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Lasri A, Shahrezaei V, Sturrock M. Benchmarking imputation methods for network inference using a novel method of synthetic scRNA-seq data generation. BMC Bioinformatics 2022; 23:236. [PMID: 35715748 PMCID: PMC9204969 DOI: 10.1186/s12859-022-04778-9] [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: 08/17/2021] [Accepted: 05/31/2022] [Indexed: 11/30/2022] Open
Abstract
Background Single cell RNA-sequencing (scRNA-seq) has very rapidly become the new workhorse of modern biology providing an unprecedented global view on cellular diversity and heterogeneity. In particular, the structure of gene-gene expression correlation contains information on the underlying gene regulatory networks. However, interpretation of scRNA-seq data is challenging due to specific experimental error and biases that are unique to this kind of data including drop-out (or technical zeros). Methods To deal with this problem several methods for imputation of zeros for scRNA-seq have been developed. However, it is not clear how these processing steps affect inference of genetic networks from single cell data. Here, we introduce Biomodelling.jl, a tool for generation of synthetic scRNA-seq data using multiscale modelling of stochastic gene regulatory networks in growing and dividing cells. Results Our tool produces realistic transcription data with a known ground truth network topology that can be used to benchmark different approaches for gene regulatory network inference. Using this tool we investigate the impact of different imputation methods on the performance of several network inference algorithms. Conclusions Biomodelling.jl provides a versatile and useful tool for future development and benchmarking of network inference approaches using scRNA-seq data. Supplementary Information The online version contains supplementary material available at 10.1186/s12859-022-04778-9
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Affiliation(s)
- Ayoub Lasri
- Department of Physiology and Medical Physics, Royal College of Surgeons in Ireland, Dublin, Ireland
| | - Vahid Shahrezaei
- Department of Mathematics, Faculty of Natural Sciences, Imperial College London, London, SW7 2AZ, UK
| | - Marc Sturrock
- Department of Physiology and Medical Physics, Royal College of Surgeons in Ireland, Dublin, Ireland.
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Lasri A, Sturrock M. The influence of methylation status on a stochastic model of MGMT dynamics in glioblastoma: Phenotypic selection can occur with and without a downshift in promoter methylation status. J Theor Biol 2021; 521:110662. [PMID: 33684406 DOI: 10.1016/j.jtbi.2021.110662] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2020] [Revised: 02/26/2021] [Accepted: 03/01/2021] [Indexed: 01/02/2023]
Abstract
Glioblastoma originates in the brain and is one of the most aggressive cancer types. Glioblastoma represents 15% of all brain tumours, with a median survival of 15 months. Although the current standard of care for such a tumour (the Stupp protocol) has shown positive results for the prognosis of patients, O-6-methylguanine-DNA methyltransferase (MGMT) driven drug resistance has been an issue of increasing concern and hence requires innovative approaches. In addition to the well established drug resistance factors such as tumour location and blood brain barriers, it is also important to understand how the genetic and epigenetic dynamics of the glioblastoma cells can play a role. One important aspect of this is the study of methylation status of MGMT following administration of temozolomide. In this paper, we extend our previously published model that simulated MGMT expression in glioblastoma cells to incorporate the promoter methylation status of MGMT. This methylation status has clinical significance and is used as a marker for patient outcomes. Using this model, we investigate the causative relationship between temozolomide treatment and the methylation status of the MGMT promoter in a population of cells. In addition by constraining the model to relevant biological data using Approximate Bayesian Computation, we were able to identify parameter regimes that yield different possible modes of resistances, namely, phenotypic selection of MGMT, a downshift in the methylation status of the MGMT promoter or both simultaneously. We analysed each of the parameter sets associated with the different modes of resistance, presenting representative solutions as well as discovering some similarities between them as well as unique requirements for each of them. Finally, we used them to devise optimal strategies for inhibiting MGMT expression with the aim of minimising live glioblastoma cell numbers.
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Affiliation(s)
- Ayoub Lasri
- Department of Physiology and Medical Physics, Royal College of Surgeons in Ireland, York house, Dublin, Ireland.
| | - Marc Sturrock
- Department of Physiology and Medical Physics, Royal College of Surgeons in Ireland, York house, Dublin, Ireland
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3
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Trigilio AD, Marien YW, Van Steenberge PHM, D’hooge DR. Gillespie-Driven kinetic Monte Carlo Algorithms to Model Events for Bulk or Solution (Bio)Chemical Systems Containing Elemental and Distributed Species. Ind Eng Chem Res 2020. [DOI: 10.1021/acs.iecr.0c03888] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Alessandro D. Trigilio
- Laboratory for Chemical Technology, Ghent University, Technologiepark 125, 9052 Gent, Belgium
| | - Yoshi W. Marien
- Laboratory for Chemical Technology, Ghent University, Technologiepark 125, 9052 Gent, Belgium
| | | | - Dagmar R. D’hooge
- Laboratory for Chemical Technology, Ghent University, Technologiepark 125, 9052 Gent, Belgium
- Centre for Textile Science and Engineering, Ghent University, Technologiepark 70a, 9052 Gent, Belgium
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4
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A critical analysis of Powell's results on the interdivision time distribution. Sci Rep 2019; 9:8165. [PMID: 31160635 PMCID: PMC6546743 DOI: 10.1038/s41598-019-44606-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2019] [Accepted: 05/07/2019] [Indexed: 11/09/2022] Open
Abstract
The cell-age and interdivision-time probability density functions (PDFs) have been extensively investigated since the 1940s due to their fundamental role in cell growth. The pioneering work of Powell established the first relationship between the interdivision-time and cell-age PDFs. In the literature, two definitions for the interdivision-time PDF have been proposed. One stands for the age-at-rupture PDF and is experimentally observable, whereas the other is the probability density that a cell divides at a certain age and is unobservable. From Powell’s results pertaining to the unobservable interdivision-time PDF, Painter and Marr derived an inequality that is true but is incorrectly used by experimentalists to analyse single-cell data. Unfortunately, the confusion between these two PDFs persists. To dissipate this confusion, exact relationships between the cell-age and the interdivision-time PDFs are derived in this work from an age-structured model, which can be used by experimentalists to analyse cell growth in batch and continuous culture modes.
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5
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Jędrak J, Kwiatkowski M, Ochab-Marcinek A. Exactly solvable model of gene expression in a proliferating bacterial cell population with stochastic protein bursts and protein partitioning. Phys Rev E 2019; 99:042416. [PMID: 31108597 DOI: 10.1103/physreve.99.042416] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2018] [Indexed: 06/09/2023]
Abstract
Many of the existing stochastic models of gene expression contain the first-order decay reaction term that may describe active protein degradation or dilution. If the model variable is interpreted as the molecule number, and not concentration, the decay term may also approximate the loss of protein molecules due to cell division as a continuous degradation process. The seminal model of that kind leads to gamma distributions of protein levels, whose parameters are defined by the mean frequency of protein bursts and mean burst size. However, such models (whether interpreted in terms of molecule numbers or concentrations) do not correctly account for the noise due to protein partitioning between daughter cells. We present an exactly solvable stochastic model of gene expression in cells dividing at random times, where we assume description in terms of molecule numbers with a constant mean protein burst size. The model is based on a population balance equation supplemented with protein production in random bursts. If protein molecules are partitioned equally between daughter cells, we obtain at steady state the analytical expressions for probability distributions similar in shape to gamma distributions, yet with quite different values of mean burst size and mean burst frequency than would result from fitting of the classical continuous-decay model to these distributions. For random partitioning of protein molecules between daughter cells, we obtain the moment equations for the protein number distribution and thus the analytical formulas for the squared coefficient of variation.
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Affiliation(s)
- Jakub Jędrak
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
| | | | - Anna Ochab-Marcinek
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
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6
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Charlebois DA, Balázsi G. Modeling cell population dynamics. In Silico Biol 2019; 13:21-39. [PMID: 30562900 PMCID: PMC6598210 DOI: 10.3233/isb-180470] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2018] [Revised: 09/13/2018] [Accepted: 10/16/2018] [Indexed: 12/27/2022]
Abstract
Quantitative modeling is quickly becoming an integral part of biology, due to the ability of mathematical models and computer simulations to generate insights and predict the behavior of living systems. Single-cell models can be incapable or misleading for inferring population dynamics, as they do not consider the interactions between cells via metabolites or physical contact, nor do they consider competition for limited resources such as nutrients or space. Here we examine methods that are commonly used to model and simulate cell populations. First, we cover simple models where analytic solutions are available, and then move on to more complex scenarios where computational methods are required. Overall, we present a summary of mathematical models used to describe cell population dynamics, which may aid future model development and highlights the importance of population modeling in biology.
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Affiliation(s)
- Daniel A. Charlebois
- The Louis and Beatrice Laufer Center for Physical and Quantitative Biology, Stony Brook University, NY, USA
- Department of Physics, University of Alberta, Edmonton, AB, Canada
| | - Gábor Balázsi
- The Louis and Beatrice Laufer Center for Physical and Quantitative Biology, Stony Brook University, NY, USA
- Department of Biomedical Engineering, Stony Brook University, NY, USA
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7
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Abstract
Quantitative modeling is quickly becoming an integral part of biology, due to the ability of mathematical models and computer simulations to generate insights and predict the behavior of living systems. Single-cell models can be incapable or misleading for inferring population dynamics, as they do not consider the interactions between cells via metabolites or physical contact, nor do they consider competition for limited resources such as nutrients or space. Here we examine methods that are commonly used to model and simulate cell populations. First, we cover simple models where analytic solutions are available, and then move on to more complex scenarios where computational methods are required. Overall, we present a summary of mathematical models used to describe cell population dynamics, which may aid future model development and highlights the importance of population modeling in biology.
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Affiliation(s)
- Daniel A Charlebois
- The Louis and Beatrice Laufer Center for Physical and Quantitative Biology, Stony Brook University, NY, USA.,Department of Physics, University of Alberta, Edmonton, AB, Canada
| | - Gábor Balázsi
- The Louis and Beatrice Laufer Center for Physical and Quantitative Biology, Stony Brook University, NY, USA.,Department of Biomedical Engineering, Stony Brook University, NY, USA
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8
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Waldherr S. Estimation methods for heterogeneous cell population models in systems biology. J R Soc Interface 2018; 15:20180530. [PMID: 30381346 PMCID: PMC6228475 DOI: 10.1098/rsif.2018.0530] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2018] [Accepted: 10/04/2018] [Indexed: 12/19/2022] Open
Abstract
Heterogeneity among individual cells is a characteristic and relevant feature of living systems. A range of experimental techniques to investigate this heterogeneity is available, and multiple modelling frameworks have been developed to describe and simulate the dynamics of heterogeneous populations. Measurement data are used to adjust computational models, which results in parameter and state estimation problems. Methods to solve these estimation problems need to take the specific properties of data and models into account. The aim of this review is to give an overview on the state of the art in estimation methods for heterogeneous cell population data and models. The focus is on models based on the population balance equation, but stochastic and individual-based models are also discussed. It starts with a brief discussion of common experimental approaches and types of measurement data that can be obtained in this context. The second part describes computational modelling frameworks for heterogeneous populations and the types of estimation problems occurring for these models. The third part starts with a discussion of observability and identifiability properties, after which the computational methods to solve the various estimation problems are described.
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9
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A Framework for the Development of Integrated and Computationally Feasible Models of Large-Scale Mammalian Cell Bioreactors. Processes (Basel) 2018. [DOI: 10.3390/pr6070082] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
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10
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Quedeville V, Ouazaite H, Polizzi B, Fox R, Villedieu P, Fede P, Létisse F, Morchain J. A two-dimensional population balance model for cell growth including multiple uptake systems. Chem Eng Res Des 2018. [DOI: 10.1016/j.cherd.2018.02.025] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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11
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Chrysinas P, Kavousanakis ME, Boudouvis AG. Effect of cell heterogeneity on isogenic populations with the synthetic genetic toggle switch network: Bifurcation analysis of two-dimensional cell population balance models. Comput Chem Eng 2018. [DOI: 10.1016/j.compchemeng.2018.01.021] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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12
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A population balance model for bioreactors combining interdivision time distributions and micromixing concepts. Biochem Eng J 2017. [DOI: 10.1016/j.bej.2016.09.005] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
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13
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Farzan P, Ierapetritou MG. Integrated modeling to capture the interaction of physiology and fluid dynamics in biopharmaceutical bioreactors. Comput Chem Eng 2017. [DOI: 10.1016/j.compchemeng.2016.11.037] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
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14
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Review of the important challenges and opportunities related to modeling of mammalian cell bioreactors. AIChE J 2016. [DOI: 10.1002/aic.15442] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
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15
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Belete MK, Balázsi G. Optimality and adaptation of phenotypically switching cells in fluctuating environments. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062716. [PMID: 26764736 DOI: 10.1103/physreve.92.062716] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2015] [Indexed: 06/05/2023]
Abstract
Stochastic switching between alternative phenotypic states is a common cellular survival strategy during unforeseen environmental fluctuations. Cells can switch between different subpopulations that proliferate at different rates in different environments. Optimal population growth is typically assumed to occur when phenotypic switching rates match environmental switching rates. However, it is not well understood how this optimum behaves as a function of the growth rates of phenotypically different cells. In this study, we use mathematical and computational models to test how the actual parameters associated with optimal population growth differ from those assumed to be optimal. We find that the predicted optimum is practically always valid if the environmental durations are long. However, the regime of validity narrows as environmental durations shorten, especially if subpopulation growth rate differences differ from each other (are asymmetric) in two environments. Furthermore, we study the fate of mutants with switching rates previously predicted to be optimal. We find that mutants which match their phenotypic switching rates with the environmental ones can only sweep the population if the assumed optimum is valid, but not otherwise.
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Affiliation(s)
- Merzu Kebede Belete
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York, USA
- Department of Biomedical Engineering, Stony Brook University, Stony Brook, New York, USA
- Department of Physics, University of Houston, Houston, Texas, USA
| | - Gábor Balázsi
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York, USA
- Department of Biomedical Engineering, Stony Brook University, Stony Brook, New York, USA
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16
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Morales-Oyervides L, Oliveira J, Sousa-Gallagher M, Méndez-Zavala A, Montañez J. Quantitative assessment of the impact of the type of inoculum on the kinetics of cell growth, substrate consumption and pigment productivity by Penicillium purpurogenum GH2 in liquid culture with an integrated stochastic approach. FOOD AND BIOPRODUCTS PROCESSING 2015. [DOI: 10.1016/j.fbp.2015.08.004] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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17
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Aviziotis IG, Kavousanakis ME, Boudouvis AG. Effect of Intrinsic Noise on the Phenotype of Cell Populations Featuring Solution Multiplicity: An Artificial lac Operon Network Paradigm. PLoS One 2015; 10:e0132946. [PMID: 26185999 PMCID: PMC4506119 DOI: 10.1371/journal.pone.0132946] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2015] [Accepted: 06/21/2015] [Indexed: 11/19/2022] Open
Abstract
Heterogeneity in cell populations originates from two fundamentally different sources: the uneven distribution of intracellular content during cell division, and the stochastic fluctuations of regulatory molecules existing in small amounts. Discrete stochastic models can incorporate both sources of cell heterogeneity with sufficient accuracy in the description of an isogenic cell population; however, they lack efficiency when a systems level analysis is required, due to substantial computational requirements. In this work, we study the effect of cell heterogeneity in the behaviour of isogenic cell populations carrying the genetic network of lac operon, which exhibits solution multiplicity over a wide range of extracellular conditions. For such systems, the strategy of performing solely direct temporal solutions is a prohibitive task, since a large ensemble of initial states needs to be tested in order to drive the system--through long time simulations--to possible co-existing steady state solutions. We implement a multiscale computational framework, the so-called "equation-free" methodology, which enables the performance of numerical tasks, such as the computation of coarse steady state solutions and coarse bifurcation analysis. Dynamically stable and unstable solutions are computed and the effect of intrinsic noise on the range of bistability is efficiently investigated. The results are compared with the homogeneous model, which neglects all sources of heterogeneity, with the deterministic cell population balance model, as well as with a stochastic model neglecting the heterogeneity originating from intrinsic noise effects. We show that when the effect of intrinsic source of heterogeneity is intensified, the bistability range shifts towards higher extracellular inducer concentration values.
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Affiliation(s)
- Ioannis G. Aviziotis
- School of Chemical Engineering, National Technical University of Athens, Athens, Greece
| | | | - Andreas G. Boudouvis
- School of Chemical Engineering, National Technical University of Athens, Athens, Greece
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18
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Investigating the interactions between physical and biological heterogeneities in bioreactors using compartment, population balance and metabolic models. Chem Eng Sci 2015. [DOI: 10.1016/j.ces.2014.11.035] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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19
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Aviziotis IG, Kavousanakis ME, Bitsanis IA, Boudouvis AG. Coarse-grained analysis of stochastically simulated cell populations with a positive feedback genetic network architecture. J Math Biol 2014; 70:1457-84. [PMID: 24929336 DOI: 10.1007/s00285-014-0799-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2013] [Revised: 05/26/2014] [Indexed: 11/29/2022]
Abstract
Among the different computational approaches modelling the dynamics of isogenic cell populations, discrete stochastic models can describe with sufficient accuracy the evolution of small size populations. However, for a systematic and efficient study of their long-time behaviour over a wide range of parameter values, the performance of solely direct temporal simulations requires significantly high computational time. In addition, when the dynamics of the cell populations exhibit non-trivial bistable behaviour, such an analysis becomes a prohibitive task, since a large ensemble of initial states need to be tested for the quest of possibly co-existing steady state solutions. In this work, we study cell populations which carry the lac operon network exhibiting solution multiplicity over a wide range of extracellular conditions (inducer concentration). By adopting ideas from the so-called "equation-free" methodology, we perform systems-level analysis, which includes numerical tasks such as the computation of coarse steady state solutions, coarse bifurcation analysis, as well as coarse stability analysis. Dynamically stable and unstable macroscopic (population level) steady state solutions are computed by means of bifurcation analysis utilising short bursts of fine-scale simulations, and the range of bistability is determined for different sizes of cell populations. The results are compared with the deterministic cell population balance model, which is valid for large populations, and we demonstrate the increased effect of stochasticity in small size populations with asymmetric partitioning mechanisms.
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Affiliation(s)
- I G Aviziotis
- National Technical University of Athens, School of Chemical Engineering, 15780 , Athens, Greece,
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20
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Mathematical models for CFSE labelled lymphocyte dynamics: asymmetry and time-lag in division. J Math Biol 2013; 69:1547-83. [PMID: 24337680 DOI: 10.1007/s00285-013-0741-z] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2013] [Revised: 11/07/2013] [Indexed: 12/17/2022]
Abstract
Since their invention in 1994, fluorescent dyes such as carboxyfluorescein diacetate succinimidyl ester (CFSE) are used for cell proliferation analysis in flow cytometry. Importantly, the interpretation of such assays relies on the assumption that the label is divided equally between the daughter cells upon cell division. However, recent experimental studies indicate that division of cells is not perfectly symmetric and there is unequal distribution of protein between sister cell pairs. The uneven partition of protein or mass to daughter cells can lead to an overlap in the generations of CFSE-labelled cells with straightforward consequences for the resolution of individual generations. Numerous mathematical models developed so far for the analysis of CFSE proliferation assay incorporate the premise that the CFSE fluorescence intensity is halved in the two daughter cells. Here, we propose a novel modelling approach for the analysis of the CFSE cell proliferation assays which are characterized by poorly resolved peaks of cell generations in flow cytometric histograms. We formulate a mathematical model in the form of a system of delay hyperbolic partial differential equations which provides a good agreement with the CFSE histograms time-series data and allows an analytical treatment. The model is a further generalization of the recently proposed class of division- and label-structured models as it considers an asymmetric cell division. In addition, the basic structure of the cell cycle, i.e. the resting and cycling cell compartments, is taken into account. The model is used to estimate fundamental parameters such as activation rate, duration of the cell cycle, apoptosis rate, CFSE decay rate and asymmetry factor in cell division of monoclonal T cells during cognate interaction with dendritic cells.
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21
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Cell population balance and hybrid modeling of population dynamics for a single gene with feedback. Comput Chem Eng 2013. [DOI: 10.1016/j.compchemeng.2013.02.006] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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22
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Gonze D. Modeling the effect of cell division on genetic oscillators. J Theor Biol 2013; 325:22-33. [DOI: 10.1016/j.jtbi.2013.02.001] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2012] [Revised: 01/22/2013] [Accepted: 02/01/2013] [Indexed: 02/07/2023]
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23
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Chatzidoukas C, Penloglou G, Kiparissides C. Development of a structured dynamic model for the production of polyhydroxybutyrate (PHB) in Azohydromonas lata cultures. Biochem Eng J 2013. [DOI: 10.1016/j.bej.2012.11.015] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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24
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Discussion on research methods of bacterial resistant mutation mechanisms under selective culture--uncertainty analysis of data from the Luria-Delbrück fluctuation experiment. SCIENCE CHINA-LIFE SCIENCES 2012; 55:1007-21. [PMID: 23160830 DOI: 10.1007/s11427-012-4395-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2012] [Accepted: 10/09/2012] [Indexed: 10/27/2022]
Abstract
Whether bacterial drug-resistance is drug-induced or results from rapid propagation of random spontaneous mutations in the flora prior to exposure, remains a long-term key issue concerned and debated in both genetics and medicinal fields. In a pioneering study, Luria and Delbrück exposed E. coli to T1 phage, to investigate whether the number of resistant colonies followed the Poisson distribution. They deduced that the development of resistant colonies is independent of phage presence. Similar results have since been obtained on solid medium containing antibacterial agents. Luria and Delbrück's conclusions were long considered a gold standard for analyzing drug resistance mutations. More recently, the concept of adaptive mutation has triggered controversy over this approach. Microbiological observation shows that, following exposure to drugs of various concentrations, drug-resistant cells emerge and multiply depending on the time course, and show a process function, inconsistent with the definition of Poisson distribution (which assumes not only that resistance is independent of drug quantity but follows no specific time course). At the same time, since cells tend to aggregate after division rather than separating, colonies growing on drug plates arise from the multiplication of resistant bacteria cells of various initial population sizes. Thus, statistical analysis based on equivalence of initial populations will yield erroneous results. In this paper, 310 data from the Luria-Delbrück fluctuation experiment were reanalyzed from this perspective. In most cases, a high-end abnormal value, resulting from the non-synchronous variation of the two above-mentioned time variables, was observed. Therefore, the mean value cannot be regarded as an unbiased expectation estimate. The ratio between mean value and variance was similarly incomparable, because two different sampling methods were used. In fact, the Luria-Delbrück data appear to follow an aggregated, rather than Poisson distribution. In summary, the statistical analysis of Luria and Delbrück is insufficient to describe rules of resistant mutant development and multiplication. Correction of this historical misunderstanding will enable new insight into bacterial resistance mechanisms.
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Spetsieris K, Zygourakis K. Single-cell behavior and population heterogeneity: solving an inverse problem to compute the intrinsic physiological state functions. J Biotechnol 2012; 158:80-90. [PMID: 21930163 PMCID: PMC3432406 DOI: 10.1016/j.jbiotec.2011.08.018] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2011] [Revised: 07/31/2011] [Accepted: 08/10/2011] [Indexed: 11/16/2022]
Abstract
The dynamics of isogenic cell populations can be described by cell population balance models that account for phenotypic heterogeneity. To utilize the predictive power of these models, however, we must know the rates of single-cell reaction and division and the bivariate partition probability density function. These three intrinsic physiological state (IPS) functions can be obtained by solving an inverse problem that requires knowledge of the phenotypic distributions for the overall cell population, the dividing cell subpopulation and the newborn cell subpopulation. We present here a robust computational procedure that can accurately estimate the IPS functions for heterogeneous cell populations. A detailed parametric analysis shows how the accuracy of the inverse solution is affected by discretization parameters, the type of non-parametric estimators used, the qualitative characteristics of phenotypic distributions and the unknown partitioning probability density function. The effect of finite sampling and measurement errors on the accuracy of the recovered IPS functions is also assessed. Finally, we apply the procedure to estimate the IPS functions of an E. coli population carrying an IPTG-inducible genetic toggle network. This study completes the development of an integrated experimental and computational framework that can become a powerful tool for quantifying single-cell behavior using measurements from heterogeneous cell populations.
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Affiliation(s)
- Konstantinos Spetsieris
- Department of Chemical and Biomolecular Engineering, MS-362, Rice University, 6100 Main Street, Houston, TX 77005, USA
| | - Kyriacos Zygourakis
- Department of Chemical and Biomolecular Engineering, MS-362, Rice University, 6100 Main Street, Houston, TX 77005, USA
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Chauhan SS, Chiney A, Kumar S. On the solution of bivariate population balance equations for aggregation: X–discretization of space for expansion and contraction of computational domain. Chem Eng Sci 2012. [DOI: 10.1016/j.ces.2011.10.005] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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27
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MODELING OF GENE REGULATORY PROCESSES BY POPULATION MEDIATED SIGNALING. NEW APPLICATIONS OF POPULATION BALANCES. Chem Eng Sci 2011; 70:188-199. [PMID: 22581980 DOI: 10.1016/j.ces.2011.07.062] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Population balance modeling is considered for cell populations in gene regulatory processes in which one or more intracellular variables undergo stochastic dynamics as determined by Ito stochastic differential equations. This paper addresses formulation and computational issues with sample applications to the spread of drug resistance among bacterial cells. It is shown that predictions from population balances can display qualitative differences from those made with single cell models which are usually encountered in the literature. Such differences are deemed to be important.
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Stamatakis M, Zygourakis K. Deterministic and stochastic population-level simulations of an artificial lac operon genetic network. BMC Bioinformatics 2011; 12:301. [PMID: 21791088 PMCID: PMC3181209 DOI: 10.1186/1471-2105-12-301] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2011] [Accepted: 07/26/2011] [Indexed: 11/26/2022] Open
Abstract
BACKGROUND The lac operon genetic switch is considered as a paradigm of genetic regulation. This system has a positive feedback loop due to the LacY permease boosting its own production by the facilitated transport of inducer into the cell and the subsequent de-repression of the lac operon genes. Previously, we have investigated the effect of stochasticity in an artificial lac operon network at the single cell level by comparing corresponding deterministic and stochastic kinetic models. RESULTS This work focuses on the dynamics of cell populations by incorporating the above kinetic scheme into two Monte Carlo (MC) simulation frameworks. The first MC framework assumes stochastic reaction occurrence, accounts for stochastic DNA duplication, division and partitioning and tracks all daughter cells to obtain the statistics of the entire cell population. In order to better understand how stochastic effects shape cell population distributions, we develop a second framework that assumes deterministic reaction dynamics. By comparing the predictions of the two frameworks, we conclude that stochasticity can create or destroy bimodality, and may enhance phenotypic heterogeneity. CONCLUSIONS Our results show how various sources of stochasticity act in synergy with the positive feedback architecture, thereby shaping the behavior at the cell population level. Further, the insights obtained from the present study allow us to construct simpler and less computationally intensive models that can closely approximate the dynamics of heterogeneous cell populations.
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Affiliation(s)
- Michail Stamatakis
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, TX 77005, USA
| | - Kyriacos Zygourakis
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, TX 77005, USA
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Luni C, Doyle FJ, Elvassore N. Cell population modelling describes intrinsic heterogeneity: a case study for hematopoietic stem cells. IET Syst Biol 2011; 5:164-73. [PMID: 21639590 DOI: 10.1049/iet-syb.2009.0059] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022] Open
Abstract
The control of stem cell properties during in vitro expansion is of paramount importance for their clinical use. According to Food and Drug Administration (FDA) guidelines, phenotypic heterogeneity is a critical aspect influencing therapeutic response. Even if the authors ability to reduce heterogeneity were limited, the sources from which it arises should be well understood for safe clinical applications. The aim of this work was to describe theoretically the intrinsic cell population heterogeneity that is present even when cells are cultured in a perfectly homogeneous environment. A bivariate population balance model is developed to account for the heterogeneity in the number of receptors and receptor-ligand complexes per cell, and is coupled with a ligand conservation equation. As a case study, the model is applied to the hematopoietic stem cell expansion, considering the c-Kit receptor and stem cell factor pair. Results show the dependence of intrinsic heterogeneity from ligand concentration and the kinetics of its administration. By tracking the cell generations within the total population, the authors highlight intra- and an inter-generational contributions to total population heterogeneity. In terms of dimensionless variables, intrinsic heterogeneity is dependent on the ratio of the characteristic time of cell division to that needed by a newborn cell to reach its single-cell steady state. [Includes supplementary material].
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Affiliation(s)
- C Luni
- University of Padova, Dipartimento di Principi e Impianti di Ingegneria Chimica, Padova, Italy
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Mancuso L, Scanu M, Pisu M, Concas A, Cao G. Experimental analysis and modelling of in vitro HUVECs proliferation in the presence of various types of drugs. Cell Prolif 2010; 43:617-28. [PMID: 21040000 PMCID: PMC6496246 DOI: 10.1111/j.1365-2184.2010.00711.x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2010] [Accepted: 06/17/2010] [Indexed: 01/13/2023] Open
Abstract
OBJECTIVES This study focuses on experimental analysis and corresponding mathematical simulation of in vitro HUVECs (human umbilical vein endothelial cells) proliferation in the presence of various types of drugs. MATERIALS AND METHODS HUVECs, once seeded in Petri dishes, were expanded to confluence. Temporal profiles of total count obtained by classic haemocytometry and cell size distribution measured using an electronic Coulter counter, are quantitatively simulated by a suitable model based on the population balance approach. Influence of drugs on cell proliferation is also properly simulated by accounting for suitable kinetic equations. RESULTS AND DISCUSSION The models' parameters have been determined by comparison with experimental data related to cell population expansion and cell size distribution in the absence of drugs. Inhibition constant for each type of drug has been estimated by comparing the experimental data with model results concerning temporal profiles of total cell count. The reliability of the model and its predictive capability have been tested by simulating cell size distribution for experiments performed in the presence of drugs. The proposed model will be useful in interpreting effects of selected drugs on expansion of readily available human cells.
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Affiliation(s)
- L. Mancuso
- Department of Chemical Engineering and Materials, University of Cagliari, Research Unit of Consorzio Interuniversitario Nazionale “La Chimica per l’Ambiente”, Piazza d’Armi, Cagliari, Italy
| | - M. Scanu
- Department of Chemical Engineering and Materials, University of Cagliari, Research Unit of Consorzio Interuniversitario Nazionale “La Chimica per l’Ambiente”, Piazza d’Armi, Cagliari, Italy
| | - M. Pisu
- CRS4 (Center for Advanced Studies, Research and Development in Sardinia), Piscinamanna Site, Building 1, Pula, Cagliari, Italy
| | - A. Concas
- CRS4 (Center for Advanced Studies, Research and Development in Sardinia), Piscinamanna Site, Building 1, Pula, Cagliari, Italy
| | - G. Cao
- Department of Chemical Engineering and Materials, University of Cagliari, Research Unit of Consorzio Interuniversitario Nazionale “La Chimica per l’Ambiente”, Piazza d’Armi, Cagliari, Italy
- CRS4 (Center for Advanced Studies, Research and Development in Sardinia), Piscinamanna Site, Building 1, Pula, Cagliari, Italy
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31
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A mathematical and computational approach for integrating the major sources of cell population heterogeneity. J Theor Biol 2010; 266:41-61. [PMID: 20685607 DOI: 10.1016/j.jtbi.2010.06.002] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2009] [Revised: 04/08/2010] [Accepted: 06/01/2010] [Indexed: 11/20/2022]
Abstract
Several approaches have been used in the past to model heterogeneity in bacterial cell populations, with each approach focusing on different source(s) of heterogeneity. However, a holistic approach that integrates all the major sources into a comprehensive framework applicable to cell populations is still lacking. In this work we present the mathematical formulation of a cell population master equation (CPME) that describes cell population dynamics and takes into account the major sources of heterogeneity, namely stochasticity in reaction, DNA-duplication, and division, as well as the random partitioning of species contents into the two daughter cells. The formulation also takes into account cell growth and respects the discrete nature of the molecular contents and cell numbers. We further develop a Monte Carlo algorithm for the simulation of the stochastic processes considered here. To benchmark our new framework, we first use it to quantify the effect of each source of heterogeneity on the intrinsic and the extrinsic phenotypic variability for the well-known two-promoter system used experimentally by Elowitz et al. (2002). We finally apply our framework to a more complicated system and demonstrate how the interplay between noisy gene expression and growth inhibition due to protein accumulation at the single cell level can result in complex behavior at the cell population level. The generality of our framework makes it suitable for studying a vast array of artificial and natural genetic networks. Using our Monte Carlo algorithm, cell population distributions can be predicted for the genetic architecture of interest, thereby quantifying the effect of stochasticity in intracellular reactions or the variability in the rate of physiological processes such as growth and division. Such in silico experiments can give insight into the behavior of cell populations and reveal the major sources contributing to cell population heterogeneity.
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Mancuso L, Liuzzo MI, Fadda S, Pisu M, Cincotti A, Arras M, La Nasa G, Concas A, Cao G. In vitro ovine articular chondrocyte proliferation: experiments and modelling. Cell Prolif 2010; 43:310-20. [PMID: 20412130 DOI: 10.1111/j.1365-2184.2010.00676.x] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022] Open
Abstract
This study focuses on analysis of in vitro cultures of chondrocytes from ovine articular cartilage. Isolated cells were seeded in Petri dishes, then expanded to confluence and phenotypically characterized by flow cytometry. The sigmoidal temporal profile of total counts was obtained by classic haemocytometry and corresponding cell size distributions were measured electronically using a Coulter Counter. A mathematical model recently proposed (1) was adopted for quantitative interpretation of these experimental data. The model is based on a 1-D (that is, mass-structured), single-staged population balance approach capable of taking into account contact inhibition at confluence. The model's parameters were determined by fitting measured total cell counts and size distributions. Model reliability was verified by predicting cell proliferation counts and corresponding size distributions at culture times longer than those used when tuning the model's parameters. It was found that adoption of cell mass as the intrinsic characteristic of a growing chondrocyte population enables sigmoidal temporal profiles of total counts in the Petri dish, as well as cell size distributions at 'balanced growth', to be adequately predicted.
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Affiliation(s)
- L Mancuso
- Dipartimento di Ingegneria Chimica e Materiali, Università degli Studi di Cagliari, Cagliari, Italy
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33
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Stamatakis M. Cell population balance, ensemble and continuum modeling frameworks: Conditional equivalence and hybrid approaches. Chem Eng Sci 2010. [DOI: 10.1016/j.ces.2009.09.054] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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34
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Lowengrub JS, Frieboes HB, Jin F, Chuang YL, Li X, Macklin P, Wise SM, Cristini V. Nonlinear modelling of cancer: bridging the gap between cells and tumours. NONLINEARITY 2010; 23:R1-R9. [PMID: 20808719 PMCID: PMC2929802 DOI: 10.1088/0951-7715/23/1/r01] [Citation(s) in RCA: 224] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
Despite major scientific, medical and technological advances over the last few decades, a cure for cancer remains elusive. The disease initiation is complex, and including initiation and avascular growth, onset of hypoxia and acidosis due to accumulation of cells beyond normal physiological conditions, inducement of angiogenesis from the surrounding vasculature, tumour vascularization and further growth, and invasion of surrounding tissue and metastasis. Although the focus historically has been to study these events through experimental and clinical observations, mathematical modelling and simulation that enable analysis at multiple time and spatial scales have also complemented these efforts. Here, we provide an overview of this multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis. While we briefly review discrete modelling, our focus is on the continuum approach. We limit the scope further by considering models of tumour progression that do not distinguish tumour cells by their age. We also do not consider immune system interactions nor do we describe models of therapy. We do discuss hybrid-modelling frameworks, where the tumour tissue is modelled using both discrete (cell-scale) and continuum (tumour-scale) elements, thus connecting the micrometre to the centimetre tumour scale. We review recent examples that incorporate experimental data into model parameters. We show that recent mathematical modelling predicts that transport limitations of cell nutrients, oxygen and growth factors may result in cell death that leads to morphological instability, providing a mechanism for invasion via tumour fingering and fragmentation. These conditions induce selection pressure for cell survivability, and may lead to additional genetic mutations. Mathematical modelling further shows that parameters that control the tumour mass shape also control its ability to invade. Thus, tumour morphology may serve as a predictor of invasiveness and treatment prognosis.
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Affiliation(s)
- J S Lowengrub
- Department of Biomedical Engineering, Center for Mathematical and Computational Biology, University of California at Irvine, Irvine, CA 92697, USA
| | - H B Frieboes
- School of Health Information Sciences, University of Texas Health Science Center, Houston, TX 77030, USA
- Department of Mathematics, University of California at Irvine, Irvine, CA 92697, USA
| | - F Jin
- School of Health Information Sciences, University of Texas Health Science Center, Houston, TX 77030, USA
- Department of Mathematics, University of California at Irvine, Irvine, CA 92697, USA
| | - Y-L Chuang
- School of Health Information Sciences, University of Texas Health Science Center, Houston, TX 77030, USA
| | - X Li
- Department of Mathematics, University of California at Irvine, Irvine, CA 92697, USA
| | - P Macklin
- School of Health Information Sciences, University of Texas Health Science Center, Houston, TX 77030, USA
| | - S M Wise
- Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA
| | - V Cristini
- School of Health Information Sciences, University of Texas Health Science Center, Houston, TX 77030, USA
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35
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Abstract
Cell-to-cell variability of gene expression in clonal populations of mammalian cells is ubiquitous. However, because molecular biologists habitually assume uniformity of the cell populations that serve as starting material for experimental analysis, attention to such non-genetic heterogeneity has been scant. As awareness of, and interest in, understanding its biological significance increases, this Primer attempts to clarify the confusing terminologies used in an emerging field that often conflates heterogeneity with noise, and provides a qualitative introduction to the fundamental dynamic principles that underlie heterogeneity. It thus aims to present a useful conceptual framework to organize, analyze and communicate observations made at the resolution of individual cells that indicate that heterogeneity of cell populations plays a biological role, such as in multipotency and cell fate decision.
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Affiliation(s)
- Sui Huang
- Institute for Biocomplexity and Informatics, Biological Sciences Bldg, Room 539D, University of Calgary, Calgary, AB T3A 0Y1, Canada.
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36
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37
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Lee MW, Vassiliadis VS, Park JM. Individual-based and stochastic modeling of cell population dynamics considering substrate dependency. Biotechnol Bioeng 2009; 103:891-9. [PMID: 19365871 DOI: 10.1002/bit.22327] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
In this article, we propose an individual-based and stochastic modeling approach that is capable of describing the bacterial cell population dynamics during a batch culture. All stochastic nature inherent in intracellular molecular level reactions and cell division processes were considered in a single model framework by embedding a sub-model describing individual cell's growth kinetics in a discrete event simulation algorithm. The resultant unique feature of the model is that the effects of the stochasticities on the cell population dynamics can be investigated for different substrate-dependent cell growth kinetics. When Monod kinetics was used as the sub-model, the stochasticities only slightly affected the cell mass increase and substrate consumption profiles during the batch culture although they were still important in describing the changes of cell population distributions. When Andrews substrate inhibition kinetics was used, however, it was revealed that the overall cell population dynamics could be seriously influenced by the stochasticities. Under a critical initial substrate level, the cell population could proliferate against the substrate inhibition only when the stochasticities were considered.
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Affiliation(s)
- Min Woo Lee
- Department of Chemical Engineering, School of Environmental Science and Engineering, POSTECH, San 31, Hyoja-dong, Pohang, Kyungbuk 790-784, Korea
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38
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Mancuso L, Liuzzo MI, Fadda S, Pisu M, Cincotti A, Arras M, Desogus E, Piras F, Piga G, La Nasa G, Concas A, Cao G. Experimental analysis and modelling of in vitro proliferation of mesenchymal stem cells. Cell Prolif 2009; 42:602-16. [PMID: 19614674 DOI: 10.1111/j.1365-2184.2009.00626.x] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022] Open
Abstract
OBJECTIVES Stem cell therapies based on differentiation of adult or embryonic stem cells into specialized ones appear to be effective for treating several human diseases. This work addresses the mathematical simulation of proliferation kinetics of stem cells. MATERIALS AND METHODS Sheep bone marrow mesenchymal stem cells (phenotype characterized by flow cytometry analysis) seeded at different initial concentrations in Petri dishes were expanded to confluence. Sigmoid temporal profiles of total counts obtained through classic haemocytometry were quantitatively interpreted by both a phenomenological logistic equation and a novel model based on a one-dimensional, single-staged population balance approach capable of taking into account contact inhibition at confluence. The models' parameters were determined by comparison with experimental data on population expansion starting from single seeding concentration. Reliability of the models was tested by predicting cell proliferation carried out starting from different seeding concentrations. RESULTS AND DISCUSSION It was found that the proposed population balance modelling approach was successful in predicting the experimental data over the whole range of initial cell numbers investigated, while prediction capability of phenomenological logistic equation was more limited.
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Affiliation(s)
- L Mancuso
- Department of Chemical Engineering and Materials Science, University of Cagliari, Cagliari, Italy
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39
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Sherer E, Hannemann RE, Rundell AE, Ramkrishna D. Application of stochastic equations of population balances to sterilization processes. Chem Eng Sci 2009. [DOI: 10.1016/j.ces.2008.05.011] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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40
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Gilbert A, Srienc F. Optimized evolution in the cytostat: a Monte Carlo simulation. Biotechnol Bioeng 2008; 102:221-31. [PMID: 18781685 DOI: 10.1002/bit.22045] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Rational genetic alterations of a microorganism for a specific purpose are not possible in many situations where our knowledge of the relationship between phenotype and genotype is limited. In such cases evolutionary techniques must be applied. Evolutionary methods are usually time consuming; therefore, more efficient techniques are highly desirable. In this work we present the optimization of strain development in a cytostat. The time required for mutant strain isolation is dependent on the total cells present, the wild-type specific growth rate, the beneficial mutation probability, the mutant specific growth rate, and several bioreactor operating conditions. These parameters are highly related, and a theoretical model, as developed here, is needed to define the conditions that optimize the isolation. The model is based on a discrete, stochastic description of mutant formation and selection in the background of abundant wild-type cells. Using the model, we determined the optimal cytostat operating strategy for mutant isolation that varies according to the probability of beneficial mutations. It is also shown that mutants with as little as a 5% growth advantage can be isolated in less than 15 days which is significantly faster than in a chemostat. The described optimal mutant isolation procedure is expected to be particularly useful for the generation of industrial strains that are robust in challenging growth conditions.
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Affiliation(s)
- Alan Gilbert
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota, USA
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41
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Friedlander T, Brenner N. Cellular properties and population asymptotics in the population balance equation. PHYSICAL REVIEW LETTERS 2008; 101:018104. [PMID: 18764157 DOI: 10.1103/physrevlett.101.018104] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2007] [Indexed: 05/26/2023]
Abstract
Proliferating cell populations at steady-state growth often exhibit broad protein distributions with exponential tails. The sources of this variation and its universality are of much theoretical interest. Here we address the problem by asymptotic analysis of the population balance equation. We show that the steady-state distribution tail is determined by a combination of protein production and cell division and is insensitive to other model details. Under general conditions this tail is exponential with a dependence on parameters consistent with experiment. We discuss the conditions for this effect to be dominant over other sources of variation and the relation to experiments.
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Affiliation(s)
- Tamar Friedlander
- Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel
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42
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Affiliation(s)
- Eric Sherer
- School of Chemical Engineering Purdue University West Lafayette, Indiana 47907
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43
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Monine MI, Haugh JM. Cell population-based model of dermal wound invasion with heterogeneous intracellular signaling properties. Cell Adh Migr 2008; 2:137-46. [PMID: 19262100 DOI: 10.4161/cam.2.2.6511] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022] Open
Abstract
A deterministic model of dermal wound invasion, which accounts for the platelet-derived growth factor (PDGF) gradient sensing mechanism in fibroblasts mediated by cell surface receptors and the phosphoinositide 3-kinase (PI3K) signal transduction pathway, was previously described (Biophys J 2006; 90:2297-308). Here, we extend that work and implement a hybrid modeling strategy that treats fibroblasts as discrete entities endowed with heterogeneous properties, namely receptor, PI3K and 3' phosphoinositide phosphatase expression levels. Analysis of the model suggests that the wound environment fosters the advancement of cells within the population that are better fit to migrate and/or proliferate in response to PDGF stimulation. Thus, cell-to-cell variability results in a significantly higher rate of wound invasion as compared with the deterministic model, in a manner that depends on the way in which individual cell properties are sampled or inherited upon cell division.
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Affiliation(s)
- Michael I Monine
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, New Mexico, USA
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44
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Mantzaris NV. From single-cell genetic architecture to cell population dynamics: quantitatively decomposing the effects of different population heterogeneity sources for a genetic network with positive feedback architecture. Biophys J 2007; 92:4271-88. [PMID: 17384073 PMCID: PMC1877777 DOI: 10.1529/biophysj.106.100271] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2006] [Accepted: 02/15/2007] [Indexed: 11/18/2022] Open
Abstract
Phenotypic cell-to-cell variability or cell population heterogeneity originates from two fundamentally different sources: unequal partitioning of cellular material at cell division and stochastic fluctuations associated with intracellular reactions. We developed a mathematical and computational framework that can quantitatively isolate both heterogeneity sources and applied it to a genetic network with positive feedback architecture. The framework consists of three vastly different mathematical formulations: a), a continuum model, which completely neglects population heterogeneity; b), a deterministic cell population balance model, which accounts for population heterogeneity originating only from unequal partitioning at cell division; and c), a fully stochastic model accommodating both sources of population heterogeneity. The framework enables the quantitative decomposition of the effects of the different population heterogeneity sources on system behavior. Our results indicate the importance of cell population heterogeneity in accurately predicting even average population properties. Moreover, we find that unequal partitioning at cell division and sharp division rates shrink the region of the parameter space where the population exhibits bistable behavior, a characteristic feature of networks with positive feedback architecture. In addition, intrinsic noise at the single-cell level due to slow operator fluctuations and small numbers of molecules further contributes toward the shrinkage of the bistability regime at the cell population level. Finally, the effect of intrinsic noise at the cell population level was found to be markedly different than at the single-cell level, emphasizing the importance of simulating entire cell populations and not just individual cells to understand the complex interplay between single-cell genetic architecture and behavior at the cell population level.
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Affiliation(s)
- Nikos V Mantzaris
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA.
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45
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46
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Sherer E, Hannemann RE, Rundell A, Ramkrishna D. Estimation of likely cancer cure using first- and second-order product densities of population balance models. Ann Biomed Eng 2007; 35:903-15. [PMID: 17440813 DOI: 10.1007/s10439-007-9310-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2006] [Accepted: 03/30/2007] [Indexed: 10/23/2022]
Abstract
The objective of chemotherapy is to eradicate all cancerous cells. However, due to the stochastic behavior of cells, the elimination of all cancerous cells must be discussed probabilistically. We hypothesize, and demonstrate in the results, that the mean and standard deviation of a cancer cell population, derived through the probabilistic interpretation of population balance equations, are sufficient to estimate the likelihood of cancer eradication. Our analysis of a binary cell division model reveals that an expected cancer population that is six standard deviations less than one cell provides a good estimate for the treatment durations that nearly ensures treatment successes. This approximation is evaluated and tested on two other physiologically likely scenarios: variable patient response to chemotherapy and the presence of a dormant population. We find that early identification of individual patient susceptibility to the chemotherapeutic agent is extremely important to all patients as treatment adjustments for non-responders greatly enhances their likelihood of cure while responders need not be subjected to needlessly harsh treatments. Presence of a dormant population increases both the required treatment duration and population variability, but the same estimation method holds. This work is a step toward using stochastic models for a quantitative evaluation of chemotherapy.
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Affiliation(s)
- Eric Sherer
- School of Chemical Engineering, Forney Hall of Chemical Engineering, Purdue University, West Lafayette, IN 47907, USA
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