1
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Mao S, Chou T, D'Orsogna MR. A probabilistic model of relapse in drug addiction. Math Biosci 2024; 372:109184. [PMID: 38582296 DOI: 10.1016/j.mbs.2024.109184] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2024] [Accepted: 03/25/2024] [Indexed: 04/08/2024]
Abstract
More than 60% of individuals recovering from substance use disorder relapse within one year. Some will resume drug consumption even after decades of abstinence. The cognitive and psychological mechanisms that lead to relapse are not completely understood, but stressful life experiences and external stimuli that are associated with past drug-taking are known to play a primary role. Stressors and cues elicit memories of drug-induced euphoria and the expectation of relief from current anxiety, igniting an intense craving to use again; positive experiences and supportive environments may mitigate relapse. We present a mathematical model of relapse in drug addiction that draws on known psychiatric concepts such as the "positive activation; negative activation" paradigm and the "peak-end" rule to construct a relapse rate that depends on external factors (intensity and timing of life events) and individual traits (mental responses to these events). We analyze which combinations and ordering of stressors, cues, and positive events lead to the largest relapse probability and propose interventions to minimize the likelihood of relapse. We find that the best protective factor is exposure to a mild, yet continuous, source of contentment, rather than large, episodic jolts of happiness.
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Affiliation(s)
- Sayun Mao
- Department of Computational Medicine, UCLA, Los Angeles, 90095-1766, CA, USA.
| | - Tom Chou
- Department of Computational Medicine, UCLA, Los Angeles, 90095-1766, CA, USA.
| | - Maria R D'Orsogna
- Department of Computational Medicine, UCLA, Los Angeles, 90095-1766, CA, USA; Department of Mathematics, California State University at Northridge, Los Angeles, 91330, CA, USA.
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2
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Xia M, Li X, Chou T. Overcompensation of transient and permanent death rate increases in age-structured models with cannibalistic interactions. ArXiv 2024:arXiv:2303.00864v2. [PMID: 36911278 PMCID: PMC10002760] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 03/14/2023]
Abstract
There has been renewed interest in understanding the mathematical structure of ecological population models that lead to overcompensation, the process by which a population recovers to a higher level after suffering a permanent increase in predation or harvesting. Here, we apply a recently formulated kinetic population theory to formally construct an age-structured single-species population model that includes a cannibalistic interaction in which older individuals prey on younger ones. Depending on the age-dependent structure of this interaction, our model can exhibit transient or steady-state overcompensation of an increased death rate as well as oscillations of the total population, both phenomena that have been observed in ecological systems. Analytic and numerical analysis of our model reveals sufficient conditions for overcompensation and oscillations. We also show how our structured population partial integrodifferential equation (PIDE) model can be reduced to coupled ODE models representing piecewise constant parameter domains, providing additional mathematical insight into the emergence of overcompensation.
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Affiliation(s)
- Mingtao Xia
- Courant Institute of Mathematical Sciences, New York University, New York, 10012-1185, New York, USA
| | - Xiangting Li
- Department of Computational Medicine, UCLA, Los Angeles, 90095-1766, CA, USA
| | - Tom Chou
- Department of Computational Medicine, UCLA, Los Angeles, 90095-1766, CA, USA
- Department of Mathematics, UCLA, Los Angeles, 90095-1555, CA, USA
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3
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Wang Y, Shtylla B, Chou T. Order-of-Mutation Effects on Cancer Progression: Models for Myeloproliferative Neoplasm. Bull Math Biol 2024; 86:32. [PMID: 38363386 PMCID: PMC10873249 DOI: 10.1007/s11538-024-01257-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Accepted: 01/08/2024] [Indexed: 02/17/2024]
Abstract
In some patients with myeloproliferative neoplasms (MPN), two genetic mutations are often found: JAK2 V617F and one in the TET2 gene. Whether one mutation is present influences how the other subsequent mutation will affect the regulation of gene expression. In other words, when a patient carries both mutations, the order of when they first arose has been shown to influence disease progression and prognosis. We propose a nonlinear ordinary differential equation, the Moran process, and Markov chain models to explain the non-additive and non-commutative mutation effects on recent clinical observations of gene expression patterns, proportions of cells with different mutations, and ages at diagnosis of MPN. Combined, these observations are used to shape our modeling framework. Our key proposal is that bistability in gene expression provides a natural explanation for many observed order-of-mutation effects. We also propose potential experimental measurements that can be used to confirm or refute predictions of our models.
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Affiliation(s)
- Yue Wang
- Department of Computational Medicine, UCLA, Los Angeles, CA, 90095, USA
- Department of Statistics, Irving Institute for Cancer Dynamics, Columbia University, New York, NY, 10027, USA
| | - Blerta Shtylla
- Mathematics Department, Pomona College, Claremont, CA, 91711, USA
- Pharmacometrics and Systems Pharmacology, Pfizer Research and Development, San Diego, CA, 92121, USA
| | - Tom Chou
- Department of Computational Medicine, UCLA, Los Angeles, CA, 90095, USA.
- Department of Mathematics, UCLA, Los Angeles, CA, 90095, USA.
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4
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Böttcher L, Chou T, D’Orsogna MR. Forecasting drug-overdose mortality by age in the United States at the national and county levels. PNAS Nexus 2024; 3:pgae050. [PMID: 38725534 PMCID: PMC11079616 DOI: 10.1093/pnasnexus/pgae050] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/14/2023] [Accepted: 01/25/2024] [Indexed: 05/12/2024]
Abstract
The drug-overdose crisis in the United States continues to intensify. Fatalities have increased 5-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 interventions and efficiently delivering treatment is forecasting age-specific overdose patterns at the local level. To address this need, 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.
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Affiliation(s)
- Lucas Böttcher
- Department of Computational Science and Philosophy, Frankfurt School of Finance and Management, 60322 Frankfurt am Main, Germany
| | - Tom Chou
- Department of Computational Medicine, University of California, Los Angeles, Los Angeles, CA 90095-1766, USA
| | - Maria R D’Orsogna
- Department of Computational Medicine, University of California, Los Angeles, Los Angeles, CA 90095-1766, USA
- Department of Mathematics, California State University at Northridge, Los Angeles, CA 91330-8313, USA
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5
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Li X, Chou T. Stochastic nucleosome disassembly mediated by remodelers and histone fragmentation. J Chem Phys 2023; 159:204107. [PMID: 38010331 PMCID: PMC10684310 DOI: 10.1063/5.0165136] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2023] [Accepted: 10/14/2023] [Indexed: 11/29/2023] Open
Abstract
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 solutions 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.
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Affiliation(s)
- Xiangting Li
- Department of Computational Medicine, University of California, Los Angeles, California 90095-1766, USA
| | - Tom Chou
- Author to whom correspondence should be addressed:
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6
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Li X, Habibipour S, Chou T, Yang OO. The role of APOBEC3-induced mutations in the differential evolution of monkeypox virus. Virus Evol 2023; 9:vead058. [PMID: 37841642 PMCID: PMC10569380 DOI: 10.1093/ve/vead058] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2023] [Revised: 09/03/2023] [Accepted: 09/18/2023] [Indexed: 10/17/2023] Open
Abstract
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 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.
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Affiliation(s)
- Xiangting Li
- Department of Computational Medicine, UCLA, Los Angeles, CA, United States
| | - Sara Habibipour
- Departments of Medicine and Microbiology, Immunology, and Molecular Genetics, UCLA, Los Angeles, CA, United States
| | - Tom Chou
- Department of Computational Medicine, UCLA, Los Angeles, CA, United States
- Department of Mathematics, UCLA, Los Angeles, CA, United States
| | - Otto O Yang
- Departments of Medicine and Microbiology, Immunology, and Molecular Genetics, UCLA, Los Angeles, CA, United States
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7
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Böttcher L, Wald S, Chou T. Mathematical Characterization of Private and Public Immune Receptor Sequences. Bull Math Biol 2023; 85:102. [PMID: 37707621 PMCID: PMC10501991 DOI: 10.1007/s11538-023-01190-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 07/26/2023] [Indexed: 09/15/2023]
Abstract
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.
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Affiliation(s)
- Lucas Böttcher
- Department of Computational Science and Philosophy, Frankfurt School of Finance and Management, 60322 Frankfurt am Main, Germany
- Department of Computational Medicine, University of California, Los Angeles, 621 Charles E. Young Dr. S., Los Angeles, 90095-1766 CA USA
- Department of Medicine, University of Florida, Gainesville, 32610 FL USA
| | - Sascha Wald
- Statistical Physics Group, Centre for Fluid and Complex Systems, Coventry University, Priory Street, Coventry, CV1 5FB UK
| | - Tom Chou
- Department of Computational Medicine, University of California, Los Angeles, 621 Charles E. Young Dr. S., Los Angeles, 90095-1766 CA USA
- Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, 90095-1555 CA USA
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8
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Li X, Chou T. Stochastic nucleosome disassembly mediated by remodelers and histone fragmentation. ArXiv 2023:arXiv:2309.02736v1. [PMID: 37731652 PMCID: PMC10508821] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 09/22/2023]
Abstract
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.
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Affiliation(s)
- Xiangting Li
- Department of Computational Medicine, University of California, Los Angeles, CA 90095-1766 USA
| | - Tom Chou
- Department of Computational Medicine, University of California, Los Angeles, CA 90095-1766 USA
- Department of Mathematics, University of California, Los Angeles, CA 90095-1555 USA
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9
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Wang Y, Shtylla B, Chou T. Order-of-mutation effects on cancer progression: models for myeloproliferative neoplasm. medRxiv 2023:2023.08.16.23294177. [PMID: 37662184 PMCID: PMC10473807 DOI: 10.1101/2023.08.16.23294177] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/05/2023]
Abstract
In some patients with myeloproliferative neoplasms (MPN), two genetic mutations are often found, JAK2 V617F and one in the TET2 gene. 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. We propose a nonlinear ordinary differential equation (ODE), Moran process, and Markov chain models to explain the non-additive and non-commutative mutation effects on recent clinical observations of gene expression patterns, proportions of cells with different mutations, and ages at diagnosis of MPN. These observations consistently shape our modeling framework. Our key proposal is that bistability in gene expression provides a natural explanation for many observed order-of-mutation effects. We also propose potential experimental measurements that can be used to confirm or refute predictions of our models.
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Affiliation(s)
- Yue Wang
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095
- Irving Institute for Cancer Dynamics and Department of Statistics, Columbia University, New York, NY 10027
| | - Blerta Shtylla
- Mathematics Department, Pomona College, Claremont, CA, 91711
- Quantitative Systems Pharmacology, Oncology, Pfizer, San Diego, CA 92121
| | - Tom Chou
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095
- Dept. of Mathematics, UCLA, Los Angeles, CA 90095
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10
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Wang Y, Shtylla B, Chou T. Order-of-mutation effects on cancer progression: models for myeloproliferative neoplasm. ArXiv 2023:arXiv:2308.09941v1. [PMID: 37645049 PMCID: PMC10462171] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Subscribe] [Scholar Register] [Indexed: 08/31/2023]
Abstract
In some patients with myeloproliferative neoplasms (MPN), two genetic mutations are often found, JAK2 V617F and one in the TET2 gene. 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. We propose a nonlinear ordinary differential equation (ODE), Moran process, and Markov chain models to explain the non-additive and non-commutative mutation effects on recent clinical observations of gene expression patterns, proportions of cells with different mutations, and ages at diagnosis of MPN. These observations consistently shape our modeling framework. Our key proposal is that bistability in gene expression provides a natural explanation for many observed order-of-mutation effects. We also propose potential experimental measurements that can be used to confirm or refute predictions of our models.
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Affiliation(s)
- Yue Wang
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095
- Irving Institute for Cancer Dynamics and Department of Statistics, Columbia University, New York, NY 10027
| | - Blerta Shtylla
- Mathematics Department, Pomona College, Claremont, CA, 91711
- Quantitative Systems Pharmacology, Oncology, Pfizer, San Diego, CA 92121
| | - Tom Chou
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095
- Dept. of Mathematics, UCLA, Los Angeles, CA 90095
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11
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Li X, Habibipour S, Chou T, Yang OO. The role of APOBEC3-induced mutations in the differential evolution of monkeypox virus. ArXiv 2023:arXiv:2308.03714v1. [PMID: 37608930 PMCID: PMC10441442] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 08/24/2023]
Abstract
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.
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Affiliation(s)
- Xiangting Li
- Department of Computational Medicine, UCLA, Los Angeles, CA, United States
| | - Sara Habibipour
- Depts. of Medicine and Microbiology, Immunology, and Molecular Genetics, UCLA, Los Angeles, CA, United States
| | - Tom Chou
- Department of Computational Medicine, UCLA, Los Angeles, CA, United States
- Department of Mathematics, UCLA, Los Angeles, CA, United States
| | - Otto O Yang
- Depts. of Medicine and Microbiology, Immunology, and Molecular Genetics, UCLA, Los Angeles, CA, United States
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12
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Böttcher L, Chou T, D’Orsogna MR. Modeling and forecasting age-specific drug overdose mortality in the United States. Eur Phys J Spec Top 2023; 232:1-10. [PMID: 37359186 PMCID: PMC10132445 DOI: 10.1140/epjs/s11734-023-00801-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Accepted: 02/24/2023] [Indexed: 06/28/2023]
Abstract
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 fivefold; 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.
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Affiliation(s)
- Lucas Böttcher
- Department of Computational Science and Philosophy, Frankfurt School of Finance and Management, 60322 Frankfurt am Main, Germany
| | - Tom Chou
- Department of Computational Medicine, University of California, Los Angeles, Los Angeles, 90095 CA USA
- Department of Mathematics, University of California, Los Angeles, Los Angeles, 90095 CA USA
| | - Maria R. D’Orsogna
- Department of Computational Medicine, University of California, Los Angeles, Los Angeles, 90095 CA USA
- Department of Mathematics, California State University at Northridge, Los Angeles, 91330 CA USA
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13
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Böttcher L, Chou T, D'Orsogna MR. Modeling and forecasting age-specific drug overdose mortality in the United States. ArXiv 2023:arXiv:2303.16172v1. [PMID: 37033462 PMCID: PMC10081349] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
Abstract
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.
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14
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D’Orsogna MR, Böttcher L, Chou T. Fentanyl-driven acceleration of racial, gender and geographical disparities in drug overdose deaths in the United States. PLOS Glob Public Health 2023; 3:e0000769. [PMID: 36962959 PMCID: PMC10032521 DOI: 10.1371/journal.pgph.0000769] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Accepted: 02/13/2023] [Indexed: 03/24/2023]
Abstract
We examine trends in drug overdose deaths by race, gender, and geography in the United States during the period 2013-2020. Race and gender specific crude rates were extracted from the final National Vital Statistics System multiple cause-of-death mortality files for several jurisdictions and used to calculate the male-to-female ratios of crude rates between 2013 and 2020. We established 2013-2019 temporal trends for four major drug types: psychostimulants with addiction potential (T43.6, such as methamphetamines); heroin (T40.1); natural and semi-synthetic opioids (T40.2, such as those contained in prescription pain-killers); synthetic opioids (T40.4, such as fentanyl and its derivatives) through a quadratic regression and determined whether changes in the pandemic year 2020 were statistically significant. We also identified which race, gender and states were most impacted by drug overdose deaths. Nationwide, the year 2020 saw statistically significant increases in overdose deaths from all drug categories except heroin, surpassing predictions based on 2013-2019 trends. Crude rates for Black individuals of both genders surpassed those for White individuals for fentanyl and psychostimulants in 2018, creating a gap that widened through 2020. In some regions, mortality among White persons decreased while overdose deaths for Black persons kept rising. The largest 2020 mortality statistic is for Black males in the District of Columbia, with a record 134 overdose deaths per 100,000 due to fentanyl, 9.4 times more than the fatality rate among White males. Male overdose crude rates in 2020 remain larger than those of females for all drug categories except in Idaho, Utah and Arkansas where crude rates of overdose deaths by natural and semisynthetic opioids for females exceeded those of males. Drug prevention, mitigation and no-harm strategies should include racial, geographical and gender-specific efforts, to better identify and serve at-risk groups.
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Affiliation(s)
- Maria R. D’Orsogna
- Department of Computational Medicine, University of California at Los Angeles, Los Angeles, California, United States of America
- Department of Mathematics, California State University at Northridge, Los Angeles, California, United States of America
| | - Lucas Böttcher
- Department of Computational Science and Philosophy, Frankfurt School of Finance and Management, Frankfurt am Main, Germany
| | - Tom Chou
- Department of Computational Medicine, University of California at Los Angeles, Los Angeles, California, United States of America
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15
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Masoomy H, Chou T, Böttcher L. Impact of random and targeted disruptions on information diffusion during outbreaks. Chaos 2023; 33:033145. [PMID: 37003816 DOI: 10.1063/5.0139844] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2022] [Accepted: 03/02/2023] [Indexed: 06/19/2023]
Abstract
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 measures can be effective at containing an infectious disease, particularly during 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 (e.g., errors and intentional attacks on communication infrastructure) impact the total proportion of infections, peak prevalence (i.e., the maximum proportion of infections), and the time to reach peak prevalence. We calibrate our model to the early outbreak stages of the SARS-CoV-2 pandemic in 2020. Mitigation campaigns 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 of infection. Our results emphasize the importance of the availability of a robust communication infrastructure during an outbreak that can withstand both random and targeted disruptions.
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Affiliation(s)
- Hosein Masoomy
- Department of Physics, Shahid Beheshti University, 1983969411 Tehran, Iran
| | - Tom Chou
- Department of Computational Medicine and Department of Mathematics, UCLA, Los Angeles, California 90095, USA
| | - Lucas Böttcher
- Department of Computational Science and Philosophy, Frankfurt School of Finance and Management, 60322 Frankfurt am Main, Germany
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16
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Li X, Chou T. Stochastic dynamics and ribosome-RNAP interactions in transcription-translation coupling. Biophys J 2023; 122:254-266. [PMID: 36199250 PMCID: PMC9822797 DOI: 10.1016/j.bpj.2022.09.041] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2022] [Revised: 09/22/2022] [Accepted: 09/27/2022] [Indexed: 01/11/2023] Open
Abstract
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 against premature termination, 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.
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Affiliation(s)
- Xiangting Li
- Department of Computational Medicine, University of California, Los Angeles, Los Angeles, California
| | - Tom Chou
- Department of Computational Medicine, University of California, Los Angeles, Los Angeles, California; Department of Mathematics, University of California, Los Angeles, Los Angeles, California.
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17
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Wang Y, Mistry BA, Chou T. Discrete stochastic models of SELEX: Aptamer capture probabilities and protocol optimization. J Chem Phys 2022; 156:244103. [DOI: 10.1063/5.0094307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Antibodies are important biomolecules that are often designed to recognize target antigens. However, they are expensive to produce and their relatively large size prevents their transport across lipid membranes. An alternative to antibodies is aptamers, short ([Formula: see text] bp) oligonucleotides (and amino acid sequences) with specific secondary and tertiary structures that govern their affinity to specific target molecules. Aptamers are typically generated via solid phase oligonucleotide synthesis before selection and amplification through Systematic Evolution of Ligands by EXponential enrichment (SELEX), a process based on competitive binding that enriches the population of certain strands while removing unwanted sequences, yielding aptamers with high specificity and affinity to a target molecule. Mathematical analyses of SELEX have been formulated in the mass action limit, which assumes large system sizes and/or high aptamer and target molecule concentrations. In this paper, we develop a fully discrete stochastic model of SELEX. While converging to a mass-action model in the large system-size limit, our stochastic model allows us to study statistical quantities when the system size is small, such as the probability of losing the best-binding aptamer during each round of selection. Specifically, we find that optimal SELEX protocols in the stochastic model differ from those predicted by a deterministic model.
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Affiliation(s)
- Yue Wang
- Department of Computational Medicine, University of California, Los Angeles, California 90095-1766, USA
| | - Bhaven A. Mistry
- Department of Mathematical Sciences, Claremont McKenna College, Claremont, California 91711, USA
| | - Tom Chou
- Department of Computational Medicine, University of California, Los Angeles, California 90095-1766, USA
- Department of Mathematics, University of California, Los Angeles, California 90095-1555, USA
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18
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Wang Y, Dessalles R, Chou T. Modelling the impact of birth control policies on China's population and age: effects of delayed births and minimum birth age constraints. R Soc Open Sci 2022. [PMID: 35706677 DOI: 10.5281/zenodo.6394805] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
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.
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Affiliation(s)
- Yue Wang
- Department of Computational Medicine, UCLA, Los Angeles, CA 90095-1766, USA
| | | | - Tom Chou
- Department of Computational Medicine, UCLA, Los Angeles, CA 90095-1766, USA
- Department of Mathematics, UCLA, Los Angeles, CA 90095-1555, USA
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19
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Wang Y, Dessalles R, Chou T. Modelling the impact of birth control policies on China's population and age: effects of delayed births and minimum birth age constraints. R Soc Open Sci 2022; 9:211619. [PMID: 35706677 PMCID: PMC9174737 DOI: 10.1098/rsos.211619] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/12/2021] [Accepted: 05/16/2022] [Indexed: 05/03/2023]
Abstract
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.
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Affiliation(s)
- Yue Wang
- Department of Computational Medicine, UCLA, Los Angeles, CA 90095-1766, USA
| | | | - Tom Chou
- Department of Computational Medicine, UCLA, Los Angeles, CA 90095-1766, USA
- Department of Mathematics, UCLA, Los Angeles, CA 90095-1555, USA
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20
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Dessalles R, Pan Y, Xia M, Maestrini D, D'Orsogna MR, Chou T. How Naive T-Cell Clone Counts Are Shaped By Heterogeneous Thymic Output and Homeostatic Proliferation. Front Immunol 2022; 12:735135. [PMID: 35250963 PMCID: PMC8891377 DOI: 10.3389/fimmu.2021.735135] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2021] [Accepted: 12/06/2021] [Indexed: 11/13/2022] Open
Abstract
The specificity of T cells is that each T cell has only one T cell receptor (TCR). A T cell clone represents a collection of T cells with the same TCR sequence. Thus, the number of different T cell clones in an organism reflects the number of different T cell receptors (TCRs) that arise from recombination of the V(D)J gene segments during T cell development in the thymus. TCR diversity and more specifically, the clone abundance distribution, are important factors in immune functions. Specific recombination patterns occur more frequently than others while subsequent interactions between TCRs and self-antigens are known to trigger proliferation and sustain naive T cell survival. These processes are TCR-dependent, leading to clone-dependent thymic export and naive T cell proliferation rates. We describe the heterogeneous steady-state population of naive T cells (those that have not yet been antigenically triggered) by using a mean-field model of a regulated birth-death-immigration process. After accounting for random sampling, we investigate how TCR-dependent heterogeneities in immigration and proliferation rates affect the shape of clone abundance distributions (the number of different clones that are represented by a specific number of cells, or “clone counts”). By using reasonable physiological parameter values and fitting predicted clone counts to experimentally sampled clone abundances, we show that realistic levels of heterogeneity in immigration rates cause very little change to predicted clone-counts, but that modest heterogeneity in proliferation rates can generate the observed clone abundances. Our analysis provides constraints among physiological parameters that are necessary to yield predictions that qualitatively match the data. Assumptions of the model and potentially other important mechanistic factors are discussed.
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Affiliation(s)
- Renaud Dessalles
- Department of Computational Medicine, University of California at Los Angeles (UCLA), Los Angeles, CA, United States
| | - Yunbei Pan
- Department of Mathematics, California State University at Northridge, Los Angeles, CA, United States
| | - Mingtao Xia
- Department of Mathematics, University of California at Los Angeles (UCLA), Los Angeles, CA, United States
| | - Davide Maestrini
- Department of Computational Medicine, University of California at Los Angeles (UCLA), Los Angeles, CA, United States
| | - Maria R D'Orsogna
- Department of Computational Medicine, University of California at Los Angeles (UCLA), Los Angeles, CA, United States.,Department of Mathematics, California State University at Northridge, Los Angeles, CA, United States
| | - Tom Chou
- Department of Computational Medicine, University of California at Los Angeles (UCLA), Los Angeles, CA, United States.,Department of Mathematics, University of California at Los Angeles (UCLA), Los Angeles, CA, United States
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21
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Lin Y, Lin J, Chang T, Chou T, Hung L, Huang C. PO-1329 Predictive factors for pathologic good response after the neoadjuvant CRT of rectal cancer. Radiother Oncol 2022. [DOI: 10.1016/s0167-8140(22)03293-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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22
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Abstract
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, drug-induced incentive salience, and opponent process theory. 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.
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Affiliation(s)
- Tom Chou
- Department of Computational Medicine, UCLA, Los Angeles, California 90095-1766, USA
| | - Maria R. D’Orsogna
- Department of Mathematics, California State University at Northridge, Los Angeles, California 91130-8313, USA
- Also at: Department of Computational Medicine, UCLA, Los Angeles, CA 90095-1766, USA. Author to whom correspondence should be addressed:
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23
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Böttcher L, D'Orsogna MR, Chou T. A statistical model of COVID-19 testing in populations: effects of sampling bias andtesting errors. Philos Trans A Math Phys Eng Sci 2022; 380:20210121. [PMID: 34802274 PMCID: PMC8607147 DOI: 10.1098/rsta.2021.0121] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 06/21/2021] [Indexed: 05/11/2023]
Abstract
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. This article is part of the theme issue 'Data science approach to infectious disease surveillance'.
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Affiliation(s)
- Lucas Böttcher
- Department of Computational Medicine, University of California, Los Angeles, 90095-1766 Los Angeles, CA, USA
- Computational Social Science, Frankfurt School of Finance and Management, 60322 Frankfurt am Main, Germany
| | - Maria R. D'Orsogna
- Department of Computational Medicine, University of California, Los Angeles, 90095-1766 Los Angeles, CA, USA
- Department of Mathematics, California State University at Northridge, Los Angeles, 91330-8313 CA, USA
| | - Tom Chou
- Department of Computational Medicine, University of California, Los Angeles, 90095-1766 Los Angeles, CA, USA
- Department of Mathematics, University of California, Los Angeles, 90095-1766 Los Angeles, CA, USA
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24
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Abstract
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 noncognate or "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 for error correction and incorporation given an initial local RNAP configuration. Using these results, we propose an effective interacting-RNAP lattice that can be readily simulated.
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Affiliation(s)
- Xinzhe Zuo
- Department of Mathematics, University of California - Los Angeles, Los Angeles, CA 90095-1555, USA, Los Angeles, California, 90095, UNITED STATES
| | - Tom Chou
- Department of Mathematics, University of California - Los Angeles, Los Angeles, CA 90095-1555, USA, Los Angeles, California, 90095, UNITED STATES
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25
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Spero M, Jones J, Lomenick B, Zareian S, Chou T, Newman D. 428: Mechanisms of chlorate toxicity and resistance in Pseudomonas aeruginosa. J Cyst Fibros 2021. [DOI: 10.1016/s1569-1993(21)01852-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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26
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Findlay A, Paing M, Daw J, Pittman S, Bengoechea R, Chou T, Weihl C. LGMD. Neuromuscul Disord 2021. [DOI: 10.1016/j.nmd.2021.07.201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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27
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Pardridge WM, Chou T. Mathematical Models of Blood-Brain Barrier Transport of Monoclonal Antibodies Targeting the Transferrin Receptor and the Insulin Receptor. Pharmaceuticals (Basel) 2021; 14:535. [PMID: 34205013 PMCID: PMC8226686 DOI: 10.3390/ph14060535] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2021] [Revised: 05/29/2021] [Accepted: 06/01/2021] [Indexed: 02/07/2023] Open
Abstract
We develop and analyze mathematical models for receptor-mediated transcytosis of monoclonal antibodies (MAb) targeting the transferrin receptor (TfR) or the insulin receptor (IR), which are expressed at the blood-brain barrier (BBB). The mass-action kinetic model for both the TfR and IR antibodies were solved numerically to generate predictions for the concentrations of all species in all compartments considered. Using these models, we estimated the rates of MAb endocytosis into brain capillary endothelium, which forms the BBB in vivo, the rates of MAb exocytosis from the intra-endothelial compartment into brain extracellular space, and the rates of receptor recycling from the endothelial space back to the luminal endothelial plasma membrane. Our analysis highlights the optimal rates of MAb association with the targeted receptor. An important role of the endogenous ligand, transferrin (Tf) or insulin, in receptor-mediated-transport (RMT) of the associated MAb was found and was attributed to the five order magnitude difference between plasma concentrations of Tf (25,000 nM) and insulin (0.3 nM). Our modeling shows that the very high plasma concentration of Tf leads to only 5% of the endothelial TfR expressed on the luminal endothelial membrane.
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Affiliation(s)
| | - Tom Chou
- Departments of Computational Medicine and Mathematics, UCLA, Los Angeles, CA 90095, USA;
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28
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Böttcher L, D’Orsogna MR, Chou T. A statistical model of COVID-19 testing in populations: effects of sampling bias and testing errors. medRxiv 2021:2021.05.22.21257643. [PMID: 34075386 PMCID: PMC8168390 DOI: 10.1101/2021.05.22.21257643] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
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.
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Affiliation(s)
- Lucas Böttcher
- Dept. of Computational Medicine, University of California, Los Angeles, 90095-1766, Los Angeles, CA, United States
- Computational Social Science, Frankfurt School of Finance and Management, 60322 Frankfurt am Main, Germany
| | - Maria R. D’Orsogna
- Dept. of Computational Medicine, University of California, Los Angeles, 90095-1766, Los Angeles, CA, United States
- Dept. of Mathematics, California State University at Northridge, Los Angeles, 91330-8313, CA, United States
| | - Tom Chou
- Dept. of Computational Medicine, University of California, Los Angeles, 90095-1766, Los Angeles, CA, United States
- Dept. of Mathematics, University of California, Los Angeles, 90095-1766, Los Angeles, CA, United States
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29
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Abstract
Factors such as varied 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 from January 2020 until February 2021 is 9[Formula: see text] 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 statistically insignificant or even negative excess deaths for at least most of 2020 in places such as Germany, Denmark, and Norway.
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Affiliation(s)
- Lucas Böttcher
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095-1766 USA
- Computational Social Science, Frankfurt School of Finance and Management, Frankfurt am Main, 60322 Germany
| | - Maria R. D’Orsogna
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095-1766 USA
- Dept. of Mathematics, California State University at Northridge, Los Angeles, CA 91330-8313 USA
| | - Tom Chou
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095-1766 USA
- Dept. of Mathematics, UCLA, Los Angeles, CA 90095-1555 USA
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30
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Wylie J, Chou T. Uniformly accurate nonlinear transmission rate models arising from disease spread through pair contacts. Phys Rev E 2021; 103:032306. [PMID: 33862712 DOI: 10.1103/physreve.103.032306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2020] [Accepted: 02/23/2021] [Indexed: 11/07/2022]
Abstract
We derive and asymptotically analyze mass-action models for disease spread that include transient pair formation and dissociation. Populations of unpaired susceptible individuals and infected individuals are distinguished from the population of three types of pairs of individuals: both susceptible, one susceptible and one infected, and both infected. Disease transmission can occur only within a pair consisting of one susceptible individual and one infected individual. We use perturbation expansion to formally derive uniformly valid approximations for the dynamics of the total infected and susceptible populations under different conditions including combinations of fast association, fast transmission, and fast dissociation limits. The effective equations are derived from the fundamental mass-action system without implicitly imposing transmission mechanisms, such as those used in frequency-dependent models. Our results represent submodels that show how effective nonlinear transmission can arise from pairing dynamics and are juxtaposed with density-based mass-action and frequency-based models.
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Affiliation(s)
- Jonathan Wylie
- Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong
| | - Tom Chou
- Department of Computational Medicine and Department of Mathematics, UCLA, Los Angeles, California 90095, USA
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31
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Abstract
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.
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Affiliation(s)
- Lucas Böttcher
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095-1766
| | - Maria R. D’Orsogna
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095-1766
- Dept. of Mathematics, California State University at Northridge, Los Angeles, CA 91330-8313
| | - Tom Chou
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095-1766
- Dept. of Mathematics, UCLA, Los Angeles, CA 90095-1555
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32
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Böttcher L, D’Orsogna MR, Chou T. Using excess deaths and testing statistics to improve estimates of COVID-19 mortalities. ArXiv 2021:arXiv:2101.03467v1. [PMID: 33442558 PMCID: PMC7805454] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
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.
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Affiliation(s)
- Lucas Böttcher
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095-1766
| | - Maria R. D’Orsogna
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095-1766
- Dept. of Mathematics, California State University at Northridge, Los Angeles, CA 91330-8313
| | - Tom Chou
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095-1766
- Dept. of Mathematics, UCLA, Los Angeles, CA 90095-1555
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33
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Affiliation(s)
- Sam C. P. Norris
- Department of Bioengineering, University of California, Los Angeles, Los Angeles, California 90095-1600, United States
| | - Andrea M. Kasko
- Department of Bioengineering, University of California, Los Angeles, Los Angeles, California 90095-1600, United States
| | - Tom Chou
- Department of Biomathematics, University of California, Los Angeles, Los Angeles, California 90095-1766, United States
- Department of Mathematics, University of California, Los Angeles, Los Angeles, California 0095-1555, United States
| | - Maria R. D’Orsogna
- Department of Mathematics, California State University, Northridge, Northridge, California 91330-8313, United States
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34
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Yang Z, Olszewski D, He C, Pintea G, Lian J, Chou T, Chen RC, Shtylla B. Machine learning and statistical prediction of patient quality-of-life after prostate radiation therapy. Comput Biol Med 2020; 129:104127. [PMID: 33333364 DOI: 10.1016/j.compbiomed.2020.104127] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2020] [Revised: 10/26/2020] [Accepted: 11/15/2020] [Indexed: 12/25/2022]
Abstract
Thanks to advancements in diagnosis and treatment, prostate cancer patients have high long-term survival rates. Currently, an important goal is to preserve quality of life during and after treatment. The relationship between the radiation a patient receives and the subsequent side effects he experiences is complex and difficult to model or predict. Here, we use machine learning algorithms and statistical models to explore the connection between radiation treatment and post-treatment gastro-urinary function. Since only a limited number of patient datasets are currently available, we used image flipping and curvature-based interpolation methods to generate more data to leverage transfer learning. Using interpolated and augmented data, we trained a convolutional autoencoder network to obtain near-optimal starting points for the weights. A convolutional neural network then analyzed the relationship between patient-reported quality-of-life and radiation doses to the bladder and rectum. We also used analysis of variance and logistic regression to explore organ sensitivity to radiation and to develop dosage thresholds for each organ region. Our findings show no statistically significant association between the bladder and quality-of-life scores. However, we found a statistically significant association between the radiation applied to posterior and anterior rectal regions and changes in quality of life. Finally, we estimated radiation therapy dose thresholds for each organ. Our analysis connects machine learning methods with organ sensitivity, thus providing a framework for informing cancer patient care using patient reported quality-of-life metrics.
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Affiliation(s)
- Zhijian Yang
- New York University, New York, NY, 10012, USA; Applied Mathematics and Computational Science Program, University of Pennsylvania, Philadelphia, PA, 19104, USA
| | - Daniel Olszewski
- Carroll College, Helena, MT, 59625, USA; Computer, Information Science and Engineering Department, University of Florida, Gainesville, FL, 32611, USA
| | - Chujun He
- Smith College, Northampton, MA, 01063, USA
| | - Giulia Pintea
- Simmons University, Boston, MA, USA; Department of Psychology, Tufts University, Boston, MA, 02111, USA
| | - Jun Lian
- Department of Radiation Oncology, The University of North Carolina, Chapel Hill, NC, 27599, USA
| | - Tom Chou
- Depts. of Computational Medicine and Mathematics, UCLA, Los Angeles, CA, 90095-1766, USA
| | - Ronald C Chen
- Department of Radiation Oncology, University of Kansas Medical Center, Kansas City, KS, 66160, USA
| | - Blerta Shtylla
- Department of Mathematics, Pomona College, Claremont, CA, 91711, USA; Early Clinical Development, Pfizer Worldwide Research, Development, and Medical, Pfizer Inc, San Diego, CA, 92121, USA.
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Cheng X, D'Orsogna MR, Chou T. Mathematical modeling of depressive disorders: Circadian driving, bistability and dynamical transitions. Comput Struct Biotechnol J 2020; 19:664-690. [PMID: 33510869 PMCID: PMC7815682 DOI: 10.1016/j.csbj.2020.10.035] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2020] [Revised: 10/30/2020] [Accepted: 10/30/2020] [Indexed: 11/30/2022] Open
Abstract
The hypothalamus-pituitary-adrenal (HPA) axis is a key neuroendocrine system implicated in stress response, major depression disorder, and post-traumatic stress disorder. We present a new, compact dynamical systems model for the response of the HPA axis to external stimuli, representing stressors or therapeutic intervention, in the presence of a circadian input. Our work builds upon previous HPA axis models where hormonal dynamics are separated into slow and fast components. Several simplifications allow us to derive an effective model of two equations, similar to a multiplicative-input FitzHugh-Nagumo system, where two stable states, a healthy and a diseased one, arise. We analyze the effective model in the context of state transitions driven by external shocks to the hypothalamus, but also modulated by circadian rhythms. Our analyses provide mechanistic insight into the effects of the circadian cycle on input driven transitions of the HPA axis and suggest a circadian influence on exposure or cognitive behavioral therapy in depression, or post-traumatic stress disorder treatment.
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Affiliation(s)
- Xiaoou Cheng
- School of Mathematical Sciences, Peking University, Haidian District, Beijing 100871, China
| | - Maria R D'Orsogna
- Dept. of Mathematics, California State University, Northridge, CA 91330, United States
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095, United States
| | - Tom Chou
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095, United States
- Dept. of Mathematics, UCLA, Los Angeles, CA 90095, United States
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36
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Leleu X, Beksac M, Chou T, Dimopoulos M, Yoon S, Prince H, Chari A, Oriol A, Siegel D, Khurana M, Qi M, Obreja M, Pour L, Shelekhova T. EFFICACY AND SAFETY OF CARFILZOMIB, DEXAMETHASONE, DARATUMUMAB TWICE-WEEKLY AT 56 MG/M2 AND ONCE-WEEKLY AT 70 MG/M2 IN RELAPSED OR REFRACTORY MULTIPLE MYELOMA: CROSS-STUDY COMPARISON OF CANDOR AND MMY1001. Hematol Transfus Cell Ther 2020. [DOI: 10.1016/j.htct.2020.10.431] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022] Open
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Abstract
Different ways of calculating mortality during epidemics have yielded very different results, particularly during the current COVID-19 pandemic. For example, the “CFR” has been interchangeably called the case fatality ratio, case fatality rate, and case fatality risk, often without standard mathematical definitions. The most commonly used CFR is the case fatality ratio, typically constructed using the estimated number of deaths to date divided by the estimated total number of confirmed infected cases to date. How does this CFR relate to an infected individual’s probability of death? To explore such issues, we formulate both a survival probability model and an associated infection duration-dependent SIR model to define individual- and population-based estimates of dynamic mortality measures to show that neither of these are directly represented by the case fatality ratio. The key parameters that affect the dynamics of different mortality estimates are the incubation period and the time individuals were infected before confirmation of infection. Using data on the recent SARS-CoV-2 outbreaks, we estimate and compare the different dynamic mortality estimates and highlight their differences. Informed by our modeling, we propose more systematic methods to determine mortality during epidemic outbreaks and discuss sensitivity to confounding effects and uncertainties in the data arising from, e.g., undertesting and heterogeneous populations.
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Affiliation(s)
- Lucas Böttcher
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095-1766, United States of America
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Abstract
Different ways of calculating mortality ratios during epidemics can yield widely different results, particularly during the COVID-19 pandemic. We formulate both a survival probability model and an associated infection duration-dependent SIR model to define individual- and population-based estimates of dynamic mortality ratios. The key parameters that affect the dynamics of the different mortality estimates are the incubation period and the length of time individuals were infected before confirmation of infection. We stress that none of these ratios are accurately represented by the often misinterpreted case fatality ratio (CFR), the number of deaths to date divided by the total number of infected cases to date. Using available data on the recent SARS-CoV-2 outbreaks and simple assumptions, we estimate and compare the different dynamic mortality ratios and highlight their differences. Informed by our modeling, we propose a more systematic method to determine mortality ratios during epidemic outbreaks and discuss sensitivity to confounding effects and errors in the data.
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Affiliation(s)
- Lucas Böttcher
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095-1766
| | - Mingtao Xia
- Dept. of Mathematics, UCLA, Los Angeles, CA 90095-1555
| | - Tom Chou
- Dept. of Computational Medicine, UCLA, Los Angeles, CA 90095-1766
- Dept. of Mathematics, UCLA, Los Angeles, CA 90095-1555
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Abstract
Diversity indices are useful single-number metrics for characterizing a complex distribution of a set of attributes across a population of interest. The utility of these different metrics or sets of metrics depends on the context and application, and whether a predictive mechanistic model exists. In this topical review, we first summarize the relevant mathematical principles underlying heterogeneity in a large population, before outlining the various definitions of 'diversity' and providing examples of scientific topics in which its quantification plays an important role. We then review how diversity has been a ubiquitous concept across multiple fields, including ecology, immunology, cellular barcoding experiments, and socioeconomic studies. Since many of these applications involve sampling of populations, we also review how diversity in small samples is related to the diversity in the entire population. Features that arise in each of these applications are highlighted.
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Affiliation(s)
- Song Xu
- Center for Biomedical Informatics Research, Department of Medicine, Stanford University, Stanford, CA, United States of America
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Abstract
Cell division is a process that involves many biochemical steps and complex biophysical mechanisms. To simplify the understanding of what triggers cell division, three basic models that subsume more microscopic cellular processes associated with cell division have been proposed. Cells can divide based on the time elapsed since their birth, their size, and/or the volume added since their birth-the timer, sizer, and adder models, respectively. Here, we propose unified adder-sizer models and investigate some of the properties of different adder processes arising in cellular proliferation. Although the adder-sizer model provides a direct way to model cell population structure, we illustrate how it is mathematically related to the well-known model in which cell division depends on age and size. Existence and uniqueness of weak solutions to our 2+1-dimensional PDE model are proved, leading to the convergence of the discretized numerical solutions and allowing us to numerically compute the dynamics of cell population densities. We then generalize our PDE model to incorporate recent experimental findings of a system exhibiting mother-daughter correlations in cellular growth rates. Numerical experiments illustrating possible average cell volume blowup and the dynamical behavior of cell populations with mother-daughter correlated growth rates are carried out. Finally, motivated by new experimental findings, we extend our adder model cases where the controlling variable is the added size between DNA replication initiation points in the cell cycle.
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Affiliation(s)
- Mingtao Xia
- Department of Mathematics, UCLA, Los Angeles, CA 90095-1555
| | - Chris D Greenman
- School of Computing Sciences, University of East Anglia, Norwich, UK NR4 7TJ
| | - Tom Chou
- Departments of Computational Medicine and Mathematics, UCLA, Los Angeles, CA 90095-1766
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Ho H, Yeh Y, Chou T. P1.09-30 Molecular Characterization of Preinvasive and Invasive Lesions in Multifocal Pulmonary Adenocarcinomas. J Thorac Oncol 2019. [DOI: 10.1016/j.jtho.2019.08.1059] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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42
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Lin S, Lin C, Shih N, Liu H, Wang W, Lin K, Lin Y, Yeh Y, Minato H, Fujii T, Wu Y, Chen M, Chou T. MA15.01 Cellular Prion Protein Transcriptionally Regulated by NFIL3 Enhances Lung Cancer Cell Lamellipodium Formation and Migration. J Thorac Oncol 2019. [DOI: 10.1016/j.jtho.2019.08.619] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Abstract
Naive human T cells are produced and developed in the thymus, which atrophies abruptly and severely in response to physical or psychological stress. To understand how an instance of stress affects the size and "diversity" of the peripheral naive T cell pool, we derive a mean-field autonomous ODE model of T cell replenishment that allows us to track the clone abundance distribution (the mean number of different TCRs each represented by a specific number of cells). We identify equilibrium solutions that arise at different rates of T cell production, and derive analytic approximations to the dominant eigenvalues and eigenvectors of the mathematical model linearized about these equilibria. From the forms of the eigenvalues and eigenvectors, we estimate rates at which counts of clones of different sizes converge to and depart from equilibrium values-that is, how the number of clones of different sizes "adjusts" to the changing rate of T cell production. Under most physiological realizations of our model, the dominant eigenvalue (representing the slowest dynamics of the clone abundance distribution) scales as a power law in the thymic output for low output levels, but saturates at higher T cell production rates. Our analysis provides a framework for quantitatively understanding how the clone abundance distribution evolves under small changes in the overall T cell production rate.
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Affiliation(s)
| | - Yao-Li Chuang
- Department of Mathematics, CalState Northridge, Northridge, CA 91330, USA
| | - Tom Chou
- Department of Mathematics, UCLA, Los Angeles, CA, 90095-1555, USA
- Department of Biomathematics, UCLA, Los Angeles, CA, 90095-1766, USA
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Mistry BA, Chou T. Nonspecific probe binding and automatic gating in flow cytometry and fluorescence activated cell sorting (FACS). Math Biosci Eng 2019; 16:4477-4490. [PMID: 31499672 DOI: 10.3934/mbe.2019223] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Flow cytometry is extensively used in cell biology to differentiate cells of interest (mutants) from control cells (wild-types). For mutant cells characterized by expression of a distinct membrane surface structure, fluorescent marker probes can be designed to bind specifically to these structures while the cells are in suspension, resulting in a sufficiently high fluorescence intensity measurement by the cytometer to identify a mutant cell. However, cell membranes may have relatively weak, nonspecific binding affinity to the probes, resulting in false positive results. Furthermore, the same effect would be present on mutant cells, allowing both specific and nonspecific binding to a single cell. We derive and analyze a kinetic model of fluorescent probe binding dynamics by tracking populations of mutant and wild-type cells with differing numbers of probes bound specifically and nonspecifically. By assuming the suspension is in chemical equilibrium prior to cytometry, we use a two-species Langmuir adsorption model to analyze the confounding effects of non-specific binding on the assay. Furthermore, we analytically derive an expectation maximization method to infer an appropriate estimate of the total number of mutant cells as an alternative to existing, heuristic methods. Lastly, using our model, we propose a new method to infer physical and experimental parameters from existing protocols. Our results provide improved ways to quantitatively analyze flow cytometry data.
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Affiliation(s)
- Bhaven A Mistry
- Department of Biomathematics, UCLA, Los Angeles, CA, 90095-1766, USA
| | - Tom Chou
- Department of Biomathematics, UCLA, Los Angeles, CA, 90095-1766, USA
- Department of Mathematics, UCLA, Los Angeles, CA, 90095-1555, USA
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Manuchehrfar F, Tian W, Chou T, Liang J. Evolution of Coagulation-Fragmentation Stochastic Processes Using Accurate Chemical Master Equation Approach. Commun Inf Syst 2019; 19:37-55. [PMID: 34421394 DOI: 10.4310/cis.2019.v19.n1.a3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Coagulation and fragmentation (CF) is a fundamental process in which smaller particles attach to each other to form larger clusters while existing clusters break up into smaller particles . It is a ubiquitous process that plays important roles in many physical and biological phenomena. CF is typically a stochastic process that often occurs in confined spaces with a limited number of available particles . Here, we study the CF process formulated with the discrete Chemical Master Equation (dCME). Using the newly developed Accurate Chemical Master Equation (ACME) method, we examine the time-dependent behavior of the CF system. We investigate the effects of a number of important factors that influence the overall behavior of the system, including the dimensionality, the ratio of attachment to detachment rates among clusters, and the initial conditions. By comparing CF in one and three dimensions, we conclude that systems in three dimensions are more likely to form large clusters. We also demonstrate how the ratio of the attachment to detachment rates affects the dynamics and the steady-state of the system. Finally, we demonstrate the relationship between the formation of large clusters and the initial condition.
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Affiliation(s)
- Farid Manuchehrfar
- Department of Bioengineering, University of Illinois at Chicago (UIC), Chicago, Illinois, USA
| | - Wei Tian
- Department of Bioengineering, University of Illinois at Chicago (UIC), Chicago, Illinois, USA
| | - Tom Chou
- Departments of Biomathematics and Mathematics, University of California at Los Angeles (UCLA), Los Angeles, California
| | - Jie Liang
- Department of Bioengineering, University of Illinois at Chicago (UIC), Chicago, Illinois, USA
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Chang SS, Chou T. A Dynamical Bifurcation Model of Bipolar Disorder Based on Learned Expectation and Asymmetry in Mood Sensitivity. Comput Psychiatr 2018; 2:205-222. [PMID: 30627671 PMCID: PMC6317753 DOI: 10.1162/cpsy_a_00021] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/10/2018] [Accepted: 09/17/2018] [Indexed: 11/16/2022]
Abstract
Bipolar disorder is a common psychiatric dysfunction characterized by recurring episodes of mania and depression. Despite its prevalence, the causes and mechanisms of bipolar disorder remain largely unknown. Recently, theories focusing on the interaction between emotion and behavior, including those based on dysregulation of the so-called behavioral approach system (BAS), have gained popularity. Mathematical models built on this principle predict bistability in mood and do not invoke intrinsic biological rhythms that may arise from interactions between mood and expectation. Here we develop and analyze a model with clinically meaningful and modifiable parameters that incorporates the interaction between mood and expectation. Our nonlinear model exhibits a transition to limit cycle behavior when a mood-sensitivity parameter exceeds a threshold value, signaling a transition to a bipolar state. The model also predicts that asymmetry in response to positive and negative events can induce unipolar depression/mania, consistent with clinical observations. We analyze the model with asymmetric mood sensitivities and show that large unidirectional mood sensitivity can lead to bipolar disorder. Finally, we show how observed effects of lithium- and antidepressant-induced mania can be explained within the framework of our proposed model.
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Affiliation(s)
- Shyr-Shea Chang
- Department of Mathematics, University of California, Los Angeles, Los Angeles, California, USA
| | - Tom Chou
- Department of Mathematics, University of California, Los Angeles, Los Angeles, California, USA
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Xu S, Kim S, Chen ISY, Chou T. Modeling large fluctuations of thousands of clones during hematopoiesis: The role of stem cell self-renewal and bursty progenitor dynamics in rhesus macaque. PLoS Comput Biol 2018; 14:e1006489. [PMID: 30335762 PMCID: PMC6218102 DOI: 10.1371/journal.pcbi.1006489] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2017] [Revised: 11/05/2018] [Accepted: 09/05/2018] [Indexed: 01/13/2023] Open
Abstract
In a recent clone-tracking experiment, millions of uniquely tagged hematopoietic stem cells (HSCs) and progenitor cells were autologously transplanted into rhesus macaques and peripheral blood containing thousands of tags were sampled and sequenced over 14 years to quantify the abundance of hundreds to thousands of tags or “clones.” Two major puzzles of the data have been observed: consistent differences and massive temporal fluctuations of clone populations. The large sample-to-sample variability can lead clones to occasionally go “extinct” but “resurrect” themselves in subsequent samples. Although heterogeneity in HSC differentiation rates, potentially due to tagging, and random sampling of the animals’ blood and cellular demographic stochasticity might be invoked to explain these features, we show that random sampling cannot explain the magnitude of the temporal fluctuations. Moreover, we show through simpler neutral mechanistic and statistical models of hematopoiesis of tagged cells that a broad distribution in clone sizes can arise from stochastic HSC self-renewal instead of tag-induced heterogeneity. The very large clone population fluctuations that often lead to extinctions and resurrections can be naturally explained by a generation-limited proliferation constraint on the progenitor cells. This constraint leads to bursty cell population dynamics underlying the large temporal fluctuations. We analyzed experimental clone abundance data using a new statistic that counts clonal disappearances and provided least-squares estimates of two key model parameters in our model, the total HSC differentiation rate and the maximum number of progenitor-cell divisions. Hematopoiesis of virally tagged cells in rhesus macaques is analyzed in the context of a mechanistic and statistical model. We find that the clone size distribution and the temporal variability in the abundance of each clone (viral tag) in peripheral blood are consistent with (i) stochastic HSC self-renewal during bone marrow repair, (ii) clonal aging that restricts the number of generations of progenitor cells, and (iii) infrequent and small-size samples. By fitting data, we infer two key parameters that control the level of fluctuations of clone sizes in our model: the total HSC differentiation rate and the maximum proliferation capacity of progenitor cells. Our analysis provides insight into the mechanisms of hematopoiesis and a framework to guide future multiclone barcoding/lineage tracking measurements.
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Affiliation(s)
- Song Xu
- Center for Biomedical Informatics Research, Department of Medicine, Stanford University, Stanford, California, United States of America
| | - Sanggu Kim
- Department of Veterinary Biosciences, The Ohio State University, Columbus, Ohio, United States of America
| | - Irvin S. Y. Chen
- UCLA AIDS Institute and Department of Microbiology, Immunology, and Molecular Genetics, University of California, Los Angeles, Los Angeles, California, United States of America
| | - Tom Chou
- Center for Biomedical Informatics Research, Department of Medicine, Stanford University, Stanford, California, United States of America
- Department of Mathematics, University of California, Los Angeles, Los Angeles, California, United States of America
- * E-mail:
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48
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Chou T. MTE02.02 Update on WHO Classification and Staging of Lung Cancer. J Thorac Oncol 2018. [DOI: 10.1016/j.jtho.2018.08.050] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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49
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Manuchehrfar F, Tian W, Chou T, Liang J. Stochastic Analysis of Coagulation and Fragmentation of Self-Assembly by Solving Discrete Chemical Master Equation (dCME) with Acme. Biophys J 2018. [DOI: 10.1016/j.bpj.2017.11.3582] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022] Open
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50
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Kim LU, D’Orsogna MR, Chou T. Perturbing the Hypothalamic-Pituitary-Adrenal Axis: A Mathematical Model for Interpreting PTSD Assessment Tests. Comput Psychiatr 2018; 2:28-49. [PMID: 30090861 PMCID: PMC6067831 DOI: 10.1162/cpsy_a_00013] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/03/2017] [Accepted: 08/15/2017] [Indexed: 12/05/2022]
Abstract
We use a dynamical systems model of the hypothalamic-pituitary-adrenal (HPA) axis to understand the mechanisms underlying clinical protocols used to probe patient stress response. Specifically, we address dexamethasone (DEX) and ACTH challenge tests, which probe pituitary and adrenal gland responses, respectively. We show that some previously observed features and experimental responses can arise from a bistable mathematical model containing two steady-states, rather than relying on specific and permanent parameter changes due to physiological disruption. Moreover, we show that the timing of a perturbation relative to the intrinsic oscillation of the HPA axis can affect challenge test responses. Conventional mechanistic hypotheses supported and refuted by the challenge tests are reexamined by varying parameters in our mathematical model associated with these hypotheses. We show that (a) adrenal hyposensitivity can give rise to the responses seen in ACTH challenge tests and (b) enhanced cortisol-mediated suppression of the pituitary in subjects with PTSD is not necessary to explain the responses observed in DEX stress tests. We propose a new two-stage DEX/external stressor protocol to more clearly distinguish between the conventional hypothesis of enhanced suppression of the pituitary and bistable dynamics hypothesized in our model.
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Affiliation(s)
- Lae Un Kim
- Department of Biomathematics, University of California, Los Angeles, USA
| | | | - Tom Chou
- Department of Biomathematics, University of California, Los Angeles, USA
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