Computational Modeling for the Activation Cycle of G-proteins
by G-protein-coupled Receptors
Yifei Bao, Adriana B. Compagnoni, Joseph S. Glavy, Tommy E. White
Introduction
Traditionally, biologists have used ordinary differential equations (ODEs) to model biological processes and simulate the evolution of species over time. However, the past decade has seen the emergence of a family of formalisms dedicated to modeling biological behavior (kinetics). Stemming from formal languages designed to capture concurrent computation and communicating processes, these new formalisms range from graphical formalisms to algebraic languages.
In this work we survey five different computational modeling formalisms, and we show how to simulate the activation cycle of G-proteins by G-protein coupled receptors in each of them.
Figure 1: Activation cycle of G-proteins by G-protein-coupled receptors. When a ligand activates the receptor, a conformation change occurs in the receptor that exchanges GDP for GTP on the α subunit and this triggers the dissociation of the α subunit from β γ dimer and the receptor. After the free α unit works on target proteins, GTP will be hydrolyzed to GDP. The GTPase activity is enhanced by binding of the RGS.
Methods
1. ODEs Modeling
2. Stochastic Pi-Calculus Modeling
The stochastic Pi-calculus is a process algebra where stochastic rates are imposed
on processes, allowing for more accurate description of biological systems. A process can be
depicted as a collection of interacting automata with two kinds of reactions: delay@r
and interaction@r on ch.
Figure 2: Graphical representation of Stochastic Pi-calculus modeling .
3. Kappa Languange Modeling
In the Kappa language, reaction rules are described by rewriting rules between lists of agents.
Each agent has a name and binding sites. Agents can become bound, and the two end points
of a link between two agents is Indicated by !i, for some index ~value specifies the
internal state of a site on the agent, -> specifies a bidirectional reaction, <-> specifies an
unidirectional reaction, and @value specifies the reaction rate.
4. Petri Nets Modeling
The basic Petri Net is a directed bipartite graph with two kinds of nodes which are either
places or transitions and directed arcs which connect nodes. In modeling biological
processes, place nodes represent molecular species and transition nodes represent reactions.
Figure.3 Petri Nets for G-protein Cycle.
Results
We show here consistent experimental simulation results. SPiM, Cell Illustrator, Cellucidate, and Bio- PEPA all use Gillespie’s algorithm for simulation. Figure 4(a), 4(b), 4(c), 4(d), 4(e) shows that the results from those four simulations are consistent with the result of the original ODEs modeling. The plots show that RL is consumed as the reaction proceeds. The curves of G and Ga decline and increase oppositely, and the sum of these two species is a constant, which is equal to the initial amount of G-protein, so the conservation relationships mentioned by Yi. et. al. are confirmed ([Gbg] = Gt − [G], [Gd] = Gt − [G] − [Ga]) .
Figure 4 (a)ODEs simulation by Matlab. Figure 4(b) Pi-calculus simulation by SPiM.
Figure 4(c) Petri Nets simulation by Cell Figure 4(d) Kappa simulation by Cellucidate . Illustrator .
Figure 4(d) BioPepa
Conclusion
In our study, the models we build using stochastic modeling approaches can represent the G-
protein cycle quite convincingly, which shows that stochastic modeling approaches could be
efficient instruments to assist in biomedical research.
We develop a high level notation that can be systematically translated into SPiM programs
to hide Pi-calculus communication primitives and enable modeling using only terminology
directly obtained from biological processes (not shown).
