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1. Inferring delays in partially observed gene regulation processes

   https://doi.org/10.1093/bioinformatics/btad670  

   Hong, Hyukpyo ; Cortez, Mark_Jayson ; Cheng, Yu-Yu ; Kim, Hang_Joon ; Choi, Boseung ; Josić, Krešimir ; Kim, Jae_Kyoung ; Martelli, ed., Pier_Luigi ( November 2023 , Bioinformatics)

   Cell function is regulated by gene regulatory networks (GRNs) defined by protein-mediated interaction between constituent genes. Despite advances in experimental techniques, we can still measure only a fraction of the processes that govern GRN dynamics. To infer the properties of GRNs using partial observation, unobserved sequential processes can be replaced with distributed time delays, yielding non-Markovian models. Inference methods based on the resulting model suffer from the curse of dimensionality.

   We develop a simulation-based Bayesian MCMC method employing an approximate likelihood for the efficient and accurate inference of GRN parameters when only some of their products are observed. We illustrate our approach using a two-step activation model: an activation signal leads to the accumulation of an unobserved regulatory protein, which triggers the expression of observed fluorescent proteins. With prior information about observed fluorescent protein synthesis, our method successfully infers the dynamics of the unobserved regulatory protein. We can estimate the delay and kinetic parameters characterizing target regulation including transcription, translation, and target searching of an unobserved protein from experimental measurements of the products of its target gene. Our method is scalable and can be used to analyze non-Markovian models with hidden components.

   Our code is implemented in R and is freely available with a simple example data at https://github.com/Mathbiomed/SimMCMC.

    

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2. A Variational Inference Approach to Single-Cell Gene Regulatory Network Inference using Probabilistic Matrix Factorization

   https://doi.org/10.1101/2022.09.09.507305  

   Mahmood, Omar ; Skok Gibbs, Claudia ; Bonneau, Richard ; Cho, Kyunghyun ( March 2023 , ICML 2023)

   Inferring gene regulatory networks (GRNs) from single-cell gene expression datasets is a challenging task. Existing methods are often designed heuristically for specific datasets and lack the flexibility to incorporate additional information or compare against other algorithms. Further, current GRN inference methods do not provide uncertainty estimates with respect to the interactions that they predict, making inferred networks challenging to interpret. To overcome these challenges, we introduce Probabilistic Matrix Factorization for Gene Regulatory Network inference (PMF-GRN). PMF-GRN uses single-cell gene expression data to learn latent factors representing transcription factor activity as well as regulatory relationships between transcription factors and their target genes. This approach incorporates available experimental evidence into prior distributions over latent factors and scales well to single-cell gene expression datasets. By utilizing variational inference, we facilitate hyperparameter search for principled model selection and direct comparison to other generative models. To assess the accuracy of our method, we evaluate PMF-GRN using the model organisms Saccharomyces cerevisiae and Bacillus subtilis, benchmarking against database-derived gold standard interactions. We discover that, on average, PMF-GRN infers GRNs more accurately than current state-of-the-art single-cell GRN inference methods. Moreover, our PMF-GRN approach offers well-calibrated uncertainty estimates, as it performs gene regulatory network (GRN) inference in a probabilistic setting. These estimates are valuable for validation purposes, particularly when validated interactions are limited or a gold standard is incomplete. 

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3. Generation of multicellular spatiotemporal models of population dynamics from ordinary differential equations, with applications in viral infection

   https://doi.org/10.1186/s12915-021-01115-z  

   Sego, T. J. ; Aponte-Serrano, Josua O. ; Gianlupi, Juliano F. ; Glazier, James A. ( September 2021 , BMC Biology)

   The biophysics of an organism span multiple scales from subcellular to organismal and include processes characterized by spatial properties, such as the diffusion of molecules, cell migration, and flow of intravenous fluids. Mathematical biology seeks to explain biophysical processes in mathematical terms at, and across, all relevant spatial and temporal scales, through the generation of representative models. While non-spatial, ordinary differential equation (ODE) models are often used and readily calibrated to experimental data, they do not explicitly represent the spatial and stochastic features of a biological system, limiting their insights and applications. However, spatial models describing biological systems with spatial information are mathematically complex and computationally expensive, which limits the ability to calibrate and deploy them and highlights the need for simpler methods able to model the spatial features of biological systems.

   In this work, we develop a formal method for deriving cell-based, spatial, multicellular models from ODE models of population dynamics in biological systems, and vice versa. We provide examples of generating spatiotemporal, multicellular models from ODE models of viral infection and immune response. In these models, the determinants of agreement of spatial and non-spatial models are the degree of spatial heterogeneity in viral production and rates of extracellular viral diffusion and decay. We show how ODE model parameters can implicitly represent spatial parameters, and cell-based spatial models can generate uncertain predictions through sensitivity to stochastic cellular events, which is not a feature of ODE models. Using our method, we can test ODE models in a multicellular, spatial context and translate information to and from non-spatial and spatial models, which help to employ spatiotemporal multicellular models using calibrated ODE model parameters. We additionally investigate objects and processes implicitly represented by ODE model terms and parameters and improve the reproducibility of spatial, stochastic models.

   We developed and demonstrate a method for generating spatiotemporal, multicellular models from non-spatial population dynamics models of multicellular systems. We envision employing our method to generate new ODE model terms from spatiotemporal and multicellular models, recast popular ODE models on a cellular basis, and generate better models for critical applications where spatial and stochastic features affect outcomes.

    

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4. PMF-GRN: a variational inference approach to single-cell gene regulatory network inference using probabilistic matrix factorization

   https://doi.org/10.1186/s13059-024-03226-6  

   Skok Gibbs, Claudia ; Mahmood, Omar ; Bonneau, Richard ; Cho, Kyunghyun ( April 2024 , Genome Biology)

   Inferring gene regulatory networks (GRNs) from single-cell data is challenging due to heuristic limitations. Existing methods also lack estimates of uncertainty. Here we present Probabilistic Matrix Factorization for Gene Regulatory Network Inference (PMF-GRN). Using single-cell expression data, PMF-GRN infers latent factors capturing transcription factor activity and regulatory relationships. Using variational inference allows hyperparameter search for principled model selection and direct comparison to other generative models. We extensively test and benchmark our method using real single-cell datasets and synthetic data. We show that PMF-GRN infers GRNs more accurately than current state-of-the-art single-cell GRN inference methods, offering well-calibrated uncertainty estimates.

    

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5. Generalizing Graph ODE for Learning Complex System Dynamics across Environments

   https://doi.org/10.1145/3580305.3599362  

   Huang, Zijie ; Sun, Yizhou ; Wang, Wei ( August 2023 , Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD ’23))

   Learning multi-agent system dynamics has been extensively studied for various real-world applications, such as molecular dynamics in biology, multi-body system in physics, and particle dynamics in material science. Most of the existing models are built to learn single system dynamics, which learn the dynamics from observed historical data and predict the future trajectory. In practice, however, we might observe multiple systems that are generated across different environments, which differ in latent exogenous factors such as temperature and gravity. One simple solution is to learn multiple environment-specific models, but it fails to exploit the potential commonalities among the dynamics across environments and offers poor prediction results where per-environment data is sparse or limited. Here, we present GG-ODE (Generalized Graph Ordinary Differential Equations), a machine learning framework for learning continuous multi-agent system dynamics across environments. Our model learns system dynamics using neural ordinary differential equations (ODE) parameterized by Graph Neural Networks (GNNs) to capture the continuous interaction among agents. We achieve the model generalization by assuming the dynamics across different environments are governed by common physics laws that can be captured via learning a shared ODE function. The distinct latent exogenous factors learned for each environment are incorporated into the ODE function to account for their differences. To improve model performance, we additionally design two regularization losses to (1) enforce the orthogonality between the learned initial states and exogenous factors via mutual information minimization; and (2) reduce the temporal variance of learned exogenous factors within the same system via contrastive learning. Experiments over various physical simulations show that our model can accurately predict system dynamics, especially in the long range, and can generalize well to new systems with few observations. 

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