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 Bortolussi 1 Agostino Dovier 1 Federico Fogolari 2 1 Department of Mathematics and Computer Science University of Udine 2 Department of Biomedical Science and Technologies University of Udine BCI, Dobbiaco, 16 th September 2005 L. Bortolussi, A. Dovier, F. Fogolari Multi-Agent Simulation of Protein Folding

Proteins: a Quick Introduction Multi-Agent Scheme for PSP Results Outline Proteins: a Quick Introduction 1 Biological Background Protein Structure Prediction Multi-Agent Scheme for PSP 2 Multi-Agent Optimization Searching Level Strategy Level Cooperative Level Results 3 Implementation Experimental Results 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: Ala nine (A), Cys teine (C), Asp artic Acid (D), Glu tamic Acid (E), Phe nylalanine (F), Gly cine (G), His tidine (H), I so le ucine (I), Lys ine (K), Leu cine (L), Met hionine (M), As paragi n e (N), Pro line (P), Gl utami n e (Q), Arg inine (R), Ser ine (S), Thr eonine (T), Val ine (V), Tr y p tophan (W), Tyr osine (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 Levinthal’s Paradox The space of accessible spatial configurations for a protein is very big. If protein folding proceeded through random sampling of state space, it would take thousand years to fold a protein. It actually takes milliseconds. There must exists a folding code that makes protein folding possible. Levinthal’s paradox (1968) J. Chim. Phys. Vol. 65, pp. 44-55. 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 one. 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; we used one available in literature: De Mori et alt., J. Phys. Chem. B , 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 x new from a box centered in its current position x old . Then, it computes the potential w.r.t its old position ( E old ) and the new one ( E new ), and accepts the move using a Monte Carlo criterion (i.e. Enew − Eold with probability min { 1 , e } ). 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 others (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 of “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