Two central aspects of chemical processing in living systems are

  • spatial self-organization via  reaction properties
  • spatial self-organization via dynamic membrane structures

and both depend on the combinatorial complexity of the molecules involved. Whereas much work in biophysics emphasizes structural aspects, our primary goal was to extend chemical kinetic simulations to include a first approximation to effects induced by dynamic structures.

Membranes provide a two-dimensional reaction environment in which collective self-organization of embedded structures is utilized by the cell. Any mesoscale simulation method must reflect both topological membrane dynamics and chemical reaction kinetics, whereby their combination poses a considerable challenge. In order to serve as a chemical reaction environment, simulated membranes must be sufficiently fluid in order to allow diffusive transport. On the other hand, the membranes as a whole must remain structurally stable (even under perturbations far stronger than those in statistical equilibrium).

So what are the options for a simulation platform that is capable of representing chemical kinetics and morphological dynamics of membrane systems? The major rationale for DPD and our major extension to multipole reactive DPD, compared with fine-grained techniques such as MD (molecular dynamics) is computational efficiency. Lattice methods such as Lattice Gas or Lattice Boltzmann, although potnetially even more efficient, are burdened by their difficulty in simulating extended (especially rotating) objects and their intrinsic breaking of Galilean invariance, which means that extended objects with a non-vanishing velocity are hard to simulate. DPD is generically a well-suited tool for the study of extended objects. Not only stationary properties, as in equilibrium phase diagrams, but also mesoscale dynamical properties emerge properly from completely local interactions.

Classical DPD involves the interaction of point-particles interacting by central forces.

In order to get self-organized membranes, the interactions between particles must show more structure than can result from simple isotropic forces, independently of how complex the distance dependence may be. Simplified chain molecule based extensions, analagous to Larson's extensions to spin lattice models, have proved to be quite successful for studies close to the molecular length scale and for short timescales (e.g. microseconds). However, in the context of endocytosis for example, the dynamics of reacting vesicles needs to be simulated on larger scales and for longer time periods. In contrast with other work, we extended the DPD framework by equiping the DPD-particles with (mathematical) dipole moments and including angle dependent interactions derived from the corresponding Lagrangian. The motivation behind this extension is the idea that a DPD-particle’s dipole moment defines a local direction and can be understood as a surface element that can be used to build up extended curved two-dimensional objects embedded in space. We have discovered that multipolar interactions – for membrane dipoles are sufficient – are a valid and efficient alternative to dedicated particle-assemblies such as the chainlike structures, employed in various DPD-based studies of membranes [1-4].

In keeping with our system chemical kinetics focus, we have added chemical reactions at the level of single mesoscale particles to mprDPD. Chemical reactions can induce changes in the properties of mprDPD particle interaction, which can then lead to changes in the spatial behaviour of entities. In particular, reactive mprDPD enables the study of cellular reactions which modify complex mesoscale entities such as membrane bound compartments.

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