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1. Different paths, same destination: divergent action potential responses produce conserved cardiac fight‐or‐flight response in mouse and rabbit hearts

   https://doi.org/10.1113/JP278016  

   Wang, Lianguo ; Morotti, Stefano ; Tapa, Srinivas ; Francis Stuart, Samantha D. ; Jiang, Yanyan ; Wang, Zhen ; Myles, Rachel C. ; Brack, Kieran E. ; Ng, G. André ; Bers, Donald M. ; et al ( July 2019 , The Journal of Physiology)

   Cardiac electrophysiology and Ca²⁺handling change rapidly during the fight‐or‐flight response to meet physiological demands.

   Despite dramatic differences in cardiac electrophysiology, the cardiac fight‐or‐flight response is highly conserved across species.

   In this study, we performed physiological sympathetic nerve stimulation (SNS) while optically mapping cardiac action potentials and intracellular Ca²⁺transients in innervated mouse and rabbit hearts.

   Despite similar heart rate and Ca²⁺handling responses between mouse and rabbit hearts, we found notable species differences in spatio‐temporal repolarization dynamics during SNS.

   Species‐specific computational models revealed that these electrophysiological differences allowed for enhanced Ca²⁺handling (i.e. enhanced inotropy) in each species, suggesting that electrophysiological responses are fine‐tuned across species to produce optimal cardiac fight‐or‐flight responses.

   Sympathetic activation of the heart results in positive chronotropy and inotropy, which together rapidly increase cardiac output. The precise mechanisms that produce the electrophysiological and Ca²⁺handling changes underlying chronotropic and inotropic responses have been studied in detail in isolated cardiac myocytes. However, few studies have examined the dynamic effects of physiological sympathetic nerve activation on cardiac action potentials (APs) and intracellular Ca²⁺transients (CaTs) in the intact heart. Here, we performed bilateral sympathetic nerve stimulation (SNS) in fully innervated, Langendorff‐perfused rabbit and mouse hearts. Dual optical mapping with voltage‐ and Ca²⁺‐sensitive dyes allowed for analysis of spatio‐temporal AP and CaT dynamics. The rabbit heart responded to SNS with a monotonic increase in heart rate (HR), monotonic decreases in AP and CaT duration (APD, CaTD), and a monotonic increase in CaT amplitude. The mouse heart had similar HR and CaT responses; however, a pronounced biphasic APD response occurred, with initial prolongation (50.9 ± 5.1 ms att = 0 svs. 60.6 ± 4.1 ms att = 15 s,P < 0.05) followed by shortening (46.5 ± 9.1 ms att = 60 s,P = NSvs. t = 0). We determined the biphasic APD response in mouse was partly due to dynamic changes in HR during SNS and was exacerbated by β‐adrenergic activation. Simulations with species‐specific cardiac models revealed that transient APD prolongation in mouse allowed for greater and more rapid CaT responses, suggesting more rapid increases in contractility; conversely, the rabbit heart requires APD shortening to produce optimal inotropic responses. Thus, while the cardiac fight‐or‐flight response is highly conserved between species, the underlying mechanisms orchestrating these effects differ significantly.

    

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2. Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic Real-World Simulations

   https://doi.org/10.3389/fphys.2021.667828  

   Toledo-Marín, J. Quetzalcóatl ; Fox, Geoffrey ; Sluka, James P. ; Glazier, James A. ( June 2021 , Frontiers in Physiology)

   In many mechanistic medical, biological, physical, and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs), especially for diffusion, fluid flow and mechanical relaxation, can make simulations impractically slow. Biological models of tissues and organs often require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. One clinical example where rapid calculation of a diffusing field is of use is the estimation of oxygen gradients in the retina, based on imaging of the retinal vasculature, to guide surgical interventions in diabetic retinopathy. Furthermore, the ability to predict blood perfusion and oxygenation may one day guide clinical interventions in diverse settings, i.e., from stent placement in treating heart disease to BOLD fMRI interpretation in evaluating cognitive function (Xie et al., 2019 ; Lee et al., 2020 ). Since the quasi-steady-state solutions required for fast-diffusing chemical species like oxygen are particularly computationally costly, we consider the use of a neural network to provide an approximate solution to the steady-state diffusion equation. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. Surrogates of PDEs could enable use of larger and more detailed models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. Often the practical applications of such models require thousands to millions of replica simulations, for example for parameter identification and uncertainty quantification, each of which gains speed from surrogate use and rapidly recovers the up-front costs of surrogate generation. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. Such a configuration caricatures the chemical concentration field of a fast-diffusing species like oxygen in a tissue with two parallel blood vessels in a cross section perpendicular to the two blood vessels. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1000 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application. We briefly discuss some of the issues we encountered with overfitting, mismapping of the field values and the geometrical conditions that lead to large absolute and relative errors in the approximate solution. 

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3. Synchronizing and Desynchronizing Neural Populations through Phase Distribution Control

   Monga, Bharat ; Froyland, Gary ; Moehlis, Jeff ( January 2018 , Proceedings of the ... American Control Conference)

   In this article, we devise two related control algorithms to change the degree of synchrony of a population of noise-free, identical, uncoupled neural oscillators using a single control input. The algorithms are based on phase reduction, and use a population-level partial differential equation formulation to change the phase distribution of the neurons as desired. Motivated by the pathological neural synchronization hypothesized to be present in patients suffering from essential and parkinsonian tremor, we take our control objective to be the desynchronization of an initially synchronized neural population. Through numerical simulations, we are able to show that our algorithms work for both Type I and Type II neural populations. To demonstrate the versatility of our control algorithms, we also show that they can be applied to synchronize an initially desynchronized neural population as well. For the systems considered in this paper, the control algorithms can be applied to achieve any desired traveling-wave neural phase distribution, as long as the combination of initial and desired phase distributions is non-degenerate. 

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4. Comparison Theorems for Stochastic Chemical Reaction Networks

   https://doi.org/10.1007/s11538-023-01136-5  

   Campos, Felipe A. ; Bruno, Simone ; Fu, Yi ; Del Vecchio, Domitilla ; Williams, Ruth J. ( March 2023 , Bulletin of Mathematical Biology)

   Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady-state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. These tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. When propensity functions are bounded, our method of proof gives an explicit method for coupling two comparable SCRNs, which can be used to simultaneously simulate their sample paths in a comparable manner. We illustrate our results with applications to models of enzymatic kinetics and epigenetic regulation by chromatin modifications.

    

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5. Dysregulation of temporal dynamics of synchronous neural activity in adolescents on autism spectrum

   https://doi.org/10.1002/aur.2219  

   Malaia, Evie A. ; Ahn, Sungwoo ; Rubchinsky, Leonid L. ( November 2019 , Autism Research)

   Autism spectrum disorder is increasingly understood to be based on atypical signal transfer among multiple interconnected networks in the brain. Relative temporal patterns of neural activity have been shown to underlie both the altered neurophysiology and the altered behaviors in a variety of neurogenic disorders. We assessed brain network dynamics variability in autism spectrum disorders (ASD) using measures of synchronization (phase‐locking) strength, and timing of synchronization and desynchronization of neural activity (desynchronization ratio) across frequency bands of resting‐state electroencephalography (EEG). Our analysis indicated that frontoparietal synchronization is higher in ASD but with more short periods of desynchronization. It also indicates that the relationship between the properties of neural synchronization and behavior is different in ASD and typically developing populations. Recent theoretical studies suggest that neural networks with a high desynchronization ratio have increased sensitivity to inputs. Our results point to the potential significance of this phenomenon to the autistic brain. This sensitivity may disrupt the production of an appropriate neural and behavioral responses to external stimuli. Cognitive processes dependent on the integration of activity from multiple networks maybe, as a result, particularly vulnerable to disruption.Autism Res2020, 13: 24–31. © 2019 International Society for Autism Research, Wiley Periodicals, Inc.

   Parts of the brain can work together by synchronizing the activity of the neurons. We recorded the electrical activity of the brain in adolescents with autism spectrum disorder and then compared the recording to that of their peers without the diagnosis. We found that in participants with autism, there were a lot of very short time periods of non‐synchronized activity between frontal and parietal parts of the brain. Mathematical models show that the brain system with this kind of activity is very sensitive to external events.

    

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