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Short-term synaptic dynamics differ markedly across connections and strongly regulate how action potentials communicate information. To model the range of synaptic dynamics observed in experiments, we have developed a flexible mathematical framework based on a linear-nonlinear operation. This model can capture various experimentally observed features of synaptic dynamics and different types of heteroskedasticity. Despite its conceptual simplicity, we show that it is more adaptable than previous models. Combined with a standard maximum likelihood approach, synaptic dynamics can be accurately and efficiently characterized using naturalistic stimulation patterns. These results make explicit that synaptic processing bears algorithmic similarities with information processing in convolutional neural networks.
Recent advances in sensor technologies and predictive analytics are fueling the growth in point-of-care (POC) therapies for obstructive sleep apnea (OSA) and other sleep disorders. The effectiveness of POC therapies can be enhanced by providing personalized and real-time prediction of OSA episode onsets. Previous attempts at OSA prediction are limited to capturing the nonlinear, nonstationary dynamics of the underlying physiological processes. This paper reports an investigation into heart rate dynamics aiming to predict in real time the onsets of OSA episode before the clinical symptoms appear. A prognosis method based on a nonparametric statistical Dirichlet-Process Mixture-Gaussian-Process (DPMG) model to estimate the transition from normal states to an anomalous (apnea) state is utilized to estimate the remaining time until the onset of an impending OSA episode. The approach was tested using three datasets including (1) 20 records from 14 OSA subjects in benchmark ECG apnea databases (Physionet.org), (2) records of 10 OSA patients from the University of Dublin OSA database and (3) records of eight subjects from previous work. Validation tests suggest that the model can be used to track the time until the onset of an OSA episode with the likelihood of correctly predicting apnea onset in 1 min to 5 mins ahead is 83.6 ± 9.3%, 80 ± 8.1%, 76.2 ± 13.3%, 66.9 ± 15.4%, and 61.1 ± 16.7%, respectively. The present prognosis approach can be integrated with wearable devices, enhancing proactive treatment of OSA and real-time wearable sensor-based of sleep disorders.
Microbiome dynamics are both crucial indicators and potential drivers of human health, agricultural output, and industrial bio-applications. However, predicting microbiome dynamics is notoriously difficult because communities often show abrupt structural changes, such as "dysbiosis" in human microbiomes.
Mathematical modeling can provide unique insights and predictions about a signaling pathway. Parameter variations allow identification of key reactions that govern signaling features such as the response time that may have a direct impact on the functional outcome. The effect of varying one parameter, however, may depend on values of another. To address the issue, we performed multi-parameter variations of an experimentally validated mathematical model of NF-κB regulatory network, and analyzed the inter-relationships of the parameters in shaping key dynamic features. We find that nonlinear dependencies are ubiquitous among parameters. Such phenomena may underlie the emergence of cell type-specific behaviors from essentially the same molecular network. Our results from a multivariate ensemble of models highlight the hypothesis that cell type specificity in signaling phenotype can arise from quantitatively altered strength of reactions in the pathway, in the absence of tissue-specific factors that re-wire the network for a new topology.
Contamination of oysters with a variety of viruses is one key pathway to trigger outbreaks of massive oyster mortality as well as human illnesses, including gastroenteritis and hepatitis. Much effort has gone into examining the fate of viruses in contaminated oysters, yet the current state of knowledge of nonlinear virus-oyster interactions is not comprehensive because most studies have focused on a limited number of processes under a narrow range of experimental conditions. A framework is needed for describing the complex nonlinear virus-oyster interactions. Here, we introduce a mathematical model that includes key processes for viral dynamics in oysters, such as oyster filtration, viral replication, the antiviral immune response, apoptosis, autophagy, and selective accumulation. We evaluate the model performance for two groups of viruses, those that replicate in oysters (e.g., ostreid herpesvirus) and those that do not (e.g., norovirus), and show that this model simulates well the viral dynamics in oysters for both groups. The model analytically explains experimental findings and predicts how changes in different physiological processes and environmental conditions nonlinearly affect in-host viral dynamics, for example, that oysters at higher temperatures may be more resistant to infection by ostreid herpesvirus. It also provides new insight into food treatment for controlling outbreaks, for example, that depuration for reducing norovirus levels is more effective in environments where oyster filtration rates are higher. This study provides the foundation of a modeling framework to guide future experiments and numerical modeling for better prediction and management of outbreaks. IMPORTANCE The fate of viruses in contaminated oysters has received a significant amount of attention in the fields of oyster aquaculture, food quality control, and public health. However, intensive studies through laboratory experiments and in situ observations are often conducted under a narrow range of experimental conditions and for a specific purpose in their respective fields. Given the complex interactions of various processes and nonlinear viral responses to changes in physiological and environmental conditions, a theoretical framework fully describing the viral dynamics in oysters is warranted to guide future studies from a top-down design. Here, we developed a process-based, in-host modeling framework that builds a bridge for better communications between different disciplines studying virus-oyster interactions.
The main finding of this paper is that the human visual cortex responds in a very nonlinear manner to the color contrast of pure color patterns. We examined human cortical responses to color checkerboard patterns at many color contrasts, measuring the chromatic visual evoked potential (cVEP) with a dense electrode array. Cortical topography of the cVEPs showed that they were localized near the posterior electrode at position Oz, indicating that the primary cortex (V1) was the major source of responses. The choice of fine spatial patterns as stimuli caused the cVEP response to be driven by double-opponent neurons in V1. The cVEP waveform revealed nonlinear color signal processing in the V1 cortex. The cVEP time-to-peak decreased and the waveform's shape was markedly narrower with increasing cone contrast. Comparison of the linear dynamics of retinal and lateral geniculate nucleus responses with the nonlinear dynamics of the cortical cVEP indicated that the nonlinear dynamics originated in the V1 cortex. The nature of the nonlinearity is a kind of automatic gain control that adjusts cortical dynamics to be faster when color contrast is greater.
The inherent nonlinear magnetization dynamics in spintronic devices make them suitable candidates for neuromorphic hardware. Among spintronic devices, spin torque oscillators such as spin transfer torque oscillators and spin Hall oscillators have shown the capability to perform recognition tasks. In this paper, with the help of micromagnetic simulations, we model and demonstrate that the magnetization dynamics of a single spin Hall oscillator can be nonlinearly transformed by harnessing input pulse streams and can be utilized for classification tasks. The spin Hall oscillator utilizes the microwave spectral characteristics of its magnetization dynamics for processing a binary data input. The spectral change due to the nonlinear magnetization dynamics assists in real-time feature extraction and classification of 4-binary digit input patterns. The performance was tested for the classification of the standard MNIST handwritten digit data set and achieved an accuracy of 83.1% in a simple linear regression model. Our results suggest that modulating time-driven input data can generate diverse magnetization dynamics in the spin Hall oscillator that can be suitable for temporal or sequential information processing.
Persistent sodium current (INaP) in the spinal locomotor network promotes two distinct nonlinear firing patterns: a self-sustained spiking triggered by a brief excitation in bistable motoneurons and bursting oscillations in interneurons of the central pattern generator (CPG). Here, we identify the NaV channels responsible for INaP and their role in motor behaviors. We report the axonal Nav1.6 as the main molecular player for INaP in lumbar motoneurons. The inhibition of Nav1.6, but not of Nav1.1, in motoneurons impairs INaP, bistability, postural tone, and locomotor performance. In interneurons of the rhythmogenic CPG region, both Nav1.6 and Nav1.1 equally mediate INaP. Inhibition of both channels is required to abolish oscillatory bursting activities and the locomotor rhythm. Overall, Nav1.6 plays a significant role both in posture and locomotion by governing INaP-dependent bistability in motoneurons and working in tandem with Nav1.1 to provide INaP-dependent rhythmogenic properties of the CPG.
Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations.
The pairwise maximum entropy model (pMEM) has recently gained widespread attention to exploring the nonlinear characteristics of brain state dynamics observed in resting-state functional magnetic resonance imaging (rsfMRI). Despite its unique advantageous features, the practical application of pMEM for individuals is limited as it requires a much larger sample than conventional rsfMRI scans. Thus, this study proposes an empirical Bayes estimation of individual pMEM using the variational expectation-maximization algorithm (VEM-MEM). The performance of the VEM-MEM is evaluated for several simulation setups with various sample sizes and network sizes. Unlike conventional maximum likelihood estimation procedures, the VEM-MEM can reliably estimate the individual model parameters, even with small samples, by effectively incorporating the group information as the prior. As a test case, the individual rsfMRI of children with attention deficit hyperactivity disorder (ADHD) is analyzed compared to that of typically developed children using the default mode network, executive control network, and salient network, obtained from the Healthy Brain Network database. We found that the nonlinear dynamic properties uniquely established on the pMEM differ for each group. Furthermore, pMEM parameters are more sensitive to group differences and are better associated with the behavior scores of ADHD compared to the Pearson correlation-based functional connectivity. The simulation and experimental results suggest that the proposed method can reliably estimate the individual pMEM and characterize the dynamic properties of individuals by utilizing empirical information of the group brain state dynamics.
Because most humans live and work in populated environments, researchers recently took into account that people may not only experience first-hand stress, but also second-hand stress related to the ability to empathically share another person's stress response. Recently, researchers have begun to more closely examine the existence of such empathic stress and highlighted the human propensity to physiologically resonate with the stress responses of others. As in case of first-hand stress, empathic stress could be deleterious for health if people experience exacerbated activation of hypothalamic-pituitary-adrenal and autonomic nervous systems. Thus, exploring empathic stress in an observer watching someone else experiencing stress is critical to gain a better understanding of physiological resonance and conduct strategies for health prevention. In the current study, we investigated the influence of empathic stress responses on heart rate variability (HRV) with a specific focus on nonlinear dynamics. Classic and nonlinear markers of HRV time series were computed in both targets and observers during a modified Trier social stress test (TSST). We capitalized on multiscale entropy, a reliable marker of complexity for depicting neurovisceral interactions (brain-to-heart and heart-to-brain) and their role in physiological resonance. State anxiety and affect were evaluated as well. While classic markers of HRV were not impacted by empathic stress, we showed that the complexity marker reflected the existence of empathic stress in observers. More specifically, a linear model highlighted a physiological resonance phenomenon. We conclude on the relevance of entropy in HRV dynamics, as a marker of complexity in neurovisceral interactions reflecting physiological resonance in empathic stress.
In synapses, calcium is required for modulating synaptic transmission, plasticity, synaptogenesis, and synaptic pruning. The regulation of calcium dynamics within neurons involves cellular mechanisms such as synaptically activated channels and pumps, calcium buffers, and calcium sequestrating organelles. Many experimental studies tend to focus on only one or a small number of these mechanisms, as technical limitations make it difficult to observe all features at once. Computational modeling enables incorporation of many of these properties together, allowing for more complete and integrated studies. However, the scale of existing detailed models is often limited to synaptic and dendritic compartments as the computational burden rapidly increases when these models are integrated in cellular or network level simulations. In this article we present a computational model of calcium dynamics at the postsynaptic spine of a CA1 pyramidal neuron, as well as a methodology that enables its implementation in multi-scale, large-scale simulations. We first present a mechanistic model that includes individually validated models of various components involved in the regulation of calcium at the spine. We validated our mechanistic model by comparing simulated calcium levels to experimental data found in the literature. We performed additional simulations with the mechanistic model to determine how the simulated calcium activity varies with respect to presynaptic-postsynaptic stimulation intervals and spine distance from the soma. We then developed an input-output (IO) model that complements the mechanistic calcium model and provide a computationally efficient representation for use in larger scale modeling studies; we show the performance of the IO model compared to the mechanistic model in terms of accuracy and speed. The models presented here help achieve two objectives. First, the mechanistic model provides a comprehensive platform to describe spine calcium dynamics based on individual contributing factors. Second, the IO model is trained on the main dynamical features of the mechanistic model and enables nonlinear spine calcium modeling on the cell and network level simulation scales. Utilizing both model representations provide a multi-level perspective on calcium dynamics, originating from the molecular interactions at spines and propagating the effects to higher levels of activity involved in network behavior.
We have designed and built a versatile modularized software library-ODYN-that wraps a comprehensive set of advanced data analysis methods meant to facilitate the study of turbulence, nonlinear dynamics, and complexity in space plasmas. The Python programming language is used for the algorithmic implementation of models and methods devised to understand fundamental phenomena of space plasma physics like elements of spectral analysis, probability distribution functions and their moments, multifractal analysis, or information theory. ODYN is an open-source software analysis tool and freely available to any user interested in turbulence and nonlinear dynamics analysis and provides a tool to perform automatic analysis on large collections of space measurements, in situ or simulations, a feature that distinguishes ODYN from other similar software. A user-friendly configurator is provided, which allows customization of key parameters of the analysis methods, most useful for nonprogrammers.
Electrophysiological recordings during perceptual decision tasks in monkeys suggest that the degree of confidence in a decision is based on a simple neural signal produced by the neural decision process. Attractor neural networks provide an appropriate biophysical modeling framework, and account for the experimental results very well. However, it remains unclear whether attractor neural networks can account for confidence reports in humans. We present the results from an experiment in which participants are asked to perform an orientation discrimination task, followed by a confidence judgment. Here we show that an attractor neural network model quantitatively reproduces, for each participant, the relations between accuracy, response times and confidence. We show that the attractor neural network also accounts for confidence-specific sequential effects observed in the experiment (participants are faster on trials following high confidence trials). Remarkably, this is obtained as an inevitable outcome of the network dynamics, without any feedback specific to the previous decision (that would result in, e.g., a change in the model parameters before the onset of the next trial). Our results thus suggest that a metacognitive process such as confidence in one's decision is linked to the intrinsically nonlinear dynamics of the decision-making neural network.
The way in which single neurons transform input into output spike trains has fundamental consequences for network coding. Theories and modeling studies based on standard Integrate-and-Fire models implicitly assume that, in response to increasingly strong inputs, neurons modify their coding strategy by progressively reducing their selective sensitivity to rapid input fluctuations. Combining mathematical modeling with in vitro experiments, we demonstrate that, in L5 pyramidal neurons, the firing threshold dynamics adaptively adjust the effective timescale of somatic integration in order to preserve sensitivity to rapid signals over a broad range of input statistics. For that, a new Generalized Integrate-and-Fire model featuring nonlinear firing threshold dynamics and conductance-based adaptation is introduced that outperforms state-of-the-art neuron models in predicting the spiking activity of neurons responding to a variety of in vivo-like fluctuating currents. Our model allows for efficient parameter extraction and can be analytically mapped to a Generalized Linear Model in which both the input filter--describing somatic integration--and the spike-history filter--accounting for spike-frequency adaptation--dynamically adapt to the input statistics, as experimentally observed. Overall, our results provide new insights on the computational role of different biophysical processes known to underlie adaptive coding in single neurons and support previous theoretical findings indicating that the nonlinear dynamics of the firing threshold due to Na+-channel inactivation regulate the sensitivity to rapid input fluctuations.
Selection modulates gene sequence evolution in different ways by constraining potential changes of amino acid sequences (purifying selection) or by favoring new and adaptive genetic variants (positive selection). The number of nonsynonymous differences in a pair of protein-coding sequences can be used to quantify the mode and strength of selection. To control for regional variation in substitution rates, the proportionate number of nonsynonymous differences (d(N)) is divided by the proportionate number of synonymous differences (d(S)). The resulting ratio (d(N)/d(S)) is a widely used indicator for functional divergence to identify particular genes that underwent positive selection. With the ever-growing amount of genome data, summary statistics like mean d(N)/d(S) allow gathering information on the mode of evolution for entire species. Both applications hinge on the assumption that d(S) and mean d(S) (approximately branch length) are neutral and adequately control for variation in substitution rates across genes and across organisms, respectively. We here explore the validity of this assumption using empirical data based on whole-genome protein sequence alignments between human and 15 other vertebrate species and several simulation approaches. We find that d(N)/d(S) does not appropriately reflect the action of selection as it is strongly influenced by its denominator (d(S)). Particularly for closely related taxa, such as human and chimpanzee, d(N)/d(S) can be misleading and is not an unadulterated indicator of selection. Instead, we suggest that inconsistencies in the behavior of d(N)/d(S) are to be expected and highlight the idea that this behavior may be inherent to taking the ratio of two randomly distributed variables that are nonlinearly correlated. New null hypotheses will be needed to adequately handle these nonlinear dynamics.
This paper introduces an intensive discussion for the dynamical model of the love triangle in both integer and fractional-order domains. Three different types of nonlinearities soft, hard, and mixed between soft and hard, are used in this study. MATLAB numerical simulations for the different three categories are presented. Also, a discussion for how the kind of personalities affects the behavior of chaotic attractors is introduced. This paper suggests some explanations for the complex love relationships depending on the impact of memory (IoM) principle. Lyapunov exponents, Kaplan-Yorke dimension, and bifurcation diagrams for three different integer-order cases show a significant dependency on system parameters. Hardware digital realization of the system is done using the Xilinx Artix-7 XC7A100T FPGA kit. Version 14.7 from the Xilinx ISE platform is used in both Verilog simulation and hardware implementation stages. The digital approach of such a system opens the door to predict the love relation after sensing the human personality. Also, this study will help in justifying more human emotions like happiness, panic, and fear accurately. Perhaps shortly, this study may combine with artificial intelligence to demonstrate Human-Computer interaction products.
The information processing capability of the brain decreases during unconscious states. Capturing this decrease during anesthesia-induced unconsciousness has been attempted using standard spectral analyses as these correlate relatively well with breakdowns in corticothalamic networks. Much of this work has involved the use of propofol to perturb brain activity, as it is one of the most widely used anesthetics for routine surgical anesthesia. Propofol administration alone produces EEG spectral characteristics similar to most hypnotics; however, inter-individual and drug variation render spectral measures inconsistent. Complexity measures of EEG signals could offer better measures to distinguish brain states, because brain activity exhibits nonlinear behavior at several scales during transitions of consciousness. We tested the potential of complexity analyses from nonlinear dynamics to identify loss and recovery of consciousness at clinically relevant timepoints. Patients undergoing propofol general anesthesia for various surgical procedures were identified as having changes in states of consciousness by the loss and recovery of response to verbal stimuli after induction and upon cessation of anesthesia, respectively. We demonstrate that nonlinear dynamics analyses showed more significant differences between consciousness states than spectral measures. Notably, attractors in conscious and anesthesia-induced unconscious states exhibited significantly different shapes. These shapes have implications for network connectivity, information processing, and the total number of states available to the brain at these different levels. They also reflect some of our general understanding of the network effects of consciousness in a way that spectral measures cannot. Thus, complexity measures could provide a universal means for reliably capturing depth of consciousness based on EEG changes at the beginning and end of anesthesia administration.
Neurons exhibit diverse intrinsic dynamics, which govern how they integrate synaptic inputs to produce spikes. Intrinsic dynamics are often plastic during development and learning, but the effects of these changes on stimulus encoding properties are not well known. To examine this relationship, we simulated auditory responses to zebra finch song using a linear-dynamical cascade model, which combines a linear spectrotemporal receptive field with a dynamical, conductance-based neuron model, then used generalized linear models to estimate encoding properties from the resulting spike trains. We focused on the effects of a low-threshold potassium current (KLT) that is present in a subset of cells in the zebra finch caudal mesopallium and is affected by early auditory experience. We found that KLT affects both spike adaptation and the temporal filtering properties of the receptive field. The direction of the effects depended on the temporal modulation tuning of the linear (input) stage of the cascade model, indicating a strongly nonlinear relationship. These results suggest that small changes in intrinsic dynamics in tandem with differences in synaptic connectivity can have dramatic effects on the tuning of auditory neurons.
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