Sparse Regression Based Structure Learning of Stochastic Reaction Networks from Single Cell Snapshot Time Series

Klimovskaia, Anna; Ganscha, Stefan; Claassen, Manfred

doi:10.1371/journal.pcbi.1005234

Cited by 23 publications

(27 citation statements)

References 41 publications

(60 reference statements)

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“…These hypotheses can be falsified using model selection criteria such as the Akaike Information Criterion (AIC) [30], or Bayesian Information Criterion (BIC) [31]. For large models, a high number of mutually non-exclusive hypotheses is not uncommon and typically leads to a combinatorial explosion of the number of model candidates (see, e.g., [32,33,34]). Computing the AIC or BIC for all model candidates for comparison would require parameter inference for each model candidate and may seem futile, given that parameter inference for a single model can already be challenging.…”

Section: Introductionmentioning

confidence: 99%

Scalable Inference of Ordinary Differential Equation Models of Biochemical Processes

Fröhlich

Loos

Hasenauer

2018

Methods in Molecular Biology

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Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about the behavior of latent variables or the process under new experimental conditions. Complementarily, inference of model structure can be used to identify the most plausible model structure from a set of candidates, and, thus, gain novel biological insight. Several toolboxes can infer model parameters and structure for small-to medium-scale mechanistic models out of the box. However, models for highly multiplexed datasets can require hundreds to thousands of state variables and parameters. For the analysis of such large-scale models, most algorithms require intractably high computation times. This chapter provides an overview of state-of-the-art methods for parameter and model inference, with an emphasis on scalability.

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Section: Introductionmentioning

confidence: 99%

Scalable Inference of Ordinary Differential Equation Models of Biochemical Processes

Fröhlich

Loos

Hasenauer

2018

Methods in Molecular Biology

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“…We now summarize some asymptotic properties of the function G ǫ in (32). Given ǫ > 0, recall that G ǫ (x) = ǫ ln 1 + e x/ǫ , for all x ∈ R , whose first and second derivatives are…”

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confidence: 99%

Learning Chemical Reaction Networks from Trajectory Data

Zhang¹,

Klus²,

Conrad³

et al. 2019

SIAM J. Appl. Dyn. Syst.

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We develop a data-driven method to learn chemical reaction networks from trajectory data. Modeling the reaction system as a continuous-time Markov chain and assuming the system is fully observed, our method learns the propensity functions of the system with predetermined basis functions by maximizing the likelihood function of the trajectory data under l 1 sparse regularization. We demonstrate our method with numerical examples using synthetic data and carry out an asymptotic analysis of the proposed learning procedure in the infinite-data limit.

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“…High-dimensional 2 single-cell molecularly resolved time series data is becoming a key data source for this task [1,2]. However, 3 these technologies are destructive, and consequently result in snapshot time series data originating from 4 batches of cells collected at time points of interest. A longstanding and still challenging problem is to 5 reconstruct dynamic biological processes from this data, to the end of identifying dynamically important 6 states, i.e.…”

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confidence: 99%

“…However, by 16 means of high-dimensional measurements, we typically observe larger systems comprising at least dozens of 17 components with largely a priori undefined interactions. This situation results in a combinatorial explosion 18 of model variants that cannot be exhaustively evaluated [4,5]. Alternative approaches are agnostic with 19 regards to parametric form and model structure and use a probabilistically-motivated rule to map between 20 distributions, e.g., one optimal transport method maps neighbours at one time point to the nearest neighbour 21 at the next time point [6].…”

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confidence: 99%

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Dynamic Distribution Decomposition for Single-Cell Snapshot Time Series Identifies Subpopulations and Trajectories during iPSC Reprogramming

Taylor-King

Riseth

Claassen

2018

Preprint

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Recent high-dimensional single-cell technologies such as mass cytometry are enabling time series experiments to monitor the temporal evolution of cell state distributions and to identify dynamically important cell states, such as fate decision states in differentiation. However, these technologies are destructive, and require analysis approaches that temporally map between cell state distributions across time points. Current approaches to approximate the single-cell time series as a dynamical system suffer from too restrictive assumptions about the type of kinetics, or link together pairs of sequential measurements in a discontinuous fashion.We propose Dynamic Distribution Decomposition (DDD), an operator approximation approach to infer a continuous distribution map between time points. On the basis of single-cell snapshot time series data, DDD approximates the continuous time Perron-Frobenius operator by means of a finite set of basis functions. This procedure can be interpreted as a continuous time Markov chain over a continuum of states. By only assuming a memoryless Markov (autonomous) process, the types of dynamics represented are more general than those represented by other common models, e.g., chemical reaction networks, stochastic differential equations. Additionally, the continuity assumption ensures that the same dynamical system maps between all time points, not arbitrarily changing at each time point. We demonstrate the ability of DDD to reconstruct dynamically important cell states and their transitions both on synthetic data, as well as on mass cytometry time series of iPSC reprogramming of a fibroblast system. We use DDD to find previously identified subpopulations of cells and to visualize differentiation trajectories.Dynamic Distribution Decomposition allows interpreting high-dimensional snapshot time series data as a low-dimensional Markov process, thereby enabling an interpretable dynamics analysis for a variety of biological processes by means of identifying their dynamically important cell states. Author summaryHigh-dimensional single-cell snapshot measurements are now increasingly utilized to study dynamic processes. Such measurements enable us to evaluate cell population distributions and their evolution over time. However, it is not trivial to map these distribution across time and to identify dynamically important cell states, i.e. bottleneck regions of state space exhibiting a high degree of change. We present Dynamic Distribution Decomposition (DDD) achieving this task by encoding single-cell measurements as linear combination of basis function distributions and evolving these as a linear system. We demonstrate reconstruction of dynamically important states for synthetic data of a bifurcated diffusion process and mass cytometry data for iPSC reprogramming.

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Sparse Regression Based Structure Learning of Stochastic Reaction Networks from Single Cell Snapshot Time Series

Cited by 23 publications

References 41 publications

Scalable Inference of Ordinary Differential Equation Models of Biochemical Processes

Scalable Inference of Ordinary Differential Equation Models of Biochemical Processes

Learning Chemical Reaction Networks from Trajectory Data

Dynamic Distribution Decomposition for Single-Cell Snapshot Time Series Identifies Subpopulations and Trajectories during iPSC Reprogramming

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