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Protein Folding Problem: Given sequence of polypeptide, find the 3D arrangement of all atomsin the polypeptide in its physiological environment.

Central Dogma of Molecular Biology:Sequence Structure Function

Tentative Definition of Knowledge Based Pseudopotential:The free energy function corresponding to a statistical mechanical model of a proteinderived from the experimentally determined structural coordinates of several differentproteins.

An Introduction to Knowledge Based PseudopotentialsFor Proteins

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Protein Modeling Methods-ab initio - methods based on potential

functions that describe the

physics of the situation.(ie.. Blue Gene)

-Knowledge based - methods based upondatabase statistics.- Homology Modeling- Threading- Fold Recognition

Knowledge

BasedPseudo-Potentials ?

Physicist Perspective -

An N-body problemBiologist Perspective -

Information

Genomics Proteomics

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Perspective

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Methods Developed by BiologistsDefinitions:Neutral drift - the random mutations which, throughout time, change a proteins primary

structure but do not significantly change its function (some unknown element of

structure is conserved).Homologous proteins - evolutionarily related proteins.Analogous proteins - proteins which have low sequence identity, but can be well superimposed.

They have different functions and their structural similarity is the result of convergentevolution.

Concepts: The primary structures of a given protein from related species closely resemble one another.

If the species have evolved from a common ancestor, then the proteins have evolved from thecorresponding protein in that ancestor.

If a protein is well adapted to its function and is not subject to any real physiologicalimprovement, it will, nevertheless continue to evolve (neutral drift).

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Knowledge Based PseudopotentialsGoal: Concoct a formulation for the determination of the most probableconfiguration of atoms in a protein using only information from

a structural database.Simplified Protein Representations:

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Proteins as solutions- Tanaka and Scheraga:

Model is a mirror of the regular solution(Bragg-Williams latticemodel of solutions)

Assumptions:1) Liquid solution of components A and B are packed closely resembling a crystal2) A and B are similar in molecular size and shape to allow perfectly random mixing

in the lattice.

3) Intermolecular forces are appreciable only for nearest neighbors.

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- Miyazawa and Jernigan:Model mirrors the Bethe - Peierl quasichemical approximation(also a lattice model)

- Sidechain Centroid is the reduced representationqini

2= nij

j= 0

20

! 0 is for solvent

W = niiw

ii+ n

jjw

jj + n

ijw

ij

QN(V,T) = [q1I

(T)e! q1w11/ 2kT]

n1 [q2I

(T)e!q2w22/ 2 kT]

n2"(n1

n12

# , n2 ,n12)en12w / 2kT

w =w11+w

22! 2w

12

"(n1n12

# ,n2,n12) =N!

n1!n

2!

Quasichemical Approx. for species i and j:ii + jj 2ij

nij2

niinjj! exp(2wij "wii "wjj)

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The Pair PMF Approach

w(r) =!kTln[g(r)]

where,

g(r) = g(2 )

(!r

1,!r

2) =

f ( 2) (!r

1, !r

2)

f

(1)

(

!r1)f

(1)

(

!r2 )

=

1

"

2

#

zN

$

3N

(N! 2 )!N=

2

%

& ...V

' e!(U({q})

' d3(N!2)

q

so,

)w(r)

)!r1

=

!kT

g(r)

)g(r )

)!r1

=

zN

$3N(N!2)!N=2

%

& ...V

' e! (U({q}) )U({q})

)!r1

*

+,-

./'d3(N!2 )q

zN

$3N

(N! 2 )!N=2

%

& ...V'

e!(U({q})

'd

3(N! 2)q

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g(r) =nobs (r)

nhom

(r)=

nobs (r)

4!r2"r#

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Further Critique of PMF approach:The PMF of a protein is:

w({r}) = !kTlng(!r1,

!r2 ,...,

!rN) " !kTln[g(r12)g(r23)...etc.]

or,

w({r}) " w(r12) + w(r23)+ ...

In some cases this superposition principle is a good approximation,but never completely

trueNot even for clusters as small as three particles.

Approximation was developed to solve integral equations of Born, Green, and Kirkwood.

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Correspondence of PMFs in ProteinsAnd Liquids

By Shan and Zhou (JCP: 9/15/00)1)Use a configuration after 1billion collisions of a hard

sphere liquid (500 spheres).2)Generate chains 90 res long from the configuration using

some algorithm.3)3.7 million chains found with pairwise connectivity

less than 1.5!4)Select 90 residues from each of a set of real 210

nonhomologous proteins which correspondto the smallest radius of gyration in the protein.- convert identities to a 2-letter alphabet: N/P

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5)Calculate interaction energies using some pairwise contact parameters.

6)Select 10,000 structures for each of the 210 sequences w/ lowest energy.7)Calculate PMF using..

8)Chain connectivity of model proteins was modeled with a gauusian distributionfor the reference state.

9)The liquid state PMF was calculated as usual.

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Protein Liquid