A novel algorithm helps discover a fundamental effect in chemical kinetics

This article contains a fundamental contribution to chemical reaction theory in small volumes, which may primarily find applications in biochemistry and nanotechnology. Chemical reactions are among the most important phenomena in our world and daily lives. From the chemical and pharmaceutical industry to medical analytics to biological cells, chemical reactions are everywhere.

Chemical reactions are conventionally described using "rate equations", as also taught in school. Rate equations are valid for large molecular populations, where individual molecules do not matter. For small populations, however, the fact that individual molecules are distinct particles becomes important. Rate equations are then invalid and predict wrong concentrations. This situation is frequently found in biological cells. Of many molecules there are only a few tens to hundreds of copies in a cell. Genes are present in only one or two copies.

The present work has shown for the first time that the error in the rate equation prediction can grow so large that the ordering of species is wrongly predicted. Correctly accounting for the particle nature of molecules, one finds that if species A is more abundant than species B at high population, the reverse can be true at populations below a critical limit, for the same reaction rates and the same input concentrations. This concentration inversion effect is not predicted by rate equations and is described here for the first time.

The present work also provides a theory that allows estimating the critical population or volume for any reaction network, as well as the correct ordering of concentrations for populations below the critical limit. This work used a combination of theoretical and computational approaches. The corresponding computer simulation algorithm has earlier been developed in the MOSAIC Group.

For most biochemical reaction networks, the critical volumes are comparable to the sizes of cells or intra-cellular organelles. This suggests that cells could use the inversion effect described here to, e.g., tune the sensitivity of signalling pathways or to sense its own size. In biological systems, the relative ordering of chemical concentrations is frequently more important than their absolute values. Being able to predict the correct ranking of molecule abundances, and to determine when conventional rate equations fail to do so, is key to biological modeling.

About the MOSAIC Group

The MOSAIC Group does research in the methodology and applications of Computational Science. It aims at addressing significant scientific challenges using novel computational methods and algorithms, without which the problems could not be solved. The MOSAIC Group is an experiment in interdisciplinary creativity, combining expertise from Computer Science, mathematics, engineering, physics, and biology.

The MOSAIC Group was founded and is headed by Prof. Ivo F. Sbalzarini. The group is currently affiliated with the Institute of Theoretical Computer Science in the Department of Computer Science at ETH Zurich. As per July 31, 2012, the MOSAIC Group and Professor Sbalzarini are going to relocate to the new Max Planck Center for Systems Biology in Dresden, Germany.

The history leading to the results

The MOSAIC Group has earlier developed a novel simulation algorithm for exact chemical kinetics, enabling computer simulations at a fraction of the computational cost incurred by previous algorithms. For this work, Rajesh Ramaswamy has been honoured with the SIB Best Graduate Paper Award in 2010, a competitive Swiss national prize annually awarded by the Swiss Institute of Bioinformatics.

This algorithm has earlier allowed identifying novel dynamics of chemical reaction networks around non-equilibrium states, as frequently found in biology, and has led to the discovery of a novel effect of molecular population on the frequency of chemical oscillators. The latter has implications, e.g., for biological clocks, such as the circadian clocks that determine the daily rhythm of our body.