MOTIVATION: Biological functions are governed by gene regulatory networks (GRNs). Accurately inferring GRNs from high-dimensional and noisy single-cell data remains a major challenge in systems biology. Conventional approaches often struggle with robustness and interpretability, particularly when applied to complex biological processes such as cell fate decisions and complex diseases. RESULTS: In this study, we propose GGANO, a hybrid framework that integrates Gaussian Graphical Models for conditional independence learning with Neural Ordinary Differential Equations for dynamic modeling and inference. Benchmark analyzes show that GGANO achieves superior accuracy and stability compared to existing methods, particularly under high-noise conditions. Furthermore, GGANO enables the inference of stochastic dynamics from single-cell data. Applying GGANO to the EMT datasets, we uncover intermediate cellular states and key regulatory genes driving EMT progression. AVAILABILITY AND IMPLEMENTATION: The source code is available at GitHub: https://github.com/ChenFeng87/GGANO.

Understanding the ecological mechanisms associated with the collapse and restoration is especially critical in promoting harmonious coexistence between humans and nature. So far, it remains challenging to elucidate the mechanisms of stochastic dynamical transitions for ecological systems. Using an example of plant-pollinator network, we quantified the energy landscape of ecological system. The landscape displays multiple attractors characterizing the high, low and intermediate abundance stable states. Interestingly, we detected the intermediate states under pollinator decline, and demonstrated the indispensable role of the intermediate state in state transitions. From the landscape, we define the barrier height (BH) as a global quantity to evaluate the transition feasibility. We propose that the BH can serve as a new early-warning signal (EWS) for upcoming catastrophic breakdown, which provides an earlier and more accurate warning signal than traditional metrics based on time series. Our results promote developing better management strategies to achieve environmental sustainability.

Waddington's epigenetic landscape is a framework depicting the processes of cell differentiation and reprogramming under the control of a gene regulatory network (GRN). Traditional model-driven methods for landscape quantification focus on the Boolean network or differential equation-based models of GRN, which need sophisticated prior knowledge and hence hamper their practical applications. To resolve this problem, we combine data-driven methods for inferring GRNs from gene expression data with model-driven approach to the landscape mapping. Specifically, we build an end-to-end pipeline to link data-driven and model-driven methods and develop a software tool named TMELand for GRN inference, visualizing Waddington's epigenetic landscape, and calculating state transition paths between attractors to uncover the intrinsic mechanism of cellular transition dynamics. By integrating GRN inference from real transcriptomic data with landscape modeling, TMELand can facilitate studies of computational systems biology, such as predicting cellular states and visualizing the dynamical trends of cell fate determination and transition dynamics from single-cell transcriptomic data.

The dynamical properties of many complex physical and biological systems can be quantified from the energy landscape theory. Previous approaches focused on estimating the transition rate from landscape reconstruction based on data. However, for general non-equilibrium systems (such as gene regulatory systems), both the energy landscape and the probability flux are important to determine the transition rate between attractors. In this work, we proposed a data-driven approach to estimate non-equilibrium transition rate, which combines the kernel density estimation and non-equilibrium transition rate theory. Our approach shows superior performance in estimating transition rate from data, compared with previous methods, due to the introduction of a nonparametric density estimation method and the new saddle point by considering the effects of flux. We demonstrate the practical validity of our approach by applying it to a simplified cell fate decision model and a high-dimensional stem cell differentiation model. Our approach can be applied to other biological and physical systems.

Understanding the underlying dynamical mechanisms of the brain and controlling it is a crucial issue in brain science. The energy landscape and transition path approach provides a possible route to address these challenges. Here, taking working memory as an example, we quantified its landscape based on a large-scale macaque model. The working memory function is governed by the change of landscape and brain-wide state switching in response to the task demands. The kinetic transition path reveals that information flow follows the direction of hierarchical structure. Importantly, we propose a landscape control approach to manipulate brain state transition by modulating external stimulation or inter-areal connectivity, demonstrating the crucial roles of associative areas, especially prefrontal and parietal cortical areas in working memory performance. Our findings provide new insights into the dynamical mechanism of cognitive function, and the landscape control approach helps to develop therapeutic strategies for brain disorders.

Multistep cell fate transitions with stepwise changes of transcriptional profiles are common to many developmental, regenerative and pathological processes. The multiple intermediate cell lineage states can serve as differentiation checkpoints or branching points for channeling cells to more than one lineages. However, mechanisms underlying these transitions remain elusive. Here, we explored gene regulatory circuits that can generate multiple intermediate cellular states with stepwise modulations of transcription factors. With unbiased searching in the network topology space, we found a motif family containing a large set of networks can give rise to four attractors with the stepwise regulations of transcription factors, which limit the reversibility of three consecutive steps of the lineage transition. We found that there is an enrichment of these motifs in a transcriptional network controlling the early T cell development, and a mathematical model based on this network recapitulates multistep transitions in the early T cell lineage commitment. By calculating the energy landscape and minimum action paths for the T cell model, we quantified the stochastic dynamics of the critical factors in response to the differentiation signal with fluctuations. These results are in good agreement with experimental observations and they suggest the stable characteristics of the intermediate states in the T cell differentiation. These dynamical features may help to direct the cells to correct lineages during development. Our findings provide general design principles for multistep cell linage transitions and new insights into the early T cell development. The network motifs containing a large family of topologies can be useful for analyzing diverse biological systems with multistep transitions.

Cellular reprogramming has been recently intensively studied experimentally. We developed a global potential landscape and kinetic path framework to explore a human stem cell developmental network composed of 52 genes. We uncovered the underlying landscape for the stem cell network with two basins of attractions representing stem and differentiated cell states, quantified and exhibited the high dimensional biological paths for the differentiation and reprogramming process, connecting the stem cell state and differentiated cell state. Both the landscape and non-equilibrium curl flux determine the dynamics of cell differentiation jointly. Flux leads the kinetic paths to be deviated from the steepest descent gradient path, and the corresponding differentiation and reprogramming paths are irreversible. Quantification of paths allows us to find out how the differentiation and reprogramming occur and which important states they go through. We show the developmental process proceeds as moving from the stem cell basin of attraction to the differentiation basin of attraction. The landscape topography characterized by the barrier heights and transition rates quantitatively determine the global stability and kinetic speed of cell fate decision process for development. Through the global sensitivity analysis, we provided some specific predictions for the effects of key genes and regulation connections on the cellular differentiation or reprogramming process. Key links from sensitivity analysis and biological paths can be used to guide the differentiation designs or reprogramming tactics.