Systems biology informed deep learning for inferring parameters and hidden dynamics

Yazdani, Alireza; Lu, Lu; Raissi, Maziar; Karniadakis, George Em

doi:10.1101/865063

Cited by 45 publications

(64 citation statements)

References 33 publications

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“…In this final example, the performance of the proposed algorithms applied to a realistic problem in systems biology is investigated. To this end, a yeast glycolysis process is considered and described by a seven-dimensional dynamical system [1,52] as dS1dt=J0−k1S1A3[1+(A3KI)q]−1,dS2dt=2k1S1A3[1+(A3KI)q]−1−k2S2N1−k6S2N2,dS3dt=k2S2N1−k3S3A2,dS4dt=k3S3<...>…”

Section: Resultsmentioning

confidence: 99%

“…Such a task would involve physics-informed regularization on the unknown latent dynamics of the system. Approaches used in [52] could be helpful for solving this problem. A third open question is how to adapt the proposed method to stochastic dynamical systems where the dynamics itself may be driven by a stochastic process.…”

Section: Discussionmentioning

confidence: 99%

“…In this case, one can parametrize the unknown dynamical system using black-box function approximators such as deep neural networks [15,16,20], or aim to distil a more parsimonious and interpretable representation by constructing a comprehensive dictionary over all possible interactions and try to infer a predictive, yet minimal, model form [17,18,21]. The second class of problems contains cases where a model form for the underlying dynamics is prescribed by domain knowledge, but a number of unknown parameters need to be calibrated in order to accurately explain the observed data [31,52]. Finally, a third class of problems arises as a hybrid of the aforementioned settings, in which some parts of the model form may be known from domain knowledge, but there exists additional functional terms that need to be inferred [14].…”

Section: Methodsmentioning

confidence: 99%

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Bayesian differential programming for robust systems identification under uncertainty

2020

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This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling. This allows an efficient inference of the posterior distributions over plausible models with quantified uncertainty, while the use of sparsity-promoting priors enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed methods, including nonlinear oscillators, predator–prey systems and examples from systems biology. Taken together, our findings put forth a flexible and robust workflow for data-driven model discovery under uncertainty. All codes and data accompanying this article are available at https://bit.ly/34FOJMj .

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Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Bayesian differential programming for robust systems identification under uncertainty

2020

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“…Additionally, r trainable variables ψ 1 ,…, ψ r are included to represent ‘phase shifts’. Problem-specific temporal features, like the ones we consider, have been successfully employed in existing deep learning methods for ODE-based reaction network models (see, e.g., [38] and the references therein). Note that the mapping between time t and the temporal features is one-to-one and hence no information is lost by substituting time inputs with temporal features.…”

Section: Deepcme: Deep Learning Formulation For Cmementioning

confidence: 99%

DeepCME: A deep learning framework for solving the Chemical Master Equation

Gupta

Schwab

Khammash

2021

Preprint

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Stochastic models of biomolecular reaction networks are commonly employed in systems and synthetic biology to study the effects of stochastic fluctuations emanating from reactions involving species with low copy-numbers. For such models, the Kolmogorov's forward equation is called the chemical master equation (CME), and it is a fundamental system of linear ordinary differential equations (ODEs) that describes the evolution of the probability distribution of the random state-vector representing the copy-numbers of all the reacting species. The size of this system is given by the number of states that are accessible by the chemical system, and for most examples of interest this number is either very large or infinite. Moreover, approximations that reduce the size of the system by retaining only a finite number of important chemical states (e.g. those with non-negligible probability) result in high-dimensional ODE systems, even when the number of reacting species is small. Consequently, accurate numerical solution of the CME is very challenging, despite the linear nature of the underlying ODEs. One often resorts to estimating the solutions via computationally intensive stochastic simulations. The goal of the present paper is to develop a novel deep-learning approach for solving high-dimensional CMEs by reformulating the stochastic dynamics using Kolmogorov's backward equation. The proposed method leverages superior approximation properties of Deep Neural Networks (DNNs) and is algorithmically based on reinforcement learning. It only requires a moderate number of stochastic simulations (in comparison to typical simulation-based approaches) to train the "policy function". This allows not just the numerical approximation of the CME solution but also of its sensitivities to all the reaction network parameters (e.g. rate constants). We provide four examples to illustrate our methodology and provide several directions for future research.

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“…To this end, a first-principle based mechanistic model has been a preferred choice for modeling an intracellular signaling pathway. Specifically, a system of nonlinear ordinary differential equations (ODEs) is constructed based on the current knowledge about a system, where its differential equations are derived using kinetic laws such as mass-action and Michaelis-Menten kinetics [4][5][6]. Since a first-principle model represents the current understandings of a system, its ODEs are physically meaningful, and its predictions are valid over a wide range of conditions [7,8].…”

Section: Introductionmentioning

confidence: 99%

Development of a hybrid model for a partially known intracellular signaling pathway through correction term estimation and neural network modeling

2020

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Developing an accurate first-principle model is an important step in employing systems biology approaches to analyze an intracellular signaling pathway. However, an accurate first-principle model is difficult to be developed since it requires in-depth mechanistic understandings of the signaling pathway. Since underlying mechanisms such as the reaction network structure are not fully understood, significant discrepancy exists between predicted and actual signaling dynamics. Motivated by these considerations, this work proposes a hybrid modeling approach that combines a first-principle model and an artificial neural network (ANN) model so that predictions of the hybrid model surpass those of the original model. First, the proposed approach determines an optimal subset of model states whose dynamics should be corrected by the ANN by examining the correlation between each state and outputs through relative order. Second, an L2-regularized least-squares problem is solved to infer values of the correction terms that are necessary to minimize the discrepancy between the model predictions and available measurements. Third, an ANN is developed to generalize relationships between the values of the correction terms and the system dynamics. Lastly, the original first-principle model is coupled with the developed ANN to finalize the hybrid model development so that the model will possess generalized prediction capabilities while retaining the model interpretability. We have successfully validated the proposed methodology with two case studies, simplified apoptosis and lipopolysaccharide-induced NFκB signaling pathways, to develop hybrid models with in silico and in vitro measurements, respectively.

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Systems biology informed deep learning for inferring parameters and hidden dynamics

Cited by 45 publications

References 33 publications

Bayesian differential programming for robust systems identification under uncertainty

Bayesian differential programming for robust systems identification under uncertainty

DeepCME: A deep learning framework for solving the Chemical Master Equation

Development of a hybrid model for a partially known intracellular signaling pathway through correction term estimation and neural network modeling

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