A maximum likelihood estimator for parameter distributions in heterogeneous cell populations

Hasenauer, Jan; Waldherr, Steffen; Radde, Nicole; Doszczak, Malgorzata; Scheurich, Peter; Allgöwer, Frank

doi:10.1016/j.procs.2010.04.185

Cited by 15 publications

(18 citation statements)

References 11 publications

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“…More generally, mechanistic models are obtained by assuming that biological systems are built up from actual or perceived components which are governed by physical laws (Fröhlich et al, 2017;Hasenauer, 2013;Pullen and Morris, 2014;White et al, 2016). It is a different strategy to empirical models which are reverse engineered from observations (Bronstein et al, 2015;Dattner, 2015;Geffen et al, 2008).…”

Section: Review Of Modeling Strategies For Brnsmentioning

confidence: 99%

“…Reduced stochastic description of BRN exploiting time scale separation is studied in (Thomas et al, 2012). If deterministic ODEs cannot be solved analytically, one can use Langevin and Fokker-Planck equations as stochastic diffusion approximations of CME (Schnoerr et al, 2017;Hasenauer, 2013). Fokker-Planck equation can be solved to obtain deterministic time evolution of system state distribution (Kügler, 2012;Liao et al, 2015a;Schnoerr et al, 2017).…”

Section: Modeling Brns By Differential Equationsmentioning

confidence: 99%

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Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

2019

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The key processes in biological and chemical systems are described by networks of chemical reactions. From molecular biology to biotechnology applications, computational models of reaction networks are used extensively to elucidate their non-linear dynamics. The model dynamics are crucially dependent on the parameter values which are often estimated from observations. Over the past decade, the interest in parameter and state estimation in models of (bio-) chemical reaction networks (BRNs) grew considerably. The related inference problems are also encountered in many other tasks including model calibration, discrimination, identifiability, and checking, and optimum experiment design, sensitivity analysis, and bifurcation analysis. The aim of this review paper is to examine the developments in literature to understand what BRN models are commonly used, and for what inference tasks and inference methods. The initial collection of about 700 documents concerning estimation problems in BRNs excluding books and textbooks in computational biology and chemistry were screened to select over 270 research papers and 20 graduate research theses. The paper selection was facilitated by text mining scripts to automate the search for relevant keywords and terms. The outcomes are presented in tables revealing the levels of interest in different inference tasks and methods for given models in the literature as well as the research trends are uncovered. Our findings indicate that many combinations of models, tasks and methods are still relatively unexplored, and there are many new research opportunities to explore combinations that have not been considered—perhaps for good reasons. The most common models of BRNs in literature involve differential equations, Markov processes, mass action kinetics, and state space representations whereas the most common tasks are the parameter inference and model identification. The most common methods in literature are Bayesian analysis, Monte Carlo sampling strategies, and model fitting to data using evolutionary algorithms. The new research problems which cannot be directly deduced from the text mining data are also discussed.

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Section: Review Of Modeling Strategies For Brnsmentioning

confidence: 99%

Section: Modeling Brns By Differential Equationsmentioning

confidence: 99%

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

2019

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“…As is often the case in inverse problems the problem here is about rearranging and putting together these different pieces of partial information to get the full information content. 3. This figure illustrates the problem that is at the core of our inverse problem: the reconstruction of an unknown density p 0 from its integrals along the sets (Ce At ) −1 (B y ) for different t ≥ 0 and B y ∈ B(R m ).…”

Section: A the Inverse Problemmentioning

confidence: 99%

“…From an applied point of view, the estimation of an initial distribution from the evolution of some distribution of output measurements has been considered by many research groups [5], [2], [3], [6]. Widely used and indeed natural seeming approaches are based on finding distributions that match the output snapshots best, i.e.…”

Section: Introductionmentioning

confidence: 99%

An inverse problem of tomographic type in population dynamics

Zeng

Waldherr

Allgöwer

2014

53rd IEEE Conference on Decision and Control

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In this paper we address an inverse problem on populations described by probability distributions. From a theoretical point of view, this problem can be seen as a natural extension to the classical observability problem. We consider a population that is described by a classical linear finite-dimensional system in which the initial state is a random vector subject to a non-parametric probability distribution. The problem is to reconstruct this initial state distribution from the time-evolution of the probability distribution of the output. We reveal as a novel viewpoint, that, at its core, this problem is a tomography problem which is a well-known subject in the field of inverse problems. Furthermore we show how this tomography problem is inherently linked with the observability properties of the finite-dimensional system thereby establishing a beautiful link between a control theoretic question and tomography problems. 53rd IEEE Conference on Decision and Control

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“…They cannot, however, be used alone to address the observed cell-to-cell variability because it is well known that the extrinsic component is, in general, the dominant source of variability [3,8]. In the context of parameter inference, extrinsic heterogeneity has only been included into differential equation models [21]. Therein, individual cells are modeled by reaction rate equations, and the parameters of which vary from cell to cell but are drawn from a common distribution.…”

Section: Introductionmentioning

confidence: 99%

Accounting for extrinsic variability in the estimation of stochastic rate constants

Koeppl

Zechner

Ganguly

et al. 2012

Intl J Robust & Nonlinear

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Single-cell recordings of transcriptional and post-transcriptional processes reveal the inherent stochasticity of cellular events. However, to a large extent, the observed variability in isogenic cell populations is due to extrinsic factors, such as difference in expression capacity, cell volume and cell cycle stage-to name a few. Thus, such experimental data represents a convolution of effects from stochastic kinetics and extrinsic noise sources. Recent parameter inference schemes for single-cell data just account for variability because of molecular noise. Here, we present a Bayesian inference scheme that deconvolutes the two sources of variability and enables us to obtain optimal estimates of stochastic rate constants of low copy-number events and extract statistical information about cell-to-cell variability. In contrast to previous attempts, we model extrinsic noise by a variability in the abundance of mass-conserved species, rather than a variability in kinetic parameters. We apply the scheme to a simple model of the osmostressinduced transcriptional activation in budding yeast. SUMMARYSingle-cell recordings of transcriptional and post-transcriptional processes reveal the inherent stochasticity of cellular events. However, to a large extent the observed variability in isogenic cell populations is due to extrinsic factors, such as difference in expression capacity, cell volume and cell cycle stage -to name a few. Thus, such experimental data represents a convolution of effects from stochastic kinetics and extrinsic noise sources. Recent parameter inference schemes for single-cell data just account for variability due to molecular noise. Here we present a Bayesian inference scheme which de-convolutes the two sources of variability and enables us to obtain optimal estimates of stochastic rate constants of low copy-number events and extract statistical information about cell-to-cell variability. In contrast to previous attempts, we model extrinsic noise by a variability in the abundance of mass-conserved species, rather than a variability in kinetic parameters. We apply the scheme to a simple model of the osmo-stress induced transcriptional activation in budding yeast.

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A maximum likelihood estimator for parameter distributions in heterogeneous cell populations

Cited by 15 publications

References 11 publications

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

An inverse problem of tomographic type in population dynamics

Accounting for extrinsic variability in the estimation of stochastic rate constants

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