Multi-Agent Simulation of Protein Folding Luca Bortolussi 1 Agostino - - PowerPoint PPT Presentation

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results

Multi-Agent Simulation of Protein Folding

Luca Bortolussi1 Agostino Dovier1 Federico Fogolari2

1Department of Mathematics and Computer Science

University of Udine

2Department of Biomedical Science and Technologies

University of Udine

MAS-BIOMED, Utrecht, 25th July 2005

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results

Outline

1

Proteins: a Quick Introduction Biological Background Protein Structure Prediction The Energy Function

2

Multi-Agent Scheme for PSP Multi-Agent Optimization Searching Level Strategy Level Cooperative Level

3

Results Implementation Experimental Results Future Work

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Biological Background

Proteins: the Bricks of Life

Proteins are fundamental to life. They have a very wide range of biological functions. For example:

Enzymes—biological catalysts Storage (e.g. ferritin in liver) Transport (e.g. haemoglobin) Messengers (transmission of nervous impulses—hormones) Antibodies Regulation (during the process to synthesize proteins) Structural proteins (mechanical support, e.g. hair, bone)

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Biological Background

Primary Structure

A Protein is a polymer chain (a list) made of monomers (aminoacids). This list is called the Primary Structure. The typical length is 50–500. Aminoacids are of 20 different types:

Alanine (A), Cysteine (C), Aspartic Acid (D), Glutamic Acid (E), Phenylalanine (F), Glycine (G), Histidine (H), Isoleucine (I), Lysine (K), Leucine (L), Methionine (M), Asparagine (N), Proline (P), Glutamine (Q), Arginine (R), Serine (S), Threonine (T), Valine (V), Tryptophan (W), Tyrosine (Y).

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Biological Background

Tertiary Structure

The complete 3D conformation of a protein is called the Tertiary Structure. The tertiary structure determines the function of a Protein. ∼ 31500 structures (most of them redundant) are stored in the PDB.

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Biological Background

Tertiary Structure

Proteins fold in a determined environment (e.g. water) to form a very specific geometric pattern (native state). The native conformation is relatively stable and unique and is the state with minimum free energy (Anfinsen’s hypothesis).

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Biological Background

Secondary Structure

Locally, a protein presents some repetitive motifs, known as secondary structure: α-helices; β-sheets.

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Protein Structure Prediction

Approaches to PSP

The Protein Structure Prediction (PSP) is the problem of predicting the tertiary structure of a protein, given the primary

• ne.

It basically consists in minimizing a suitable energy function. We focused on simplified models, where aminoacids are represented as spheres. One crucial point is the choice of this energy function:

it must discriminate between native states and spurious configurations;

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results The Energy Function

The Energy Model

The aminoacids are represented as a single center of interaction (coarse model). The energy function is very simple (used for generating coarse models to throw into molecular dynamics). E(x, t) = Ecooperative(x, t) + Epairwise(x, t) + Echiral(x, t) +Esteric(x) + Echircst(x) + Edist(x).

• G. M. S. De Mori, C. Micheletti, and G. Colombo. All-atom folding simulations of the villin headpiece from

stochastically selected coarse-grained structures. Journal Of Physical Chemistry B 108(33):12267–12270, 2004.

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Multi-Agent Optimization

The MAGMA Scheme for Optimization

Parallel or Concurrent Optimization Algorithms can be designed in a multi-agent fashion. We follow the MAGMA scheme, which distinguish 4 types of agents, sorted by their power: (level 0) Agents generating an initial solution. (level 1) Agents searching the state space. (level 2) Agents performing global strategic tasks. (level 3) Agents deciding cooperation strategies.

M.Milano, A.Roli. MAGMA: A Multiagent Architecture for Metaheuristics.IEEE Trans. on Systems, Man and Cybernetics - Part B, Vol.34, Issue 2, April 2004.

• M. Resende, P

. Pardalos, S. Duni Ek¸ sio˜

• glu. Parallel Metaheuristics for Combinatorial Optimization. Models

for Parallel and Distributed Computation - Theory, Algorithmic Techniques and Applications, R. Correa et al. Eds., Kluwer Academic, 179-206, 2002.

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Searching Level

The Searching Agents

We associate an independent agent to every aminoacid. These agents move in the 3D-space, interact and communicate. The exploration of the state space is guided by their current knowledge about the position of other aminoacids. The agents interact by communicating each other their respective spatial position.

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Searching Level

The Searching Agents

Movement Strategy Each amino agent chooses randomly a new point xnew from a box centered in its current position xold. Then, it computes the potential w.r.t its old position (Eold) and the new

• ne (Enew), and accepts the move

using a Monte Carlo criterion (i.e. with probability min{1, e

Enew −Eold T

}).

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Searching Level

The Searching Agents

Communication Strategy The energy function for an aminoacid depends essentially from the position of its spatial neighbours. To avoid continuous broadcasting of information, each aminoacid communicates more often with its spatial neighbours, and less with all the rest of aminoacids. Therefore an aminoacid may not know the exact position of all the

• thers (errors in the energy).
• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Strategy Level

Exploration and Environment

Improving the Space Exploration We need to enhance the space exploration, and allow the aminoacid to visit more configurations. This is achieved by a strategic agent (the “orchestra director”), which possesses the exact knowledge of the position of all aminoacids. Every now and then, it “freezes” the amino agents, and it “shakes” the chain.

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Strategy Level

Exploration and Environment

The environment The environment in which the aminoacids are embedded is characterized by a single parameter: the temperature (it governs the acceptance ratio of hill-climbing moves). we use a simulated annealing scheme: temperature is gradually lowered according to a cooling schedule. This cooling schedule is controlled by a dedicated strategic agent.

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Cooperative Level

Making Agents Cooperate

We would like that amino agents cooperate to create favorable configurations. These configurations we have in mind are local structures which are willing to appear in a protein:

secondary structure elements small recurrent oligomers

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Cooperative Level

Making Agents Cooperate

Cooperation Cooperation is achieved by a variant

• f “Computational Fields”, i.e. by

introducing perturbations in the force field to make agents form certain spatial patterns.

• M. Mamei, F. Zambonelli, L. Leonardi. A Physically Grounded Approach to

Coordinate Movements in a Team. Proceedings of ICDCS, 2002.

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Cooperative Level

Making Agents Cooperate

Cooperation

In our case, this effect is obtained by introducing a modification in the potential energy: we add terms that penalize all configurations but the one we want. These modifications are different from aminoacid to aminoacid, to induce local effects. The cooperation is coordinated by a dedicated agent, who has full knowledge of the current configuration, plus external one.

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Implementation

Implementation and Expectations

Implementation We have two different implementations of the program: SICStus Prolog and LINDA (declarative). Energy is computed by external C functions. It is very slow. Multithread version in C++. Faster, but runs on a sequential machine.

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Experimental Results

Experimental Results

Without Cooperation Protein RMSD energy 1LE0 4.21

• 10.253

1KVG 3.89

• 19.41

1PG1 7.25

• 54.56

1VII 7.22

• 51.06

1E0M 8.65

• 76.47

With Cooperation Protein RMSD energy 1LE0 2.99

• 5.75

1KVG 1.29

• 9.27

1PG1 2.73

• 23.04

1VII 6.81

• 32.13

1E0M 5.96

• 22.18
• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Experimental Results

Experimental Results

1PG1 without cooperation 1PG1 with cooperation 1PG1 from PDB

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Experimental Results

Experimental Results

1PG1 without cooperation 1PG1 with cooperation 1PG1 from PDB

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Experimental Results

Experimental Results

1PG1 without cooperation 1PG1 with cooperation 1PG1 from PDB

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Future Work

Future Work

Using a more detailed potential (statistical, with local terms, with side chain centroids) Implementing a true parallel version in MPI. Enhancing the exploration of the state space by using spherical coordinates (and grouping aminoacids together) Using a more refined minimization scheme than simulated annealing Enhancing the cooperation (mimicking hydrophobic effect)

• L. Bortolussi, A. Dovier, F. Fogolari

Multi-Agent Simulation of Protein Folding