The dynamic and thermodynamic origin of dissipative chaos: chemical Lorenz system

Global dynamics, thermodynamics and non-equilibrium origin of bifurcations for single neuron dynamics

The understanding of neural excitability and oscillations in single neuron dynamics remains incomplete in terms of global stabilities and the underlying mechanisms for phase formation and associated phase transitions. In this study, we investigate the mechanism of single neuron excitability and spontaneous oscillations by analyzing the potential landscape and curl flux. The topological features of the landscape play a crucial role in assessing the stability of resting states and the robustness/coherence of oscillations. We analyze the excitation characteristics in Class I and Class II neurons and establish their relation to biological function. Our findings reveal that the average curl flux and associated entropy production exhibit significant changes near bifurcation or phase transition points. Moreover, the curl flux and entropy production offer insights into the dynamical and thermodynamical origins of nonequilibrium phase transitions and exhibit distinct behaviors in Class I and Class II neurons. Additionally, we quantify time irreversibility through the difference in cross-correlation functions in both forward and backward time, providing potential indicators for the emergence of nonequilibrium phase transitions in single neurons.

Nonequilibrium indicator for the onset of epileptic seizure

The occurrence of spontaneous bursts of uncontrolled electrical activity between neurons can disrupt normal brain function and lead to epileptic seizures. Despite extensive research, the mechanisms underlying seizure onset remain unclear. This study investigates the onset of seizures from the perspective of nonequilibrium statistical physics. By analyzing the probability flux within the framework of the nonequilibrium potential-flux landscape, we establish a connection between seizure dynamics and nonequilibrium. Our findings demonstrate that the degree of nonequilibrium is sensitive to the onset of epileptic seizures. This result offers an alternative perspective on assessing seizure onset in epilepsy.

Perspectives on the landscape and flux theory for describing emergent behaviors of the biological systems

We give a review on the landscape theory of the equilibrium biological systems and landscape-flux theory of the nonequilibrium biological systems as the global driving force. The emergences of the behaviors, the associated thermodynamics in terms of the entropy and free energy and dynamics in terms of the rate and paths have been quantitatively demonstrated. The hierarchical organization structures have been discussed. The biological applications ranging from protein folding, biomolecular recognition, specificity, biomolecular evolution and design for equilibrium systems as well as cell cycle, differentiation and development, cancer, neural networks and brain function, and evolution for nonequilibrium systems, cross-scale studies of genome structural dynamics and experimental quantifications/verifications of the landscape and flux are illustrated. Together, this gives an overall global physical and quantitative picture in terms of the landscape and flux for the behaviors, dynamics and functions of biological systems.

The onset of dissipative chaos driven by nonequilibrium conditions

Dissipative chaos appears widely in various nonequilibrium systems; however, it is not clear how dissipative chaos originates from nonequilibrium. We discuss a framework based on the potential-flux approach to study chaos from the perspective of nonequilibrium dynamics. In this framework, chaotic systems possess a wide basin on the potential landscape, in which the rotational flux dominates the system dynamics, and chaos occurs with the appearance of this basin. In contrast, the probability flux is particularly associated with the detailed balance-breaking in nonequilibrium systems. This implies that the appearance of dissipative chaos is driven by nonequilibrium conditions.

Noise distorts the epigenetic landscape and shapes cell-fate decisions

The Waddington epigenetic landscape has become an iconic representation of the cellular differentiation process. Recent single-cell transcriptomic data provide new opportunities for quantifying this originally conceptual tool, offering insight into the gene regulatory networks underlying cellular development. While many methods for constructing the landscape have been proposed, by far the most commonly employed approach is based on computing the landscape as the negative logarithm of the steady-state probability distribution. Here, we use simple models to highlight the complexities and limitations that arise when reconstructing the potential landscape in the presence of stochastic fluctuations. We consider how the landscape changes in accordance with different stochastic systems and show that it is the subtle interplay between the deterministic and stochastic components of the system that ultimately shapes the landscape. We further discuss how the presence of noise has important implications for the identifiability of the regulatory dynamics from experimental data. A record of this paper's transparent peer review process is included in the supplemental information.