arXiv subjects

Tom Chou

Publications and source records attributed to Tom Chou.

At least 37 records · Page 2Linked to original sources

arXiv2023

Forecasting drug overdose mortality by age in the United States at the national and county levels

The drug overdose crisis in the United States continues to intensify. Fatalities have increased five-fold since 1999 reaching a record high of 108,000 deaths in 2021. The epidemic has unfolded through distinct waves of different drug types, uniquely impacting various age, gender, race and ethnic groups in specific geographical areas. One major challenge in designing effective interventions is the forecasting of age-specific overdose patterns at the local level so that prevention and preparedness can be effectively delivered. We develop a forecasting method that assimilates observational data obtained from the CDC WONDER database with an age-structured model of addiction and overdose mortality. We apply our method nationwide and to three select areas: Los Angeles County, Cook County and the five boroughs of New York City, providing forecasts of drug-overdose mortality and estimates of relevant epidemiological quantities, such as mortality and age-specific addiction rates.

stat.AP↗

arXiv2023

Stochastic nucleosome disassembly mediated by remodelers and histone fragmentation

We construct and analyze monomeric and multimeric models of the stochastic disassembly of a single nucleosome. Our monomeric model predicts the time needed for a number of histone-DNA contacts to spontaneously break, leading to dissociation of a non-fragmented histone from DNA. The dissociation process can be facilitated by DNA binding proteins or processing molecular motors that compete with histones for histone-DNA contact sites. Eigenvalue analysis of the corresponding master equation allows us to evaluate histone detachment times under both spontaneous detachment and protein-facilitated processes. We find that competitive DNA binding of remodeling proteins can significantly reduce the typical detachment time but only if these remodelers have DNA-binding affinities comparable to those of histone-DNA contact sites. In the presence of processive motors, the histone detachment rate is shown to be proportional to the product of the histone single-bond dissociation constant and the speed of motor protein procession. Our simple intact-histone model is then extended to allow for multimeric nucleosome kinetics that reveal additional pathways of disassembly. In addition to a dependence of complete disassembly times on subunit-DNA contact energies, we show how histone subunit concentrations in bulk solution can mediate the disassembly process by rescuing partially disassembled nucleosomes. Moreover, our kinetic model predicts that remodeler binding can also bias certain pathways of nucleosome disassembly, with higher remodeler binding rates favoring intact-histone detachment.

q-bio.BM↗

arXiv2023

Mathematical Characterization of Private and Public Immune Repertoire Sequences

Diverse T and B cell repertoires play an important role in mounting effective immune responses against a wide range of pathogens and malignant cells. The number of unique T and B cell clones is characterized by T and B cell receptors (TCRs and BCRs), respectively. Although receptor sequences are generated probabilistically by recombination processes, clinical studies found a high degree of sharing of TCRs and BCRs among different individuals. In this work, we use a general probabilistic model for T/B cell receptor clone abundances to define "publicness" or "privateness" and information-theoretic measures for comparing the frequency of sampled sequences observed across different individuals. We derive mathematical formulae to quantify the mean and the variances of clone richness and overlap. Our results can be used to evaluate the effect of different sampling protocols on abundances of clones within an individual as well as the commonality of clones across individuals. Using synthetic and empirical TCR amino acid sequence data, we perform simulations to study expected clonal commonalities across multiple individuals. Based on our formulae, we compare these simulated results with the analytically predicted mean and variances of the repertoire overlap. Complementing the results on simulated repertoires, we derive explicit expressions for the richness and its uncertainty for specific, single-parameter truncated power-law probability distributions. Finally, the information loss associated with grouping together certain receptor sequences, as is done in spectratyping, is also evaluated. Our approach can be, in principle, applied under more general and mechanistically realistic clone generation models.

q-bio.QM↗

arXiv2023

Order-of-mutation effects on cancer progression: models for myeloproliferative neoplasm

We develop a modeling framework for cancer progression that distinguishes the order of two possible mutations. Recent observations and information on myeloproliferative neoplasms are analyzed within our framework. In some patients with myeloproliferative neoplasms, two genetic mutations can be found, JAK2 V617F and TET2. Whether or not one mutation is present will influence how the other subsequent mutation affects the regulation of gene expression. When both mutations are present, the order of their occurrence has been shown to influence disease progression and prognosis. In this paper, we propose a nonlinear ordinary differential equation (ODE) and Markov chain models to explain the non-additive and non-commutative clinical observations with respect to different orders of mutations: gene expression patterns, proportions of cells with different mutations, and ages at diagnosis. We also propose potential experiments measurements that can be used to verify our models.

q-bio.MN↗

arXiv2023

The role of APOBEC3-induced mutations in the differential evolution of monkeypox virus

Recent studies show that newly sampled monkeypox virus (MPXV) genomes exhibit mutations consistent with Apolipoprotein B mRNA Editing Catalytic Polypeptide-like3 (APOBEC3)-mediated editing, compared to MPXV genomes collected earlier. It is unclear whether these single nucleotide polymorphisms (SNPs) result from APOBEC3-induced editing or are a consequence of genetic drift within one or more MPXV animal reservoirs. We develop a simple method based on a generalization of the General-Time-Reversible (GTR) model to show that the observed SNPs are likely the result of APOBEC3-induced editing. The statistical features allow us to extract lineage information and estimate evolutionary events.

q-bio.PE↗

arXiv2023

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.

stat.AP↗

arXiv2023

Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problems

Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient numerical methods that can resolve the dependence of the PDE on the unbounded variable over at least several orders of magnitude. We propose a solution to such problems by combining two classes of numerical methods: (i) adaptive spectral methods and (ii) physics-informed neural networks (PINNs). The numerical approach that we develop takes advantage of the ability of physics-informed neural networks to easily implement high-order numerical schemes to efficiently solve PDEs and extrapolate numerical solutions at any point in space and time. We then show how recently introduced adaptive techniques for spectral methods can be integrated into PINN-based PDE solvers to obtain numerical solutions of unbounded domain problems that cannot be efficiently approximated by standard PINNs. Through a number of examples, we demonstrate the advantages of the proposed spectrally adapted PINNs in solving PDEs and estimating model parameters from noisy observations in unbounded domains.

cs.LG↗

arXiv2023

Impact of random and targeted disruptions on information diffusion during outbreaks

Outbreaks are complex multi-scale processes that are impacted not only by cellular dynamics and the ability of pathogens to effectively reproduce and spread, but also by population-level dynamics and the effectiveness of mitigation measures. A timely exchange of information related to the spread of novel pathogens, stay-at-home orders, and other containment measures can be effective at containing an infectious disease, particularly during in the early stages when testing infrastructure, vaccines, and other medical interventions may not be available at scale. Using a multiplex epidemic model that consists of an information layer (modeling information exchange between individuals) and a spatially embedded epidemic layer (representing a human contact network), we study how random and targeted disruptions in the information layer (\eg, errors and intentional attacks on communication infrastructure) impact outbreak dynamics. We calibrate our model to the early outbreak stages of the SARS-CoV-2 pandemic in 2020. Mitigation campaign can still be effective under random disruptions, such as failure of information channels between a few individuals. However, targeted disruptions or sabotage of hub nodes that exchange information with a large number of individuals can abruptly change outbreak characteristics such as the time to reach the peak infection. Our results emphasize the importance of using a robust communication infrastructure that can withstand both random and targeted disruptions.

physics.soc-ph↗

arXiv2022

Stochastic dynamics and ribosome-RNAP interactions in Transcription-Translation Coupling

Under certain cellular conditions, transcription and mRNA translation in prokaryotes appear to be "coupled," in which the formation of mRNA transcript and production of its associated protein are temporally correlated. Such transcription-translation coupling (TTC) has been evoked as a mechanism that speeds up the overall process, provides protection during the transcription, and/or regulates the timing of transcript and protein formation. What molecular mechanisms underlie ribosome-RNAP coupling and how they can perform these functions have not been explicitly modeled. We develop and analyze a continuous-time stochastic model that incorporates ribosome and RNAP elongation rates, initiation and termination rates, RNAP pausing, and direct ribosome and RNAP interactions (exclusion and binding). Our model predicts how distributions of delay times depend on these molecular features of transcription and translation. We also propose additional measures for TTC: a direct ribosome-RNAP binding probability and the fraction of time the translation-transcription process is "protected" from attack by transcription-terminating proteins. These metrics quantify different aspects of TTC and differentially depend on parameters of known molecular processes. We use our metrics to reveal how and when our model can exhibit either acceleration or deceleration of transcription, as well as protection from termination. Our detailed mechanistic model provides a basis for designing new experimental assays that can better elucidate the mechanisms of TTC.

q-bio.SC↗

arXiv2022

A mathematical model of reward-mediated learning in drug addiction

Substances of abuse are known to activate and disrupt neuronal circuits in the brain reward system. We propose a simple and easily interpretable dynamical systems model to describe the neurobiology of drug addiction that incorporates the psychiatric concepts of reward prediction error (RPE), drug-induced incentive salience (IST), and opponent process theory (OPT). Drug-induced dopamine releases activate a biphasic reward response with pleasurable, positive "a-processes" (euphoria, rush) followed by unpleasant, negative "b-processes" (cravings, withdrawal). Neuroadaptive processes triggered by successive intakes enhance the negative component of the reward response, which the user compensates for by increasing drug dose and/or intake frequency. This positive feedback between physiological changes and drug self-administration leads to habituation, tolerance and eventually to full addiction. Our model gives rise to qualitatively different pathways to addiction that can represent a diverse set of user profiles (genetics, age) and drug potencies. We find that users who have, or neuroadaptively develop, a strong b-process response to drug consumption are most at risk for addiction. Finally, we include possible mechanisms to mitigate withdrawal symptoms, such as through the use of methadone or other auxiliary drugs used in detoxification.

q-bio.NC↗

arXiv2022

Adaptive Hermite Spectral Methods in Unbounded Domains

Recently, new adaptive techniques were developed that greatly improved the efficiency of solving PDEs using spectral methods. These adaptive spectral techniques are especially suited for accurately solving problems in unbounded domains and require the monitoring and dynamic adjustment of three key tunable parameters: the scaling factor, the displacement of the basis functions, and the spectral expansion order. There have been few analyses of numerical methods for unbounded domain problems. Specifically, there is no analysis of adaptive spectral methods to provide insight into how to increase efficiency and accuracy through dynamical adjustment of parameters. In this paper, we perform the first numerical analysis of the adaptive spectral method using generalized Hermite functions in both one- and multi-dimensional problems. Our analysis reveals why adaptive spectral methods work well when a "frequency indicator" of the numerical solution is controlled. We then investigate how the implementation of the adaptive spectral methods affects numerical results, thereby providing guidelines for the proper tuning of parameters. Finally, we further improve performance by extending the adaptive methods to allow bidirectional basis function translation, and the prospect of carrying out similar numerical analysis to solving PDEs arising from realistic difficult-to-solve unbounded models with adaptive spectral methods is also briefly discussed.

math.NA↗

arXiv2022

Modeling the impact of birth control policies on China's population and age: effects of delayed births and minimum birth age constraints

We consider age-structured models with an imposed refractory period between births. These models can be used to formulate alternative population control strategies to China's one-child policy. By allowing any number of births, but with an imposed delay between births, we show how the total population can be decreased and how a relatively older age distribution can be generated. This delay represents a more "continuous" form of population management for which the strict one-child policy is a limiting case. Such a policy approach could be more easily accepted by society. Our analyses provide an initial framework for studying demographics and how social constraints influence population structure.

q-bio.PE↗

arXiv2021

Controlling epidemics through optimal allocation of test kits and vaccine doses across networks

Efficient testing and vaccination protocols are critical aspects of epidemic management. To study the optimal allocation of limited testing and vaccination resources in a heterogeneous contact network of interacting susceptible, recovered, and infected individuals, we present a degree-based testing and vaccination model for which we use control-theoretic methods to derive optimal testing and vaccination policies. Within our framework, we find that optimal intervention policies first target high-degree nodes before shifting to lower-degree nodes in a time-dependent manner. Using such optimal policies, it is possible to delay outbreaks and reduce incidence rates to a greater extent than uniform and reinforcement-learning-based interventions, particularly on certain scale-free networks.

q-bio.PE↗

arXiv2021

A statistical model of COVID-19 testing in populations: effects of sampling bias and testing errors

We develop a statistical model for the testing of disease prevalence in a population. The model assumes a binary test result, positive or negative, but allows for biases in sample selection and both type I (false positive) and type II (false negative) testing errors. Our model also incorporates multiple test types and is able to distinguish between retesting and exclusion after testing. Our quantitative framework allows us to directly interpret testing results as a function of errors and biases. By applying our testing model to COVID-19 testing data and actual case data from specific jurisdictions, we are able to estimate and provide uncertainty quantification of indices that are crucial in a pandemic, such as disease prevalence and fatality ratios.

stat.AP↗

arXiv2021

Density- and elongation speed-dependent error correction in RNA polymerization

Backtracking of RNA polymerase (RNAP) is an important pausing mechanism during DNA transcription that is part of the error correction process that enhances transcription fidelity. We model the backtracking mechanism of RNA polymerase, which usually happens when the polymerase tries to incorporate a mismatched nucleotide triphosphate. Previous models have made simplifying assumptions such as neglecting the trailing polymerase behind the backtracking polymerase or assuming that the trailing polymerase is stationary. We derive exact analytic solutions of a stochastic model that includes locally interacting RNAPs by explicitly showing how a trailing RNAP influences the probability that an error is corrected or incorporated by the leading backtracking RNAP. We also provide two related methods for computing the mean times to error correction or incorporation given an initial local RNAP configuration.

q-bio.SC↗

arXiv2021

Using excess deaths and testing statistics to improve estimates of COVID-19 mortalities

Factors such as non-uniform definitions of mortality, uncertainty in disease prevalence, and biased sampling complicate the quantification of fatality during an epidemic. Regardless of the employed fatality measure, the infected population and the number of infection-caused deaths need to be consistently estimated for comparing mortality across regions. We combine historical and current mortality data, a statistical testing model, and an SIR epidemic model, to improve estimation of mortality. We find that the average excess death across the entire US is 13$\%$ higher than the number of reported COVID-19 deaths. In some areas, such as New York City, the number of weekly deaths is about eight times higher than in previous years. Other countries such as Peru, Ecuador, Mexico, and Spain exhibit excess deaths significantly higher than their reported COVID-19 deaths. Conversely, we find negligible or negative excess deaths for part and all of 2020 for Denmark, Germany, and Norway.

q-bio.QM↗

arXiv2021

Kinetic theory for structured populations: application to stochastic sizer-timer models of cell proliferation

We derive the full kinetic equations describing the evolution of the probability density distribution for a structured population such as cells distributed according to their ages and sizes. The kinetic equations for such a "sizer-timer" model incorporates both demographic and individual cell growth rate stochasticities. Averages taken over the densities obeying the kinetic equations can be used to generate a second order PDE that incorporates the growth rate stochasticity. On the other hand, marginalizing over the densities yields a modified birth-death process that shows how age and size influence demographic stochasticity. Our kinetic framework is thus a more complete model that subsumes both the deterministic PDE and birth-death master equation representations for structured populations.

q-bio.PE↗

arXiv2020

A frequency-dependent $p$-adaptive technique for spectral methods

When using spectral methods, a question arises as how to determine the expansion order, especially for time-dependent problems in which emerging oscillations may require adjusting the expansion order. In this paper, we propose a frequency-dependent $p$-adaptive technique that adaptively adjusts the expansion order based on a frequency indicator. Using this $p$-adaptive technique, combined with recently proposed scaling and moving techniques, we are able to devise an adaptive spectral method in unbounded domains that can capture and handle diffusion, advection, and oscillations. As an application, we use this adaptive spectral method to numerically solve the Schrödinger equation in the whole domain and successfully capture the solution's oscillatory behavior at infinity.

math.NA↗