Interparticle gap distributions on one-dimensional lattices

We analyse the successive binding of two species of particles on a one-dimensional discrete lattice, where the second variety is deposited only after complete adsorption of the first. We consider the two extreme cases of a perfectly irreversible initial deposition, with non-sliding particles, and that of a fully equilibrated one. For the latter we construct the exact gap distribution from the Tonks gas partition function. This distribution is contrasted with that obtained from the random sequential adsorption process. We discuss implications for the kinetics of adsorption of the second species, as well as experimental relevance of our results

The Effects of Statistical Multiplicity of Infection on Virus Quantification and Infectivity Assays

Many biological assays are employed in virology to quantify parameters of interest. Two such classes of assays, virus quantification assays (VQA) and infectivity assays (IA), aim to estimate the number of viruses present in a solution, and the ability of a viral strain to successfully infect a host cell, respectively. VQAs operate at extremely dilute concentrations and results can be subject to stochastic variability in virus-cell interactions. At the other extreme, high viral particle concentrations are used in IAs, resulting in large numbers of viruses infecting each cell, enough for measurable change in total transcription activity. Furthermore, host cells can be infected at any concentration regime by multiple particles, resulting in a statistical multiplicity of infection (SMOI) and yielding potentially significant variability in the assay signal and parameter estimates. We develop probabilistic models for SMOI at low and high viral particle concentration limits and apply them to the plaque (VQA), endpoint dilution (VQA), and luciferase reporter (IA) assays. A web-based tool implementing our models and analysis is also developed and presented. We test our proposed new methods for inferring experimental parameters from data using numerical simulations and show improvement on existing procedures in all limits.Comment: 19 pages, 11 figures, 1 tabl

Onset, timing, and exposure therapy of stress disorders: mechanistic insight from a mathematical model of oscillating neuroendocrine dynamics

The hypothalamic-pituitary-adrenal (HPA) axis is a neuroendocrine system that regulates numerous physiological processes. Disruptions in the activity of the HPA axis are correlated with many stress-related diseases such as post-traumatic stress disorder (PTSD) and major depressive disorder. In this paper, we characterize "normal" and "diseased" states of the HPA axis as basins of attraction of a dynamical system describing the inhibition of peptide hormones such as corticotropin-releasing hormone (CRH) and adrenocorticotropic hormone (ACTH) by circulating glucocorticoids such as cortisol (CORT). In addition to including key physiological features such as ultradian oscillations in cortisol levels and self-upregulation of CRH neuron activity, our model distinguishes the relatively slow process of cortisol-mediated CRH biosynthesis from rapid trans-synaptic effects that regulate the CRH secretion process. Crucially, we find that the slow regulation mechanism mediates external stress-driven transitions between the stable states in novel, intensity, duration, and timing-dependent ways. These results indicate that the timing of traumatic events may be an important factor in determining if and how patients will exhibit hallmarks of stress disorders. Our model also suggests a mechanism whereby exposure therapy of stress disorders such as PTSD may act to normalize downstream dysregulation of the HPA axis.Comment: 30 pages, 16 figures, submitted to BMC Biology Direc

Modeling and forecasting age-specific drug overdose mortality in the United States

Drug overdose deaths continue to increase in the United States for all major drug categories. Over the past two decades the total number of overdose fatalities has increased more than five-fold; since 2013 the surge in overdose rates is primarily driven by fentanyl and methamphetamines. Different drug categories and factors such as age, gender, and ethnicity are associated with different overdose mortality characteristics that may also change in time. For example, the average age at death from a drug overdose has decreased from 1940 to 1990 while the overall mortality rate has steadily increased. To provide insight into the population-level dynamics of drug-overdose mortality, we develop an age-structured model for drug addiction. Using an augmented ensemble Kalman filter (EnKF), we show through a simple example how our model can be combined with synthetic observation data to estimate mortality rate and an age-distribution parameter. Finally, we use an EnKF to combine our model with observation data on overdose fatalities in the United States from 1999 to 2020 to forecast the evolution of overdose trends and estimate model parameters.Comment: 10 pages, 4 figure

Recidivism and rehabilitation of criminal offenders: A carrot and stick evolutionary game

Motivated by recent efforts by the criminal justice system to treat and rehabilitate nonviolent offenders rather than focusing solely on their punishment, we introduce an evolutionary game theoretic model to study the effects of ???carrot and stick??? intervention programs on criminal recidivism. We use stochastic simulations to study the evolution of a population where individuals may commit crimes depending on their past history, surrounding environment and, in the case of recidivists, on any counseling, educational or training programs available to them after being punished for their previous crimes. These sociological factors are embodied by effective parameters that determine the decision making probabilities. Players may decide to permanently reform or continue engaging in criminal activity, eventually reaching a state where they are considered incorrigible. Depending on parameter choices, the outcome of the game is a society with a majority of virtuous, rehabilitated citizens or incorrigibles. Since total resources may be limited, we constrain the combined punishment and rehabilitation costs per crime to be fixed, so that increasing one effort will necessarily decrease the other. We find that the most successful strategy in reducing crime is to optimally allocate resources so that after being punished, criminals experience impactful intervention programs, especially during the first stages of their return to society. Excessively harsh or lenient punishments are less effective. We also develop a system of coupled ordinary differential equations with memory effects to give a qualitative description of our simulated societal dynamics. We discuss our findings and sociological implications.This work was supported by the National Science Foundation through grants DMS-1021850 (to MRD) and DMS-1021818 (to TC), and by the ARO through the MURI grant W911NF-11-1-0332 (to MRD) and grant 58386MA (to TC). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript