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Cellular signaling, crucial for biological processes like immune response and homeostasis, relies on specificity and fidelity in signal transduction to accurately respond to stimuli amidst biological noise. Kinetic proofreading (KPR) is a key mechanism enhancing signaling specificity through time-delayed steps, although its effectiveness is debated due to intrinsic noise potentially reducing signal fidelity. In this study, we reformulate the theory of kinetic proofreading (KPR) by convolving multiple intermediate states into a single state and then define an overall processing time required to traverse these states. This simplification allows us to succinctly describe kinetic proofreading in terms of a single waiting time parameter, facilitating a more direct evaluation and comparison of KPR performance across different biological contexts such as DNA replication and T cell receptor (TCR) signaling. We find that loss of fidelity for longer proofreading steps relies on the specific strategy of information extraction and show that in the first-passage time (FPT) discrimination strategy, longer proofreading steps can exponentially improve the accuracy of KPR at the cost of speed. Thus, KPR can still be an effective discrimination mechanism in the high noise regime. However, in a product concentration-based discrimination strategy, longer proofreading steps do not necessarily lead to an increase in performance. However, by introducing activation thresholds on product concentrations, can we decompose the product-based strategy into a series of FPT-based strategies to better resolve the subtleties of KPR-mediated product discrimination. Our findings underscore the importance of understanding KPR in the context of how information is extracted and processed in the cell.

BackgroundAn understanding of epidemiological dynamics, once confined to mathematical epidemiologists and applied mathematicians, can be disseminated to a non-mathematical community of health care professionals and applied biologists through simple-to-use simulation applications. We used Numerus Model Builder RAMP Ⓡ (Runtime Alterable Model Platform) technology, to construct deterministic and stochastic versions of compartmental SIR (Susceptible, Infectious, Recovered with immunity) models as simple-to-use, freely available, epidemic simulation application programs.ResultsWe take the reader through simulations used to demonstrate the following concepts: 1) disease prevalence curves of unmitigated outbreaks have a single peak and result in epidemics that 'burn' through the population to become extinguished when the proportion of the susceptible population drops below a critical level; 2) if immunity in recovered individuals wanes sufficiently fast then the disease persists indefinitely as an endemic state, with possible dampening oscillations following the initial outbreak phase; 3) the steepness and initial peak of the prevalence curve are influenced by the basic reproductive value R0, which must exceed 1 for an epidemic to occur; 4) the probability that a single infectious individual in a closed population (i.e. no migration) gives rise to an epidemic increases with the value of R0>1; 5) behavior that adaptively decreases the contact rate among individuals with increasing prevalence has major effects on the prevalence curve including dramatic flattening of the prevalence curve along with the generation of multiple prevalence peaks; 6) the impacts of treatment are complicated to model because they effect multiple processes including transmission, recovery and mortality; 7) the impacts of vaccination policies, constrained by a fixed number of vaccination regimens and by the rate and timing of delivery, are crucially important to maximizing the ability of vaccination programs to reduce mortality.ConclusionOur presentation makes transparent the key assumptions underlying SIR epidemic models. Our RAMP simulators are meant to augment rather than replace classroom material when teaching epidemiological dynamics. They are sufficiently versatile to be used by students to address a range of research questions for term papers and even dissertations.

Advances in single-cell technologies allow scrutinizing of heterogeneous cell states, however, detecting cell-state transitions from snap-shot single-cell transcriptome data remains challenging. To investigate cells with transient properties or mixed identities, we present MuTrans, a method based on multiscale reduction technique to identify the underlying stochastic dynamics that prescribes cell-fate transitions. By iteratively unifying transition dynamics across multiple scales, MuTrans constructs the cell-fate dynamical manifold that depicts progression of cell-state transitions, and distinguishes stable and transition cells. In addition, MuTrans quantifies the likelihood of all possible transition trajectories between cell states using coarse-grained transition path theory. Downstream analysis identifies distinct genes that mark the transient states or drive the transitions. The method is consistent with the well-established Langevin equation and transition rate theory. Applying MuTrans to datasets collected from five different single-cell experimental platforms, we show its capability and scalability to robustly unravel complex cell fate dynamics induced by transition cells in systems such as tumor EMT, iPSC differentiation and blood cell differentiation. Overall, our method bridges data-driven and model-based approaches on cell-fate transitions at single-cell resolution.

COVID-19's high virus transmission rates have caused a pandemic that is exacerbated by the high rates of asymptomatic and presymptomatic infections. These factors suggest that face masks and social distance could be paramount in containing the pandemic. We examined the efficacy of each measure and the combination of both measures using an agent-based model within a closed space that approximated real-life interactions. By explicitly considering different fractions of asymptomatic individuals, as well as a realistic hypothesis of face masks protection during inhaling and exhaling, our simulations demonstrate that a synergistic use of face masks and social distancing is the most effective intervention to curb the infection spread. To control the pandemic, our models suggest that high adherence to social distance is necessary to curb the spread of the disease, and that wearing face masks provides optimal protection even if only a small portion of the population comply with social distance. Finally, the face mask effectiveness in curbing the viral spread is not reduced if a large fraction of population is asymptomatic. Our findings have important implications for policies that dictate the reopening of social gatherings.

Transcription-replication interactions occur when DNA replication encounters genomic regions undergoing transcription. Both replication and transcription are essential for life and use the same DNA template making conflicts unavoidable. R-loops, DNA supercoiling, DNA secondary structure, and chromatin-binding proteins are all potential obstacles for processive replication or transcription and pose an even more potent threat to genome integrity when these processes co-occur. It is critical to maintaining high fidelity and processivity of transcription and replication while navigating through a complex chromatin environment, highlighting the importance of defining cellular pathways regulating transcription-replication interaction formation, evasion, and resolution. Here we discuss how transcription influences replication fork stability, and the safeguards that have evolved to navigate transcription-replication interactions and maintain genome integrity in mammalian cells.

Neurons rely on localized mitochondria to fulfill spatially heterogeneous metabolic demands. Mitochondrial aging occurs on timescales shorter than the neuronal lifespan, necessitating transport of fresh material from the soma. Maintaining an optimal distribution of healthy mitochondria requires an interplay between a stationary pool localized to sites of high metabolic demand and a motile pool capable of delivering new material. Interchange between these pools can occur via transient fusion / fission events or by halting and restarting entire mitochondria. Our quantitative model of neuronal mitostasis identifies key parameters that govern steady-state mitochondrial health at discrete locations. Very infrequent exchange between stationary and motile pools optimizes this system. Exchange via transient fusion allows for robust maintenance, which can be further improved by selective recycling through mitophagy. These results provide a framework for quantifying how perturbations in organelle transport and interactions affect mitochondrial homeostasis in neurons, a key aspect underlying many neurodegenerative disorders.

To study viral evolutionary processes within patients, mathematical models have been instrumental. Yet, the need for stochastic simulations of minority mutant dynamics can pose computational challenges, especially in heterogeneous systems where very large and very small sub-populations coexist. Here, we describe a hybrid stochastic-deterministic algorithm to simulate mutant evolution in large viral populations, such as acute HIV-1 infection, and further include the multiple infection of cells. We demonstrate that the hybrid method can approximate the fully stochastic dynamics with sufficient accuracy at a fraction of the computational time, and quantify evolutionary end points that cannot be expressed by deterministic models, such as the mutant distribution or the probability of mutant existence at a given infected cell population size. We apply this method to study the role of multiple infection and intracellular interactions among different virus strains (such as complementation and interference) for mutant evolution. Multiple infection is predicted to increase the number of mutants at a given infected cell population size, due to a larger number of infection events. We further find that viral complementation can significantly enhance the spread of disadvantageous mutants, but only in select circumstances: it requires the occurrence of direct cell-to-cell transmission through virological synapses, as well as a substantial fitness disadvantage of the mutant, most likely corresponding to defective virus particles. This, however, likely has strong biological consequences because defective viruses can carry genetic diversity that can be incorporated into functional virus genomes via recombination. Through this mechanism, synaptic transmission in HIV might promote virus evolvability.

FLASH radiotherapy delivers a high dose (≥10 Gy) at a high rate (≥40 Gy/s). In this way, particles are delivered in pulses as short as a few nanoseconds. At that rate, intertrack reactions between chemical species produced within the same pulse may affect the heterogeneous chemistry stage of water radiolysis. This stochastic process suits the capabilities of the Monte Carlo method, which can model intertrack effects to aid in radiobiology research, including the design and interpretation of experiments. In this work, the TOPAS-nBio Monte Carlo track-structure code was expanded to allow simulations of intertrack effects in the chemical stage of water radiolysis. Simulation of the behavior of radiolytic yields over a long period of time (up to 50 s) was verified by simulating radiolysis in a Fricke dosimeter irradiated by 60Co γ rays. In addition, LET-dependent G values of protons delivered in single squared pulses of widths, 1 ns, 1 µs and 10 µs, were obtained and compared to simulations using no intertrack considerations. The Fricke simulation for the calculated G value of Fe3+ ion at 50 s was within 0.4% of the accepted value from ICRU Report 34. For LET-dependent G values at the end of the chemical stage, intertrack effects were significant at LET values below 2 keV/µm. Above 2 keV/µm the reaction kinetics remained limited locally within each track and thus, effects of intertrack reactions remained low. Therefore, when track structure simulations are used to investigate the biological damage of FLASH irradiation, these intertrack reactions should be considered. The TOPAS-nBio framework with the expansion to intertrack chemistry simulation provides a useful tool to assist in this task.

Pure (single) cultures of microorganisms and mixed microbial communities (microbiomes) have been important for centuries in providing renewable energy, clean water and food products to human society and will continue to play a crucial role to pursue the Sustainable Development Goals. To use microorganisms effectively, microbial engineered processes require adequate control. Microbial communities are shaped by manageable deterministic processes, but also by stochastic processes, which can promote unforeseeable variations and adaptations. Here, we highlight the impact of stochasticity in single culture and microbiome engineering. First, we discuss the concepts and mechanisms of stochasticity in relation to microbial ecology of single cultures and microbiomes. Second, we discuss the consequences of stochasticity in relation to process performance and human health, which are reflected in key disadvantages and important opportunities. Third, we propose a suitable decision tool to deal with stochasticity in which monitoring of stochasticity and setting the boundaries of stochasticity by regulators are central aspects. Stochasticity may give rise to some risks, such as the presence of pathogens in microbiomes. We argue here that by taking the necessary precautions and through clever monitoring and interpretation, these risks can be mitigated.

Political orientation is one of the most important and consequential individual attributes studied by social scientists. Yet, we know relatively little about the temporal evolution of political orientation, especially at periods in the life course during which individuals are forming new social relationships and transitioning to new relational contexts. Here we use Stochastic Actor-Oriented models (SAOMs) to examine the co-evolution of political orientation and social networks using two feature-rich, temporal network datasets from samples of students making the transition to college at the University of Notre Dame (i.e. the NetSense and NetHealth studies). Overall, we find a great deal of stability in political orientation, with a slight tendency for the 2011 NetSense study participants to become more conservative during their first four semesters in college, but not the 2015 NetHealth study participants. Partisanship is the best predictor of changes in political orientation, with students who identify or vote as Republicans becoming more conservative over time. Neither network influence nor selection processes seem to be driving observed changes. During this formative period, relatively stable identities such as party affiliation predict changes in political orientation independently of local network dynamics, selection processes, socio-demographic traits, and dispositional factors.

Chaos, or exponential sensitivity to small perturbations, appears everywhere in nature. Moreover, chaos is predicted to play diverse functional roles in living systems. A method for detecting chaos from empirical measurements should therefore be a key component of the biologist's toolkit. But, classic chaos-detection tools are highly sensitive to measurement noise and break down for common edge cases, making it difficult to detect chaos in domains, like biology, where measurements are noisy. However, newer tools promise to overcome these limitations. Here, we combine several such tools into an automated processing pipeline, and show that our pipeline can detect the presence (or absence) of chaos in noisy recordings, even for difficult edge cases. As a first-pass application of our pipeline, we show that heart rate variability is not chaotic as some have proposed, and instead reflects a stochastic process in both health and disease. Our tool is easy-to-use and freely available.

Ion channels are often found arranged into dense clusters in the plasma membranes of excitable cells, but the mechanisms underlying the formation and maintenance of these functional aggregates are unknown. Here, we tested the hypothesis that channel clustering is the consequence of a stochastic self-assembly process and propose a model by which channel clusters are formed and regulated in size. Our hypothesis is based on statistical analyses of the size distributions of the channel clusters we measured in neurons, ventricular myocytes, arterial smooth muscle, and heterologous cells, which in all cases were described by exponential functions, indicative of a Poisson process (i.e., clusters form in a continuous, independent, and memory-less fashion). We were able to reproduce the observed cluster distributions of five different types of channels in the membrane of excitable and tsA-201 cells in simulations using a computer model in which channels are "delivered" to the membrane at randomly assigned locations. The model's three parameters represent channel cluster nucleation, growth, and removal probabilities, the values of which were estimated based on our experimental measurements. We also determined the time course of cluster formation and membrane dwell time for CaV1.2 and TRPV4 channels expressed in tsA-201 cells to constrain our model. In addition, we elaborated a more complex version of our model that incorporated a self-regulating feedback mechanism to shape channel cluster formation. The strong inference we make from our results is that CaV1.2, CaV1.3, BK, and TRPV4 proteins are all randomly inserted into the plasma membranes of excitable cells and that they form homogeneous clusters that increase in size until they reach a steady state. Further, it appears likely that cluster size for a diverse set of membrane-bound proteins and a wide range of cell types is regulated by a common feedback mechanism.

Heterogeneity in transmission is a challenge for infectious disease dynamics and control. An 80-20 "Pareto" rule has been proposed to describe this heterogeneity whereby 80% of transmission is accounted for by 20% of individuals, herein called super-spreaders. It is unclear, however, whether super-spreading can be attributed to certain individuals or whether it is an unpredictable and unavoidable feature of epidemics. Here, we investigate heterogeneous malaria transmission at three sites in Uganda and find that super-spreading is negatively correlated with overall malaria transmission intensity. Mosquito biting among humans is 90-10 at the lowest transmission intensities declining to less than 70-30 at the highest intensities. For super-spreaders, biting ranges from 70-30 down to 60-40. The difference, approximately half the total variance, is due to environmental stochasticity. Super-spreading is thus partly due to super-spreaders, but modest gains are expected from targeting super-spreaders.

T cell receptor (TCR) stimulation activates diverse kinase pathways, which include the mitogen-activated protein kinases (MAPKs) ERK and p38, the phosphoinositide 3-kinases (PI3Ks), and the kinase mTOR. Although TCR stimulation activates the p38 pathway through a "classical" MAPK cascade that is mediated by the adaptor protein LAT, it also stimulates an "alternative" pathway in which p38 is activated by the kinase ZAP70. Here, we used dual-parameter, phosphoflow cytometry and in silico computation to investigate how both classical and alternative p38 pathways contribute to T cell activation. We found that basal ZAP70 activation in resting T cell lines reduced the threshold ("primed") TCR-stimulated activation of the classical p38 pathway. Classical p38 signals were reduced after T cell-specific deletion of the guanine nucleotide exchange factors Sos1 and Sos2, which are essential LAT signalosome components. As a consequence of Sos1/2 deficiency, production of the cytokine IL-2 was impaired, differentiation into regulatory T cells was reduced, and the autoimmune disease EAE was exacerbated in mice. These data suggest that the classical and alternative p38 activation pathways exist to generate immune balance.

Leucine-rich repeat (LRR) domains are evolutionarily conserved in proteins that function in development and immunity. Here we report strict exonic modularity of LRR domains of several human gene families, which is a precondition for alternative splicing (AS). We provide evidence for AS of LRR domain within several Nod-like receptors, most prominently the inflammasome sensor NLRP3. Human NLRP3, but not mouse NLRP3, is expressed as two major isoforms, the full-length variant and a variant lacking exon 5. Moreover, NLRP3 AS is stochastically regulated, with NLRP3 ∆ exon 5 lacking the interaction surface for NEK7 and hence loss of activity. Our data thus reveals unexpected regulatory roles of AS through differential utilization of LRRs modules in vertebrate innate immunity.

RationaleAs part of the End TB Strategy, the World Health Organization calls for low-tuberculosis (TB) incidence settings to achieve pre-elimination (

Epidemiological models are dominated by compartmental models, of which SIR formulations are the most commonly used. These formulations can be continuous or discrete (in either the state-variable values or time), deterministic or stochastic, or spatially homogeneous or heterogeneous, the latter often embracing a network formulation. Here we review the continuous and discrete deterministic and discrete stochastic formulations of the SIR dynamical systems models, and we outline how they can be easily and rapidly constructed using Numerus Model Builder, a graphically-driven coding platform. We also demonstrate how to extend these models to a metapopulation setting using NMB network and mapping tools.

Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SE[Formula: see text]I[Formula: see text]R models with [Formula: see text] concatenated E compartments and [Formula: see text] concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity. Here we formulate discrete-time deterministic analogs of the Erlang models, and their stochastic extension, based on a time-to-go distributional principle. Depending on which distributions are used (e.g. discretized Erlang, Gamma, Beta, or Uniform distributions), we demonstrate that our formulation represents both a discretization of Erlang epidemic models and generalizations thereof. We consider the challenges of fitting SE[Formula: see text]I[Formula: see text]R models and our discrete-time analog to data (the recent outbreak of Ebola in Liberia). We demonstrate that the latter performs much better than the former; although confining fits to strict SEIR formulations reduces the numerical challenges, but sacrifices best-fit likelihood scores by at least 7%.

BackgroundEvidence suggests that aspects of the neighborhood environment may influence risk of problematic drug use among adolescents. Our objective was to examine mediating roles of aspects of the school and peer environments on the effect of receiving a Section 8 housing voucher and using it to move out of public housing on adolescent substance use outcomes.MethodsWe used data from the Moving to Opportunity (MTO) experiment that randomized receipt of a Section 8 housing voucher. Hypothesized mediators included school climate, safety, peer drug use, and participation in an after-school sport or club. We applied a doubly robust, semiparametric estimator to longitudinal MTO data to estimate stochastic direct and indirect effects of randomization on cigarette use, marijuana use, and problematic drug use. Stochastic direct and indirect effects differ from natural direct and indirect effects in that they do not require assuming no posttreatment confounder of the mediator-outcome relationship. Such an assumption would be at odds with any causal model that reflects an intervention affecting a mediator and outcome through adherence to treatment assignment.ResultsHaving friends who use drugs and involvement in after-school sports or clubs partially mediated the effect of housing voucher receipt on adolescent substance use (e.g., stochastic indirect effect 0.45% [95% confidence interval: 0.12%, 0.79%] for having friends who use drugs and 0.04% [95% confidence interval: -0.02%, 0.10%] for involvement in after-school sports or clubs mediating the relationship between housing voucher receipt and marijuana use among boys). However, these mediating effects were small, contributing only fractions of a percent to the effect of voucher receipt on probability of substance use. No school environment variables were mediators.ConclusionsMeasured school- and peer-environment variables played little role in mediating the effect of housing voucher receipt on subsequent adolescent substance use.

BackgroundTransitions into and out of the anaesthetised state exhibit resistance to state transitions known as neural inertia. As a consequence, emergence from anaesthesia occurs at a consistently lower anaesthetic concentration than induction. Motivated by stochastic switching between discrete activity patterns observed at constant anaesthetic concentration, we investigated the consequences of such switching for neural inertia.MethodsWe simulated stochastic switching in MATLAB as Brownian motion on an energy landscape or equivalently as a discrete Markov process. Effects of anaesthetics were modelled as changing stability of the awake and the anaesthetised states. Simulation results were compared with re-analysed neural inertia data from mice and Drosophila.ResultsDiffusion on a two-well energy landscape gives rise to hysteresis. With additive noise, hysteresis collapses. This collapse occurs over a mixing time that is independent from pharmacokinetics. The two-well potential gives rise to the leftward shift for the emergence dose-response curve. Yet, from in vivo data, ΔEC50 and Δ Hill slope are strongly negatively correlated (R2=0.45, P

Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating finite-time transition probabilities of bivariate processes, however, has restricted statistical inference in these models. Researchers rely on computationally expensive methods such as matrix exponentiation or Monte Carlo approximation, restricting likelihood-based inference to small systems, or indirect methods such as approximate Bayesian computation. In this paper, we introduce the birth/birth-death process, a tractable bivariate extension of the birth-death process, where rates are allowed to be nonlinear. We develop an efficient algorithm to calculate its transition probabilities using a continued fraction representation of their Laplace transforms. Next, we identify several exemplary models arising in molecular epidemiology, macro-parasite evolution, and infectious disease modeling that fall within this class, and demonstrate advantages of our proposed method over existing approaches to inference in these models. Notably, the ubiquitous stochastic susceptible-infectious-removed (SIR) model falls within this class, and we emphasize that computable transition probabilities newly enable direct inference of parameters in the SIR model. We also propose a very fast method for approximating the transition probabilities under the SIR model via a novel branching process simplification, and compare it to the continued fraction representation method with application to the 17th century plague in Eyam. Although the two methods produce similar maximum a posteriori estimates, the branching process approximation fails to capture the correlation structure in the joint posterior distribution.

The mammalian skin epidermis is a stratified epithelium composed of multiple layers of epithelial cells that exist in appropriate sizes and proportions, and with distinct boundaries separating each other. How the epidermis develops from a single layer of committed precursor cells to form a complex multilayered structure of multiple cell types remains elusive. Here, we construct stochastic, three-dimensional, and multiscale models consisting of a lineage of multiple cell types to study the control of epidermal development. Symmetric and asymmetric cell divisions, stochastic cell fate transitions within the lineage, extracellular morphogens, cell-to-cell adhesion forces, and cell signaling are included in model. A GPU algorithm was developed and implemented to accelerate the simulations. These simulations show that a balance between cell proliferation and differentiation during lineage progression is crucial for the development and maintenance of the epidermal tissue. We also find that selective intercellular adhesion is critical to sharpening the boundary between layers and to the formation of a highly ordered structure. The long-range action of a morphogen provides additional feedback regulations, enhancing the robustness of overall layer formation. Our model is built upon previous experimental findings revealing the role of Ovol transcription factors in regulating epidermal development. Direct comparisons of experimental and simulation perturbations show remarkable consistency. Taken together, our results highlight the major determinants of a well-stratified epidermis: balanced proliferation and differentiation, and a combination of both short- (symmetric/asymmetric division and selective cell adhesion) and long-range (morphogen) regulations. These underlying principles have broad implications for other developmental or regenerative processes leading to the formation of multilayered tissue structures, as well as for pathological processes such as epidermal wound healing.

In order to maintain homeostasis, mature cells removed from the top compartment of hierarchical tissues have to be replenished by means of differentiation and self-renewal events happening in the more primitive compartments. As each cell division is associated with a risk of mutation, cell division patterns have to be optimized, in order to minimize or delay the risk of malignancy generation. Here we study this optimization problem, focusing on the role of division tree length, that is, the number of layers of cells activated in response to the loss of terminally differentiated cells, which is related to the balance between differentiation and self-renewal events in the compartments. Using both analytical methods and stochastic simulations in a metapopulation-style model, we find that shorter division trees are advantageous if the objective is to minimize the total number of one-hit mutants in the cell population. Longer division trees on the other hand minimize the accumulation of two-hit mutants, which is a more likely evolutionary goal given the key role played by tumor suppressor genes in cancer initiation. While division tree length is the most important property determining mutant accumulation, we also find that increasing the size of primitive compartments helps to delay two-hit mutant generation.

Influenza is responsible for up to 500,000 deaths every year, and antigenic variability represents much of its epidemiological burden. To visualize antigenic differences across many viral strains, antigenic cartography methods use multidimensional scaling on binding assay data to map influenza antigenicity onto a low-dimensional space. Analysis of such assay data ideally leads to natural clustering of influenza strains of similar antigenicity that correlate with sequence evolution. To understand the dynamics of these antigenic groups, we present a framework that jointly models genetic and antigenic evolution by combining multidimensional scaling of binding assay data, Bayesian phylogenetic machinery and nonparametric clustering methods. We propose a phylogenetic Chinese restaurant process that extends the current process to incorporate the phylogenetic dependency structure between strains in the modeling of antigenic clusters. With this method, we are able to use the genetic information to better understand the evolution of antigenicity throughout epidemics, as shown in applications of this model to H1N1 influenza. Copyright © 2017 John Wiley & Sons, Ltd.

Nosocomial pathogens such as methicillin-resistant Staphylococcus aureus (MRSA) and vancomycin-resistant Enterococci (VRE) are the cause of significant morbidity and mortality among hospital patients. It is important to be able to assess the efficacy of control measures using data on patient outcomes. In this paper, we describe methods for analysing such data using patient-level stochastic models which seek to describe the underlying unobserved process of transmission. The methods are applied to detailed longitudinal patient-level data on vancomycin-resistant Enterococci from a study in a US hospital with eight intensive care units (ICUs). The data comprise admission and discharge dates, dates and results of screening tests, and dates during which precautionary measures were in place for each patient during the study period. Results include estimates of the efficacy of the control measures, the proportion of unobserved patients colonized with vancomycin-resistant Enterococci, and the proportion of patients colonized on admission.

The concurrent or sequential usage of multiple substances during adolescence is a serious public health problem. Given the importance of understanding interdependence in substance use during adolescence, the purpose of this study is to examine the co-evolution of cigarette smoking, alcohol, and marijuana use within the ever-changing landscape of adolescent friendship networks, which are a primary socialization context for adolescent substance use. Utilizing Stochastic Actor-Based models, we examine how multiple simultaneous social processes co-evolve with adolescent smoking, drinking, and marijuana use within adolescent friendship networks using two school samples from early waves of the National Longitudinal Study of Adolescent to Adult Health (Add Health). We also estimate two separate models examining the effects from using one substance to the initiation and cessation of other substances for each sample. Based on the initial model results, we simulate the model forward in time by turning off one key effect in the estimated model at a time, and observe how the distribution of use of each substance changes. We find evidence of a unilateral causal relationship from marijuana use to subsequent smoking and drinking behaviors, resulting in the initiation of drinking behavior. Marijuana use is also associated with smoking initiation in a school with a low substance use level, and smoking cessation in a school with a high substance use level. In addition, in a simulation model excluding the effect from marijuana use to smoking and drinking behavior, the number of smokers and drinkers decreases precipitously. Overall, our findings indicate some evidence of sequential drug use, as marijuana use increased subsequent smoking and drinking behavior and indicate that an adolescent's level of marijuana use affects the initiation and continuation of smoking and drinking.

Current health policy calls for greater use of evidence-based care delivery services to improve patient quality and safety outcomes. Care delivery is complex, with interacting and interdependent components that challenge traditional statistical analytic techniques, in particular, when modeling a time series of outcomes data that might be "interrupted" by a change in a particular method of health care delivery. Interrupted time series (ITS) is a robust quasi-experimental design with the ability to infer the effectiveness of an intervention that accounts for data dependency. Current standardized methods for analyzing ITS data do not model changes in variation and correlation following the intervention. This is a key limitation since it is plausible for data variability and dependency to change because of the intervention. Moreover, present methodology either assumes a prespecified interruption time point with an instantaneous effect or removes data for which the effect of intervention is not fully realized. In this paper, we describe and develop a novel robust interrupted time series (robust-ITS) model that overcomes these omissions and limitations. The robust-ITS model formally performs inference on (1) identifying the change point; (2) differences in preintervention and postintervention correlation; (3) differences in the outcome variance preintervention and postintervention; and (4) differences in the mean preintervention and postintervention. We illustrate the proposed method by analyzing patient satisfaction data from a hospital that implemented and evaluated a new nursing care delivery model as the intervention of interest. The robust-ITS model is implemented in an R Shiny toolbox, which is freely available to the community.

Understanding the mechanisms controlling community diversity, functions, succession, and biogeography is a central, but poorly understood, topic in ecology, particularly in microbial ecology. Although stochastic processes are believed to play nonnegligible roles in shaping community structure, their importance relative to deterministic processes is hotly debated. The importance of ecological stochasticity in shaping microbial community structure is far less appreciated. Some of the main reasons for such heavy debates are the difficulty in defining stochasticity and the diverse methods used for delineating stochasticity. Here, we provide a critical review and synthesis of data from the most recent studies on stochastic community assembly in microbial ecology. We then describe both stochastic and deterministic components embedded in various ecological processes, including selection, dispersal, diversification, and drift. We also describe different approaches for inferring stochasticity from observational diversity patterns and highlight experimental approaches for delineating ecological stochasticity in microbial communities. In addition, we highlight research challenges, gaps, and future directions for microbial community assembly research.

Ciliopathies, including nephronophthisis (NPHP), Meckel syndrome (MKS) and Joubert syndrome (JBTS), can be caused by mutations affecting components of the transition zone, a domain near the base of the cilium that controls the protein composition of its membrane. We defined the three-dimensional arrangement of key proteins in the transition zone using two-colour stochastic optical reconstruction microscopy (STORM). NPHP and MKS complex components form nested rings comprised of nine-fold doublets. JBTS-associated mutations in RPGRIP1L or TCTN2 displace certain transition-zone proteins. Diverse ciliary proteins accumulate at the transition zone in wild-type cells, suggesting that the transition zone is a waypoint for proteins entering and exiting the cilium. JBTS-associated mutations in RPGRIP1L disrupt SMO accumulation at the transition zone and the ciliary localization of SMO. We propose that the disruption of transition-zone architecture in JBTS leads to a failure of SMO to accumulate at the transition zone and cilium, disrupting developmental signalling in JBTS.

Threshold generation in fate-selection circuits is often achieved through deterministic bistability, which requires cooperativity (i.e., nonlinear activation) and associated hysteresis. However, the Tat positive-feedback loop that controls HIV's fate decision between replication and proviral latency lacks self-cooperativity and deterministic bistability. Absent cooperativity, it is unclear how HIV can temporarily remain in an off-state long enough for the kinetically slower epigenetic silencing mechanisms to act-expression fluctuations should rapidly trigger active positive feedback and replication, precluding establishment of latency. Here, using flow cytometry and single-cell imaging, we find that the Tat circuit exhibits a transient activation threshold. This threshold largely disappears after ∼40 h-accounting for the lack of deterministic bistability-and promoter activation shortens the lifetime of this transient threshold. Continuous differential equation models do not recapitulate this phenomenon. However, chemical reaction (master equation) models where the transcriptional transactivator and promoter toggle between inactive and active states can recapitulate the phenomenon because they intrinsically create a single-molecule threshold transiently requiring excess molecules in the inactive state to achieve at least one molecule (rather than a continuous fractional value) in the active state. Given the widespread nature of promoter toggling and transcription factor modifications, transient thresholds may be a general feature of inducible promoters.

While studies suggest that peer influence can in some cases encourage adolescent substance use, recent work demonstrates that peer influence may be on average protective for cigarette smoking, raising questions about whether this effect occurs for other substance use behaviors. Herein, we focus on adolescent drinking, which may follow different social dynamics than smoking. We use a data-calibrated Stochastic Actor-Based (SAB) Model of adolescent friendship tie choice and drinking behavior to explore the impact of manipulating the size of peer influence and selection effects on drinking in two school-based networks. We first fit a SAB Model to data on friendship tie choice and adolescent drinking behavior within two large schools (n = 2178 and n = 976) over three time points using data from the National Longitudinal Study of Adolescent to Adult Health. We then alter the size of the peer influence and selection parameters with all other effects fixed at their estimated values and simulate the social systems forward 1000 times under varying conditions. Whereas peer selection appears to contribute to drinking behavior similarity among adolescents, there is no evidence that it leads to higher levels of drinking at the school level. A stronger peer influence effect lowers the overall level of drinking in both schools. There are many similarities in the patterning of findings between this study of drinking and previous work on smoking, suggesting that peer influence and selection may function similarly with respect to these substances.

A critical event in mammalian embryo development is construction of an inner cell mass surrounded by a trophoectoderm (a shell of cells that later form extraembryonic structures). We utilize multi-scale, stochastic modeling to investigate the design principles responsible for robust establishment of these structures. This investigation makes three predictions, each supported by our quantitative imaging. First, stochasticity in the expression of critical genes promotes cell plasticity and has a critical role in accurately organizing the developing mouse blastocyst. Second, asymmetry in the levels of noise variation (expression fluctuation) of Cdx2 and Oct4 provides a means to gain the benefits of noise-mediated plasticity while ameliorating the potentially detrimental effects of stochasticity. Finally, by controlling the timing and pace of cell fate specification, the embryo temporally modulates plasticity and creates a time window during which each cell can continually read its environment and adjusts its fate. These results suggest noise has a crucial role in maintaining cellular plasticity and organizing the blastocyst.

Cardiac myocytes normally initiate action potentials in response to a current stimulus that depolarizes the membrane above an excitation threshold. Aberrant excitation can also occur due to spontaneous calcium (Ca2+) release (SCR) from intracellular stores after the end of a preceding action potential. SCR drives the Na+/Ca2+ exchange current inducing a "delayed afterdepolarization" that can in turn trigger an action potential if the excitation threshold is reached. This "triggered activity" is known to cause arrhythmias, but how it is initiated and terminated is not understood. Using computer simulations of a ventricular myocyte model, we show that initiation and termination are inherently random events. We determine the probability of those events from statistical measurements of the number of beats before initiation and before termination, respectively, which follow geometric distributions. Moreover, we elucidate the origin of randomness by a statistical analysis of SCR events, which do not follow a Poisson process observed in other eukaryotic cells. Due to synchronization of Ca2+ releases during the action potential upstroke, waiting times of SCR events after the upstroke are narrowly distributed, whereas SCR amplitudes follow a broad normal distribution with a width determined by fluctuations in the number of independent Ca2+ wave foci. This distribution enables us to compute the probabilities of initiation and termination of bursts of triggered activity that are maintained by a positive feedback between the action potential upstroke and SCR. Our results establish a theoretical framework for interpreting complex and varied manifestations of triggered activity relevant to cardiac arrhythmias.

We extend a technique of approximation of the long-term behavior of a supercritical stochastic epidemic model, using the WKB approximation and a Hamiltonian phase space, to the subcritical case. The limiting behavior of the model and approximation are qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from its deterministic subsystem. This yields a novel, general technique of approximation of the quasistationary distribution of stochastic epidemic and birth-death models and may lead to techniques for analysis of these models beyond the quasistationary distribution. For a classic SIS model, the approximation found for the quasistationary distribution is very similar to published approximations but not identical. For a birth-death process without depletion of susceptibles, the approximation is exact. Dynamics on the phase plane similar to those predicted by the Hamiltonian analysis are demonstrated in cross-sectional data from trachoma treatment trials in Ethiopia, in which declining prevalences are consistent with subcritical epidemic dynamics.

We seek to elucidate the role of macromolecular crowding in transcription and translation. It is well known that stochasticity in gene expression can lead to differential gene expression and heterogeneity in a cell population. Recent experimental observations by Tan et al. have improved our understanding of the functional role of macromolecular crowding. It can be inferred from their observations that macromolecular crowding can lead to robustness in gene expression, resulting in a more homogeneous cell population. We introduce a spatial stochastic model to provide insight into this process. Our results show that macromolecular crowding reduces noise (as measured by the kurtosis of the mRNA distribution) in a cell population by limiting the diffusion of transcription factors (i.e. removing the unstable intermediate states), and that crowding by large molecules reduces noise more efficiently than crowding by small molecules. Finally, our simulation results provide evidence that the local variation in chromatin density as well as the total volume exclusion of the chromatin in the nucleus can induce a homogenous cell population.

Angiogenesis is a multiscale process by which blood vessels grow from existing ones and carry oxygen to distant organs. Angiogenesis is essential for normal organ growth and wounded tissue repair but it may also be induced by tumours to amplify their own growth. Mathematical and computational models contribute to understanding angiogenesis and developing anti-angiogenic drugs, but most work only involves numerical simulations and analysis has lagged. A recent stochastic model of tumour-induced angiogenesis including blood vessel branching, elongation, and anastomosis captures some of its intrinsic multiscale structures, yet allows one to extract a deterministic integropartial differential description of the vessel tip density. Here we find that the latter advances chemotactically towards the tumour driven by a soliton (similar to the famous Korteweg-de Vries soliton) whose shape and velocity change slowly. Analysing these collective coordinates paves the way for controlling angiogenesis through the soliton, the engine that drives this process.

The inability to maintain balance during varying postural control conditions can lead to falls, a significant cause of mortality and serious injury among older adults. However, our understanding of the underlying dynamical and stochastic processes in human postural control have not been fully explored. To further our understanding of the underlying dynamical processes, we examine a novel conceptual framework for studying human postural control using the center of pressure (COP) velocity autocorrelation function (COP-VAF) and compare its results to Stabilogram Diffusion Analysis (SDA). Eleven healthy young participants were studied under quiet unipedal or bipedal standing conditions with eyes either opened or closed. COP trajectories were analyzed using both the traditional posturographic measure SDA and the proposed COP-VAF. It is shown that the COP-VAF leads to repeatable, physiologically meaningful measures that distinguish postural control differences in unipedal versus bipedal stance trials with and without vision in healthy individuals. More specifically, both a unipedal stance and lack of visual feedback increased initial values of the COP-VAF, magnitude of the first minimum, and diffusion coefficient, particularly in contrast to bipedal stance trials with open eyes. Use of a stochastic postural control model, based on an Ornstein-Uhlenbeck process that accounts for natural weight-shifts, suggests an increase in spring constant and decreased damping coefficient when fitted to experimental data. This work suggests that we can further extend our understanding of the underlying mechanisms behind postural control in quiet stance under varying stance conditions using the COP-VAF and provides a tool for quantifying future neurorehabilitative interventions.

Conformation capture technologies (e.g., Hi-C) chart physical interactions between chromatin regions on a genome-wide scale. However, the structural variability of the genome between cells poses a great challenge to interpreting ensemble-averaged Hi-C data, particularly for long-range and interchromosomal interactions. Here, we present a probabilistic approach for deconvoluting Hi-C data into a model population of distinct diploid 3D genome structures, which facilitates the detection of chromatin interactions likely to co-occur in individual cells. Our approach incorporates the stochastic nature of chromosome conformations and allows a detailed analysis of alternative chromatin structure states. For example, we predict and experimentally confirm the presence of large centromere clusters with distinct chromosome compositions varying between individual cells. The stability of these clusters varies greatly with their chromosome identities. We show that these chromosome-specific clusters can play a key role in the overall chromosome positioning in the nucleus and stabilizing specific chromatin interactions. By explicitly considering genome structural variability, our population-based method provides an important tool for revealing novel insights into the key factors shaping the spatial genome organization.

Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements-important genetic markers in molecular epidemiology. Estimation of the effects of individual covariates on the birth, death, and shift rates of the process can be accomplished by analyzing patient data, but inferring these rates in a discretely and unevenly observed setting presents computational challenges. We propose a multi-type branching process approximation to BDS processes and develop a corresponding expectation maximization algorithm, where we use spectral techniques to reduce calculation of expected sufficient statistics to low-dimensional integration. These techniques yield an efficient and robust optimization routine for inferring the rates of the BDS process, and apply broadly to multi-type branching processes whose rates can depend on many covariates. After rigorously testing our methodology in simulation studies, we apply our method to study intrapatient time evolution of IS6110 transposable element, a genetic marker frequently used during estimation of epidemiological clusters of Mycobacterium tuberculosis infections.

BackgroundWe studied the evolution of information-seeking networks over a 2-year period during which an organization-wide intervention was implemented to promote evidence-informed decision-making (EIDM) in three public health units in Ontario, Canada. We tested whether engagement of staff in the intervention and their EIDM behavior were associated with being chosen as information source and how the trend of inter-divisional communications and the dominance of experts evolved over time.MethodsLocal managers at each health unit selected a group of staff to get engage in Knowledge Broker-led workshops and development of evidence summaries to address local public health problems. The staff were invited to answer three online surveys (at baseline and two annual follow-ups) including name generator questions eliciting the list of the staff they would turn to for help integrating research evidence into practice. We used stochastic actor-oriented modeling to study the evolution of networks. We tested the effect of engagement in the intervention, EIDM behavior scores, organizational divisions, and structural dynamics of social networks on the tendency of staff to select information sources, and the change in its trend between year 1 and year 2 of follow-up.ResultsIn all the three health units, and especially in the two units with higher levels of engagement in the intervention, the network evolved towards a more centralized structure, with an increasing significance of already central staff. The staff showed greater tendencies to seek information from peers with higher EIDM behavior scores. In the public health unit that had highest engagement and stronger leadership support, the engaged staff became more central. In all public health units, the engaged staff showed an increasing tendency towards forming clusters. The staff in the three public health units showed a tendency towards limiting their connections within their divisions.ConclusionsThe longitudinal analysis provided us with a means to study the microstructural changes in public health units, clues to the sustainability of the implementation. The hierarchical transformation of networks towards experts and formation of clusters among staff who were engaged in the intervention show how implementing organizational interventions to promote EIDM may affect the knowledge flow and distribution in health care communities, which may lead to unanticipated consequences.

The antibody repertoire of each individual is continuously updated by the evolutionary process of B-cell receptor (BCR) mutation and selection. It has recently become possible to gain detailed information concerning this process through high-throughput sequencing. Here, we develop modern statistical molecular evolution methods for the analysis of B-cell sequence data, and then apply them to a very deep short-read dataset of BCRs. We find that the substitution process is conserved across individuals but varies significantly across gene segments. We investigate selection on BCRs using a novel method that side-steps the difficulties encountered by previous work in differentiating between selection and motif-driven mutation; this is done through stochastic mapping and empirical Bayes estimators that compare the evolution of in-frame and out-of-frame rearrangements. We use this new method to derive a per-residue map of selection, which provides a more nuanced view of the constraints on framework and variable regions.

The hippocampus and striatum are thought to have different functional roles in learning and memory. It is unknown under what experimental conditions their contributions are dissimilar or converge, and the extent to which they interact over the course of learning. In order to evaluate both the functional contributions of as well as the interactions between the human hippocampus and striatum, the present study used high-resolution functional magnetic resonance imaging (fMRI) and variations of a conditional visuomotor associative learning task that either taxed arbitrary associative learning (Experiment 1) or stimulus-response learning (Experiment 2). In the first experiment, we observed changes in activity in the hippocampus and anterior caudate that reflect differences between the two regions consistent with distinct computational principles. In the second experiment, we observed activity in the putamen that reflected content specific representations during the learning of arbitrary conditional visuomotor associations. In both experiments, the hippocampus and ventral striatum demonstrated dynamic functional coupling during the learning of new arbitrary associations, but not during retrieval of well-learned arbitrary associations using control variants of the tasks that did not preferentially tax one system versus the other. These findings suggest that both the hippocampus and subregions of the dorsal striatum contribute uniquely to the learning of arbitrary associations while the hippocampus and ventral striatum interact over the course of learning.

Drug combinations can improve angiostatic cancer treatment efficacy and enable the reduction of side effects and drug resistance. Combining drugs is non-trivial due to the high number of possibilities. We applied a feedback system control (FSC) technique with a population-based stochastic search algorithm to navigate through the large parametric space of nine angiostatic drugs at four concentrations to identify optimal low-dose drug combinations. This implied an iterative approach of in vitro testing of endothelial cell viability and algorithm-based analysis. The optimal synergistic drug combination, containing erlotinib, BEZ-235 and RAPTA-C, was reached in a small number of iterations. Final drug combinations showed enhanced endothelial cell specificity and synergistically inhibited proliferation (p < 0.001), but not migration of endothelial cells, and forced enhanced numbers of endothelial cells to undergo apoptosis (p < 0.01). Successful translation of this drug combination was achieved in two preclinical in vivo tumor models. Tumor growth was inhibited synergistically and significantly (p < 0.05 and p < 0.01, respectively) using reduced drug doses as compared to optimal single-drug concentrations. At the applied conditions, single-drug monotherapies had no or negligible activity in these models. We suggest that FSC can be used for rapid identification of effective, reduced dose, multi-drug combinations for the treatment of cancer and other diseases.

Studying the emergence of novel infectious agents involves many processes spanning host species, spatial scales, and scientific disciplines. Mathematical models play an essential role in combining insights from these investigations and drawing robust inferences from field and experimental data. We describe nine challenges in modelling the emergence of novel pathogens, emphasizing the interface between models and data.

We consider dosing regimens designed to cure patients by eradicating colony forming units (CFU) such as bacteria. In the field of "population" pharmaco-kinetics/dynamics (PK/PD), inter-individual variability (IIV) of patients is estimated using model parameter statistical distributions. We consider a more probabilistic approach to IIV called stochastic process theory, motivated by the fact that tumor treatment planning uses both approaches. Stochastic process PD can supply additional insights and suggest different dosing regimens due to its emphasis on the probability of complete CFU eradication and its predictions on "pure chance" fluctuations of CFU number per patient when treatment has reduced this integer to less than ~100. To exemplify the contrast between stochastic process PD models and standard deterministic PD models, which track only average CFU number, we analyze, neglecting immune responses, neonatal intravenous gentamicin dosing regimens directed against Escherichia coli. Our stochastic calculations predict that the first dose is crucial for CFU eradication. For example, a single 6 mg/kg dose is predicted to have a higher eradication probability than four daily 4 mg/kg doses. We conclude: (1) neonatal gentamicin dosing regimens with larger first doses but smaller total doses deserve investigation; (2) in general, if standard PK/PD models predict average CFU number drops substantially below 100, the models should be modified to incorporate stochastic effects more accurately, and will then usually make more favorable, or less unfavorable, predictions for front boosting ("hit hard early"). Various caveats against over-interpreting the calculations are given.

We present a stochastic transmission chain simulation model for Ebola viral disease (EVD) in West Africa, with the salutary result that the virus may be more controllable than previously suspected. The ongoing tactics to detect cases as rapidly as possible and isolate individuals as safely as practicable is essential to saving lives in the current outbreaks in Guinea, Liberia, and Sierra Leone. Equally important are educational campaigns that reduce contact rates between susceptible and infectious individuals in the community once an outbreak occurs. However, due to the relatively low R 0 of Ebola (around 1.5 to 2.5 next generation cases are produced per current generation case in naïve populations), rapid isolation of infectious individuals proves to be highly efficacious in containing outbreaks in new areas, while vaccination programs, even with low efficacy vaccines, can be decisive in curbing future outbreaks in areas where the Ebola virus is maintained in reservoir populations.

Correlative fluorescence light microscopy and electron microscopy allows the imaging of spatial distributions of specific biomolecules in the context of cellular ultrastructure. Recent development of super-resolution fluorescence microscopy allows the location of molecules to be determined with nanometer-scale spatial resolution. However, correlative super-resolution fluorescence microscopy and electron microscopy (EM) still remains challenging because the optimal specimen preparation and imaging conditions for super-resolution fluorescence microscopy and EM are often not compatible. Here, we have developed several experiment protocols for correlative stochastic optical reconstruction microscopy (STORM) and EM methods, both for un-embedded samples by applying EM-specific sample preparations after STORM imaging and for embedded and sectioned samples by optimizing the fluorescence under EM fixation, staining and embedding conditions. We demonstrated these methods using a variety of cellular targets.

BackgroundFrom 2012 through 2014, the United States experienced acute shortages and price escalations of several first-line anti-tuberculosis (TB) medications. Because secondary TB drug regimens are longer and adverse events occur more frequently with them, we sought to conservatively estimate the cost, to patients and the health care system, of TB treatment and medication adverse events from alternative regimens during drug shortages.MethodsWe assessed the cost of treatment for TB disease in the absence of isoniazid (INH), rifampin (RIF), or pyrazinamide (PZA), or both INH and RIF. We simulated adverse events based on published probabilities using a monthly discrete-time stochastic model. For total costs, we summed costs of medications, routine testing, and treatment of adverse events using procedural terminology codes. We report average cost ratios of TB treatment during drug shortages to standard TB treatment.ResultsThe cost ratio of TB treatment without INH, RIF, or PZA to standard treatment was 1.7 (Range: 1.2, 2.3), 4.9 (Range: 3.2, 7.3), and 1.1 (Range: 0.7, 1.7) times higher, respectively. Without both INH and RIF, the cost ratio was 18.6 (Range: 10.0, 39.0) times higher. When the prices for INH, RIF and PZA were increased, the cost for standard treatment increased by a factor of 2.7 (Range: 1.9, 3.0). The percentage of patients experiencing at least one adverse event while taking standard therapy was 3.9% (Range: 1.3%, 11.8%). This percentage increased to 51.5% (Range: 20.1%, 83.8%) when RIF was unavailable, and increased to 82.5% (Range: 41.2%, 98.5%) when both INH and RIF were unavailable.ConclusionsOur conservative model illustrates that an interruption in first-line anti-TB medications leads to appreciable additional costs and adverse events for patients. The availability of these drugs in the United States should be ensured. Models that incorporate the effectiveness of alternative regimens, delays in treatment initiation, and TB transmission can provide broader perspectives on the impact of drug shortages.

The spreading of evolutionary novelties across populations is the central element of adaptation. Unless populations are well mixed (like bacteria in a shaken test tube), the spreading dynamics depend not only on fitness differences but also on the dispersal behavior of the species. Spreading at a constant speed is generally predicted when dispersal is sufficiently short ranged, specifically when the dispersal kernel falls off exponentially or faster. However, the case of long-range dispersal is unresolved: Although it is clear that even rare long-range jumps can lead to a drastic speedup--as air-traffic-mediated epidemics show--it has been difficult to quantify the ensuing stochastic dynamical process. However, such knowledge is indispensable for a predictive understanding of many spreading processes in natural populations. We present a simple iterative scaling approximation supported by simulations and rigorous bounds that accurately predicts evolutionary spread, which is determined by a trade-off between frequency and potential effectiveness of long-distance jumps. In contrast to the exponential laws predicted by deterministic "mean-field" approximations, we show that the asymptotic spatial growth is according to either a power law or a stretched exponential, depending on the tails of the dispersal kernel. More importantly, we provide a full time-dependent description of the convergence to the asymptotic behavior, which can be anomalously slow and is relevant even for long times. Our results also apply to spreading dynamics on networks with a spectrum of long-range links under certain conditions on the probabilities of long-distance travel: These are relevant for the spread of epidemics.

Many biochemical reaction networks are inherently multiscale in time and in the counts of participating molecular species. A standard technique to treat different time scales in the stochastic kinetics framework is averaging or quasi-steady-state analysis: it is assumed that the fast dynamics reaches its equilibrium (stationary) distribution on a time scale where the slowly varying molecular counts are unlikely to have changed. We derive analytic equilibrium distributions for various simple biochemical systems, such as enzymatic reactions and gene regulation models. These can be directly inserted into simulations of the slow time-scale dynamics. They also provide insight into the stimulus-response of these systems. An important model for which we derive the analytic equilibrium distribution is the binding of dimer transcription factors (TFs) that first have to form from monomers. This gene regulation mechanism is compared to the cases of the binding of simple monomer TFs to one gene or to multiple copies of a gene, and to the cases of the cooperative binding of two or multiple TFs to a gene. The results apply equally to ligands binding to enzyme molecules.