Michael Shelley

Suryanarayana Maddu, Victor Chardès, Michael J. Shelley

Cellular differentiation is governed by gene regulatory networks, the high-dimensional stochastic biochemical systems that determine the transcriptional landscape and mediate cellular responses to signals and perturbations. Although single-cell RNA sequencing provides quantitative snapshots of the transcriptome, current methods for inferring gene-regulatory dynamics often lack mechanistic interpretability and fail to generalize to unseen conditions. Here we introduce Probability Flow Matching (PFM), a scalable framework for learning biophysically consistent stochastic processes directly from time-resolved single-cell measurements. Applying PFM to three hematopoiesis datasets, we show that models with similar interpolation accuracy can encode fundamentally different dynamics, with only biophysically consistent formulations accurately capturing mechanisms of lineage transitions, fate specification, and gene perturbation responses. We further demonstrate that PFM accommodates unbalanced populations, enabling simultaneous inference of cellular proliferation and death dynamics. Together, these results establish PFM as a flexible, scalable framework for integrating mechanistic modeling with single-cell omics.

Victor Chardès, Suryanarayana Maddu, Michael J. Shelley

Inferring dynamical models from low-resolution temporal data continues to be a significant challenge in biophysics, especially within transcriptomics, where separating molecular programs from noise remains an important open problem. We explore a common scenario in which we have access to an adequate amount of cross-sectional samples at a few time-points, and assume that our samples are generated from a latent diffusion process. We propose an approach that relies on the probability flow associated with an underlying diffusion process to infer an autonomous, nonlinear force field interpolating between the distributions. Given a prior on the noise model, we employ score-matching to differentiate the force field from the intrinsic noise. Using relevant biophysical examples, we demonstrate that our approach can extract non-conservative forces from non-stationary data, that it learns equilibrium dynamics when applied to steady-state data, and that it can do so with both additive and multiplicative noise models.

Zijun Zhang, Adam R. Lamson, Michael Shelley et al.

Finely-tuned enzymatic pathways control cellular processes, and their dysregulation can lead to disease. Creating predictive and interpretable models for these pathways is challenging because of the complexity of the pathways and of the cellular and genomic contexts. Here we introduce Elektrum, a deep learning framework which addresses these challenges with data-driven and biophysically interpretable models for determining the kinetics of biochemical systems. First, it uses in vitro kinetic assays to rapidly hypothesize an ensemble of high-quality Kinetically Interpretable Neural Networks (KINNs) that predict reaction rates. It then employs a novel transfer learning step, where the KINNs are inserted as intermediary layers into deeper convolutional neural networks, fine-tuning the predictions for reaction-dependent in vivo outcomes. Elektrum makes effective use of the limited, but clean in vitro data and the complex, yet plentiful in vivo data that captures cellular context. We apply Elektrum to predict CRISPR-Cas9 off-target editing probabilities and demonstrate that Elektrum achieves state-of-the-art performance, regularizes neural network architectures, and maintains physical interpretability.

Wen Yan, Michael Shelley

An important but missing component in the application of the kernel independent fast multipole method (KIFMM) is the capability for flexibly and efficiently imposing singly, doubly, and triply periodic boundary conditions. In most popular packages such periodicities are imposed with the hierarchical repetition of periodic boxes, which may give an incorrect answer due to the conditional convergence of some kernel sums. Here we present an efficient method to properly impose periodic boundary conditions using a near-far splitting scheme. The near-field contribution is directly calculated with the KIFMM method, while the far-field contribution is calculated with a multipole-to-local (M2L) operator which is independent of the source and target point distribution. The M2L operator is constructed with the far-field portion of the kernel function to generate the far-field contribution with the downward equivalent source points in KIFMM. This method guarantees the sum of the near-field \& far-field converge pointwise to results satisfying periodicity and compatibility conditions. The computational cost of the far-field calculation observes the same $\mathcal{O}(N)$ complexity as FMM and is designed to be small by reusing the data computed by KIFMM for the near-field. The far-field calculations require no additional control parameters, and observes the same theoretical error bound as KIFMM. We present accuracy and timing test results for the Laplace kernel in singly periodic domains and the Stokes velocity kernel in doubly and triply periodic domains.