arXiv subjects

Eric W. Jones

Publications and source records attributed to Eric W. Jones.

5 recordsLinked to original sources

arXiv2023

Signal in the noise: temporal variation in exponentially growing populations

In exponential population growth, variability in the timing of individual division events and environmental factors (including stochastic inoculation) compound to produce variable growth trajectories. In several stochastic models of exponential growth we show power-law relationships that relate variability in the time required to reach a threshold population size to growth rate and inoculum size. Population-growth experiments in E. coli and S. aureus with inoculum sizes ranging between 1 and 100 are consistent with these relationships. We quantify how noise accumulates over time, finding that it encodes -- and can be used to deduce -- information about the early growth rate of a population.

q-bio.PE↗

arXiv2020

Aging-induced fragility of the immune system

The adaptive and innate branches of the vertebrate immune system work in close collaboration to protect organisms from harmful pathogens. As an organism ages its immune system undergoes immunosenescence, characterized by declined performance or malfunction in either immune branch, which can lead to disease and death. In this study we develop a mathematical framework of coupled innate and adaptive immune responses, namely the integrated immune branch (IIB) model. This model describes dynamics of immune components in both branches, uses a shape-space representation to encode pathogen-specific immune memory, and exhibits three steady states -- health, septic death, and chronic inflammation -- qualitatively similar to clinically-observed immune outcomes. In this model, the immune system (initialized in the health state) is subjected to a sequence of pathogen encounters, and we use the number of prior pathogen encounters as a proxy for the "age" of the immune system. We find that repeated pathogen encounters may trigger a fragility in which any encounter with a novel pathogen will cause the system to irreversibly switch from health to chronic inflammation. This transition is consistent with the onset of "inflammaging", a condition observed in aged individuals who experience chronic low-grade inflammation even in the absence of pathogens. The IIB model predicts that the onset of chronic inflammation strongly depends on the history of encountered pathogens; the timing of onset differs drastically when the same set of infections occurs in a different order. Lastly, the coupling between the innate and adaptive immune branches generates a trade-off between rapid pathogen clearance and a delayed onset of immunosenescence.

q-bio.TO↗

arXiv2020

Navigation and control of outcomes in a generalized Lotka-Volterra model of the microbiome

The generalized Lotka-Volterra (gLV) equations model the microbiome as a collection of interacting ecological species. Here we use a particular experimentally-derived gLV model of C. difficile infection (CDI) as a case study to generate methods that are applicable to generic gLV models. We examine how to transition gLV systems between multiple steady states through the application of direct control protocols, which alter the state of the system via the instantaneous addition or subtraction of microbial species. Then, the geometry of the basins of attraction of point attractors is compressed into an attractor network, which decomposes a multistable high-dimensional landscape into web of bistable subsystems. This attractor network is used to identify efficient (total intervention volume minimizing) protocols that drive the system from one basin to another. In some cases, the most efficient control protocol is circuitous and will take the system through intermediate steady states with sequential interventions. Clinically, the efficient control of the microbiome has pertinent applications for bacteriotherapies, which seek to remedy microbiome-affiliated diseases by directly altering the composition of the gut microbiome.

q-bio.PE↗

arXiv2020

Control of ecological outcomes through deliberate parameter changes in a model of the gut microbiome

The generalized Lotka-Volterra (gLV) equations are a mathematical proxy for ecological dynamics. We focus on a gLV model of the gut microbiome, in which the evolution of the gut microbial state is determined in part by pairwise inter-species interaction parameters that encode environmentally-mediated resource competition between microbes. We develop an in silico method that controls the steady-state outcome of the system by adjusting these interaction parameters. This approach is confined to a bistable region of the gLV model. The two steady states of interest are idealized as either a "healthy" or "diseased" steady state of the gut microbiome. In this method, a dimensionality reduction technique called steady-state reduction (SSR) is first used to generate a two-dimensional (2D) gLV model that approximates the high-dimensional dynamics on the 2D subspace spanned by the two steady states. Then a bifurcation analysis of the 2D model analytically determines parameter modifications that drive a disease-prone initial condition to the healthy steady state. This parameter modification of the reduced 2D model guides parameter modifications of the original high-dimensional model, resulting in a change of steady-state outcome in the high-dimensional model. This control method, called SPARC (SSR-guided parameter change), bypasses the computational challenge of directly determining parameter modifications in the original high-dimensional system. SPARC could guide the development of indirect bacteriotherapies, which seek to change microbial compositions by deliberately modifying gut environmental variables such as gut acidity or macronutrient availability.

q-bio.PE↗

arXiv2019

Steady State Reduction of generalized Lotka-Volterra systems in the microbiome

The generalized Lotka-Volterra (gLV) equations, a classic model from theoretical ecology, describe the population dynamics of a set of interacting species. As the number of species in these systems grow in number, their dynamics become increasingly complex and intractable. We introduce Steady State Reduction (SSR), a method that reduces a gLV system of many ecological species into two-dimensional (2D) subsystems that each obey gLV dynamics and whose basis vectors are steady states of the high-dimensional model. We apply this method to an experimentally-derived model of the gut microbiome in order to observe the transition between "healthy" and "diseased" microbial states. Specifically, we use SSR to investigate how fecal microbiota transplantation, a promising clinical treatment for dysbiosis, can revert a diseased microbial state to health.

q-bio.PE↗