RESUMEN

Environmental noise can lead to complex stochastic dynamical behavior in nonlinear systems. In this paper, we studied the phenomenon of a pair of Van der Pol (VDP) oscillators with direct-indirect coupling affected by Gaussian white noise. That is to say, a noise-induced equilibrium transition oscillation was observed in three types of different parameter regions, where the deterministic system had two kinds of stable equilibrium points. Meanwhile, with the noise intensity increasing, we found that the stochastic system will constantly switch between two stable equilibrium points. To analyze the stochastic behavior, we used the stochastic sensitivity equation and confidence ellipse method. When the confidence ellipsoid crossed the boundary of the attraction basin of the equilibrium point, the system entered into the state of stochastic mixed-mode oscillations, which was consistent with the simulation results.

RESUMEN

Cell-fate transition can be modeled by ordinary differential equations (ODEs) which describe the behavior of several molecules in interaction, and for which each stable equilibrium corresponds to a possible phenotype (or 'biological trait'). In this paper, we focus on simple ODE systems modeling two molecules which each negatively (or positively) regulate the other. It is well-known that such models may lead to monostability or multistability, depending on the selected parameters. However, extensive numerical simulations have led systems biologists to conjecture that in the vast majority of cases, there cannot be more than two stable points. Our main result is a proof of this conjecture. More specifically, we provide a criterion ensuring at most bistability, which is indeed satisfied by most commonly used functions. This includes Hill functions, but also a wide family of convex and sigmoid functions. We also determine which parameters lead to monostability, and which lead to bistability, by developing a more general framework encompassing all our results.

RESUMEN

Ecological resilience refers to the ability of a system to retain its state when subject to state variables perturbations or parameter changes. While understanding and quantifying resilience is crucial to anticipate the possible regime shifts, characterizing the influence of the system parameters on resilience is the first step toward controlling the system to avoid undesirable critical transitions. In this paper, we apply tools of qualitative theory of differential equations to study the resilience of competing populations as modeled by the classical Lotka-Volterra system. Within the high interspecific competition regime, such model exhibits bistability, and the boundary between the basins of attraction corresponding to exclusive survival of each population is the stable manifold of a saddle point. Studying such manifold and its behavior in terms of the model parameters, we characterized the populations resilience: While increasing competitiveness leads to higher resilience, it is not always the case with respect to reproduction. Within a pioneering context where both populations initiate with few individuals, increasing reproduction of one population leads to an increase in its resilience; however, within an environment previously dominated by one population and then invaded by the other, an increase in the resilience of a population is obtained by decreasing its reproduction rate. Besides providing interesting insights for the dynamics of competing populations, this work brings near to each other the concepts of ecological resilience and the methods of differential equations and stimulates the development and application of new tools for ecological resilience.

Asunto(s)

RESUMEN

When a pathogen invades the body, an acute inflammatory response is activated to eliminate the intruder. In some patients, runaway activation of the immune system may lead to collateral tissue damage and, in the extreme, organ failure and death. Experimental studies have found an association between severe infections and depletion in levels of adenosine triphosphate (ATP), increase in nitric oxide production, and accumulation of lactate, suggesting that tissue energetics is compromised. In this work we present a differential equations model that incorporates the dynamics of ATP, nitric oxide, and lactate accompanying an acute inflammatory response and employ this model to explore their roles in shaping this response. The bifurcation diagram of the model system with respect to the pathogen growth rate reveals three equilibrium states characterizing the health, aseptic and septic conditions. We explore the domains of attraction of these states to inform the instantiation of heterogeneous virtual patient populations utilized in a survival analysis. We then apply the model to study alterations in the inflammatory response and survival outcomes in metabolically altered conditions such as hypoglycemia, hyperglycemia, and hypoxia.

Asunto(s)

RESUMEN

Complex natural systems with eroded resilience, such as populations, ecosystems and socio-ecological systems, respond to small perturbations with abrupt, discontinuous state shifts, or critical transitions. Theory of critical transitions suggests that such systems exhibit fold bifurcations featuring folded response curves, tipping points and alternate attractors. However, there is little empirical evidence of fold bifurcations occurring in actual complex natural systems impacted by multiple stressors. Moreover, resilience of complex systems to change currently lacks clear operational measures with generic application. Here, we provide empirical evidence for the occurrence of a fold bifurcation in an exploited fish population and introduce a generic measure of ecological resilience based on the observed fold bifurcation attributes. We analyse the multivariate development of Barents Sea cod (Gadus morhua), which is currently the world's largest cod stock, over six decades (1949-2009), and identify a population state shift in 1981. By plotting a multivariate population index against a multivariate stressor index, the shift mechanism was revealed suggesting that the observed population shift was a nonlinear response to the combined effects of overfishing and climate change. Annual resilience values were estimated based on the position of each year in relation to the fitted attractors and assumed tipping points of the fold bifurcation. By interpolating the annual resilience values, a folded stability landscape was fit, which was shaped as predicted by theory. The resilience assessment suggested that the population may be close to another tipping point. This study illustrates how a multivariate analysis, supported by theory of critical transitions and accompanied by a quantitative resilience assessment, can clarify shift mechanisms in data-rich complex natural systems.

Asunto(s)

RESUMEN

The interaction of p53 with its regulators MDM2 and MDMX plays a major role in regulating the cell cycle. Inhibition of this interaction has become an important therapeutic strategy in oncology. Although MDM2 and MDMX share a very high degree of sequence/structural similarity, the small-molecule inhibitor nutlin appears to be an efficient inhibitor only of the p53-MDM2 interaction. Here, we investigate the mechanism of interaction of nutlin with these two proteins and contrast it with that of p53 using Brownian dynamics simulations. In contrast to earlier attempts to examine the bound states of the partners, here we locate initial reaction events in these interactions by identifying the regions of space around MDM2/MDMX, where p53/nutlin experience associative encounters with prolonged residence times relative to that in bulk solution. We find that the initial interaction of p53 with MDM2 is long-lived relative to nutlin, but, unlike nutlin, it takes place at the N- and C termini of the MDM2 protein, away from the binding site, suggestive of an allosteric mechanism of action. In contrast, nutlin initially interacts with MDM2 directly at the clefts of the binding site. The interaction of nutlin with MDMX, however, is very short-lived compared with MDM2 and does not show such direct initial interactions with the binding site. Comparison of the topology of the electrostatic potentials of MDM2 and MDMX and the locations of the initial encounters with p53/nutlin in tandem with structure-based sequence alignment revealed that the origin of the diminished activity of nutlin toward MDMX relative to MDM2 may stem partly from the differing topologies of the electrostatic potentials of the two proteins. Glu25 and Lys51 residues underpin these topological differences and appear to collectively play a key role in channelling nutlin directly toward the binding site on the MDM2 surface and are absent in MDMX. The results, therefore, provide new insight into the mechanism of p53/nutlin interactions with MDM2 and MDMX and could potentially have a broader impact on anticancer drug optimization strategies.

Asunto(s)