Simulation: Efficiently simulating strongly coupled networks of chemical reactions
Chemical reactions play key roles also in biology and physics. Metabolic pathways in living cells or cell signaling networks constitute complex, interconnected networks of chemical reactions. Since the number of copies of each molecule is low in biological cells, deterministic descriptions of the reaction networks by differential equations are not always valid. Instead, stochastic simulation algorithms are available to simulate and study the behavior of the reaction networks in the computer.
If a reaction network is weakly coupled, i.e. the number of reactions that are influenced by any other reaction remains constant when the network size increases, it can be efficiently simulated using existing algorithms. Many networks in systems biology and physics are, however, strongly coupled. Examples include scale-free networks in biology, where certain hubs are strongly coupled to the rest of the network, or nucleation-and-growth processes in physics or biological membranes. In these cases, the computational cost of the available algorithms grows rapidly, preventing simulations of larger networks.
We have recently presented a new class of highly efficient stochastic simulation algorithms whose computational cost is independent of the degree of coupling of the network. This allows for the first time simulating strongly coupled real-world networks with the same efficiency as weakly coupled networks. The new algorithms allow simulations of networks with thousands of chemical species on a single laptop computer, thus providing an important tool for addressing the grand challenges in modern biology and medicine.
The plot above shows the computer time required per simulated reaction of a strongly coupled reaction network describing colloid aggregation in biomembranes of increasing size (number of monomers N). The new algorithm is orders of magnitude faster and scales better than the classical Optimized Direct Method (ODM).
R. Ramaswamy, N. González-Segredo, and I. F. Sbalzarini. A new class of highly efficient exact stochastic simulation algorithms for chemical reaction networks. J. Chem. Phys., 130(24):244104, 2009.
R. Ramaswamy and I. F. Sbalzarini. A partial-propensity variant of the composition-rejection stochastic simulation algorithm for chemical reaction networks. J. Chem. Phys., 132(4):044102, 2010.