Inferring biological processes with intrinsic noise from cross-sectional data

Abstract: Inferring dynamical models from data continues to be a significant challenge in computational biology, especially given the stochastic nature of many biological processes. We explore a common scenario in omics, where statistically independent cross-sectional samples are available at a few time points, and the goal is to infer the underlying diffusion process that generated the data. Existing inference approaches often simplify or ignore noise intrinsic to the system, compromising accuracy for the sake of optimization ease. We circumvent this compromise by inferring the phase-space probability flow that shares the same time-dependent marginal distributions as the underlying stochastic process. Our approach, probability flow inference (PFI), disentangles force from intrinsic stochasticity while retaining the algorithmic ease of ODE inference. Analytically, we prove that for Ornstein-Uhlenbeck processes the regularized PFI formalism yields a unique solution in the limit of well-sampled distributions. In practical applications, we show that PFI enables accurate parameter and force estimation in high-dimensional stochastic reaction networks, and that it allows inference of cell differentiation dynamics with molecular noise, outperforming state-of-the-art approaches.

• The paper introduces the novel Probability Flow Inference (PFI) method to infer stochastic processes, providing unique solutions for Ornstein-Uhlenbeck models.
• It effectively separates deterministic forces from intrinsic noise while achieving lower reconstruction errors and superior precision-recall metrics in gene regulatory networks.
• The approach accurately predicts gene knockdown effects and cellular differentiation dynamics, offering a robust framework for analyzing high-dimensional omics data.

Inferring Biological Processes with Intrinsic Noise from Cross-Sectional Data

The paper presents a novel approach to infer dynamical models in computational biology by focusing on stochastic processes and the intrinsic noise inherent in many biological systems. Specifically, it addresses the challenge of inferring the underlying diffusion processes from cross-sectional data, a problem often encountered in omics studies where longitudinal data is not available.

The authors introduce the Probability Flow Inference (PFI) method, which aims to infer the phase-space probability flow that mirrors the stochastic process's time-dependent marginal distributions. This method effectively separates deterministic forces from intrinsic stochasticity while maintaining the computational efficiency associated with ODE optimization. A major contribution of this work is proving that the PFI framework provides a unique solution for Ornstein-Uhlenbeck processes under well-sampled conditions. This theoretical backing ensures that the regularized PFI can disentangle the force field and intrinsic noise even in high-dimensional settings.

In practical applications, the PFI method demonstrated superior performance in estimating parameters and forces within high-dimensional stochastic reaction networks. This capability was further highlighted through the accurate inference of cellular differentiation dynamics with molecular noise, surpassing state-of-the-art methodologies.

Key Numerical Results and Claims

The paper provides strong numerical evidence for the robustness of the PFI approach. It demonstrates that the method achieves lower reconstruction errors compared to existing models. For instance, in the context of gene regulatory networks, PFI exhibited enhanced precision-recall metrics, underscoring its superior capability in reconstructing complex biological interactions.

Another noteworthy claim is the PFI model's ability to predict the effects of gene knockdown perturbations with high accuracy, a critical factor in modeling cell differentiation dynamics. This indicates that PFI does not merely interpolate observed data but accurately captures underlying biological processes.

Theoretical and Practical Implications

Theoretically, the PFI framework offers a solution to the identifiability problems that have long plagued the analysis of stochastic biological processes. By leveraging a regularized approach, it ensures unique solutions and provides a systematic way to incorporate biophysical knowledge about intrinsic noise models into the inference process.

Practically, the implications are significant for computational biology. The ability to accurately infer stochastic processes from limited omics data opens new avenues for understanding gene regulatory networks and cellular differentiation. This could enhance the predictive power of models used in synthetic biology and personalized medicine.

Speculations on Future Developments in AI

Looking forward, the integration of PFI with machine learning frameworks could further augment the predictive capabilities and generalizability of biological models. As AI continues to evolve, the incorporation of advanced noise models and hybrid approaches combining deterministic and stochastic methods might lead to more comprehensive frameworks for simulating and predicting complex biological systems.

In summary, this paper offers a well-grounded and computationally feasible methodology for inferring biological processes characterized by intrinsic noise. The contributions could have lasting impacts on both the theoretical development and practical applications in the fields of computational biology and beyond.