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.

Generative adversarial networks for construction of virtual populations of mechanistic models: simulations to study Omecamtiv Mecarbil action.

Biophysical models are increasingly used to gain mechanistic insights by fitting and reproducing experimental and clinical data. The inherent variability in the recorded datasets, however, presents a key challenge. In this study, we present a novel approach, which integrates mechanistic modeling and machine learning to analyze in vitro cardiac mechanics data and solve the inverse problem of model parameter inference. We designed a novel generative adversarial network (GAN) and employed it to construct virtual populations of cardiac ventricular myocyte models in order to study the action of Omecamtiv Mecarbil (OM), a positive cardiac inotrope. Populations of models were calibrated from mechanically unloaded myocyte shortening recordings obtained in experiments on rat myocytes in the presence and absence of OM. The GAN was able to infer model parameters while incorporating prior information about which model parameters OM targets. The generated populations of models reproduced variations in myocyte contraction recorded during in vitro experiments and provided improved understanding of OM's mechanism of action. Inverse mapping of the experimental data using our approach suggests a novel action of OM, whereby it modifies interactions between myosin and tropomyosin proteins. To validate our approach, the inferred model parameters were used to replicate other in vitro experimental protocols, such as skinned preparations demonstrating an increase in calcium sensitivity and a decrease in the Hill coefficient of the force-calcium (F-Ca) curve under OM action. Our approach thereby facilitated the identification of the mechanistic underpinnings of experimental observations and the exploration of different hypotheses regarding variability in this complex biological system.

Robustness of connectome harmonics to local gray matter and long-range white matter connectivity changes.

Recently, it has been proposed that the harmonic patterns emerging from the brain's structural connectivity underlie the resting state networks of the human brain. These harmonic patterns, termed connectome harmonics, are estimated as the Laplace eigenfunctions of the combined gray and white matters connectivity matrices and yield a connectome-specific extension of the well-known Fourier basis. However, it remains unclear how topological properties of the combined connectomes constrain the precise shape of the connectome harmonics and their relationships to the resting state networks. Here, we systematically study how alterations of the local and long-range connectivity matrices affect the spatial patterns of connectome harmonics. Specifically, the proportion of local gray matter homogeneous connectivity versus long-range white-matter heterogeneous connectivity is varied by means of weight-based matrix thresholding, distance-based matrix trimming, and several types of matrix randomizations. We demonstrate that the proportion of local gray matter connections plays a crucial role for the emergence of wide-spread, functionally meaningful, and originally published connectome harmonic patterns. This finding is robust for several different cortical surface templates, mesh resolutions, or widths of the local diffusion kernel. Finally, using the connectome harmonic framework, we also provide a proof-of-concept for how targeted structural changes such as the atrophy of inter-hemispheric callosal fibers and gray matter alterations may predict functional deficits associated with neurodegenerative conditions.

Learning Brain Dynamics With Coupled Low-Dimensional Nonlinear Oscillators and Deep Recurrent Networks.

Many natural systems, especially biological ones, exhibit complex multivariate nonlinear dynamical behaviors that can be hard to capture by linear autoregressive models. On the other hand, generic nonlinear models such as deep recurrent neural networks often require large amounts of training data, not always available in domains such as brain imaging; also, they often lack interpretability. Domain knowledge about the types of dynamics typically observed in such systems, such as a certain type of dynamical systems models, could complement purely data-driven techniques by providing a good prior. In this work, we consider a class of ordinary differential equation (ODE) models known as van der Pol (VDP) oscil lators and evaluate their ability to capture a low-dimensional representation of neural activity measured by different brain imaging modalities, such as calcium imaging (CaI) and fMRI, in different living organisms: larval zebrafish, rat, and human. We develop a novel and efficient approach to the nontrivial problem of parameters estimation for a network of coupled dynamical systems from multivariate data and demonstrate that the resulting VDP models are both accurate and interpretable, as VDP's coupling matrix reveals anatomically meaningful excitatory and inhibitory interactions across different brain subsystems. VDP outperforms linear autoregressive models (VAR) in terms of both the data fit accuracy and the quality of insight provided by the coupling matrices and often tends to generalize better to unseen data when predicting future brain activity, being comparable to and sometimes better than the recurrent neural networks (LSTMs). Finally, we demonstrate that our (generative) VDP model can also serve as a data-augmentation tool leading to marked improvements in predictive accuracy of recurrent neural networks. Thus, our work contributes to both basic and applied dimensions of neuroimaging: gaining scientific insights and improving brain-based predictive models, an area of potentially high practical importance in clinical diagnosis and neurotechnology.

Striatal network modeling in Huntington's Disease.

Medium spiny neurons (MSNs) comprise over 90% of cells in the striatum. In vivo MSNs display coherent burst firing cell assembly activity patterns, even though isolated MSNs do not burst fire intrinsically. This activity is important for the learning and execution of action sequences and is characteristically dysregulated in Huntington's Disease (HD). However, how dysregulation is caused by the various neural pathologies affecting MSNs in HD is unknown. Previous modeling work using simple cell models has shown that cell assembly activity patterns can emerge as a result of MSN inhibitory network interactions. Here, by directly estimating MSN network model parameters from single unit spiking data, we show that a network composed of much more physiologically detailed MSNs provides an excellent quantitative fit to wild type (WT) mouse spiking data, but only when network parameters are appropriate for the striatum. We find the WT MSN network is situated in a regime close to a transition from stable to strongly fluctuating network dynamics. This regime facilitates the generation of low-dimensional slowly varying coherent activity patterns and confers high sensitivity to variations in cortical driving. By re-estimating the model on HD spiking data we discover network parameter modifications are consistent across three very different types of HD mutant mouse models (YAC128, Q175, R6/2). In striking agreement with the known pathophysiology we find feedforward excitatory drive is reduced in HD compared to WT mice, while recurrent inhibition also shows phenotype dependency. We show that these modifications shift the HD MSN network to a sub-optimal regime where higher dimensional incoherent rapidly fluctuating activity predominates. Our results provide insight into a diverse range of experimental findings in HD, including cognitive and motor symptoms, and may suggest new avenues for treatment.

Dimensions of control for subthreshold oscillations and spontaneous firing in dopamine neurons.

Dopaminergic neurons (DAs) of the rodent substantia nigra pars compacta (SNc) display varied electrophysiological properties in vitro. Despite this, projection patterns and functional inputs from DAs to other structures are conserved, so in vivo delivery of consistent, well-timed dopamine modulation to downstream circuits must be coordinated. Here we show robust coordination by linear parameter controllers, discovered through powerful mathematical analyses of data and models, and from which consistent control of DA subthreshold oscillations (STOs) and spontaneous firing emerges. These units of control represent coordinated intracellular variables, sufficient to regulate complex cellular properties with radical simplicity. Using an evolutionary algorithm and dimensionality reduction, we discovered metaparameters, which when regressed against STO features, revealed a 2-dimensional control plane for the neuron's 22-dimensional parameter space that fully maps the natural range of DA subthreshold electrophysiology. This plane provided a basis for spiking currents to reproduce a large range of the naturally occurring spontaneous firing characteristics of SNc DAs. From it we easily produced a unique population of models, derived using unbiased parameter search, that show good generalization to channel blockade and compensatory intracellular mechanisms. From this population of models, we then discovered low-dimensional controllers for regulating spontaneous firing properties, and gain insight into how currents active in different voltage regimes interact to produce the emergent activity of SNc DAs. Our methods therefore reveal simple regulators of neuronal function lurking in the complexity of combined ion channel dynamics.

Novel and flexible parameter estimation methods for data-consistent inversion in mechanistic modelling.

Predictions for physical systems often rely upon knowledge acquired from ensembles of entities, e.g. ensembles of cells in biological sciences. For qualitative and quantitative analysis, these ensembles are simulated with parametric families of mechanistic models (MMs). Two classes of methodologies, based on Bayesian inference and population of models, currently prevail in parameter estimation for physical systems. However, in Bayesian analysis, uninformative priors for MM parameters introduce undesirable bias. Here, we propose how to infer parameters within the framework of stochastic inverse problems (SIPs), also termed data-consistent inversion, wherein the prior targets only uncertainties that arise due to MM non-invertibility. To demonstrate, we introduce new methods to solve SIPs based on rejection sampling, Markov chain Monte Carlo, and generative adversarial networks (GANs). In addition, to overcome limitations of SIPs, we reformulate SIPs based on constrained optimization and present a novel GAN to solve the constrained optimization problem.

Cannabinoid signaling and risk in Huntington's disease.

Dysregulated endocannabinoid (eCB) signaling and the loss of cannabinoid receptors (CB1Rs) are important phenotypes of Huntington's disease (HD) but the precise contribution that eCB signaling has at the circuit level is unknown. Using a computational model of spiking neurons, synapses, and eCB signaling, we demonstrate that eCB signaling functions as a homeostatic control mechanism, minimizing excess glutamate. Furthermore, our model demonstrates that metabolic risk, quantified by excess glutamate, increases with cortico-striatal long-term depression (LTD) and/or increased cortico-striatal activity, and replicates a progressive loss of cannabinoid receptors on inhibitory terminals as a function of the excitatory/inhibitory ratio.

Functional brain activity constrained by structural connectivity reveals cohort-specific features for serum neurofilament light chain.

Background: Neuro-axonal brain damage releases neurofilament light chain (NfL) proteins, which enter the blood. Serum NfL has recently emerged as a promising biomarker for grading axonal damage, monitoring treatment responses, and prognosis in neurological diseases. Importantly, serum NfL levels also increase with aging, and the interpretation of serum NfL levels in neurological diseases is incomplete due to lack of a reliable model for age-related variation in serum NfL levels in healthy subjects. Methods: Graph signal processing (GSP) provides analytical tools, such as graph Fourier transform (GFT), to produce measures from functional dynamics of brain activity constrained by white matter anatomy. Here, we leveraged a set of features using GFT that quantified the coupling between blood oxygen level dependent signals and structural connectome to investigate their associations with serum NfL levels collected from healthy subjects and former athletes with history of concussions. Results: Here we show that GSP feature from isthmus cingulate in the right hemisphere (r-iCg) is strongly linked with serum NfL in healthy controls. In contrast, GSP features from temporal lobe and lingual areas in the left hemisphere and posterior cingulate in the right hemisphere are the most associated with serum NfL in former athletes. Additional analysis reveals that the GSP feature from r-iCg is associated with behavioral and structural measures that predict aggressive behavior in healthy controls and former athletes. Conclusions: Our results suggest that GSP-derived brain features may be included in models of baseline variance when evaluating NfL as a biomarker of neurological diseases and studying their impact on personality traits.

Features importance in seizure classification using scalp EEG reduced to single timeseries.

Seizure detection and seizure-type classification are best performed using intra-cranial or full-scalp electroencephalogram (EEG). In embedded wearable systems however, recordings from only a few electrodes are available, reducing the spatial resolution of the signals to a handful of timeseries at most. Taking this constraint into account, we tested the performance of multiple classifiers using a subset of the EEG recordings by selecting a single trace from the montage or performing a dimensionality reduction over each hemispherical space. Our results support that Random Forest (RF) classifiers lead most efficient and stable classification performances over Support Vector Machines (SVM). Interestingly, tracking the feature importances using permutation tests reveals that classical EEG spectrum power bands display different rankings across the classifiers: low frequencies (delta, theta) are most important for SVMs while higher frequencies (alpha, gamma) are more relevant for RF and Decision Trees. We reach up to 94.3% ∓ 5.3% accuracy in classifying absence from tonic-clonic seizures using state-of-art sampling methods for unbalanced datasets and leave-patients-out 3-fold cross-validation policy.

Neuronal population models reveal specific linear conductance controllers sufficient to rescue preclinical disease phenotypes.

Preclinical drug candidates are screened for their ability to ameliorate in vitro neuronal electrophysiology, and go/no-go decisions progress drugs to clinical trials based on population means across cells and animals. However, these measures do not mitigate clinical endpoint risk. Population-based modeling captures variability across multiple electrophysiological measures from healthy, disease, and drug phenotypes. We pursued optimizing therapeutic targets by identifying coherent sets of ion channel target modulations for recovering heterogeneous wild-type (WT) population excitability profiles from a heterogeneous Huntington's disease (HD) population. Our approach combines mechanistic simulations with population modeling of striatal neurons using evolutionary optimization algorithms to design 'virtual drugs'. We introduce efficacy metrics to score populations and rank virtual drug candidates. We found virtual drugs using heuristic approaches that performed better than single target modulators and standard classification methods. We compare a real drug to virtual candidates and demonstrate a novel in silico triaging method.

Model order reduction for left ventricular mechanics via congruency training.

Computational models of the cardiovascular system and specifically heart function are currently being investigated as analytic tools to assist medical practice and clinical trials. To achieve clinical utility, models should be able to assimilate the diagnostic multi-modality data available for each patient and generate consistent representations of the underlying cardiovascular physiology. While finite element models of the heart can naturally account for patient-specific anatomies reconstructed from medical images, optimizing the many other parameters driving simulated cardiac functions is challenging due to computational complexity. With the goal of streamlining parameter adaptation, in this paper we present a novel, multifidelity strategy for model order reduction of 3-D finite element models of ventricular mechanics. Our approach is centered around well established findings on the similarity between contraction of an isolated muscle and the whole ventricle. Specifically, we demonstrate that simple linear transformations between sarcomere strain (tension) and ventricular volume (pressure) are sufficient to reproduce global pressure-volume outputs of 3-D finite element models even by a reduced model with just a single myocyte unit. We further develop a procedure for congruency training of a surrogate low-order model from multi-scale finite elements, and we construct an example of parameter optimization based on medical images. We discuss how the presented approach might be employed to process large datasets of medical images as well as databases of echocardiographic reports, paving the way towards application of heart mechanics models in the clinical practice.

Global Sensitivity Analysis of Ventricular Myocyte Model-Derived Metrics for Proarrhythmic Risk Assessment.

Multiscale computational models of the heart are being extensively investigated for improved assessment of drug-induced torsades de pointes (TdP) risk, a fatal side effect of many drugs. Model-derived metrics such as action potential duration and net charge carried by ionic currents (qNet) have been proposed as potential candidates for TdP risk stratification after being tested on small datasets. Unlike purely statistical approaches, model-derived metrics are thought to provide mechanism-based classification. In particular, qNet has been recently proposed as a surrogate metric for early afterdepolarizations (EADs), which are known to be cellular triggers of TdP. Analysis of critical model components and of the ion channels that have major impact on model-derived metrics can lead to improvements in the confidence of the prediction. In this paper, we analyze large populations of virtual drugs to systematically examine the influence of different ion channels on model-derived metrics that have been proposed for proarrhythmic risk assessment. We demonstrate via global sensitivity analysis (GSA) that model-derived metrics are most sensitive to different sets of input parameters. Similarly, important differences in sensitivity to specific channel blocks are highlighted when classifying drugs into different risk categories by either qNet or a metric directly based on simulated EADs. In particular, the higher sensitivity of qNet to the block of the late sodium channel might explain why its classification accuracy is better than that of the EAD-based metric, as shown for a small set of known drugs. Our results highlight the need for a better mechanistic interpretation of promising metrics like qNet based on a formal analysis of models. GSA should, therefore, constitute an essential component of the in silico workflow for proarrhythmic risk assessment, as an improved understanding of the structure of model-derived metrics could increase confidence in model-predicted risk.

Classification of TMS evoked potentials using ERP time signatures and SVM versus deep learning.

Modeling transcranial magnetic stimulation (TMS) evoked potentials (TEP) begins with classification of stereotypical single-pulse TMS responses in order to select validation targets for generative dynamical models. Several dimensionality reduction techniques are commonly in use to extract statistically independent features from experimental data for regression against model parameters. Here, we first designed a 3-dimensional feature space based on commonly described event-related potentials (ERP) from the literature. We then compared classification schemes which take as inputs either the 3D projection space or the original full rank input space. Their ability to discriminate TEP recorded from different brain regions given a stimulus site were evaluated. We show that a deep learning architecture, employing Convolutional Neural Network (CNN) and Multi-Layer Perceptron (MLP), yields better accuracy than the 3D projection and raw TEP input combined with Support Vector Machines. Such supervised feature extraction models may therefore be useful for scoring neural circuit simulations based on their ability to reproduce the underlying dynamical processes responsible for differential TEP responses.

Transient, Consequential Increases in Extracellular Potassium Ions Accompany Channelrhodopsin2 Excitation.

Channelrhodopsin2 (ChR2) optogenetic excitation is widely used to study neurons, astrocytes, and circuits. Using complementary approaches in situ and in vivo, we found that ChR2 stimulation leads to significant transient elevation of extracellular potassium ions by ∼5 mM. Such elevations were detected in ChR2-expressing mice, following local in vivo expression of ChR2(H134R) with adeno-associated viruses (AAVs), in different brain areas and when ChR2 was expressed in neurons or astrocytes. In particular, ChR2-mediated excitation of striatal astrocytes was sufficient to increase medium spiny neuron (MSN) excitability and immediate early gene expression. The effects on MSN excitability were recapitulated in silico with a computational MSN model and detected in vivo as increased action potential firing in awake, behaving mice. We show that transient, physiologically consequential increases in extracellular potassium ions accompany ChR2 optogenetic excitation. This coincidental effect may be important to consider during astrocyte studies employing ChR2 to interrogate neural circuits and animal behavior.

Unsupervised segmentation with dynamical units.

In this paper, we present a novel network to separate mixtures of inputs that have been previously learned. A significant capability of the network is that it segments the components of each input object that most contribute to its classification. The network consists of amplitude-phase units that can synchronize their dynamics, so that separation is determined by the amplitude of units in an output layer, and segmentation by phase similarity between input and output layer units. Learning is unsupervised and based on a Hebbian update, and the architecture is very simple. Moreover, efficient segmentation can be achieved even when there is considerable superposition of the inputs. The network dynamics are derived from an objective function that rewards sparse coding in the generalized amplitude-phase variables. We argue that this objective function can provide a possible formal interpretation of the binding problem and that the implementation of the network architecture and dynamics is biologically plausible.

Cortico-Striatal Cross-Frequency Coupling and Gamma Genesis Disruptions in Huntington's Disease Mouse and Computational Models.

Abnormal gamma band power across cortex and striatum is an important phenotype of Huntington's disease (HD) in both patients and animal models, but neither the origin nor the functional relevance of this phenotype is well understood. Here, we analyzed local field potential (LFP) activity in freely behaving, symptomatic R6/2 and Q175 mouse models and corresponding wild-type (WT) controls. We focused on periods of quiet rest, which show strong γ activity in HD mice. Simultaneous recording from motor cortex and its target area in dorsal striatum in the R6/2 model revealed exaggerated functional coupling over that observed in WT between the phase of delta frequencies (1-4 Hz) in cortex and striatum and striatal amplitude modulation of low γ frequencies (25-55 Hz; i.e., phase-amplitude coupling, PAC), but no evidence that abnormal cortical activity alone can account for the increase in striatal γ power. Both HD mouse models had stronger coupling of γ amplitude to δ phase and more unimodal phase distributions than their WT counterparts. To assess the possible role of striatal fast-spiking interneurons (FSIs) in these phenomena, we developed a computational model based on additional striatal recordings from Q175 mice. Changes in peak γ frequency and power ratio were readily reproduced by our computational model, accounting for several experimental findings reported in the literature. Our results suggest that HD is characterized by both a reorganization of cortico-striatal drive and specific population changes related to intrastriatal synaptic coupling.

Striatal Network Models of Huntington's Disease Dysfunction Phenotypes.

We present a network model of striatum, which generates "winnerless" dynamics typical for a network of sparse, unidirectionally connected inhibitory units. We observe that these dynamics, while interesting and a good match to normal striatal electrophysiological recordings, are fragile. Specifically, we find that randomly initialized networks often show dynamics more resembling "winner-take-all," and relate this "unhealthy" model activity to dysfunctional physiological and anatomical phenotypes in the striatum of Huntington's disease animal models. We report plasticity as a potent mechanism to refine randomly initialized networks and create a healthy winnerless dynamic in our model, and we explore perturbations to a healthy network, modeled on changes observed in Huntington's disease, such as neuron cell death and increased bidirectional connectivity. We report the effect of these perturbations on the conversion risk of the network to an unhealthy state. Finally we discuss the relationship between structural and functional phenotypes observed at the level of simulated network dynamics as a promising means to model disease progression in different patient populations.

Closed-Loop Brain Model of Neocortical Information-Based Exchange.

Here we describe an "information-based exchange" model of brain function that ascribes to neocortex, basal ganglia, and thalamus distinct network functions. The model allows us to analyze whole brain system set point measures, such as the rate and heterogeneity of transitions in striatum and neocortex, in the context of neuromodulation and other perturbations. Our closed-loop model is grounded in neuroanatomical observations, proposing a novel "Grand Loop" through neocortex, and invokes different forms of plasticity at specific tissue interfaces and their principle cell synapses to achieve these transitions. By implementing a system for maximum information-based exchange of action potentials between modeled neocortical areas, we observe changes to these measures in simulation. We hypothesize that similar dynamic set points and modulations exist in the brain's resting state activity, and that different modifications to information-based exchange may shift the risk profile of different component tissues, resulting in different neurodegenerative diseases. This model is targeted for further development using IBM's Neural Tissue Simulator, which allows scalable elaboration of networks, tissues, and their neural and synaptic components toward ever greater complexity and biological realism.

Temporal encoding for auditory computation: physiology of primary afferent neurons in sound-producing fish.

Many fish rely on sounds for communication, yet the peripheral structures containing the hair cells are simple, without the morphological specializations that facilitate frequency analysis in the mammalian cochlea. Despite this, neurons in the midbrain of sound-producing fish (Pollimyrus) have complex receptive fields, extracting features from courtship sounds. Here we present an analysis of the initial encoding of sounds by the primary afferents and demonstrate that the representation of sound undergoes a substantial transformation as it ascends to the midbrain. Afferents were isolated as they coursed from the sacculus through the medulla. Tones (100 Hz-1.2 kHz) elicited synchronized spikes [vector strength (VS) >0.9] on each stimulus cycle [coefficient of variation (CV) <1.1], with little spike rate adaptation. Most afferents (67%) were spontaneously active and began synchronizing 10 dB below rate threshold. Rate thresholds for the most sensitive afferents (65 dB) were close to behavioral thresholds. The distribution of characteristic frequencies and best sensitivities was matched to the spectrum of sounds of this species and to its audiogram. Three clusters of afferents were identified, one including afferents that generated spike bursts and had v-shaped response areas (bursters), and two others that included entrained afferents with broad response areas (entrained types I and II). All afferents encoded the timing of clicks within click trains with time-locked spikes, and none showed selectivity for interclick intervals. Understanding the computations that yield complex receptive fields is an essential goal for auditory neuroscience, and these data on primary encoding advance this goal, allowing a comparison of inputs with feature-extracting midbrain neurons.