Inference for Stochastic Chemical Kinetics Using Moment Equations and System Size Expansion

Fröhlich, Fabian; Thomas, Philipp; Kazeroonian, Atefeh; Theis, Fabian J.; Grima, Ramon; Hasenauer, Jan

doi:10.1371/journal.pcbi.1005030

Cited by 85 publications

(106 citation statements)

References 93 publications

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“…The growth data from the initial conditions of N0=2, 4, & 10 were combined and fit to each of the seven candidate models using the moment closure approximation workflow described (Fig 3) (38). The BIC values for each model fit were computed and compared to the minimum BIC value ( Figure 8A) and the corresponding BIC weights were calculated ( Figure 8B) based on the goodness of fit and the complexity of the model (number of parameters) ( Figure 8C).…”

Section: Fit Of Low Seeding Density Data To All Stochastic Models Revmentioning

confidence: 99%

“…The profile likelihoods used to determine the 95% confidence intervals of the best fitting parameters of b = 0.0101[0.010068, 0.010181], d = 4.3613 x10 -5 [-7.27 x10 -5 , 1.599 x10 -4 ], A = -3.1576[-3.8593, -2.4559], and t = 7.480 [6.8871, 9.0393] are displayed in Figure 9C, D, E, & F. The discrepancy from the model mean and variance compared to the data is likely because an unbiased approach (as in (38)) was used to fit both the model mean and variance equally, using the likelihood function described in Eq. 30.…”

Section: Fit Of Low Seeding Density Data To All Stochastic Models Revmentioning

confidence: 99%

“…To account for the inherent stochasticity in population size revealed at very small population sizes, we develop seven stochastic models whose average behavior follows one of the deterministic models, with each stochastic model representing a different hypothesis of the mechanism underlying the growth kinetics. For each stochastic model, we perform a parameter estimation using the method of moments (25) and use model selection to identify the model most likely to describe the growth data (38). This is performed for both a simulated data set and the in vitro BT-474 data to test the hypotheses that our framework reveals an alternative tumor growth model that includes an Allee effect.…”

Section: Introductionmentioning

confidence: 99%

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Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect

Johnson

Howard

et al. 2019

Preprint

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Models of cancer cell population expansion assume exponential growth kinetics at low cell densities, with deviations from exponential growth only at higher densities due to limited resources such as space and nutrients. However, recent pre-clinical and clinical observations of tumor initiation or recurrence indicate the presence of tumor growth kinetics in which growth rates scale with cell numbers. These observations are analogous to the cooperative behavior of species in an ecosystem described by the ecological principle of the Allee effect. In preclinical and clinical models however, tumor growth data is limited by the lower limit of detection (i.e. a measurable lesion) and confounding variables, such as tumor microenvironment and immune responses may cause and mask deviations from exponential growth models. In this work, we present alternative growth models to investigate the presence of an Allee effect in cancer cells seeded at low cell densities in a controlled in vitro setting. We propose a stochastic modeling framework to consider the small number of cells in this low-density regime and use the moment approach for stochastic parameter estimation to calibrate the stochastic growth trajectories. We validate the framework on simulated data and apply this approach to longitudinal cell proliferation data of BT-474 luminal B breast cancer cells. We find that cell population growth kinetics are best described by a model structure that considers the Allee effect, in that the birth rate of tumor cells depends on cell number. This indicates a potentially critical role of cooperative behavior among tumor cells at low cell densities with relevance to early stage growth patterns of emerging tumors and relapse. Author SummaryThe growth kinetics of cancer cells at very low cell densities are of utmost clinical importance as the ability of a small number of newly transformed or surviving cells to grow exponentially and thus, to "take off" underlies tumor formation and relapse after treatment. Mathematical models of stochastic tumor cell growth typically assume a stochastic birth-death process of cells impacted by limited nutrients and space when cells reach high density, resulting in the widely accepted logistic growth model. Here we present an in-depth investigation of alternate growth models adopted from ecology to describe potential deviations from a simple cell autonomous birth-death model at low cell densities. We show that our stochastic modeling framework is robust and can be used to identify the underlying structure of stochastic growth trajectories from both simulated and experimental data taken from a controlled in vitro setting in which we can capture data from the relevant low cell density regime. This work suggests that the assumption of cell autonomous proliferation via a constant exponential growth rate at low cell densities may not be appropriate for all cancer cell growth dynamics. Consideration of cooperative behavior amongst tumor cells in this regime is critical for elucidating strategies for controll...

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Section: Fit Of Low Seeding Density Data To All Stochastic Models Revmentioning

confidence: 99%

Section: Fit Of Low Seeding Density Data To All Stochastic Models Revmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect

Johnson

Howard

et al. 2019

Preprint

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“…Stochastic perturbations of particular nodes in the network by e.g. small molecules can also enhance identifyability of network topologies and rate constants [8,23,24,25,26,27]. Figure 1: Experimental setup for input control and output measurement: Cells cultured in a microfluidic device can be stimulated dynamically with a noisy input signal provided by the universal chemical signal generator [16].…”

Section: Introductionmentioning

confidence: 99%

Noisy Perturbation Models Distinguish Network Specific from Embedding Variability

Piehler

2019

Preprint

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Recently, measurement technologies allowing to determine the abundance of tens signaling proteins in thousands of single cells became available. The interpretation of this high dimensional end-point time course data is often difficult, because sources of cell-to-cell abundance variation in measured species are hard to determine. Here I present an analytic tool to tackle this problem. By using a recently developed chemical signal generator to manipulate input noise of biochemical networks, measurement of state variables and modeling of input noise propagation, pathway-specific variability can be distinguished from environmental variability caused by network embedding. By employing different sources of natural input noise, changes in the output variability of the apoptosis pathway were measured, indicating that also synthetic noisy perturbations are biologically feasible. The presented analytic tool shows how signal generators can improve our understanding of the origin of cellular variability and help to interpret multiplexed single cell information.

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“…1–3 A main objective of systems biology is to characterize the topology and strength of interactions in signaling networks, thereby identifying the molecular basis for the observed phenotype. 4–6 Ultimately these parameters determine how cells process information and make decisions in response to stimuli. 7 For quantitative characterization measuring the response of a signaling network to a defined temporally changing chemical concentration input is essential.…”

Section: Introductionmentioning

confidence: 99%

Universal signal generator for dynamic cell stimulation

et al. 2017

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Dynamic cell stimulation is a powerful technique for probing gene networks and for applications in stem cell differentiation, immunomodulation and signaling. We developed a robust and flexible method and associated microfluidic devices to generate a wide-range of precisely formulated dynamic chemical signals to stimulate live cells and measure their dynamic response. This signal generator is capable of digital to analog conversion (DAC) through combinatoric selection of discrete input concentrations, and outperforms existing methods by both achievable resolution, dynamic range and simplicity in design. It requires no calibration, has minimal space requirements and can be easily integrated into microfluidic cell culture devices. The signal generator hardware and software we developed allows to choose the waveform, period and amplitude of chemical input signals and features addition of well-defined chemical noise to study the role of stochasticity in cellular information processing.

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Inference for Stochastic Chemical Kinetics Using Moment Equations and System Size Expansion

Cited by 85 publications

References 93 publications

Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect

Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect

Noisy Perturbation Models Distinguish Network Specific from Embedding Variability

Universal signal generator for dynamic cell stimulation

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