Estimation methods for heterogeneous cell population models in systems biology

Waldherr, Steffen

doi:10.1098/rsif.2018.0530

Cited by 27 publications

(29 citation statements)

References 119 publications

(178 reference statements)

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“…In the IBPM framework, the dynamics of individual cells within a cell population are represented by the following ODE:

scriptM = ({, \begin{array}{l} {\dot{x}}^{(i)} (t) & = boldf (x^{(i)}, θ^{(i)}, u; t); x^{(i)} (0) = x_{0}^{(i)}, θ^{(i)} \sim p_{θ} (θ) \\ y^{(i)} (t) & = boldg (x^{(i)}, θ^{(i)}, u; t); \forall i = 1, \dots, M \end{array})

where

boldx \in ℝ^{n_{x}}

is the state vector,

bold-italicθ \in ℝ^{n_{θ}}

is the parameter vector, u is the external stimulus as an input to the system, x 0 is the initial conditions of x ,

p_{θ} ((), θ) : ℝ_{+}^{n_{θ}} \to ℝ_{+}

is the multivariate PDF of θ ,

boldy \in ℝ^{n_{y}}

is the output vector, M represents the number of cells, and the index i represents the i th cell in the population. In this study, x 0 is obtained by running Equation with u = 0 until the system reaches an equilibrium and setting the values of x 0 at the equilibrium.…”

Section: Methodsmentioning

confidence: 99%

“…Specifically, its goal is to select a subset of θ whose PDFs can be accurately estimated from the population snapshot data. For deterministic modeling approaches that utilize ODEs, this procedure is fairly well established with various methods proposed in the past . However, the identifiability of an IBPM has not been examined as thoroughly as that of a deterministic model.…”

Section: Methodsmentioning

confidence: 99%

“…However, advances in single‐cell measurement techniques have provided new perspectives such as cell‐to‐cell variability, which are not available from the population‐level measurements . For example, individual cells even in a genetically homogeneous cell‐population exhibit substantial cell‐to‐cell variability in response to an external stimulus, which is not easily observed through assays such as Western blots . Moreover, single‐cell studies also have uncovered that the activation of a signaling pathway in response to a stimulus is an analogue process at the population level (i.e., the dose of the stimulus determines the strength of the signaling pathway), while the activation at the single‐cell level is digital, where the stimulus dose has to exceed a certain threshold in order to activate the signaling pathway .…”

Section: Introductionmentioning

confidence: 99%

“…The extrinsic source of the cellular heterogeneity is often considered as a dominating factor of the heterogenity for many biological systems while the effects of intrinsic source can be transient . Therefore, as an alternative modeling framework, individual‐based population model (IBPM) has been proposed, which explicitly accounts for the extrinsic noise …”

Section: Introductionmentioning

confidence: 99%

“…For an IBPM, the nonidentifiability of PDFs of some model parameters arises due to limited quality and quantity of measurements as well as the model structure. Consequently, the PDFs of only a small subset of model parameters are identifiable, and these subsets may not necessarily overlap with the parameter subset selected based on the priori knowledge on the system itself …”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Identification of cell‐to‐cell heterogeneity through systems engineering approaches

Lee¹,

Jayaraman²,

Kwon³

2020

AIChE Journal

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Cells in a genetically homogeneous cell‐population exhibit a significant degree of heterogeneity in their responses to an external stimulus. To understand origins and importance of this heterogeneity, individual‐based population model (IBPM), where parameters follow probability density functions (PDFs) instead of being constants, has been previously developed. However, parameter identification for an IBPM is challenging as estimating PDFs is computationally expensive. Also, because of experimental limitations and nonlinearity of models, not all parameters' PDFs are identifiable. Motivated by the above considerations, a new methodology is proposed in this study. First, a subset of parameters whose PDFs is identifiable are determined through sensitivity analysis, and only these PDFs are estimated. Second, an artificial neural network model is developed to find an empirical relation between these parameter and output PDFs to reduce computational costs of the parameter identification. The proposed approach is validated by estimating PDFs of parameters of a tumor necrosis factor‐α signaling model.

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“…In the IBPM framework, the dynamics of individual cells within a cell population are represented by the following ODE: