Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

The method of additional particles for models of self-assembly in multilevel biological systems
Ivan A Denisov, Peter I Belobrov

Last modified: 2014-03-28


Hierarchical organization of intracellular mechanics makes essential the methods of multilevel modelling for the development of whole-cell simulations. Self-assembly processes in various organization levels are related with formation of complexes. That is why the problem of simplified mechanical analogs for modelled objects exists along with the problem of adequate complexation models. In the molecular dynamics and various shape-based coarse-grain models the effective potentials approach is used to parametrize formation and breaking of bonds. However there are some contraindications like entropic forces (depletion interaction and hydrophobic forces) and various mesoscopic electronic effects on the supra-molecular level that are challenging for the search of the other bonds approximations. On the higher levels of organization the configuration of sub-levels can be dramatically changed during the bonding process what will make the analogy of effective potential even less credible.

We are suggesting the scale-invariant method of additional particles for modelling bonds in self-assembly models and the theoretical framework for modelling multilevel systems. The formation and breaking of complexes were described by the special multilevel derivative from the Langevin equation, that was called "reconstruction equation". This equation describing the evolution of system with variable amount of additional particles, which represent bonds and other new properties of complexes. Additional particles are emerging according to fixed local preconditions and forming further potential for system evolution. For porpoise of the framework demonstration the artificial multilevel systems were generated with simple rules of properties succession from one level organization to another. The evolution of model multilevel systems were studied using Runge-Kutta-Merson numerical method.

It was shown that reconstruction equations are allowing to study various stable periodic patterns, the dynamics of multilevel systems and the energy transfer through the levels of organization. The parameters that are hidden from the used mechanical analogy, lead to the changes of the potentials between model particles during the bonding process. The method of additional particles easier taking into account side effects for other particles in the system from the bond formation such us charge redistribution or conformational change. Suggested approach for complex formation can be used in multiscale theoretical frameworks such as coarse-grain models in a couple with effective potentials to increase accuracy of computations.


biological hierarchy; multilevel modelling; multiscale modelling