Analysis of heterogeneous cell populations: A density-based modeling and identification framework

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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“…It will be interesting to check this fundamental limitation in the reconstruction for existing optimization-based approaches [2], [4], [5], [6].…”

Section: Discussionmentioning

confidence: 99%

“…At this point let us note the immediate connection to our problem (4). We recognize that the output densities are nothing but some kind of Radon projections of the initial density along kerCe At .…”

Section: Solution Via Mathematical Tomographymentioning

confidence: 97%

An inverse problem of tomographic type in population dynamics

Zeng

Waldherr

Allgöwer

2014

53rd IEEE Conference on Decision and Control

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“…Such a formulation was used in [38] to model the dynamics of heterogeneous cell populations. In some cases, the growth processes of individuals may be driven by a much more complicated dynamical system such as one given by dX(t) = g(t, X(t); Z(t))dt + σ(t, X(t); Z(t))dW(t), X(0) = X 0 , where Z(t) is a stochastic process (with either discrete or continuous state space) which may be dependent on X(t).…”

Section: Discussionmentioning

confidence: 99%

Propagation of Growth Uncertainty in a Physiologically Structured Population

Banks

2012

Math. Model. Nat. Phenom.

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Abstract. In this review paper we consider physiologically structured population models that have been widely studied and employed in the literature to model the dynamics of a wide variety of populations. However in a number of cases these have been found inadequate to describe some phenomena arising in certain real-world applications such as dispersion in the structure variables due to growth uncertainty/variability. Prompted by this, we described two recent approaches that have been investigated in the literature to describe this growth uncertainty/variability in a physiologically structured population. One involves formulating growth as a Markov diffusion process while the other entails imposing a probabilistic structure on the set of possible growth rates across the entire population. Both approaches lead to physiologically structured population models with nontrivial dispersion. Even though these two approaches are conceptually quite different, they were found in [17] to have a close relationship: in some cases with properly chosen parameters and coefficient functions, the resulting stochastic processes have the same probability density function at each time.

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“…Given the probability of observing a single cell in the population with a level of fluorescence which is contained in the interval isFurthermore, as is a probability density, holds. For a more detailed introduction to probability densities we refer to [22]–[24]. The change of the population density contains all available informations about the response of the cell population.…”

Section: Methodsmentioning

confidence: 99%

Threshold-Free Population Analysis Identifies Larger DRG Neurons to Respond Stronger to NGF Stimulation

et al. 2012

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Sensory neurons in dorsal root ganglia (DRG) are highly heterogeneous in terms of cell size, protein expression, and signaling activity. To analyze their heterogeneity, threshold-based methods are commonly used, which often yield highly variable results due to the subjectivity of the individual investigator. In this work, we introduce a threshold-free analysis approach for sparse and highly heterogeneous datasets obtained from cultures of sensory neurons. This approach is based on population estimates and completely free of investigator-set parameters. With a quantitative automated microscope we measured the signaling state of single DRG neurons by immunofluorescently labeling phosphorylated, i.e., activated Erk1/2. The population density of sensory neurons with and without pain-sensitizing nerve growth factor (NGF) treatment was estimated using a kernel density estimator (KDE). By subtraction of both densities and integration of the positive part, a robust estimate for the size of the responsive subpopulations was obtained. To assure sufficiently large datasets, we determined the number of cells required for reliable estimates using a bootstrapping approach. The proposed methods were employed to analyze response kinetics and response amplitude of DRG neurons after NGF stimulation. We thereby determined the portion of NGF responsive cells on a true population basis. The analysis of the dose dependent NGF response unraveled a biphasic behavior, while the study of its time dependence showed a rapid response, which approached a steady state after less than five minutes. Analyzing two parameter correlations, we found that not only the number of responsive small-sized neurons exceeds the number of responsive large-sized neurons—which is commonly reported and could be explained by the excess of small-sized cells—but also the probability that small-sized cells respond to NGF is higher. In contrast, medium-sized and large-sized neurons showed a larger response amplitude in their mean Erk1/2 activity.

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Analysis of heterogeneous cell populations: A density-based modeling and identification framework

Cited by 31 publications

References 39 publications

An inverse problem of tomographic type in population dynamics

An inverse problem of tomographic type in population dynamics

Propagation of Growth Uncertainty in a Physiologically Structured Population

Threshold-Free Population Analysis Identifies Larger DRG Neurons to Respond Stronger to NGF Stimulation

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