Utility of constraints reflecting system stability on analyses for biological models.

Simulating complex biological models consisting of multiple ordinary differential equations can aid in the prediction of the pharmacological/biological responses; however, they are often hampered by the availability of reliable kinetic parameters. In the present study, we aimed to discover the properties of behaviors without determining an optimal combination of kinetic parameter values (parameter set). The key idea was to collect as many parameter sets as possible. Given that many systems are biologically stable and resilient (BSR), we focused on the dynamics around the steady state and formulated objective functions for BSR by partial linear approximation of the focused region. Using the objective functions and modified global cluster Newton method, we developed an algorithm for a thorough exploration of the allowable parameter space for biological systems (TEAPS). We first applied TEAPS to the NF-κB signaling model. This system shows a damped oscillation after stimulation and seems to fit the BSR constraint. By applying TEAPS, we found several directions in parameter space which stringently determines the BSR property. In such directions, the experimentally fitted parameter values were included in the range of the obtained parameter sets. The arachidonic acid metabolic pathway model was used as a model related to pharmacological responses. The pharmacological effects of nonsteroidal anti-inflammatory drugs were simulated using the parameter sets obtained by TEAPS. The structural properties of the system were partly extracted by analyzing the distribution of the obtained parameter sets. In addition, the simulations showed inter-drug differences in prostacyclin to thromboxane A2 ratio such that aspirin treatment tends to increase the ratio, while rofecoxib treatment tends to decrease it. These trends are comparable to the clinical observations. These results on real biological models suggest that the parameter sets satisfying the BSR condition can help in finding biologically plausible parameter sets and understanding the properties of biological systems.

Chaotic dynamics as a mechanism of rapid transition of hippocampal local field activity between theta and non-theta states.

We propose a dynamical model of the local hippocampal circuit realizing the transition between the theta and non-theta states. We model the interaction between hippocampal local rhythm generators and the external periodic input from the medial septum and diagonal band of Broca (MS-DBB). With our model, bifurcation of the nonlinear dynamics serves as a mechanism that realizes two distinctive oscillations in the hippocampus, where the amplitude of the oscillatory input from the MS-DBB works as a bifurcation parameter. We model the network of the hippocampal interneurons with a network of simple class 1 neuron models connected mutually with gap junctions. The model neurons exhibit highly synchronous periodic oscillations under the existence of an external force from the MS-DBB, just as the real hippocampus shows theta oscillation under the rhythmic input from the MS-DBB. The model shows diffusion-induced chaotic dynamics under an aperiodic MS-DBB activity, just as the large amplitude irregular activity appears following the disappearance of the rhythmicity of the MS-DBB neurons in the real brain. The model is consistent with both previous experimental findings reporting the existence of local rhythm generators in the hippocampus and the executive role of the MS-DBB in synchronizing theta oscillation in vivo. Our model also replicates the traveling waves of theta oscillations in two-dimensionally coupled networks.

Emergence of chaos in a compartmentalized catalytic reaction nanosystem.

In compartmentalized systems, chemical reactions may proceed in differing ways even in adjacent compartments. In compartmentalized nanosystems, the reaction behaviour may deviate from that observed on the macro- or mesoscale. In situ studies of processes in such nanosystems meet severe experimental challenges, often leaving the field to theoretical simulations. Here, a rhodium nanocrystal surface consisting of different nm-sized nanofacets is used as a model of a compartmentalized reaction nanosystem. Using field emission microscopy, different reaction modes are observed, including a transition to spatio-temporal chaos. The transitions between different modes are caused by variations of the hydrogen pressure modifying the strength of diffusive coupling between individual nanofacets. Microkinetic simulations, performed for a network of 52 coupled oscillators, reveal the origins of the different reaction modes. Since diffusive coupling is characteristic for many living and non-living compartmentalized systems, the current findings may be relevant for a wide class of reaction systems.

Chaos may enhance expressivity in cerebellar granular layer.

Recent evidence suggests that Golgi cells in the cerebellar granular layer are densely connected to each other with massive gap junctions. Here, we propose that the massive gap junctions between the Golgi cells contribute to the representational complexity of the granular layer of the cerebellum by inducing chaotic dynamics. We construct a model of cerebellar granular layer with diffusion coupling through gap junctions between the Golgi cells, and evaluate the representational capability of the network with the reservoir computing framework. First, we show that the chaotic dynamics induced by diffusion coupling results in complex output patterns containing a wide range of frequency components. Second, the long non-recursive time series of the reservoir represents the passage of time from an external input. These properties of the reservoir enable mapping different spatial inputs into different temporal patterns.

A Novel Method to Estimate Long-Term Chronological Changes From Fragmented Observations in Disease Progression.

Clinical observations of patients with chronic diseases are often restricted in terms of duration. Therefore, obtaining a quantitative and comprehensive understanding of the chronology of chronic diseases is challenging, because of the inability to precisely estimate the patient's disease stage at the time point of observation. We developed a novel method to reconstitute long-term disease progression from temporally fragmented data by extending the nonlinear mixed-effects model to incorporate the estimation of "disease time" of each subject. Application of this method to sporadic Alzheimer's disease successfully depicted disease progression over 20 years. The covariate analysis revealed earlier onset of amyloid-ß accumulation in male and female apolipoprotein E ε4 homozygotes, whereas disease progression was remarkably slower in female ε3 homozygotes compared with female ε4 carriers and males. Simulation of a clinical trial suggests patient recruitment using the information of precise disease time of each patient will decrease the sample size required for clinical trials.

Hippocampal state-dependent behavioral reflex to an identical sensory input in rats.

We examined the local field potential of the hippocampus to monitor brain states during a conditional discrimination task, in order to elucidate the relationship between ongoing brain states and a conditioned motor reflex. Five 10-week-old Wistar/ST male rats underwent a serial feature positive conditional discrimination task in eyeblink conditioning using a preceding light stimulus as a conditional cue for reinforced trials. In this task, a 2-s light stimulus signaled that the following 350-ms tone (conditioned stimulus) was reinforced with a co-terminating 100-ms periorbital electrical shock. The interval between the end of conditional cue and the onset of the conditioned stimulus was 4±1 s. The conditioned stimulus was not reinforced when the light was not presented. Animals successfully utilized the light stimulus as a conditional cue to drive differential responses to the identical conditioned stimulus. We found that presentation of the conditional cue elicited hippocampal theta oscillations, which persisted during the interval of conditional cue and the conditioned stimulus. Moreover, expression of the conditioned response to the tone (conditioned stimulus) was correlated with the appearance of theta oscillations immediately before the conditioned stimulus. These data support hippocampal involvement in the network underlying a conditional discrimination task in eyeblink conditioning. They also suggest that the preceding hippocampal activity can determine information processing of the tone stimulus in the cerebellum and its associated circuits.