Inferring Parameters of Pyramidal Neuron Excitability in Mouse Models of Alzheimer's Disease Using Biophysical Modeling and Deep Learning.

Alzheimer's disease (AD) is believed to occur when abnormal amounts of the proteins amyloid beta and tau aggregate in the brain, resulting in a progressive loss of neuronal function. Hippocampal neurons in transgenic mice with amyloidopathy or tauopathy exhibit altered intrinsic excitability properties. We used deep hybrid modeling (DeepHM), a recently developed parameter inference technique that combines deep learning with biophysical modeling, to map experimental data recorded from hippocampal CA1 neurons in transgenic AD mice and age-matched wildtype littermate controls to the parameter space of a conductance-based CA1 model. Although mechanistic modeling and machine learning methods are by themselves powerful tools for approximating biological systems and making accurate predictions from data, when used in isolation these approaches suffer from distinct shortcomings: model and parameter uncertainty limit mechanistic modeling, whereas machine learning methods disregard the underlying biophysical mechanisms. DeepHM addresses these shortcomings by using conditional generative adversarial networks to provide an inverse mapping of data to mechanistic models that identifies the distributions of mechanistic modeling parameters coherent to the data. Here, we demonstrated that DeepHM accurately infers parameter distributions of the conductance-based model on several test cases using synthetic data generated with complex underlying parameter structures. We then used DeepHM to estimate parameter distributions corresponding to the experimental data and infer which ion channels are altered in the Alzheimer's mouse models compared to their wildtype controls at 12 and 24 months. We found that the conductances most disrupted by tauopathy, amyloidopathy, and aging are delayed rectifier potassium, transient sodium, and hyperpolarization-activated potassium, respectively.

Spatial distribution of heterogeneity as a modulator of collective dynamics in pancreatic beta-cell networks and beyond.

We study the impact of spatial distribution of heterogeneity on collective dynamics in gap-junction coupled beta-cell networks comprised on cells from two populations that differ in their intrinsic excitability. Initially, these populations are uniformly and randomly distributed throughout the networks. We develop and apply an iterative algorithm for perturbing the arrangement of the network such that cells from the same population are increasingly likely to be adjacent to one another. We find that the global input strength, or network drive, necessary to transition the network from a state of quiescence to a state of synchronised and oscillatory activity decreases as network sortedness increases. Moreover, for weak coupling, we find that regimes of partial synchronisation and wave propagation arise, which depend both on network drive and network sortedness. We then demonstrate the utility of this algorithm for studying the distribution of heterogeneity in general networks, for which we use Watts-Strogatz networks as a case study. This work highlights the importance of heterogeneity in node dynamics in establishing collective rhythms in complex, excitable networks and has implications for a wide range of real-world systems that exhibit such heterogeneity.

Morphogen-directed cell fate boundaries: slow passage through bifurcation and the role of folded saddles.

One of the fundamental mechanisms in embryogenesis is the process by which cells differentiate and create tissues and structures important for functioning as a multicellular organism. Morphogenesis involves diffusive process of chemical signalling involving morphogens that pre-pattern the tissue. These morphogens influence cell fate through a highly nonlinear process of transcriptional signalling. In this paper, we consider this multiscale process in an idealised model for a growing domain. We focus on intracellular processes that lead to robust differentiation into two cell lineages through interaction of a single morphogen species with a cell fate variable that undergoes a bifurcation from monostability to bistability. In particular, we investigate conditions that result in successful and robust pattern formation into two well-separated domains, as well as conditions where this fails and produces a pinned boundary wave where only one part of the domain grows. We show that successful and unsuccessful patterning scenarios can be characterised in terms of presence or absence of a folded saddle singularity for a system with two slow variables and one fast variable; this models the interaction of slow morphogen diffusion, slow parameter drift through bifurcation and fast transcription dynamics. We illustrate how this approach can successfully model acquisition of three cell fates to produce three-domain "French flag" patterning, as well as for a more realistic model of the cell fate dynamics in terms of two mutually inhibiting transcription factors.

Somatostatin-Positive Interneurons Contribute to Seizures in SCN8A Epileptic Encephalopathy.

SCN8A epileptic encephalopathy is a devastating epilepsy syndrome caused by mutant SCN8A, which encodes the voltage-gated sodium channel NaV1.6. To date, it is unclear if and how inhibitory interneurons, which express NaV1.6, influence disease pathology. Using both sexes of a transgenic mouse model of SCN8A epileptic encephalopathy, we found that selective expression of the R1872W SCN8A mutation in somatostatin (SST) interneurons was sufficient to convey susceptibility to audiogenic seizures. Patch-clamp electrophysiology experiments revealed that SST interneurons from mutant mice were hyperexcitable but hypersensitive to action potential failure via depolarization block under normal and seizure-like conditions. Remarkably, GqDREADD-mediated activation of WT SST interneurons resulted in prolonged electrographic seizures and was accompanied by SST hyperexcitability and depolarization block. Aberrantly large persistent sodium currents, a hallmark of SCN8A mutations, were observed and were found to contribute directly to aberrant SST physiology in computational modeling and pharmacological experiments. These novel findings demonstrate a critical and previously unidentified contribution of SST interneurons to seizure generation not only in SCN8A epileptic encephalopathy, but epilepsy in general.SIGNIFICANCE STATEMENTSCN8A epileptic encephalopathy is a devastating neurological disorder that results from de novo mutations in the sodium channel isoform Nav1.6. Inhibitory neurons express NaV1.6, yet their contribution to seizure generation in SCN8A epileptic encephalopathy has not been determined. We show that mice expressing a human-derived SCN8A variant (R1872W) selectively in somatostatin (SST) interneurons have audiogenic seizures. Physiological recordings from SST interneurons show that SCN8A mutations lead to an elevated persistent sodium current which drives initial hyperexcitability, followed by premature action potential failure because of depolarization block. Furthermore, chemogenetic activation of WT SST interneurons leads to audiogenic seizure activity. These findings provide new insight into the importance of SST inhibitory interneurons in seizure initiation, not only in SCN8A epileptic encephalopathy, but for epilepsy broadly.

Investigation of the utility of the 1.1B4 cell as a model human beta cell line for study of persistent enteroviral infection.

The generation of a human pancreatic beta cell line which reproduces the responses seen in primary beta cells, but is amenable to propagation in culture, has long been an important goal in diabetes research. This is particularly true for studies focussing on the role of enteroviral infection as a potential cause of beta-cell autoimmunity in type 1 diabetes. In the present work we made use of a clonal beta cell line (1.1B4) available from the European Collection of Authenticated Cell Cultures, which had been generated by the fusion of primary human beta-cells with a pancreatic ductal carcinoma cell, PANC-1. Our goal was to study the factors allowing the development and persistence of a chronic enteroviral infection in human beta-cells. Since PANC-1 cells have been reported to support persistent enteroviral infection, the hybrid 1.1B4 cells appeared to offer an ideal vehicle for our studies. In support of this, infection of the cells with a Coxsackie virus isolated originally from the pancreas of a child with type 1 diabetes, CVB4.E2, at a low multiplicity of infection, resulted in the development of a state of persistent infection. Investigation of the molecular mechanisms suggested that this response was facilitated by a number of unexpected outcomes including an apparent failure of the cells to up-regulate certain anti-viral response gene products in response to interferons. However, more detailed exploration revealed that this lack of response was restricted to molecular targets that were either activated by, or detected with, human-selective reagents. By contrast, and to our surprise, the cells were much more responsive to rodent-selective reagents. Using multiple approaches, we then established that populations of 1.1B4 cells are not homogeneous but that they contain a mixture of rodent and human cells. This was true both of our own cell stocks and those held by the European Collection of Authenticated Cell Cultures. In view of this unexpected finding, we developed a strategy to harvest, isolate and expand single cell clones from the heterogeneous population, which allowed us to establish colonies of 1.1B4 cells that were uniquely human (h1.1.B4). However, extensive analysis of the gene expression profiles, immunoreactive insulin content, regulated secretory pathways and the electrophysiological properties of these cells demonstrated that they did not retain the principal characteristics expected of human beta cells. Our data suggest that stocks of 1.1B4 cells should be evaluated carefully prior to their use as a model human beta-cell since they may not retain the phenotype expected of human beta-cells.

Vangl2 promotes the formation of long cytonemes to enable distant Wnt/ß-catenin signaling.

Wnt signaling regulates cell proliferation and cell differentiation as well as migration and polarity during development. However, it is still unclear how the Wnt ligand distribution is precisely controlled to fulfil these functions. Here, we show that the planar cell polarity protein Vangl2 regulates the distribution of Wnt by cytonemes. In zebrafish epiblast cells, mouse intestinal telocytes and human gastric cancer cells, Vangl2 activation generates extremely long cytonemes, which branch and deliver Wnt protein to multiple cells. The Vangl2-activated cytonemes increase Wnt/ß-catenin signaling in the surrounding cells. Concordantly, Vangl2 inhibition causes fewer and shorter cytonemes to be formed and reduces paracrine Wnt/ß-catenin signaling. A mathematical model simulating these Vangl2 functions on cytonemes in zebrafish gastrulation predicts a shift of the signaling gradient, altered tissue patterning, and a loss of tissue domain sharpness. We confirmed these predictions during anteroposterior patterning in the zebrafish neural plate. In summary, we demonstrate that Vangl2 is fundamental to paracrine Wnt/ß-catenin signaling by controlling cytoneme behaviour.

Robust spike timing in an excitable cell with delayed feedback.

The initiation and regeneration of pulsatile activity is a ubiquitous feature observed in excitable systems with delayed feedback. Here, we demonstrate this phenomenon in a real biological cell. We establish a critical role of the delay resulting from the finite propagation speed of electrical impulses in the emergence of persistent multiple-spike patterns. We predict the coexistence of a number of such patterns in a mathematical model and use a biological cell subject to dynamic clamp to confirm our predictions in a living mammalian system. Given the general nature of our mathematical model and experimental system, we believe that our results capture key hallmarks of physiological excitability that are fundamental to information processing.

Variability in cyanobacteria sensitivity to antibiotics and implications for environmental risk assessment.

Once released into the environment antibiotics can kill or inhibit the growth of bacteria, and in turn potentially have effects on bacterial community structure and ecosystem function. Environmental risk assessment (ERA) seeks to establish protection limits to minimise chemical impacts on the environment, but recent evidence suggests that the current regulatory approaches for ERA for antibiotics may not be adequate for protecting bacteria that have fundamental roles in ecosystem function. In this study we assess the differences in interspecies sensitivity of eight species of cyanobacteria to seven antibiotics (cefazolin, cefotaxime, ampicillin, sufamethazine, sulfadiazine, azithromycin and erythromycin) with three different modes of action. We found that variability in the sensitivity to these antibiotics between species was dependent on the mode of action and varied by up to 70 times for ß-lactams. Probabilistic analysis using species sensitivity distributions suggest that the current predicted no effect concentration PNEC for the antibiotics may be either over or under protective of cyanobacteria dependent on the species on which it is based and the mode of action of the antibiotic; the PNECs derived for the macrolide antibiotics were over protective but PNECs for ß-lactams were generally under protective. For some geographical locations we identify a significant risk to cyanobacteria populations based upon measured environmental concentrations of selected antibiotics. We conclude that protection limits, as determined according to current regulatory guidance, may not always be protective and might be better derived using SSDs and that including toxicity data for a wider range of (cyano-) bacteria would improve confidence for the ERA of antibiotics.

Mathematical Modelling of Endocrine Systems.

Hormone rhythms are ubiquitous and essential to sustain normal physiological functions. Combined mathematical modelling and experimental approaches have shown that these rhythms result from regulatory processes occurring at multiple levels of organisation and require continuous dynamic equilibration, particularly in response to stimuli. We review how such an interdisciplinary approach has been successfully applied to unravel complex regulatory mechanisms in the metabolic, stress, and reproductive axes. We discuss how this strategy is likely to be instrumental for making progress in emerging areas such as chronobiology and network physiology. Ultimately, we envisage that the insight provided by mathematical models could lead to novel experimental tools able to continuously adapt parameters to gradual physiological changes and the design of clinical interventions to restore normal endocrine function.

Cardiopulmonary responses to maximal aerobic exercise in patients with cystic fibrosis.

Cystic fibrosis (CF) is a debilitating chronic condition, which requires complex and expensive disease management. Exercise has now been recognised as a critical factor in improving health and quality of life in patients with CF. Hence, cardiopulmonary exercise testing (CPET) is used to determine aerobic fitness of young patients as part of the clinical management of CF. However, at present there is a lack of conclusive evidence for one limiting system of aerobic fitness for CF patients at individual patient level. Here, we perform detailed data analysis that allows us to identify important systems-level factors that affect aerobic fitness. We use patients' data and principal component analysis to confirm the dependence of CPET performance on variables associated with ventilation and metabolic rates of oxygen consumption. We find that the time at which participants cross the gas exchange threshold (GET) is well correlated with their overall performance. Furthermore, we propose a predictive modelling framework that captures the relationship between ventilatory dynamics, lung capacity and function and performance in CPET within a group of children and adolescents with CF. Specifically, we show that using Gaussian processes (GP) we can predict GET at the individual patient level with reasonable accuracy given the small sample size of the available group of patients. We conclude by presenting an example and future perspectives for improving and extending the proposed framework. The modelling and analysis have the potential to pave the way to designing personalised exercise programmes that are tailored to specific individual needs relative to patient's treatment therapies.

An Analysis of Waves Underlying Grid Cell Firing in the Medial Enthorinal Cortex.

Layer II stellate cells in the medial enthorinal cortex (MEC) express hyperpolarisation-activated cyclic-nucleotide-gated (HCN) channels that allow for rebound spiking via an [Formula: see text] current in response to hyperpolarising synaptic input. A computational modelling study by Hasselmo (Philos. Trans. R. Soc. Lond. B, Biol. Sci. 369:20120523, 2013) showed that an inhibitory network of such cells can support periodic travelling waves with a period that is controlled by the dynamics of the [Formula: see text] current. Hasselmo has suggested that these waves can underlie the generation of grid cells, and that the known difference in [Formula: see text] resonance frequency along the dorsal to ventral axis can explain the observed size and spacing between grid cell firing fields. Here we develop a biophysical spiking model within a framework that allows for analytical tractability. We combine the simplicity of integrate-and-fire neurons with a piecewise linear caricature of the gating dynamics for HCN channels to develop a spiking neural field model of MEC. Using techniques primarily drawn from the field of nonsmooth dynamical systems we show how to construct periodic travelling waves, and in particular the dispersion curve that determines how wave speed varies as a function of period. This exhibits a wide range of long wavelength solutions, reinforcing the idea that rebound spiking is a candidate mechanism for generating grid cell firing patterns. Importantly we develop a wave stability analysis to show how the maximum allowed period is controlled by the dynamical properties of the [Formula: see text] current. Our theoretical work is validated by numerical simulations of the spiking model in both one and two dimensions.

Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis.

We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson (Phys Rev E 85(5):055,101(R), 2012), is known to support stationary and travelling bumps of localised activity. We pose the model on a ring and study the existence and stability of these patterns in various limits using a combination of analytical and numerical techniques. In a purely deterministic version of the model, posed on a continuum, we construct bumps and travelling waves analytically using standard interface methods from neural field theory. In a stochastic version with Heaviside firing rate, we construct approximate analytical probability mass functions associated with bumps and travelling waves. In the full stochastic model posed on a discrete lattice, where a coarse analytic description is unavailable, we compute patterns and their linear stability using equation-free methods. The lifting procedure used in the coarse time-stepper is informed by the analysis in the deterministic and stochastic limits. In all settings, we identify the synaptic profile as a mesoscopic variable, and the width of the corresponding activity set as a macroscopic variable. Stationary and travelling bumps have similar meso- and macroscopic profiles, but different microscopic structure, hence we propose lifting operators which use microscopic motifs to disambiguate them. We provide numerical evidence that waves are supported by a combination of high synaptic gain and long refractory times, while meandering bumps are elicited by short refractory times.

Spatiotemporal Dynamics of Insulitis in Human Type 1 Diabetes.

Type 1 diabetes (T1D) is an auto-immune disease characterized by the selective destruction of the insulin secreting beta cells in the pancreas during an inflammatory phase known as insulitis. Patients with T1D are typically dependent on the administration of externally provided insulin in order to manage blood glucose levels. Whilst technological developments have significantly improved both the life expectancy and quality of life of these patients, an understanding of the mechanisms of the disease remains elusive. Animal models, such as the NOD mouse model, have been widely used to probe the process of insulitis, but there exist very few data from humans studied at disease onset. In this manuscript, we employ data from human pancreases collected close to the onset of T1D and propose a spatio-temporal computational model for the progression of insulitis in human T1D, with particular focus on the mechanisms underlying the development of insulitis in pancreatic islets. This framework allows us to investigate how the time-course of insulitis progression is affected by altering key parameters, such as the number of the CD20+ B cells present in the inflammatory infiltrate, which has recently been proposed to influence the aggressiveness of the disease. Through the analysis of repeated simulations of our stochastic model, which track the number of beta cells within an islet, we find that increased numbers of B cells in the peri-islet space lead to faster destruction of the beta cells. We also find that the balance between the degradation and repair of the basement membrane surrounding the islet is a critical component in governing the overall destruction rate of the beta cells and their remaining number. Our model provides a framework for continued and improved spatio-temporal modeling of human T1D.

Limitations of perturbative techniques in the analysis of rhythms and oscillations.

Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are "sufficiently weak", an assumption that is not always valid when perturbative methods are applied. In this paper, we identify a number of concrete dynamical scenarios in which a standard perturbative technique, based on the infinitesimal phase response curve (PRC), is shown to give different predictions than the full model. Shear-induced chaos, i.e., chaotic behavior that results from the amplification of small perturbations by underlying shear, is missed entirely by the PRC. We show also that the presence of "sticky" phase­space structures tend to cause perturbative techniques to overestimate the frequencies and regularity of the oscillations. The phenomena we describe can all be observed in a simple 2D neuron model, which we choose for illustration as the PRC is widely used in mathematical neuroscience.