Molecular simulations of cellular processes

Abstract

It is, nowadays, possible to simulate biological processes in conditions that mimic the different cellular compartments. Several groups have performed these calculations using molecular models that vary in performance and accuracy. In many cases, the atomistic degrees of freedom have been eliminated, sacrificing both structural complexity and chemical specificity to be able to explore slow processes. In this review, we will discuss the insights gained from computer simulations on macromolecule diffusion, nuclear body formation, and processes involving the genetic material inside cell-mimicking spaces. We will also discuss the challenges to generate new models suitable for the simulations of biological processes on a cell scale and for cell-cycle-long times, including non-equilibrium events such as the co-translational folding, misfolding, and aggregation of proteins. A prominent role will be played by the wise choice of the structural simplifications and, simultaneously, of a relatively complex energetic description. These challenging tasks will rely on the integration of experimental and computational methods, achieved through the application of efficient algorithms.

Appendix: Diffusion and reactivity in the cell

A common order parameter used to describe the extent of macromolecular crowding is the volume fraction ϕ = V _cr/V, where V _cr and V are the volumes occupied by the crowders and the total volume of the cell or of the simulation box. While ϕ accounts only for the hard-core repulsion between crowders, other quantities might be important as well, as discussed in the paper.

Bimolecular reactions occurring in a cell can be described by summing up two times, one spent by the two molecules to diffuse nearby and the time to react once the molecules are in contact. This relationship can be expressed in terms of rates via the equation 1/k = 1/k _R + 1/k _D, where k, k _R, and k _D are, respectively, the observed rate of the reaction in the cell, the rate of the reaction when the biomolecules are in contact, and the rate of diffusional encounter. As discussed in the introduction, k depends on the crowding conditions because the diffusion of and reaction between macromolecules depend on the crowding conditions as well.

Diffusion regimes that are measured in a cell range from normal to anomalous. During normal diffusion, the mean square displacement of the system satisfies MSD(t) = 2nDt, where t indicates the time, n is the space dimensionality (n = 3 for diffusion in a volumetric space, n = 2 for diffusion on a surface, like a membrane), and D is the long-time translational diffusion coefficient, hereafter referred to as the diffusion coefficient. Normal diffusion is also observed in isolation, in which case the diffusion coefficient is D ₀. A system that diffuses anomalously satisfies MSD(t) = 2nD _α t ^α, where α is the anomalous exponent. Values of α larger than 1 indicate super-diffusion, whereas values less than 1 indicate sub-diffusion (Dix and Verkman 2008). The diffusion coefficient D _α is usually recast in terms of an apparent diffusion coefficient, which satisfies D(t) = D _α t ^α − 1. It is important to emphasize that D(t) is time-dependent when diffusion is not normal, i.e., when α ≠ 1. A thorough discussion of the conditions that yield anomalous diffusion as well as mathematical models of diffusion in crowded media can be found elsewhere (Bouchaud and Georges 1990; Höfling and Franosch 2013; Cherstvy and Metzler 2015).