A history-dependent approach for accurate initial condition estimation in epidemic models.

Mathematical modeling is a powerful tool for understanding and predicting complex dynamical systems, ranging from gene regulatory networks to population-level dynamics. However, model predictions are highly sensitive to initial conditions, which are often unknown. In infectious disease models, for instance, the initial number of exposed individuals (E) at the time the model simulation starts is frequently unknown.

Topological criterion for robust perfect adaptation of reaction fluxes in biological networks.

Robust Perfect Adaptation (RPA) is a mechanism adopted by living systems to maintain homeostasis amidst fluctuating environments. Previous studies on RPA of concentrations and fluxes (e.g.

Overcoming bias in estimating epidemiological parameters with realistic history-dependent disease spread dynamics.

Epidemiological parameters such as the reproduction number, latent period, and infectious period provide crucial information about the spread of infectious diseases and directly inform intervention strategies. These parameters have generally been estimated by mathematical models that involve an unrealistic assumption of history-independent dynamics for simplicity. This assumes that the chance of becoming infectious during the latent period or recovering during the infectious period remains constant, whereas in reality, these chances vary over time.

Density physics-informed neural networks reveal sources of cell heterogeneity in signal transduction.

The transduction time between signal initiation and final response provides valuable information on the underlying signaling pathway, including its speed and precision. Furthermore, multi-modality in a transduction-time distribution indicates that the response is regulated by multiple pathways with different transduction speeds. Here, we developed a method called density physics-informed neural networks (Density-PINNs) to infer the transduction-time distribution from measurable final stress response time traces.

Inferring delays in partially observed gene regulation processes.

Motivation: 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.

Modeling Incorporating the Severity-Reducing Long-term Immunity: Higher Viral Transmission Paradoxically Reduces Severe COVID-19 During Endemic Transition.

Natural infection with severe acute respiratory syndrome-coronavirus-2 or vaccination induces virus-specific immunity protecting hosts from infection and severe disease. While the infection-preventing immunity gradually declines, the severity-reducing immunity is relatively well preserved. Here, based on the different longevity of these distinct immunities, we develop a mathematical model to estimate courses of endemic transition of coronavirus disease 2019 (COVID-19).

Systematic inference identifies a major source of heterogeneity in cell signaling dynamics: The rate-limiting step number.

Identifying the sources of cell-to-cell variability in signaling dynamics is essential to understand drug response variability and develop effective therapeutics. However, it is challenging because not all signaling intermediate reactions can be experimentally measured simultaneously. This can be overcome by replacing them with a single random time delay, but the resulting process is non-Markovian, making it difficult to infer cell-to-cell heterogeneity in reaction rates and time delays.

Beyond the Michaelis-Menten: Bayesian Inference for Enzyme Kinetic Analysis.

Although the Michaelis-Menten (MM) rate law has been widely used to estimate enzyme kinetic parameters, it works only under the condition of extremely low enzyme concentration. Furthermore, even when this condition is satisfied, parameter estimation is often imprecise due to the parameter identifiability issue. To overcome these limitations of the canonical approach to enzyme kinetics, we developed a Bayesian approach based on a modified form of the MM rate law, which is derived with the total quasi-steady state approximation.

Universally valid reduction of multiscale stochastic biochemical systems using simple non-elementary propensities.

Biochemical systems consist of numerous elementary reactions governed by the law of mass action. However, experimentally characterizing all the elementary reactions is nearly impossible. Thus, over a century, their deterministic models that typically contain rapid reversible bindings have been simplified with non-elementary reaction functions (e.

Personalized sleep-wake patterns aligned with circadian rhythm relieve daytime sleepiness.

Shift workers and many other groups experience irregular sleep-wake patterns. This can induce excessive daytime sleepiness that decreases productivity and elevates the risk of accidents. However, the degree of daytime sleepiness is not correlated with standard sleep parameters like total sleep time, suggesting other factors are involved.

Hierarchical Bayesian models of transcriptional and translational regulation processes with delays.

Motivation: Simultaneous recordings of gene network dynamics across large populations have revealed that cell characteristics vary considerably even in clonal lines. Inferring the variability of parameters that determine gene dynamics is key to understanding cellular behavior. However, this is complicated by the fact that the outcomes and effects of many reactions are not observable directly.

Derivation of stationary distributions of biochemical reaction networks via structure transformation.

Long-term behaviors of biochemical reaction networks (BRNs) are described by steady states in deterministic models and stationary distributions in stochastic models. Unlike deterministic steady states, stationary distributions capturing inherent fluctuations of reactions are extremely difficult to derive analytically due to the curse of dimensionality. Here, we develop a method to derive analytic stationary distributions from deterministic steady states by transforming BRNs to have a special dynamic property, called complex balancing.