Life spans in size from small organisms consisting of single cells to complex organisms built up of billions of cells. Even the single-cell organisms are challenging to fully understand and study—their function is dependent on a rich set of reaction networks. Important molecules inside a cell may exist in only a few copies, and that makes them exceedingly difficult and costly to study.
The aim of our research is to develop algorithms and software that can assist in discoveries in basic science and medicine. We use mathematical models to describe how molecules move and interact inside cells, and then simulate these models to gain an understanding of how cells work. The multiscale nature of the problem is an interesting challenge. At the finest level we would consider single biomolecules and their exact molecular structure. There are models and methods for simulating systems at that level, but they are computationally expensive.
We couldn’t simulate the behavior of a large, complex system with such a method. Instead of considering the true structure of molecules, we could use a model that approximates them by spheres. At this level we can simulate medium-sized systems inside a cell on a time scale of seconds to minutes. An even more coarse-grained model doesn’t model individual molecules, but counts the number of molecules of different species in different parts of the domain. At this scale we can simulate bigger systems for hours.
We have developed methods with the aim of coupling accurate fine-grained methods with less computationally expensive coarse-grained methods. In doing so, we obtain methods that are more accurate than the coarse-grained method, but still more efficient than the fine-grained method. These methods are called multiscale methods. By adding scales to our simulations—more accurate models, incorporating some of the many complex internal structures that are vital to the function of the cell, but also more coarse-grained models, we attempt to move beyond the boundaries of what is currently possible to simulate with state-of-the-art methods.
- S. Hellander, A. Hellander, and L. Petzold (2017) Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning, Submitted.
- E. Blanc, S. Engblom, A. Hellander and P. Lötstedt (2016) Mesoscopic modeling of stochastic reaction-diffusion kinetics in the subdiffusive regime, Multiscale Model. Simul., 14(2), 668–707.
- L. Meinecke, S. Engblom, A. Hellander, P. Lötstedt (2016) Analysis and design of jump coefficients in discrete stochastic diffusion models, SIAM J. Sci. Comput. 38(1), A55–A83.
- M. Lawson, L. Petzold and A. Hellander (2015) Accuracy of the Michaelis-Menten approximation when analyzing effects of molecular noise, Roy. Soc. Interface, 12(106) 2015
- S. Hellander, L. Petzold and A. Hellander (2015), Reaction rates for mesoscopic reaction-diffusion kinetics, Phys. Rev. E., 92(2), 023312.