arXiv subjects

Elisa Franco

Publications and source records attributed to Elisa Franco.

6 recordsLinked to original sources

arXiv2024

Complex Dynamics in Reaction-Phase Separation Systems

We investigate the emergence of sustained spatio-temporal behaviors in reaction-phase separation systems. We focus on binary systems, in which either one or both species can phase separate, and we discuss the stability of the homogeneous state determining the conditions for the emergence of a Hopf-type bifurcation. We then examine the effects of a specific autocatalytic chemical reaction, and computationally determine the full solutions to the partial differential equations. We find that when both species phase separate, sustained pulsed dynamics arise in one dimension. When considered in two dimensions, the system generates persistent, complex dynamic droplets, which do not generally appear if only one of the species can phase separate. We finally discuss the emergence of dynamics with complex features, which can be understood using the framework of a cellular automata.

nlin.PS↗

arXiv2024

Generating forces in confinement via polymerization

Understanding how to produce forces using biomolecular building blocks is essential for the development of adaptive synthetic cells and living materials. Here we ask whether a dynamic polymer system can generate deformation forces in soft compartments by pure self-assembly, motivated by the fact that biological polymer networks like the cytoskeleton can exert forces, move objects, and deform membranes by simply growing, even in the absence of molecular motors. We address this question by investigating polymer force generation by varying the release rate, the structure, and the interactions of self-assembling monomers. First, we develop a toy computational model of polymerization in a soft elastic shell that reveals the emergence of spontaneous bundling which enhances shell deformation. We then extend our model to account more explicitly for monomer binding dynamics. We find that the rate at which monomers are released into the interior of the shell is a crucial parameter for achieving deformation through polymer growth. Finally, we demonstrate that the introduction of multivalent particles that can join polymers can either improve or impede polymer performance, depending on the amount and on the structure of the multivalent particles. Our results provide guidance for the experimental realization of polymer systems that can perform work at the nanoscale, for example through rationally designed self-assembling proteins or nucleic acids.

cond-mat.soft↗

arXiv2023

Robust microphase separation through chemical reaction networks

The interaction of phase-separating systems with chemical reactions is of great interest in various contexts, from biology to material science. In biology, phase separation is thought to be the driving force behind the formation of biomolecular condensates, i.e. organelles without a membrane that are associated with cellular metabolism, stress response, and development. RNA, proteins, and small molecules participating in the formation of condensates are also involved in a variety of biochemical reactions: how do the chemical reaction dynamics influence the process of phase separation? Here we are interested in finding chemical reactions that can arrest the growth of condensates, generating stable spatial patterns of finite size (microphase separation), in contrast with the otherwise spontaneous (unstable) growth of condensates. We consider a classical continuum model for phase separation coupled to a chemical reaction network (CRN), and we seek conditions for the emergence of stable oscillations of the solution in space. Given reaction dynamics with uncertain rate constants, but known structure, we derive easily computable conditions to assess whether microphase separation is impossible, possible for some parameter values, or robustly guaranteed for all parameter values within given bounds. Our results establish a framework to evaluate which classes of CRNs favor the emergence of condensates with finite size, a question that is broadly relevant to understanding and engineering life.

cond-mat.soft↗

arXiv2022

Chemical reaction motifs driving non-equilibrium behaviors in phase separating materials

Chemical reactions that couple to systems that phase separate have been implicated in diverse contexts from biology to materials science. However, how a particular set of chemical reactions (chemical reaction network, CRN) would affect the behaviors of a phase separating system is difficult to fully predict theoretically. In this paper, we analyze a mean field theory coupling CRNs to phase separating materials and expound on how the properties of the CRNs affect different classes of non-equilibrium behaviors: the emergence of microphase separation or of temporally oscillating patterns. We examine the problem of achieving microphase separated condensates by first considering tractable problems and illustrating the mathematical conditions leading to microphase separation. We then identify CRN motifs that are likely to yield size control by examining randomly generated networks and parameters. By analyzing the probabilities to observe particular states, we define simple design rules of CRNs that lead to desired non-equilibrium behavior. We show that chemical interactions generating negative feedback facilitate microphase separation, moreover, we demonstrate that the parameters important for the emergence of microphase separation differ for systems with two or four components, due to frustration. Our results provide guidance toward the design of self-regulating material CRNs and provide instructions to manage the formation, dissolution, and organization of compartments.

cond-mat.soft↗

arXiv2020

A feedback SIR (fSIR) model highlights advantages and limitations of infection-dependent mitigation strategies

Transmission rates in epidemic outbreaks may vary over time depending on the societal response. Non-pharmacological mitigation strategies such as social distancing and the adoption of protective equipment aim precisely at reducing transmission rates by reducing infectious contacts. To investigate the effects of mitigation strategies on the evolution of epidemics, nonlinear transmission rates that are influenced by the levels of infections, deaths or recoveries have been included in many variants of the classical SIR model. This class of models is particularly relevant to the COVID-19 epidemic, in which the population behavior has been affected by the unprecedented abundance and rapid distribution of global infection and death data through online platforms. This manuscript revisits a SIR model in which the reduction of transmission rate is due to knowledge of infections. Through a mean field approach that assumes individuals behave like molecules in a well-mixed solution, one derives a time-varying reproduction number that depends on infection information through a negative feedback term that is equivalent to Holling type II functions in ecology and Michaelis-Menten functions in chemistry and molecular biology. A step-by-step derivation of the model is provided, together with an overview of methods for its qualitative analysis, showing that negative feedback structurally reduces the peak of infections. At the same time, feedback may substantially extend the duration of an epidemic. Computational simulations agree with the analytical predictions, and further suggest that infection peak reduction persists even in the presence of information delays. If the mitigation strategy is linearly proportional to infections, a single parameter is added to the SIR model, making it useful to illustrate the effects of infection-dependent social distancing.

q-bio.PE↗

arXiv2020

The challenges of modeling and forecasting the spread of COVID-19

We present three data driven model-types for COVID-19 with a minimal number of parameters to provide insights into the spread of the disease that may be used for developing policy responses. The first is exponential growth, widely studied in analysis of early-time data. The second is a self-exciting branching process model which includes a delay in transmission and recovery. It allows for meaningful fit to early time stochastic data. The third is the well-known Susceptible-Infected-Resistant (SIR) model and its cousin, SEIR, with an "Exposed" component. All three models are related quantitatively, and the SIR model is used to illustrate the potential effects of short-term distancing measures in the United States.

q-bio.PE↗