petzold@engineering.ucsb.edu.

In biochemical systems, the occurrence of a rare event can be accompanied by catastrophic consequences. Precise characterization of these events using Monte Carlo simulation methods is often intractable, as the number of realizations needed to witness even a single rare event can be very large. The weighted stochastic simulation algorithm (wSSA) [J. Chem. Phys. 129, 165101 (2008)] and its subsequent extension [J. Chem. Phys. 130, 174103 (2009)] alleviate this difficulty with importance sampling, which effectively biases the system toward the desired rare event. However, extensive computation coupled with substantial insight into a given system is required, as there is currently no automatic approach for choosing wSSA parameters. We present a novel modification of the wSSA--the doubly weighted SSA (dwSSA)--that makes possible a fully automated parameter selection method. Our approach uses the information-theoretic concept of cross entropy to identify parameter values yielding minimum variance rare event probability estimates. We apply the method to four examples: a pure birth process, a birth-death process, an enzymatic futile cycle, and a yeast polarization model. Our results demonstrate that the proposed method (1) enables probability estimation for a class of rare events that cannot be interrogated with the wSSA, and (2) for all examples tested, reduces the number of runs needed to achieve comparable accuracy by multiple orders of magnitude. For a particular rare event in the yeast polarization model, our method transforms a projected simulation time of 600 years to three hours. Furthermore, by incorporating information-theoretic principles, our approach provides a framework for the development of more sophisticated influencing schemes that should further improve estimation accuracy.

The weighted stochastic simulation algorithm ͑wSSA͒ recently introduced by Kuwahara and Mura ͓J. Chem. Phys. 129, 165101 ͑2008͔͒ is an innovative variation on the stochastic simulation algorithm ͑SSA͒. It enables one to estimate, with much less computational effort than was previously thought possible using a Monte Carlo simulation procedure, the probability that a specified event will occur in a chemically reacting system within a specified time when that probability is very small. This paper presents some procedural extensions to the wSSA that enhance its effectiveness in practical applications. The paper also attempts to clarify some theoretical issues connected with the wSSA, including its connection to first passage time theory and its relation to the SSA.

BackgroundA prerequisite for the mechanistic simulation of a biochemical system is detailed knowledge of its kinetic parameters. Despite recent experimental advances, the estimation of unknown parameter values from observed data is still a bottleneck for obtaining accurate simulation results. Many methods exist for parameter estimation in deterministic biochemical systems; methods for discrete stochastic systems are less well developed. Given the probabilistic nature of stochastic biochemical models, a natural approach is to choose parameter values that maximize the probability of the observed data with respect to the unknown parameters, a.k.a. the maximum likelihood parameter estimates (MLEs). MLE computation for all but the simplest models requires the simulation of many system trajectories that are consistent with experimental data. For models with unknown parameters, this presents a computational challenge, as the generation of consistent trajectories can be an extremely rare occurrence.ResultsWe have developed Monte Carlo Expectation-Maximization with Modified Cross-Entropy Method (MCEM2): an accelerated method for calculating MLEs that combines advances in rare event simulation with a computationally efficient version of the Monte Carlo expectation-maximization (MCEM) algorithm. Our method requires no prior knowledge regarding parameter values, and it automatically provides a multivariate parameter uncertainty estimate. We applied the method to five stochastic systems of increasing complexity, progressing from an analytically tractable pure-birth model to a computationally demanding model of yeast-polarization. Our results demonstrate that MCEM2 substantially accelerates MLE computation on all tested models when compared to a stand-alone version of MCEM. Additionally, we show how our method identifies parameter values for certain classes of models more accurately than two recently proposed computationally efficient methods.ConclusionsThis work provides a novel, accelerated version of a likelihood-based parameter estimation method that can be readily applied to stochastic biochemical systems. In addition, our results suggest opportunities for added efficiency improvements that will further enhance our ability to mechanistically simulate biological processes.

The weighted stochastic simulation algorithm ͑wSSA͒ was developed by Kuwahara and Mura ͓J. Chem. Phys. 129, 165101 ͑2008͔͒ to efficiently estimate the probabilities of rare events in discrete stochastic systems. The wSSA uses importance sampling to enhance the statistical accuracy in the estimation of the probability of the rare event. The original algorithm biases the reaction selection step with a fixed importance sampling parameter. In this paper, we introduce a novel method where the biasing parameter is state-dependent. The new method features improved accuracy, efficiency, and robustness.

In recent years there has been substantial growth in the development of algorithms for characterizing rare events in stochastic biochemical systems. Two such algorithms, the state-dependent weighted stochastic simulation algorithm (swSSA) and the doubly weighted SSA (dwSSA) are extensions of the weighted SSA (wSSA) by H. Kuwahara and I. Mura [J. Chem. Phys. 129, 165101 (2008)]. The swSSA substantially reduces estimator variance by implementing system state-dependent importance sampling (IS) parameters, but lacks an automatic parameter identification strategy. In contrast, the dwSSA provides for the automatic determination of state-independent IS parameters, thus it is inefficient for systems whose states vary widely in time. We present a novel modification of the dwSSA-the state-dependent doubly weighted SSA (sdwSSA)-that combines the strengths of the swSSA and the dwSSA without inheriting their weaknesses. The sdwSSA automatically computes state-dependent IS parameters via the multilevel cross-entropy method. We apply the method to three examples: a reversible isomerization process, a yeast polarization model, and a lac operon model. Our results demonstrate that the sdwSSA offers substantial improvements over previous methods in terms of both accuracy and efficiency.

Background Pediatric diarrhea can be caused by a wide variety of pathogens, from bacteria to viruses to protozoa. Pathogen prevalence is often described as seasonal, peaking annually and associated with specific weather conditions. Although many studies have described the seasonality of diarrheal disease, these studies have occurred predominantly in temperate regions. In tropical and resource-constrained settings, where nearly all diarrhea-associated mortality occurs, the seasonality of many diarrheal pathogens has not been well characterized. As a retrospective study, we analyze the seasonal prevalence of diarrheal pathogens among children with moderate-to-severe diarrhea (MSD) over three years from the seven sites of the Global Enteric Multicenter Study (GEMS), a case–control study. Using data from this expansive study on diarrheal disease, we characterize the seasonality of different pathogens, their association with site-specific weather patterns, and consistency across study sites. Methodology/Principal findings Using traditional methodologies from signal processing, we found that certain pathogens peaked at the same time every year, but not at all sites. We also found associations between pathogen prevalence and weather or “seasons,” which are defined by applying modern machine-learning methodologies to site-specific weather data. In general, rotavirus was most prevalent during the drier “winter” months and out of phase with bacterial pathogens, which peaked during hotter and rainier times of year corresponding to “monsoon,” “rainy,” or “summer” seasons. Conclusions/Significance Identifying the seasonally-dependent prevalence for diarrheal pathogens helps characterize the local epidemiology and inform the clinical diagnosis of symptomatic children. Our multi-site, multi-continent study indicates a complex epidemiology of pathogens that does not reveal an easy generalization that is consistent across all sites. Instead, our study indicates the necessity of local data to characterizing the epidemiology of diarrheal disease. Recognition of the local associations between weather conditions and pathogen prevalence suggests transmission pathways and could inform control strategies in these settings.

Diarrheal disease is one of the leading causes of death among young children in the developing world. It is difficult to determine which of a wide variety of pathogens are most responsible for disease, since this differs by location and time of year. Here, we study the seasonal prevalence of several pathogens among children with moderate-to-severe diarrhea across study sites in Africa and South Asia. We found that several pathogens, including rotavirus, had regular annual peaks. Some pathogens were associated with weather conditions, such as heat or rain, or with general seasons of the year, such as summer or winter. We believe that describing the seasonal epidemiology of these pathogens could enable better diagnoses of symptomatic children based on the time of the year. Additionally, weather is a major driver of diarrheal pathogen transmission, and identifying the conditions associated with each pathogen could help us infer pathogen transmission pathways, predict large outbreaks, and develop intervention strategies. January 31, 2019 2/21 Pediatric diarrheal disease is caused by a wide variety of pathogens [1-3]. Various 2 studies have found that some pathogens are seasonal, peaking at different times of the 3 year [4-6]. Frequently, the seasonal periodicity of diarrheal disease is attributed to 4 weather, which could drive incidence by diverse mechanisms. For example, weather 5 conditions can favor the survival and replication of pathogens on fomites [7], the 6 transmission between human hosts through flooding and contamination of drinking 7 water [8], and the prevalence of vectors that transmit disease between hosts [9, 10]. 8 Weather has broadly been shown to be mathematically correlated with diarrhea 9 incidence [11, 12], with some computational studies claiming a causal link [13] despite 10 potential limitations to their methodology [14-16]. 11 However, most studies of disease seasonality have been conducted in temperate 12 climates, and substantially less is known about the seasonality of diseases in tropical 13 countries [17, 18], where diarrheal disease is one of the leading causes of morbidity and 14 mortality among children [19]. The wide variety of climates and populations in the 15 tropics make it challenging to uncover general patterns in the epidemiology of diarrheal 16 disease. Compounding these challenges, most studies are limited to sites within a single 17 country focused on a specific disease. Characterizing the seasonal epidemiology of these 18 pathogens could enable clinicians to better diagnose children based on the time of the 19 year. Additionally, identifying the weather conditions associated with each pathogen 20 could help us infer pathogen transmission pathways, predict large outbreaks, and 21 develop intervention strategies. 22 hydration; dysentery identified by blood in stool; or admission to the hospital for 49 diarrhea or dysentery [2]. To limit the number of enrollments and ensure balanced 50 enrollment by age, 8-9 children in each age strata (0-11 months, 12-23 months, 24-59 51 m...