 4 O THR A 5 22.819 72.747 10.228 1.00 51.19 O ATOM 5 CB THR A 5 25.221 71.703 12.416 1.00 51.94 C ATOM 6 OG1 THR A 5 26.159 72.326 13.305 1.00 53.51 O ATOM 7 CG2 THR A 5 25.849 71.583 11.046 1.00 53.33 C

04/21/23 Protein Conformation Prediction (Part III) 21

Name P(a) P(b) P(turn) f(i) f(i+1) f(i+2) f(i+3)

Alanine 142 83 66 0.06 0.076 0.035 0.058Arginine 98 93 95 0.070 0.106 0.099 0.085Aspartic Acid 101 54 146 0.147 0.110 0.179 0.081Asparagine 67 89 156 0.161 0.083 0.191 0.091Cysteine 70 119 119 0.149 0.050 0.117 0.128Glutamic Acid 151 037 74 0.056 0.060 0.077 0.064Glutamine 111 110 98 0.074 0.098 0.037 0.098Glycine 57 75 156 0.102 0.085 0.190 0.152Histidine 100 87 95 0.140 0.047 0.093 0.054Isoleucine 108 160 47 0.043 0.034 0.013 0.056Leucine 121 130 59 0.061 0.025 0.036 0.070Lysine 114 74 101 0.055 0.115 0.072 0.095Methionine 145 105 60 0.068 0.082 0.014 0.055Phenylalanine 113 138 60 0.059 0.041 0.065 0.065Proline 57 55 152 0.102 0.301 0.034 0.068Serine 77 75 143 0.120 0.139 0.125 0.106Threonine 83 119 96 0.086 0.108 0.065 0.079Tryptophan 108 137 96 0.077 0.013 0.064 0.167Tyrosine 69 147 114 0.082 0.065 0.114 0.125Valine 106 170 50 0.062 0.048 0.028 0.053