Active dynamics in cells

Abstract

Inspired by many complex biological mechanisms inside a cell, three research topics are discussed in this thesis. Because a live cell can never function in equilibrium, all three topics therefore have to do with active, i.e. non-equilibrium, processes. The first topic discusses the dynamics of a flexible polymer in a viscoelastic bath and subject to active force fluctuations. Both characteristics make it hard to analyse the dynamics of this polymer-bath system. For this reason we will mostly restrict our discussions to the memoryless viscous case, where the bath behaves in a water-like way. The active fluctuations are caused by the (un)binding of enzymes to a randomly chosen subset of monomers. These proteins push and pull the monomers in a random direction for a certain amount of time, but also in a non-equilibrium manner, thereby violating the fluctuation-dissipation theorem. The active forces are modeled by a non-Gaussian dichotomous Markov process, also called a telegraph process, such that these forces have an exponential time dependent correlation. We use a generalised Langevin equation to describe the dynamics of the monomers of the polymer. From previous research we may already expect anomalous dynamics, but in contrast to the superdiffusion observed for monopolar active forces, we obtain subdiffusive motion due to the dipolar activity of the enzymes: they act on two neighbouring monomers, in opposite directions. Furthermore, we analyse the mean squared end-to-end distance of the polymer, the velocity autocorrelation, the spatial autocorrelation and the kurtosis. This last quantity is a special one, for it can give us evidence that non-Gaussian effects really are at play in the motion of the polymer, originating from the active telegraph process. Our findings are in line with experiments on chromosomal loci. In the second research project, we look at the dynamics of a single active particle on an energy landscape. We analyse the time that this particle needs to go from one point to another, usually depicted as the two stable states where a system can reside in. The particle is modeled by run-and-tumble characteristics. In fact, its dynamics can be described by Brownian motion but we add active noise to the particle, again modeled by a telegraph process. This choice for the active force fluctuations connects the first two projects. However, the difference for run-and-tumble particles is that the active force is always present, in contrast to the first project where the active force is only operative for a certain time span after which the monomers become passive for some period. We analytically calculate the probability distribution for the transition path times of the particle for different cases including thermal fluctuations and/or an asymmetric potential energy function, which causes an asymmetry in the forward and backward probability distributions. The third topic discusses a first attempt to analyse the formation of nucleoli in the nucleus. By means of adapting a basic model for mathematically describing a phase separation, we initiate the analysis of the growth of nucleoli. By including production and annihilation terms for RNA, adding a coupling between RNA and proteins present inside the nucleus and tuning other parameters in such a way that the system resides in a meta-stable state, we can simulate blob formations representing nucleoli. We analyse the size of the blobs based on the area and height of the protein concentration profile across the blob and we anticipate a number of future research possibilities for this project, both numerical and experimental. While there are multiple arguments to consider nucleoli assembly as an active process, we will not occupy ourselves with the particulars of the active forces and ATP-dependent processes influencing nucleoli formation in this last chapter.