Protein Structure, Function and Interactions

Peptide-Protein Interactions Design of Peptides as DrugsBurak ErmanChem. and Biol. Eng. DeptKoc University, Istanbul Turkey

Overview

Peptide-Protein Interactions

The simplest short range coarse graining: The neighborhood potential, contact map in native proteins.

Statistical thermodynamics of native proteins. Fluctuations.

Probability distribution of fluctuations.

The harmonic approximation: The Gaussian Network Model, GNM

Energy-fluctuation correlations in harmonic systems.

Protein-ligand interactions. The drug binding problem.

Determination of binding sites: Energy gates of a protein as the binding sites.

Allostery. Graph perturbation. Interaction pathways and hub residues.

Peptide design

Free energy changes upon binding.

Balance of different forces:Entropy penalty. Enthalpic interactions.Solvation entropy.

Different conformations of a peptide.

Markov statistics and calculating TD variables

The contact mapResidue IndexResidue Index

Physical interpretation:

Each pair of residues in contact is connected with a linear spring. Spring constants are same for each spring.

G is the spring constants matrixWe are interested in:Fluctuations of residues subject to the harmonic potential of the springs

The system

The protein and its environment form a closed system. Protein exchanges energy with the environment.

Total energy of the protein + surroundings = constant.

Statistical thermodynamics of protein structure and function

Yogurtcu, O.N., M. Gur, and B. Erman, Statistical thermodynamics of residue fluctuations in native proteins. Journal of Chemical Physics, 2009. 130(9): p. 095103-095113.

WhereS = The mean (thermodynamic) value of the entropy, U = energy,V = volume,R = position vectors of Cas. The protein is in diathermal contact with the surrounding water a pressure (P) and a force (F) reservoir.The energy, volume and the positions of residues exhibit fluctuations.

The distribution are the instantaneous extensive variables is the Massieu transform of the entropy

H. B. Callen, Thermodynamics and an introduction to thermostatistics, Second ed. (Wiley, 1985).

Harmonic Fluctuations

f is a higher order product of the fluctuations of the extensive variables, DU, DV, DR. Fk represents any of the extensive variables DU, DV, DR, Yk represents the conjugate variables 1/T, P, F, Higher order correlations

An increase in energy (protein taking energy from surroundings) is correlated with large DRiJ2

A decrease in energy (protein giving off energy to the surroundings) is correlated with small DRiJ2

The residues i and j with large DRiJ2 are responsible for energy interactions.

These are the anticorrelated residue pairs.

Largest eigenvalue of the G matrix is associatedwith the significant contribution to DUi

DUi is the energy entering the protein from the surroundingsthrough residue i

Those residues at the surface are the Energy Gates.

Those residues that connect two surface gate residues constitute the Hubs along the Interaction Pathway.

Those residues along the interaction pathway that are anticorrelated are the important ones.

Connection to allostery is obvious.

Example: The HLA proteins: B2705 (1OGT.pdb)

DUi

The change of residue at position 116 perturbs the protein structureespecially residue 101 We now perturb the connectivity of residue 101 and observe the resulting affinity changes

Haliloglu, T. and B. Erman, Analysis of Correlations between Energy and Residue Fluctuations in Native Proteins and Determination of Specific Sites for Binding Physical Review Letters, 2009. 102: p. 088103-088106.

Haliloglu, T., E. Seyrek, and B. Erman, Prediction of Binding Sites in Receptor-Ligand Complexes with the Gaussian Network Model. Physical Review Letters, 2008. 100: p. 228102-4.

Overview

Peptide design

Different conformations of a peptide. The free energy.

Free energy changes upon binding.

Balance of different forces:Entropy penalty. Enthalpic interactions.Solvation entropy.

The neglected part: conformational changes ofThe peptide upon bindingMarkov statistics and calculating TD variables

Jackson, D.C., et al., The central role played by peptides in the immune response and the design of peptide-based vaccines against infectious diseases and cancer. Current Drug Targets, 2002. 3(2): p. 175-196. Peptides play a fundamental role in immune recognition and induction of immune responsePeptides are small proteins that consist of 5-15 amino acids

DFRB(L) : change from rigid body translation and rotation of the ligand, DFconf(L) : conformational free energy change of the ligandDFconf(P) : is from the conformational changes of the protein, DFbinding(LP) : change in free energy due to the interaction between the ligand and protein, and DF(W) : is the free energy change of water. . Free energy changes upon bindingDFRB(P) : change from rigid body translation and rotation of the protein

The ith residue of the peptide.

Ala, Glu, Lys, Met, Arg, Leu, Phe, Tyr, Trp

Ile, Val

XPr

Pro

Gly

PX (fi, yi) = NX(fi, yi)/ NX(fi, yi) PXY (yi, fi+1) = NXY (yi, fi+1)/ NXY (yi, fi+1)We can obtain the probabilities from PDB

Engin, O., M. Sayar, and B. Erman, Introduction of Hydrogen Bond and Hydrophobicity Effects into the Rotational Isomeric States Model for Conformational Analysis o Unfolded Peptides. Phys. Biol. , 2009. 6: p. 1-13.Keskin, O., et al., Relationships between amino acid sequence and backbone torsion angle preferences in proteins. Proteins-Structure Function and Bioinformatics 2004. 55: p. 992-998. References

For a three state system

Statistical weight matrix

Partition function

Partition function

Helmholtz free energy, A = E TS asFrom this, we obtain the entropy as:

Calculation of probabilities

Unal, E.B., A. Gursoy, and B. Erman, Conformational energies and entropies of peptides, and the peptide-protein binding problem. Phys Biol, 2009. 6(3): p. 36014.

Mean conformational energy of the peptideEntropy penalty

Number of possible peptide drugs of 10 residues = 2010 = 1013 We have to choose the most suitable peptide from this populationExisting successful peptide drugs have low DS and low CvThe entropy penalty seems to be a significant factor in binding

AcknowledgmentsMert GurOsman YogurtcuBesray UnalOzge EnginTurkan HalilogluMehmet Sayar

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