Noise-induced bistability in the fate of cancer phenotypic quasispecies: a bit-strings approach

Localization of Noise in Biochemical Networks

Noise, or uncertainty in biochemical networks, has become an important aspect of many biological problems. Noise can arise and propagate from external factors and probabilistic chemical reactions occurring in small cellular compartments. For species survival, it is important to regulate such uncertainties in executing vital cell functions. Regulated noise can improve adaptability, whereas uncontrolled noise can cause diseases. Simulation can provide a detailed analysis of uncertainties, but parameters such as rate constants and initial conditions are usually unknown. A general understanding of noise dynamics from the perspective of network structure is highly desirable. In this study, we extended the previously developed law of localization for characterizing noise in terms of (co)variances and developed noise localization theory. With linear noise approximation, we can expand a biochemical network into an extended set of differential equations representing a fictitious network for pseudo-components consisting of variances and covariances, together with chemical species. Through localization analysis, perturbation responses at the steady state of pseudo-components can be summarized into a sensitivity matrix that only requires knowledge of network topology. Our work allows identification of buffering structures at the level of species, variances, and covariances and can provide insights into noise flow under non-steady-state conditions in the form of a pseudo-chemical reaction. We tested noise localization in various systems, and here we discuss its implications and potential applications. Results show that this theory is potentially applicable in discriminating models, scanning network topologies with interesting noise behavior, and designing and perturbing networks with the desired response.

Constrained Langevin approximation for the Togashi-Kaneko model of autocatalytic reactions

The Togashi Kaneko model (TK model) is a simple stochastic reaction network that displays discreteness-induced transitions between meta-stable patterns. Here we study a constrained Langevin approximation (CLA) of this model. This CLA, derived under the classical scaling, is an obliquely reflected diffusion process on the positive orthant and hence respects the constraint that chemical concentrations are never negative. We show that the CLA is a Feller process, is positive Harris recurrent and converges exponentially fast to the unique stationary distribution. We also characterize the stationary distribution and show that it has finite moments. In addition, we simulate both the TK model and its CLA in various dimensions. For example, we describe how the TK model switches between meta-stable patterns in dimension six. Our simulations suggest that, when the volume of the vessel in which all of the reactions that take place is large, the CLA is a good approximation of the TK model in terms of both the stationary distribution and the transition times between patterns.

Phase transitions in virology

Viruses have established relationships with almost every other living organism on Earth and at all levels of biological organization: from other viruses up to entire ecosystems. In most cases, they peacefully coexist with their hosts, but in most relevant cases, they parasitize them and induce diseases and pandemics, such as the AIDS and the most recent avian influenza and COVID-19 pandemic events, causing a huge impact on health, society, and economy. Viruses play an essential role in shaping the eco-evolutionary dynamics of their hosts, and have been also involved in some of the major evolutionary innovations either by working as vectors of genetic information or by being themselves coopted by the host into their genomes. Viruses can be studied at different levels of biological organization, from the molecular mechanisms of genome replication, gene expression and encapsidation, to global pandemics. All these levels are different and yet connected through the presence of threshold conditions allowing for the formation of a capsid, the loss of genetic information or epidemic spreading. These thresholds, as occurs with temperature separating phases in a liquid, define sharp qualitative types of behaviour. Thesephase transitionsare very well known in physics. They have been studied by means of simple, but powerful models able to capture their essential properties, allowing us to better understand them. Can the physics of phase transitions be an inspiration for our understanding of viral dynamics at different scales? Here we review well-known mathematical models of transition phenomena in virology. We suggest that the advantages of abstract, simplified pictures used in physics are also the key to properly understanding the origins and evolution of complexity in viruses. By means of several examples, we explore this multilevel landscape and how minimal models provide deep insights into a diverse array of problems. The relevance of these transitions in connecting dynamical patterns across scales and their evolutionary and clinical implications are outlined.

An integrative model of cancer cell differentiation with immunotherapy. Phys Biol 2021;18. [PMID: 34633296 DOI: 10.1088/1478-3975/ac2e72] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

In order to improve cancer treatments, cancer cell differentiation and immunotherapy are the subjects of several studies in different branches of interdisciplinary sciences. In this work, we develop a new population model that integrates other complementary ones, thus emphasizing the relationship between cancer cells at different differentiation stages and the main immune system cells. For this new system, specific ranges were found where transdifferentiation of differentiated cancer cells can occur. In addition, a specific therapy against cancer stem cells was analysed by simulating cytotoxic cell vaccines. In reference to the latter, the different combinations of parameters that optimize it were studied.

Stationary distributions of systems with discreteness-induced transitions

We provide a theoretical analysis of some autocatalytic reaction networks exhibiting the phenomenon of discreteness-induced transitions. The family of networks that we address includes the celebrated Togashi and Kaneko model. We prove positive recurrence, finiteness of all moments and geometric ergodicity of the models in the family. For some parameter values, we find the analytic expression for the stationary distribution and discuss the effect of volume scaling on the stationary behaviour of the chain. We find the exact critical value of the volume for which discreteness-induced transitions disappear.

Noise-induced bistability in the quasi-neutral coexistence of viral RNAs under different replication modes

Evolutionary and dynamical investigations into real viral populations indicate that RNA replication can range between the two extremes represented by so-called 'stamping machine replication' (SMR) and 'geometric replication' (GR). The impact of asymmetries in replication for single-stranded (+) sense RNA viruses has been mainly studied with deterministic models. However, viral replication should be better described by including stochasticity, as the cell infection process is typically initiated with a very small number of RNA macromolecules, and thus largely influenced by intrinsic noise. Under appropriate conditions, deterministic theoretical descriptions of viral RNA replication predict a quasi-neutral coexistence scenario, with a line of fixed points involving different strands' equilibrium ratios depending on the initial conditions. Recent research into the quasi-neutral coexistence in two competing populations reveals that stochastic fluctuations fundamentally alter the mean-field scenario, and one of the two species outcompetes the other. In this article, we study this phenomenon for viral RNA replication modes by means of stochastic simulations and a diffusion approximation. Our results reveal that noise has a strong impact on the amplification of viral RNAs, also causing the emergence of noise-induced bistability. We provide analytical criteria for the dominance of (+) sense strands depending on the initial populations on the line of equilibria, which are in agreement with direct stochastic simulation results. The biological implications of this noise-driven mechanism are discussed within the framework of the evolutionary dynamics of RNA viruses with different modes of replication.