Heterogeneous stochastic bifurcations explain intrinsic oscillatory patterns in entorhinal cortical stellate cells.

Stellate cells (SC) in the medial entorhinal cortex manifest intrinsic membrane potential oscillatory patterns. Although different theoretical frameworks have been proposed to explain these patterns, a robust unifying framework that jointly accounts for intrinsic heterogeneities and stochasticity is missing. Here, we first performed in vitro patch-clamp electrophysiological recordings from rat SCs and found pronounced cell-to-cell variability in their characteristic physiological properties, including peri-threshold oscillatory patterns. We demonstrate that noise introduced into two independent populations (endowed with deterministic or stochastic ion-channel gating kinetics) of heterogeneous biophysical models yielded activity patterns that were qualitatively similar to electrophysiological peri-threshold oscillatory activity in SCs. We developed spectrogram-based quantitative metrics for the identification of valid oscillations and confirmed that these metrics reliably captured the variable-amplitude and arhythmic oscillatory patterns observed in electrophysiological recordings. Using these quantitative metrics, we validated activity patterns from both heterogeneous populations of SC models, with each model assessed with multiple trials of different levels of noise at distinct membrane depolarizations. Our analyses unveiled the manifestation of stochastic resonance (detection of the highest number of valid oscillatory traces at an optimal level of noise) in both heterogeneous populations of SC models. Finally, we show that a generalized network motif comprised of a slow negative feedback loop amplified by a fast positive feedback loop manifested stochastic bifurcations and stochastic resonance in the emergence of oscillations. Together, through a unique convergence of the degeneracy and stochastic resonance frameworks, our unifying framework centered on heterogeneous stochastic bifurcations argues for state-dependent emergence of SC oscillations.

Altered neuronal excitability in a Hodgkin-Huxley model incorporating channelopathies of the delayed rectifier potassium channel.

Channelopathies involving acquired or genetic modifications of the delayed rectifier K+ channel Kv1.1 include phenotypes characterized by enhanced neuronal excitability. Affected Kv1.1 channels exhibit combinations of altered expression, voltage sensitivity, and rates of activation and deactivation. Computational modeling and analysis can reveal the potential of particular channelopathies to alter neuronal excitability. A dynamical systems approach was taken to study the excitability and underlying dynamical structure of the Hodgkin-Huxley (HH) model of neural excitation as properties of the delayed rectifier K+ channel were altered. Bifurcation patterns of the HH model were determined as the amplitude of steady injection current was varied simultaneously with single parameters describing the delayed rectifier rates of activation and deactivation, maximal conductance, and voltage sensitivity. Relatively modest changes in the properties of the delayed rectifier K+ channel analogous to what is described for its channelopathies alter the bifurcation structure of the HH model and profoundly modify excitability of the HH model. Channelopathies associated with Kv1.1 can reduce the threshold for onset of neural activity. These studies also demonstrate how pathological delayed rectifier K+ channels could lead to the observation of the generalized Hopf bifurcation and, perhaps, other variants of the Hopf bifurcation. The observed bifurcation patterns collectively demonstrate that properties of the nominal delayed rectifier in the HH model appear optimized to permit activation of the HH model over the broadest possible range of input currents.

Quantifying Information without Entropy: Identifying Intermittent Disturbances in Dynamical Systems.

A system's response to disturbances in an internal or external driving signal can be characterized as performing an implicit computation, where the dynamics of the system are a manifestation of its new state holding some memory about those disturbances. Identifying small disturbances in the response signal requires detailed information about the dynamics of the inputs, which can be challenging. This paper presents a new method called the Information Impulse Function (IIF) for detecting and time-localizing small disturbances in system response data. The novelty of IIF is its ability to measure relative information content without using Boltzmann's equation by modeling signal transmission as a series of dissipative steps. Since a detailed expression of the informational structure in the signal is achieved with IIF, it is ideal for detecting disturbances in the response signal, i.e., the system dynamics. Those findings are based on numerical studies of the topological structure of the dynamics of a nonlinear system due to perturbated driving signals. The IIF is compared to both the Permutation entropy and Shannon entropy to demonstrate its entropy-like relationship with system state and its degree of sensitivity to perturbations in a driving signal.

Impulsive control of a nonlinear dynamical network and its application to biological networks.

The control of nonlinear dynamical systems is always a notable problem in science. According to control theory, suitable inputs for a controllable dynamical system are critical. Previous studies have shown some principles to determine control nodes and design control function. In this work, we propose a new control strategy of nonlinear systems by constructing impulsive control functions, i.e., we can realize the transition from an undesired state to a desired one by controlling appropriately chosen nodes in a discrete manner. In order to demonstrate the effectiveness of the strategy, we apply it to two biological networks: the epithelial-mesenchymal transition (EMT) network and the Notch1-Dll1-Jag1 signaling pathway. The strategy can not only be used to guide pharmacological design in a more feasible form but can also be applied into the fields of biological, medical and other multistable dynamical systems.

Sensitivity analysis and parameter identification of nonlinear hybrid systems for glycerol transport mechanisms in continuous culture.

In this paper, we establish a modified fourteen-dimensional nonlinear hybrid dynamic system with genetic regulation to describe the microbial continuous culture, in which we consider that there are three possible ways for glycerol to pass the cell's membrane and one way for 1,3-PD (passive diffusion and active transport). Then we discuss the existence, uniqueness, continuous dependence of solutions and the compactness of the solution set. We construct a global sensitivity analysis approach to reduce the number of kinetic parameters. In order to infer the most reasonable transport mechanism of glycerol, we propose a parameter identification model aiming at identifying the parameter with higher sensitivity and transport of glycerol, which takes the robustness index of the intracellular substance together with the relative error between the experimental data and the computational values of the extracellular substance as a performance index. Finally, a parallel algorithm is applied to find the optimal transport of glycerol and parameters.

Existence of reservoir with finite-dimensional output for universal reservoir computing.

In this paper, we prove the existence of a reservoir that has a finite-dimensional output and makes the reservoir computing model universal. Reservoir computing is a method for dynamical system approximation that trains the static part of a model but fixes the dynamical part called the reservoir. Hence, reservoir computing has the advantage of training models with a low computational cost. Moreover, fixed reservoirs can be implemented as physical systems. Such reservoirs have attracted attention in terms of computation speed and energy consumption. The universality of a reservoir computing model is its ability to approximate an arbitrary system with arbitrary accuracy. Two sufficient reservoir conditions to make the model universal have been proposed. The first is the combination of fading memory and the separation property. The second is the neighborhood separation property, which we proposed recently. To date, it has been unknown whether a reservoir with a finite-dimensional output can satisfy these conditions. In this study, we prove that no reservoir with a finite-dimensional output satisfies the former condition. By contrast, we propose a single output reservoir that satisfies the latter condition. This implies that, for any dimension, a reservoir making the model universal exists with the output of that specified dimension. These results clarify the practical importance of our proposed conditions.

Fast or stable: Research on dynamic behaviors of duopoly automakers under the background of energy transformation in the automobile industry.

New energy vehicles (NEVs) are crucial way to solving environmental and energy dilemmas. However, the transition from traditional energy vehicles (TEVs) to NEVs is extremely intricate. If the process for TEVs switching to NEVs falls into out order, the automobile industry will be shaken. This paper takes electric vehicles (EVs), representing NEVs, and internal combustion engine vehicles (ICEVs), representing TEVs, as research objects, and constructs a dynamic Gounod duopoly model for the production decisions of two oligopolistic automakers under the dual credit policy. Combining the nonlinear dynamic theory and Cournot game, the influence of policy, market, technology, and cost on the stability of duopoly automakers' dynamic production game equilibrium and the nonlinear evolution characteristics of Cournot-Nash equilibrium are analyzed systematically. Results show that: (1) In the transition from ICEVs to EVs, if the speed of production adjustment is too fast, the automobile system would trap into chaos and shakeouts, and the social welfare would show volatility. (2) The revised dual credit policy increases the credit ratio and decreases the credit coefficient which enhances the stability of automobile system. This revision may accelerate the transformation from ICEVs to EVs in the automobile industry. Especially, the credit coefficient plays a more significant role. (3) The consumer acceptance for vehicle prices and the range of EV are positively correlated with the production of EVs and the social welfare, and negatively correlated with the production of ICEVs. Nevertheless, the cost of the two types of vehicle had the opposite effect compared price acceptance and range of EVs.

Bifurcations and Proarrhythmic Behaviors in Cardiac Electrical Excitations.

The heart is a hierarchical dynamic system consisting of molecules, cells, and tissues, and acts as a pump for blood circulation. The pumping function depends critically on the preceding electrical activity, and disturbances in the pattern of excitation propagation lead to cardiac arrhythmia and pump failure. Excitation phenomena in cardiomyocytes have been modeled as a nonlinear dynamical system. Because of the nonlinearity of excitation phenomena, the system dynamics could be complex, and various analyses have been performed to understand the complex dynamics. Understanding the mechanisms underlying proarrhythmic responses in the heart is crucial for developing new ways to prevent and control cardiac arrhythmias and resulting contractile dysfunction. When the heart changes to a pathological state over time, the action potential (AP) in cardiomyocytes may also change to a different state in shape and duration, often undergoing a qualitative change in behavior. Such a dynamic change is called bifurcation. In this review, we first summarize the contribution of ion channels and transporters to AP formation and our knowledge of ion-transport molecules, then briefly describe bifurcation theory for nonlinear dynamical systems, and finally detail its recent progress, focusing on the research that attempts to understand the developing mechanisms of abnormal excitations in cardiomyocytes from the perspective of bifurcation phenomena.

Nonlinear causal analysis reveals an effective water level regulation approach for phytoplankton blooms controlling in reservoirs.

Reservoirs are a rapidly increasing water body providing water supply, irrigation, and many other benefits for human societies globally. However, due to changes in hydrological conditions, building reservoirs tends to bring adverse effects such as eutrophication and phytoplankton blooms, reducing the ecosystem service values. This study focuses on using the empirical dynamic modeling (EDM), an emerging approach for nonlinear analysis, to investigate the nonlinear causal relationship of water level fluctuation (WLF) on phytoplankton biomass and then develop a quantitative model guiding effective phytoplankton blooms controlling based on water level regulations in reservoirs. Specifically, with 9-year continued daily observed data in the Three Gorges Reservoir, we examined the causal effects of different WLF parameters on the dynamics of phytoplankton blooms for the first time. We found that the water level change in the past 24 h (ΔWL) has the strongest causal effect on the daily dynamics of phytoplankton biomass among all WLF parameters (ΔWL, |ΔWL|, and the water level), with a time lag of 2 days. Moreover, EDM revealed a nonlinear relationship between ΔWL and daily dynamics of phytoplankton biomass and achieved a successful prediction for the chlorophyll a concentration 2-day ahead. Further scenario analyses found that both the rise and fall of water level will significantly reduce the chlorophyll a concentration when phytoplankton blooms occur. Nevertheless, on the whole, the rising water level has a more substantial effect on phytoplankton blooms than falling the water level. This result reveals that regulating ΔWL is a simple and effective approach in controlling phytoplankton blooms in reservoirs. Our study reported the nonlinear causal effect of ΔWL on the dynamics of chlorophyll a and provided a quantitative approach guiding effective phytoplankton blooms controlling based on the water level regulation, which might have a broad application in algal blooms controlling in reservoirs and similar waterbodies.

Stabilization of nonlinear dynamical systems via intermittent control with non-instantaneous impulses and actuator saturation.

In many actual discontinuous control systems, the state might undergo some abrupt changes when the impulsive effects appear and the impulsive effect will stay active for a period of time which cannot be ignored. Obviously, the traditional instantaneous impulsive system models cannot describe the above process. Then in this paper, considering the actuator saturation and non-instantaneous impulse existing in the real environment, we formulate the new models to describe the nonlinear intermittent control system subject to actuator saturation with non-instantaneous impulsive effects occurring at the moments of system switching. Some exponential stability criteria of this considered intermittent control systems in the form of matrix inequalities are first put forward. Meanwhile, some LMI optimization problems are also proposed to design the control gain for estimating the attraction domain with a fixed decay rate. Finally, simulation results demonstrate the feasibility of the obtained theoretical results.

Quantitative implementation of the endogenous molecular-cellular network hypothesis in hepatocellular carcinoma.

A quantitative hypothesis for cancer genesis and progression-the endogenous molecular-cellular network hypothesis, intended to include both genetic and epigenetic causes of cancer-has been proposed recently. Using this hypothesis, here we address the molecular basis for maintaining normal liver and hepatocellular carcinoma (HCC), and the potential strategy to cure or relieve HCC. First, we elaborate the basic assumptions of the hypothesis and establish a core working network of HCC according to the hypothesis. Second, we quantify the working network by a nonlinear dynamical system. We show that the working network reproduces the main known features of normal liver and HCC at both the modular and molecular levels. Lastly, the validated working network reveals that (i) specific positive feedback loops are responsible for the maintenance of normal liver and HCC; (ii) inhibiting proliferation and inflammation-related positive feedback loops and simultaneously inducing a liver-specific positive feedback loop is predicated as a potential strategy to cure or relieve HCC; and (iii) the genesis and regression of HCC are asymmetric. In light of the characteristic properties of the nonlinear dynamical system, we demonstrate that positive feedback loops must exist as a simple and general molecular basis for the maintenance of heritable phenotypes, such as normal liver and HCC, and regulating the positive feedback loops directly or indirectly provides potential strategies to cure or relieve HCC.

Computational modeling of signaling pathways mediating cell cycle checkpoint control and apoptotic responses to ionizing radiation-induced DNA damage.

The shape of dose response of ionizing radiation (IR) induced cancer at low dose region, either linear non-threshold or J-shaped, has been a debate for a long time. This dose response relationship can be influenced by built-in capabilities of cells that minimize the fixation of IR-mediated DNA damage as pro-carcinogenic mutations. Key capabilities include sensing of damage, activation of cell cycle checkpoint arrests that provide time needed for repair of the damage as well as apoptosis. Here we describe computational modeling of the signaling pathways that link sensing of DNA damage and checkpoint arrest activation/apoptosis to investigate how these molecular-level interactions influence the dose response relationship for IR induced cancer. The model provides qualitatively accurate descriptions of the IR-mediated activation of cell cycle checkpoints and the apoptotic pathway, and of time-course activities and dose response of relevant regulatory proteins (e.g. p53 and p21). Linking to a two-stage clonal growth cancer model, the model described here successfully captured a monotonically increasing to a J-shaped dose response curve and identified one potential mechanism leading to the J-shape: the cell cycle checkpoint arrest time saturates with the increase of the dose.