Time-delayed model of RNA interference

Abstract

RNA interference (RNAi) is a fundamental cellular process that inhibits gene expression through cleavage and destruction of target mRNA. It is responsible for a number of important intracellular functions, from being the first line of immune defence against pathogens to regulating development and morphogenesis. In this paper we consider a mathematical model of RNAi with particular emphasis on time delays associated with two aspects of primed amplification: binding of siRNA to aberrant RNA, and binding of siRNA to mRNA, both of which result in the expanded production of dsRNA responsible for RNA silencing. Analytical and numerical stability analyses are performed to identify regions of stability of different steady states and to determine conditions on parameters that lead to instability. Our results suggest that while the original model without time delays exhibits a bi-stability due to the presence of a hysteresis loop, under the influence of time delays, one of the two steady states with the high (default) or small (silenced) concentration of mRNA can actually lose its stability via a Hopf bifurcation. This leads to the co-existence of a stable steady state and a stable periodic orbit, which has a profound effect on the dynamics of the system.

Stochastic Effects in Autoimmune Dynamics

“…For the parameter combination illustrated in Figure 4A , the deterministic model exhibits a bi-stability between a stable disease-free steady state and a periodic oscillation around the state , which biologically corresponds to an autoimmune regime. In the deterministic case, the black boundary provides a clear separation of the basins of attraction of these two dynamical states, in a manner similar to that investigated recently in the context of within-cell dynamics of RNA interference (Neofytou et al, 2017 ). For stochastic simulations, the color indicates the probability of the solution going to a disease-free state , and it shows that even in the case where deterministically the system is in the basin of attraction of one of the states, there is a non-zero probability that it will actually end up at another state, with this probability varying smoothly across the deterministic basin boundary.…”

Control of mosaic disease using microbial biostimulants: insights from mathematical modelling

“…Both of these approaches rely on supplying plants with appropriate dsRNA (double-stranded RNA) that would trigger RNAi process, and this dsRNA can be delivered into plants through various means, including development of transgenic plants [21,22], root soaking [13,23], as well as topical application (spraying) [24,25]. Recent work has demonstrated the feasibility of RNAi for control of B. tabaci whitefly [26][27][28][29][30], while mathematical models have elucidated a number of important aspects of RNAi in plants [31][32][33].…”

RNAi-Based Biocontrol of Wheat Nematodes Using Natural Poly-Component Biostimulants

“…Experimentally driven mathematical models suggest that equilibrium concentrations of chemical compounds in plants are reached very quickly, when plants are taking up compound from the soil through their roots (Briggs et al, 1983; Fryer and Collins, 2003; Rein et al, 2011). Theoretical models of RNAi (Groenenboom and Hogeweg, 2008; Neofytou et al, 2016a,b, 2017) have shown that the rate at which proliferating cells of meristematic tissue mature into healthy plant cells plays an important role in determining the success of RNAi-based plant response, which suggests that the transport of these products to different parts of the plant during its growth has a knock-on effect on their availability for consumption by nematodes. Furthermore, one should be mindful of the fact that in the case of poly-component mixtures, diffusion and uptake of different chemical components and their subsequent within-plant transport can significantly differ due to their various characteristics, such as lipophilicity, acidity, and electrical charge.…”