Stochastic simulations of minimal cells: the Ribocell model

Abstract

BackgroundOver the last two decades, lipid compartments (liposomes, lipid-coated droplets) have been extensively used as in vitro "minimal" cell models. In particular, simple and complex biomolecular reactions have been carried out inside these self-assembled micro- and nano-sized compartments, leading to the synthesis of RNA and functional proteins inside liposomes. Despite this experimental progress, a detailed physical understanding of the underlying dynamics is missing. In particular, the combination of solute compartmentalization, reactivity and stochastic effects has not yet been clarified. A combination of experimental and computational approaches can reveal interesting mechanisms governing the behavior of micro compartmentalized systems, in particular by highlighting the intrinsic stochastic diversity within a population of "synthetic cells".MethodsIn this context, we have developed a computational platform called ENVIRONMENT suitable for studying the stochastic time evolution of reacting lipid compartments. This software - which implements a Gillespie Algorithm - is an improvement over a previous program that simulated the stochastic time evolution of homogeneous, fixed-volume, chemically reacting systems, extending it to more general conditions in which a collection of similar such systems interact and change over the course of time. In particular, our approach is focused on elucidating the role of randomness in the time behavior of chemically reacting lipid compartments, such as micelles, vesicles or micro emulsions, in regimes where random fluctuations due to the stochastic nature of reacting events can lead an open system towards unexpected time evolutions.ResultsThis paper analyses the so-called Ribocell (RNA-based cell) model. It consists in a hypothetical minimal cell based on a self-replicating minimum RNA genome coupled with a self-reproducing lipid vesicle compartment. This model assumes the existence of two ribozymes, one able to catalyze the conversion of molecular precursors into lipids and the second able to replicate RNA strands. The aim of this contribution is to explore the feasibility of this hypothetical minimal cell. By deterministic kinetic analysis, the best external conditions to observe synchronization between genome self-replication and vesicle membrane reproduction are determined, while its robustness to random fluctuations is investigated using stochastic simulations, and then discussed.

Recent Theoretical Approaches to Minimal Artificial Cells

“…Based on this method we developed a software platform [26] suitable for simulating the stochastic time evolution of a collection of reacting vesicles, assuming that spatial diffusion processes can be neglected and the concentration gradients take place only across the lipid membranes. Moreover, this program allows one to study the case of vesicle self-reproduction, since it is able to follow a collection of reacting compartments that increases in number (see [26], and [33][34][35] for further details). We wish to remark here that this software is also suitable to study the influence of extrinsic stocasticity.…”

“…genome self-replication and membrane production are somehow synchronized, leading to a sustainable and recursive growth and division dynamics. Recently we have explored the feasibility of this hypothetical minimal cell [33] by determining the best external conditions to observe synchronization between genome self-replication and vesicle membrane reproduction, making use of a deterministic kinetic analysis, while the ribocell robustness to random fluctuations has been tested by stochastic simulations. The proposed metabolic mechanism is reported in Figure 9.…”

“…Although the observed cell life time stabilizes after the first 10 generations, it remains very high (about 80 days for all the k L values in the synchronization range), making the ribocell very hard to implement and study experimentally. Therefore, we investigated the robustness of the stationary growth and division regime of the ribocell in terms of the external substrate concentrations, vesicle size and initial ribozyme amount in order to define optimal external conditions for ribocell self-reproduction [33]. The influence of ribozyme length was also explored in the optimal external conditions by varying strand size from 20 to 200 bases in length and keeping all the other kinetic parameters constant.…”

“…Figure 11: Stochastic behavior of a population of 320 ribocells: population composition against time (on the left), schematic drawing of different protocells as result of vesicle division and random RNA strands distribution. Reproduced from [33] with kind permission of the author. Different protocells can emerges due to ribozymes segregation among the daughter protocells at the moment of mother protocell division: vesicles without any ribozymes (empty vesicles) or containing one lone R P or many filaments of c R P and/or c R L (inert vesicles), vesicles encapsulating R L (self-producing), vesicles containing more than one molecule of R P or both R P and c R P filaments (self-replicating genome), aggregates containing one R P filament and R L / c R L strands (reduced ribocells).…”

“…To improve this behaviour, one possibility could be to increase the working temperature in order to facilitate the dimers dissociation and increase the concentration of the free catalysers R L and R P . For further details the reader is addressed to [33,[44][45].…”