Potential Benefits of Sequential Inhibitor-Mutagen Treatments of RNA Virus Infections

Lethal mutagenesis is an antiviral strategy consisting of virus extinction associated with enhanced mutagenesis. The use of non-mutagenic antiviral inhibitors has faced the problem of selection of inhibitor-resistant virus mutants. Quasispecies dynamics predicts, and clinical results have confirmed, that combination therapy has an advantage over monotherapy to delay or prevent selection of inhibitor-escape mutants. Using ribavirin-mediated mutagenesis of foot-and-mouth disease virus (FMDV), here we show that, contrary to expectations, sequential administration of the antiviral inhibitor guanidine (GU) first, followed by ribavirin, is more effective than combination therapy with the two drugs, or than either drug used individually. Coelectroporation experiments suggest that limited inhibition of replication of interfering mutants by GU may contribute to the benefits of the sequential treatment. In lethal mutagenesis, a sequential inhibitor-mutagen treatment can be more effective than the corresponding combination treatment to drive a virus towards extinction. Such an advantage is also supported by a theoretical model for the evolution of a viral population under the action of increased mutagenesis in the presence of an inhibitor of viral replication. The model suggests that benefits of the sequential treatment are due to the involvement of a mutagenic agent, and to competition for susceptible cells exerted by the mutant spectrum. The results may impact lethal mutagenesis-based protocols, as well as current antiviral therapies involving ribavirin

The uncertain future in how a virus spreads

A new model helps clarify the limits of pandemic predictions, which are notoriously difficult for the near future and impossible for longer timescales

Viral evolution

In the last two decades, viruses have been used as model systems to study evolution in short periods of time. Due to their characteristics, virus adapt rapidly to changing conditions, thus allowing the quantification of several evolutionary features under controlled laboratory conditions. Here we review the basic biology of viruses and describe in detail a number of experiments performed with RNA viruses. Particular emphasis is devoted to the interpretation of the experiments and to the involved phenomenology. This analysis sometimes represents the basis to formulate simple evolutionary models that aim at describing the observed dynamics. In other cases, theoretical results have prompted the realization of related experiments, as we discuss. Concepts as fitness loss and fitness recovery, the error threshold, increased mutagenesis, viral sex, or viral competition and interference, are discussed in an empirical framework and from the associated theoretical point of view. © 2005 Elsevier B.V. All rights reserved.The authors acknowledge fruitful and continued discussions with friends and colleagues: U. Bastolla, C. Biebricher, C. Briones, E. Domingo, C. Escarmís, J. García-Arriaza, A. Grande-Pérez, J. Pérez-Mercader, and the support of INTA and Ministerio de Educación y Ciencia (FIS2004-06414). SCM benefits from a Ramón y Cajal contract.Support of INTA and Ministerio de Educación y Ciencia (FIS2004-06414). SCM benefits from a Ramón y Cajal contract.Peer Reviewe

Out-of-equilibrium competitive dynamics of quasispecies

6 pages, 4 figures.-- PACS nrs.: 87.10.+e; 87.23.Kg; 89.90.+n.-- ISI Article Identifier: 000245743000025.-- Printed version published Feb 2007.The composition of a quasispecies is completely characterized, in the large population and long time limit, by the matrix yielding the transition probabilities between different types in the population. Further, its asymptotic growth rate —i.e. the largest eigenvalue of the transition matrix— completely determines the winning population in an equilibrium competition. However, due to the intrinsically heterogeneous nature of quasispecies, out-of-equilibrium fluctuations in population size might change the expected fate of competition experiments. Using a simple model for a heterogeneous population we quantify the probability that, after a population bottleneck, the a priori weaker competitor wins in a competition with a population characterized by a larger asymptotic growth rate. We analyse the role played by different degrees of neutrality in the outcome of the process, and demonstrate that lower neutrality favours the weaker competitor in out-of-equilibrium situations. Our results might shed light on empirical observations in competition experiments with RNA viruses.The authors acknowledge the support of Spanish MEC (project FIS2004-06414). SCM benefits from a Ramón y Cajal contract.Peer reviewe

Effects of spatial competition on the diversity of a quasispecies

The diversity harbored by populations of RNA viruses results from high mutation rates, as well as from the characteristics of the environment where they evolve. By means of a simple model for structured quasispecies, we quantify how competition for space among phenotypic types shapes their distribution at the mutation-selection equilibrium. We introduce a general framework to treat this problem and relate mutation rate and competition strength to the quasispecies composition. For diffusion limited competition, diversity typically increases and the asymptotic growth rate of the population diminishes as diffusion decreases. Limited mobility confers a relative advantage to worse competitors. The stationary state is characterized by an over-production of viral particles. Empirical data allow an estimation of mutation rates compatible with the diversity observed in viral populations infecting cellular monolayers. © 2008 The American Physical Society.The authors acknowledge discussions with C. Briones and E. La´zaro, and the support of the Spanish Ministerio de Educacio´n y Ciencia under Project No. FIS2004-0641

Tipping points and early warning signals in the genomic composition of populations induced by environmental changes

We live in an ever changing biosphere that faces continuous and often stressing environmental challenges. From this perspective, much effort is currently devoted to understanding how natural populations succeed or fail in adapting to evolving conditions. In a different context, many complex dynamical systems experience critical transitions where their dynamical behaviour or internal structure changes suddenly. Here we connect both approaches and show that in rough and correlated fitness landscapes, population dynamics shows flickering under small stochastic environmental changes, alerting of the existence of tipping points. Our analytical and numerical results demonstrate that transitions at the genomic level preceded by early-warning signals are a generic phenomenon in constant and slowly driven landscapes affected by even slight stochasticity. As these genomic shifts are approached, the time to reach mutation-selection equilibrium dramatically increases, leading to the appearance of hysteresis in the composition of the population. Eventually, environmental changes significantly faster than the typical adaptation time may result in population extinction. Our work points out several indicators that are at reach with current technologies to anticipate these sudden and largely unavoidable transitions.The authors acknowledge financial support from Spanish MICINN (project FIS2011-27569) and from Comunidad de Madrid (MODELICO, S2009/ESP-1691).Peer reviewe

Redes de genotipos: los senderos de la evolución

Para cualquier organismo o incluso para las proteínas más simples, el espacio de genomas posibles es muchísimo mayor que todo lo que haya podido explorar la evolución desde el origen de la vida en la Tierra. Si las mutaciones aleatorias solo pueden recorrer una parte mínima de las posibilidades biológicas, ¿cómo halla la naturaleza soluciones a problemas adaptativos? ¿Cómo surge la diversidad necesaria para que la selección natural pueda actuar? La respuesta se encuentra en la compleja relación entre secuencias genéticas y fenotipos. Un nuevo marco teórico basado en la teoría de redes está comenzando a revelar la estructura subyacente que permite que la evolución darwinista tenga lugar

Fat tails and black swans: Exact results for multiplicative processes with resets

© 2020 Author(s).We consider a class of multiplicative processes which, added with stochastic reset events, give origin to stationary distributions with power-law tails—ubiquitous in the statistics of social, economic, and ecological systems. Our main goal is to provide a series of exact results on the dynamics and asymptotic behavior of increasingly complex versions of a basic multiplicative process with resets, including discrete and continuous-time variants and several degrees of randomness in the parameters that control the process. In particular, we show how the power-law distributions are built up as time elapses, how their moments behave with time, and how their stationary profiles become quantitatively determined by those parameters. Our discussion emphasizes the connection with financial systems, but these stochastic processes are also expected to be fruitful in modeling a wide variety of social and biological phenomena. City sizes, word usage, surname abundance, personal income, or stock market returns are examples of power-law distributed quantities. Such a kind of distribution, ubiquitous in the natural and social sciences, holds “atypical” properties that have awoken the interest of researchers for over a century.1–5 The dynamics of these kinds of data exhibit extreme, catastrophic, “unexpected” black-swan-like events.6 Distribution moments, such as the average or the variance, are highly volatile and poorly predict future properties of the process. In that context of uncertainty, knowledge of the dominant mechanisms underlying power-law distributions is relevant to directly compare the short-time properties of data series to actual asymptotic properties, and to eventually evaluate the reliability of forecast algorithms. Stochastic multiplicative processes (SMPs) with reset events, introduced two decades ago7 as a generic mechanism to generate power laws, have multiple applications in a variety of situations.8,9 In this contribution, we derive several finite-time properties of SMPs with reset events with the aim of improving our understanding of the poor predictability of the dynamical process. The discussion of our results in a financial context clarifies the relationship between gain and risk in investing strategies, and provides clues to control the frequency and magnitude of extreme events.S.M. is supported by Grant No. FIS2017-89773-P (MINECO/FEDER, E. U.)

Physics of diffusion in viral genome evolution

Using data from SARS-CoV-2 viral genomes sequenced during the COVID-19 pandemic, Goiriz and colleagues analyze, in PNAS (1), the way that mutational variants “move” through the space of sequences of this virus. Their analysis reveals an unexpected phenomenon known as “anomalous diffusion” in SARS-CoV-2 genomes. This means that instead of undergoing an exploration of neighboring variants through replication and unconstrained mutation (akin to normal diffusion), the virus exhibits either a hindered exploration, progressing at a slower-than-expected speed (subdiffusive spread), or an accelerated exploration, displaying a faster-than-expected spread through the sequence space (superdiffusive spread). In order to understand the deep implications of this finding, we must travel back 200 y in time. Diffusion, a well-established physical phenomenon since the early 19th century, describes the intermixing of gases or liquids. A classic example is the diffusion of an ink droplet in a glass of water. Mathematically, diffusion was described by Fick in 1855 (2) through an equation known as the diffusion equation or Fick’s law, which Fick derived by drawing from an analogy to heat conduction. However, the microscopic explanation of this phenomenon was hidden in a perplexing observation coming from an entirely different scientific discipline. Robert Brown was a renowned botanist fascinated with the mechanisms of fertilization in flowering plants. In June 1827, while studying pollen particles of Clarkia pulchella suspended in water, he witnessed the incessant agitation of these particles. His meticulous observations were supported by a pioneering and proficient use of a specially designed microscope for investigating “minute points” (3). The irregular motion he described came to be known as “Brownian motion” and became inseparably associated with his name. Brown, however, could not discern the causes underlying the behavior of those seemingly inanimate, but active, particles. It was not until 1905, when Einstein published his work on the theory of Brownian motion, that an explanation emerged (4). Einstein correctly attributed the motion of the particles to the thermal agitation of water molecules, which would push the pollen granules in random directions after each collision. On a larger scale, it is the collective behavior of numerous minute particles that causes the spread of pollen grains on water. Einstein formulation had quantifiable consequences: If a large number of tiny particles are initially positioned in a specific location, the mean square distance covered by these particles after a time follows the simple law , where D represents the diffusion constant appearing in Fick’s law. Incidentally, Einstein’s explanation of Brownian motion was considered the definitive proof of the existence of atoms—by the time a controversial hypothesis.Our research is supported by grants PID2020-113284GB-C21 (S.M.) and PGC2018-098186-B-I00 (J.A.C.), all funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe.”Peer reviewe