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DeWitt WS, Evans SN, Hiesmayr E, Hummel S. Mean-field interacting multi-type birth-death processes with a view to applications in phylodynamics. Theor Popul Biol 2024; 159:1-12. [PMID: 39019333 DOI: 10.1016/j.tpb.2024.07.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2023] [Revised: 07/09/2024] [Accepted: 07/11/2024] [Indexed: 07/19/2024]
Abstract
Multi-type birth-death processes underlie approaches for inferring evolutionary dynamics from phylogenetic trees across biological scales, ranging from deep-time species macroevolution to rapid viral evolution and somatic cellular proliferation. A limitation of current phylogenetic birth-death models is that they require restrictive linearity assumptions that yield tractable message-passing likelihoods, but that also preclude interactions between individuals. Many fundamental evolutionary processes - such as environmental carrying capacity or frequency-dependent selection - entail interactions, and may strongly influence the dynamics in some systems. Here, we introduce a multi-type birth-death process in mean-field interaction with an ensemble of replicas of the focal process. We prove that, under quite general conditions, the ensemble's stochastically evolving interaction field converges to a deterministic trajectory in the limit of an infinite ensemble. In this limit, the replicas effectively decouple, and self-consistent interactions appear as nonlinearities in the infinitesimal generator of the focal process. We investigate a special case that is rich enough to model both carrying capacity and frequency-dependent selection while yielding tractable message-passing likelihoods in the context of a phylogenetic birth-death model.
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Affiliation(s)
- William S DeWitt
- Department of Electrical Engineering & Computer Sciences, University of California, Berkeley, United States of America.
| | - Steven N Evans
- Department of Statistics, University of California, Berkeley, United States of America.
| | - Ella Hiesmayr
- Department of Statistics, University of California, Berkeley, United States of America.
| | - Sebastian Hummel
- Department of Statistics, University of California, Berkeley, United States of America.
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2
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Huang J, Morsomme R, Dunson D, Xu J. Detecting changes in the transmission rate of a stochastic epidemic model. Stat Med 2024; 43:1867-1882. [PMID: 38409877 DOI: 10.1002/sim.10050] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Revised: 10/26/2023] [Accepted: 01/03/2024] [Indexed: 02/28/2024]
Abstract
Throughout the course of an epidemic, the rate at which disease spreads varies with behavioral changes, the emergence of new disease variants, and the introduction of mitigation policies. Estimating such changes in transmission rates can help us better model and predict the dynamics of an epidemic, and provide insight into the efficacy of control and intervention strategies. We present a method for likelihood-based estimation of parameters in the stochastic susceptible-infected-removed model under a time-inhomogeneous transmission rate comprised of piecewise constant components. In doing so, our method simultaneously learns change points in the transmission rate via a Markov chain Monte Carlo algorithm. The method targets the exact model posterior in a difficult missing data setting given only partially observed case counts over time. We validate performance on simulated data before applying our approach to data from an Ebola outbreak in Western Africa and COVID-19 outbreak on a university campus.
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Affiliation(s)
- Jenny Huang
- Department of Statistical Science, Duke University, Durham, North Carolina, USA
| | - Raphaël Morsomme
- Department of Statistical Science, Duke University, Durham, North Carolina, USA
| | - David Dunson
- Department of Statistical Science, Duke University, Durham, North Carolina, USA
| | - Jason Xu
- Department of Statistical Science, Duke University, Durham, North Carolina, USA
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3
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Awasthi A, Minin VM, Huang J, Chow D, Xu J. Fitting a stochastic model of intensive care occupancy to noisy hospitalization time series during the COVID-19 pandemic. Stat Med 2023; 42:5189-5206. [PMID: 37705508 DOI: 10.1002/sim.9907] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2022] [Revised: 07/28/2023] [Accepted: 09/01/2023] [Indexed: 09/15/2023]
Abstract
Intensive care occupancy is an important indicator of health care stress that has been used to guide policy decisions during the COVID-19 pandemic. Toward reliable decision-making as a pandemic progresses, estimating the rates at which patients are admitted to and discharged from hospitals and intensive care units (ICUs) is crucial. Since individual-level hospital data are rarely available to modelers in each geographic locality of interest, it is important to develop tools for inferring these rates from publicly available daily numbers of hospital and ICU beds occupied. We develop such an estimation approach based on an immigration-death process that models fluctuations of ICU occupancy. Our flexible framework allows for immigration and death rates to depend on covariates, such as hospital bed occupancy and daily SARS-CoV-2 test positivity rate, which may drive changes in hospital ICU operations. We demonstrate via simulation studies that the proposed method performs well on noisy time series data and apply our statistical framework to hospitalization data from the University of California, Irvine (UCI) Health and Orange County, California. By introducing a likelihood-based framework where immigration and death rates can vary with covariates, we find, through rigorous model selection, that hospitalization and positivity rates are crucial covariates for modeling ICU stay dynamics and validate our per-patient ICU stay estimates using anonymized patient-level UCI hospital data.
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Affiliation(s)
- Achal Awasthi
- Department of Biostatistics and Bioinformatics, Duke University, Durham, North Carolina, USA
| | - Volodymyr M Minin
- Department of Statistics, University of California, Irvine, Irvine, California, USA
| | - Jenny Huang
- Department of Statistical Science, Duke University, Durham, North Carolina, USA
| | - Daniel Chow
- School of Medicine, University of California, Irvine, Irvine, California, USA
| | - Jason Xu
- Department of Biostatistics and Bioinformatics, Duke University, Durham, North Carolina, USA
- Department of Statistical Science, Duke University, Durham, North Carolina, USA
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4
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Saha E, Ho LST, Tran G. SPADE4: Sparsity and Delay Embedding Based Forecasting of Epidemics. Bull Math Biol 2023; 85:71. [PMID: 37335437 DOI: 10.1007/s11538-023-01174-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2023] [Accepted: 05/27/2023] [Indexed: 06/21/2023]
Abstract
Predicting the evolution of diseases is challenging, especially when the data availability is scarce and incomplete. The most popular tools for modelling and predicting infectious disease epidemics are compartmental models. They stratify the population into compartments according to health status and model the dynamics of these compartments using dynamical systems. However, these predefined systems may not capture the true dynamics of the epidemic due to the complexity of the disease transmission and human interactions. In order to overcome this drawback, we propose Sparsity and Delay Embedding based Forecasting (SPADE4) for predicting epidemics. SPADE4 predicts the future trajectory of an observable variable without the knowledge of the other variables or the underlying system. We use random features model with sparse regression to handle the data scarcity issue and employ Takens' delay embedding theorem to capture the nature of the underlying system from the observed variable. We show that our approach outperforms compartmental models when applied to both simulated and real data.
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Affiliation(s)
- Esha Saha
- Department of Applied Mathematics, University of Waterloo, Waterloo, Canada
| | - Lam Si Tung Ho
- Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada.
| | - Giang Tran
- Department of Applied Mathematics, University of Waterloo, Waterloo, Canada
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5
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Wadkin LE, Golightly A, Branson J, Hoppit A, Parker NG, Baggaley AW. Quantifying Invasive Pest Dynamics through Inference of a Two-Node Epidemic Network Model. DIVERSITY 2023. [DOI: 10.3390/d15040496] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/31/2023]
Abstract
Invasive woodland pests have substantial ecological, economic, and social impacts, harming biodiversity and ecosystem services. Mathematical modelling informed by Bayesian inference can deepen our understanding of the fundamental behaviours of invasive pests and provide predictive tools for forecasting future spread. A key invasive pest of concern in the UK is the oak processionary moth (OPM). OPM was established in the UK in 2006; it is harmful to both oak trees and humans, and its infestation area is continually expanding. Here, we use a computational inference scheme to estimate the parameters for a two-node network epidemic model to describe the temporal dynamics of OPM in two geographically neighbouring parks (Bushy Park and Richmond Park, London). We show the applicability of such a network model to describing invasive pest dynamics and our results suggest that the infestation within Richmond Park has largely driven the infestation within Bushy Park.
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6
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Wadkin LE, Branson J, Hoppit A, Parker NG, Golightly A, Baggaley AW. Inference for epidemic models with time-varying infection rates: Tracking the dynamics of oak processionary moth in the UK. Ecol Evol 2022; 12:e8871. [PMID: 35509609 PMCID: PMC9058805 DOI: 10.1002/ece3.8871] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2022] [Revised: 03/31/2022] [Accepted: 04/08/2022] [Indexed: 11/16/2022] Open
Abstract
Invasive pests pose a great threat to forest, woodland, and urban tree ecosystems. The oak processionary moth (OPM) is a destructive pest of oak trees, first reported in the UK in 2006. Despite great efforts to contain the outbreak within the original infested area of South‐East England, OPM continues to spread. Here, we analyze data consisting of the numbers of OPM nests removed each year from two parks in London between 2013 and 2020. Using a state‐of‐the‐art Bayesian inference scheme, we estimate the parameters for a stochastic compartmental SIR (susceptible, infested, and removed) model with a time‐varying infestation rate to describe the spread of OPM. We find that the infestation rate and subsequent basic reproduction number have remained constant since 2013 (with R0 between one and two). This shows further controls must be taken to reduce R0 below one and stop the advance of OPM into other areas of England. Synthesis. Our findings demonstrate the applicability of the SIR model to describing OPM spread and show that further controls are needed to reduce the infestation rate. The proposed statistical methodology is a powerful tool to explore the nature of a time‐varying infestation rate, applicable to other partially observed time series epidemic data.
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Affiliation(s)
- Laura E Wadkin
- School of Mathematics, Statistics and Physics Newcastle University Newcastle upon Tyne UK
| | - Julia Branson
- GeoData, Geography and Environmental Science University of Southampton Southampton UK
| | | | - Nicholas G Parker
- School of Mathematics, Statistics and Physics Newcastle University Newcastle upon Tyne UK
| | - Andrew Golightly
- School of Mathematics, Statistics and Physics Newcastle University Newcastle upon Tyne UK.,Department of Mathematical Sciences Durham University Durham UK
| | - Andrew W Baggaley
- School of Mathematics, Statistics and Physics Newcastle University Newcastle upon Tyne UK
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Kumar A, Zodage A, Santhanam MS. First detection of threshold crossing events under intermittent sensing. Phys Rev E 2021; 104:L052103. [PMID: 34942787 DOI: 10.1103/physreve.104.l052103] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2021] [Accepted: 10/20/2021] [Indexed: 12/14/2022]
Abstract
The time taken by a random variable to cross a threshold for the first time, known as the first passage time, is of interest in many areas of sciences and engineering. Conventionally, there is an implicit assumption that the notional "sensor" monitoring the threshold crossing event is always active. In many realistic scenarios, the sensor monitoring the stochastic process works intermittently. Then, the relevant quantity of interest is the first detection time, which denotes the time when the sensor detects the random variable to be above the threshold for the first time. In this Letter, a birth-death process monitored by a random intermittent sensor is studied for which the first detection time distribution is obtained. In general, it is shown that the first detection time is related to and is obtainable from the first passage time distribution. Our analytical results display an excellent agreement with simulations. Furthermore, this framework is demonstrated in several applications-the susceptible infected susceptible compartmental and logistic models and birth-death processes with resetting. Finally, we solve the practically relevant problem of inferring the first passage time distribution from the first detection time.
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Affiliation(s)
- Aanjaneya Kumar
- Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411008, India
| | - Aniket Zodage
- Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411008, India
| | - M S Santhanam
- Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411008, India
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Carr MJ, Simpson MJ, Drovandi C. Estimating parameters of a stochastic cell invasion model with fluorescent cell cycle labelling using approximate Bayesian computation. J R Soc Interface 2021; 18:20210362. [PMID: 34547212 PMCID: PMC8455172 DOI: 10.1098/rsif.2021.0362] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
We develop a parameter estimation method based on approximate Bayesian computation (ABC) for a stochastic cell invasion model using fluorescent cell cycle labelling with proliferation, migration and crowding effects. Previously, inference has been performed on a deterministic version of the model fitted to cell density data, and not all parameters were identifiable. Considering the stochastic model allows us to harness more features of experimental data, including cell trajectories and cell count data, which we show overcomes the parameter identifiability problem. We demonstrate that, while difficult to collect, cell trajectory data can provide more information about the parameters of the cell invasion model. To handle the intractability of the likelihood function of the stochastic model, we use an efficient ABC algorithm based on sequential Monte Carlo. Rcpp and MATLAB implementations of the simulation model and ABC algorithm used in this study are available at https://github.com/michaelcarr-stats/FUCCI.
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Affiliation(s)
- Michael J Carr
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
| | - Matthew J Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
| | - Christopher Drovandi
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
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10
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Bu F, Aiello AE, Xu J, Volfovsky A. Likelihood-Based Inference for Partially Observed Epidemics on Dynamic Networks. J Am Stat Assoc 2020. [DOI: 10.1080/01621459.2020.1790376] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Affiliation(s)
- Fan Bu
- Department of Statistical Science, Duke University, Durham, NC
| | - Allison E. Aiello
- Department of Epidemiology, Gillings School of Global Public Health, University of North Carolina at Chapel Hill, Chapel Hill, NC
| | - Jason Xu
- Department of Statistical Science, Duke University, Durham, NC
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12
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Santana LM, Ganesan S, Bhanot G. A Quasi Birth-and-Death model for tumor recurrence. J Theor Biol 2019; 480:175-191. [PMID: 31374283 DOI: 10.1016/j.jtbi.2019.07.017] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2019] [Revised: 07/04/2019] [Accepted: 07/29/2019] [Indexed: 11/24/2022]
Abstract
A major cause of chemoresistance and recurrence in tumors is the presence of dormant tumor foci that survive chemotherapy and can eventually transition to active growth to regenerate the cancer. In this paper, we propose a Quasi Birth-and-Death (QBD) model for the dynamics of tumor growth and recurrence/remission of the cancer. Starting from a discrete-state master equation that describes the time-dependent transition probabilities between states with different numbers of dormant and active tumor foci, we develop a framework based on a continuum-limit approach to determine the time-dependent probability that an undetectable residual tumor will become large enough to be detectable. We derive an exact formula for the probability of recurrence at large times and show that it displays a phase transition as a function of the ratio of the death rate μA of an active tumor focus to its doubling rate λ. We also derive forward and backward Kolmogorov equations for the transition probability density in the continuum limit and, using a first-passage time formalism, we obtain a drift-diffusion equation for the mean recurrence time and solve it analytically to leading order for a large detectable tumor size N. We show that simulations of the discrete-state model agree with the analytical results, except for O(1/N) corrections. As an example of the use of our model in a clinical setting, we show that a range of model parameters can fit Kaplan-Meier recurrence-free survival data for ovarian cancer. Finally, we show in simulations that extending the duration of chemotherapy increases both the mean recurrence time and the asymptotic (large-time) probability of no recurrence. Our results should be useful in planning optimized chemotherapy dosing and duration for cancer treatment, especially in cancer types for which no targeted therapy is available.
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Affiliation(s)
- Leonardo M Santana
- Department of Physics & Astronomy, Rutgers University, Piscataway, NJ 08854, USA.
| | - Shridar Ganesan
- Rutgers Cancer Institute of New Jersey, New Brunswick, NJ 08903, USA; Department of Medicine, Rutgers Robert Wood Johnson Medical School, Rutgers University, New Brunswick, NJ 08903, USA.
| | - Gyan Bhanot
- Department of Physics & Astronomy, Rutgers University, Piscataway, NJ 08854, USA; Rutgers Cancer Institute of New Jersey, New Brunswick, NJ 08903, USA; Department of Molecular Biology and Biochemistry, Rutgers University, Piscataway, NJ 08854, USA
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13
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Ho LST, Crawford FW, Suchard MA. Direct likelihood-based inference for discretely observed stochastic compartmental models of infectious disease. Ann Appl Stat 2018. [DOI: 10.1214/18-aoas1141] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Crawford FW, Ho LST, Suchard MA. Computational methods for birth-death processes. WILEY INTERDISCIPLINARY REVIEWS. COMPUTATIONAL STATISTICS 2018; 10:e1423. [PMID: 29942419 PMCID: PMC6014701 DOI: 10.1002/wics.1423] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
Many important stochastic counting models can be written as general birth-death processes (BDPs). BDPs are continuous-time Markov chains on the non-negative integers in which only jumps to adjacent states are allowed. BDPs can be used to easily parameterize a rich variety of probability distributions on the non-negative integers, and straightforward conditions guarantee that these distributions are proper. BDPs also provide a mechanistic interpretation - birth and death of actual particles or organisms - that has proven useful in evolution, ecology, physics, and chemistry. Although the theoretical properties of general BDPs are well understood, traditionally statistical work on BDPs has been limited to the simple linear (Kendall) process. Aside from a few simple cases, it remains impossible to find analytic expressions for the likelihood of a discretely-observed BDP, and computational difficulties have hindered development of tools for statistical inference. But the gap between BDP theory and practical methods for estimation has narrowed in recent years. There are now robust methods for evaluating likelihoods for realizations of BDPs: finite-time transition, first passage, equilibrium probabilities, and distributions of summary statistics that arise commonly in applications. Recent work has also exploited the connection between continuously- and discretely-observed BDPs to derive EM algorithms for maximum likelihood estimation. Likelihood-based inference for previously intractable BDPs is much easier than previously thought and regression approaches analogous to Poisson regression are straightforward to derive. In this review, we outline the basic mathematical theory for BDPs and demonstrate new tools for statistical inference using data from BDPs.
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Affiliation(s)
- Forrest W Crawford
- Departments of Biostatistics, Ecology & Evolutionary Biology, and School of Management, Yale University
| | - Lam Si Tung Ho
- Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada
| | - Marc A Suchard
- Departments of Biomathematics, Biostatistics and Human Genetics, University of California, Los Angeles
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Liu LL, Brumbaugh J, Bar-Nur O, Smith Z, Stadtfeld M, Meissner A, Hochedlinger K, Michor F. Probabilistic Modeling of Reprogramming to Induced Pluripotent Stem Cells. Cell Rep 2016; 17:3395-3406. [PMID: 28009305 PMCID: PMC5467646 DOI: 10.1016/j.celrep.2016.11.080] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2016] [Revised: 10/04/2016] [Accepted: 11/24/2016] [Indexed: 01/01/2023] Open
Abstract
Reprogramming of somatic cells to induced pluripotent stem cells (iPSCs) is typically an inefficient and asynchronous process. A variety of technological efforts have been made to accelerate and/or synchronize this process. To define a unified framework to study and compare the dynamics of reprogramming under different conditions, we developed an in silico analysis platform based on mathematical modeling. Our approach takes into account the variability in experimental results stemming from probabilistic growth and death of cells and potentially heterogeneous reprogramming rates. We suggest that reprogramming driven by the Yamanaka factors alone is a more heterogeneous process, possibly due to cell-specific reprogramming rates, which could be homogenized by the addition of additional factors. We validated our approach using publicly available reprogramming datasets, including data on early reprogramming dynamics as well as cell count data, and thus we demonstrated the general utility and predictive power of our methodology for investigating reprogramming and other cell fate change systems.
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Affiliation(s)
- Lin L Liu
- Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute, Boston, MA 02115, USA; Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA 02115, USA
| | - Justin Brumbaugh
- Massachusetts General Hospital Cancer Center and Center for Regenerative Medicine, Boston, MA 02114, USA; Harvard Stem Cell Institute, Cambridge, MA 02138, USA; Department of Stem Cell and Regenerative Biology, Cambridge, MA 02138, USA
| | - Ori Bar-Nur
- Massachusetts General Hospital Cancer Center and Center for Regenerative Medicine, Boston, MA 02114, USA; Harvard Stem Cell Institute, Cambridge, MA 02138, USA; Department of Stem Cell and Regenerative Biology, Cambridge, MA 02138, USA
| | - Zachary Smith
- Department of Stem Cell and Regenerative Biology, Cambridge, MA 02138, USA
| | - Matthias Stadtfeld
- The Helen L. and Martin S. Kimmel Center for Biology and Medicine, Skirball Institute of Biomolecular Medicine, Department of Cell Biology, NYU School of Medicine, New York, NY 10016, USA
| | - Alexander Meissner
- Department of Stem Cell and Regenerative Biology, Cambridge, MA 02138, USA
| | - Konrad Hochedlinger
- Massachusetts General Hospital Cancer Center and Center for Regenerative Medicine, Boston, MA 02114, USA; Harvard Stem Cell Institute, Cambridge, MA 02138, USA; Department of Stem Cell and Regenerative Biology, Cambridge, MA 02138, USA; Howard Hughes Medical Institute, Chevy Chase, MD 20815, USA
| | - Franziska Michor
- Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute, Boston, MA 02115, USA; Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA 02115, USA.
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