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

Elena

2020

Preprint

Viruses have established symbiotic 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, peacefully coexisting with their hosts, but in most relevant cases, parasitizing them and inducing diseases. Viruses are playing an essential role in shaping the eco-evolutionary dynamics of their hosts, and also have been 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 it occurs with temperatures separating phases in a liquid, define sharp qualitative types of behaviour. These {\em phase transitions} are very well known in physics. They have been studied by means of simple, but powerful models able to capture their essential properties, allowing to understand them. Can the physics of phase transitions be an inspiration for our understanding of viral dynamics at different scales? Here we review the best-known examples of transition phenomena in virology and their simplest mathematical modelling approaches. We suggest that the advantages of abstract, simplified pictures used in physics are also the key to properly understand 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 levels and their evolutionary and clinical implications are outlined.

Section: Article In Pressmentioning

confidence: 76%

Phase Transitions in Virology

Solé

Elena

2020

Preprint

“…Noiseinduced bistability is typically found in dynamical systems which display a single asymptotically stable state in their deterministic limit, while being able to achieve different alternative states due to stochasticity. Different examples of noise-induced stability, which can also be understood in terms of the noise-enhanced stability typical of metastable systems (see [28,29] for examples of cancer stochastic systems), have been described in many different systems [30][31][32][33]. Summarizing, we have analysed a particular scenario found in a simple model of complementary replication of viral RNAs giving rise to the so-called quasi-neutral coexistence [12,13].…”

Section: Resultsmentioning

confidence: 99%

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

Arderiu

Elena

et al. 2018

J. R. Soc. Interface.

Self Cite

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.

“…Different examples of noise-induced stability, which can also be understood in terms of noise-enhanced stability typical from metastable systems (see Refs. [30,31] for examples on cancer stochastic systems) have been described in many different systems [29,[32][33][34].…”

Section: Discussionmentioning

confidence: 99%

Noise-induced bistability in the quasineutral coexistence of viral RNA under different replication modes

Alarcón

Arderiu

et al. 2018

Preprint

Self Cite

Evolutionary and dynamical investigations on real viral populations indicate that RNA replication can range between two extremes given 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 up to now studied with deterministic models. However, viral replication should be better described by including stochasticity, since 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 quasineutral coexistence scenario, with a line of fixed points involving different strands' equilibrium ratios depending on the initial conditions. Recent research on the quasineutral coexistence in two competing populations reveals that stochastic fluctuations fundamentally alters the mean-field scenario, and one of the two species outcompetes the other one. In this manuscript we study this phenomenon for RNA viral 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 RNA, 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.