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.

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.

The intracellular domain of major histocompatibility class-I proteins is essential for maintaining excitatory spine density and synaptic ultrastructure in the brain.

Major histocompatibility complex class I (MHC-I) proteins are expressed in neurons, where they regulate synaptic plasticity. However, the mechanisms by which MHC-I functions in the CNS remains unknown. Here we describe the first structural analysis of a MHC-I protein, to resolve underlying mechanisms that explains its function in the brain. We demonstrate that Y321F mutation of the conserved cytoplasmic tyrosine-based endocytosis motif YXXΦ in MHC-I affects spine density and synaptic structure without affecting neuronal complexity in the hippocampus, a region of the brain intimately involved in learning and memory. Furthermore, the impact of the Y321F substitution phenocopies MHC-I knock-out (null) animals, demonstrating that reverse, outside-in signalling events sensing the external environment is the major mechanism that conveys this information to the neuron and this has a previously undescribed yet essential role in the regulation of synaptic plasticity.

Sex-Specific Neural Networks of Cued Threat Conditioning: A Pilot Study.

Cued threat conditioning is the most common preclinical model for emotional memory, which is dysregulated in anxiety disorders and post-traumatic stress disorder. Though women are twice as likely as men to develop these disorders, current knowledge of threat conditioning networks was established by studies that excluded female subjects. For unbiased investigation of sex differences in these networks, we quantified the neural activity marker c-fos across 112 brain regions in adult male and female mice after cued threat conditioning compared to naïve controls. We found that trained females engaged prelimbic cortex, lateral amygdala, cortical amygdala, dorsal peduncular cortex, and subparafasicular nucleus more than, and subparaventricular zone less than, trained males. To explore how these sex differences in regional activity impact the global network, we generated interregional cross-correlations of c-fos expression to identify regions that were co-active during conditioning and performed hub analyses to identify regional control centers within each neural network. These exploratory graph theory-derived analyses revealed sex differences in the functional coordination of the threat conditioning network as well as distinct hub regions between trained males and females. Hub identification across multiple networks constructed by sequentially pruning the least reliable connections revealed globus pallidus and ventral lateral septum as the most robust hubs for trained males and females, respectively. While low sample size and lack of non-associative controls are major limitations, these findings provide preliminary evidence of sex differences in the individual circuit components and broader global networks of threat conditioning that may confer female vulnerability to fear-based psychiatric disease.

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.

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.

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.

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.

Automated evolutionary optimization of ion channel conductances and kinetics in models of young and aged rhesus monkey pyramidal neurons.

Conductance-based compartment modeling requires tuning of many parameters to fit the neuron model to target electrophysiological data. Automated parameter optimization via evolutionary algorithms (EAs) is a common approach to accomplish this task, using error functions to quantify differences between model and target. We present a three-stage EA optimization protocol for tuning ion channel conductances and kinetics in a generic neuron model with minimal manual intervention. We use the technique of Latin hypercube sampling in a new way, to choose weights for error functions automatically so that each function influences the parameter search to a similar degree. This protocol requires no specialized physiological data collection and is applicable to commonly-collected current clamp data and either single- or multi-objective optimization. We applied the protocol to two representative pyramidal neurons from layer 3 of the prefrontal cortex of rhesus monkeys, in which action potential firing rates are significantly higher in aged compared to young animals. Using an idealized dendritic topology and models with either 4 or 8 ion channels (10 or 23 free parameters respectively), we produced populations of parameter combinations fitting the target datasets in less than 80 hours of optimization each. Passive parameter differences between young and aged models were consistent with our prior results using simpler models and hand tuning. We analyzed parameter values among fits to a single neuron to facilitate refinement of the underlying model, and across fits to multiple neurons to show how our protocol will lead to predictions of parameter differences with aging in these neurons.

Functional consequences of age-related morphologic changes to pyramidal neurons of the rhesus monkey prefrontal cortex.

Layer 3 (L3) pyramidal neurons in the lateral prefrontal cortex (LPFC) of rhesus monkeys exhibit dendritic regression, spine loss and increased action potential (AP) firing rates during normal aging. The relationship between these structural and functional alterations, if any, is unknown. To address this issue, morphological and electrophysiological properties of L3 LPFC pyramidal neurons from young and aged rhesus monkeys were characterized using in vitro whole-cell patch-clamp recordings and high-resolution digital reconstruction of neurons. Consistent with our previous studies, aged neurons exhibited significantly reduced dendritic arbor length and spine density, as well as increased input resistance and firing rates. Computational models using the digital reconstructions with Hodgkin-Huxley and AMPA channels allowed us to assess relationships between demonstrated age-related changes and to predict physiological changes that have not yet been tested empirically. For example, the models predict that in both backpropagating APs and excitatory postsynaptic currents (EPSCs), attenuation is lower in aged versus young neurons. Importantly, when identical densities of passive parameters and voltage- and calcium-gated conductances were used in young and aged model neurons, neither input resistance nor firing rates differed between the two age groups. Tuning passive parameters for each model predicted significantly higher membrane resistance (R m ) in aged versus young neurons. This R m increase alone did not account for increased firing rates in aged models, but coupling these R m values with subtle differences in morphology and membrane capacitance did. The predicted differences in passive parameters (or parameters with similar effects) are mathematically plausible, but must be tested empirically.

A spiking self-organizing map combining STDP, oscillations, and continuous learning.

The self-organizing map (SOM) is a neural network algorithm to create topographically ordered spatial representations of an input data set using unsupervised learning. The SOM algorithm is inspired by the feature maps found in mammalian cortices but lacks some important functional properties of its biological equivalents. Neurons have no direct access to global information, transmit information through spikes and may be using phasic coding of spike times within synchronized oscillations, receive continuous input from the environment, do not necessarily alter network properties such as learning rate and lateral connectivity throughout training, and learn through relative timing of action potentials across a synaptic connection. In this paper, a network of integrate-and-fire neurons is presented that incorporates solutions to each of these issues through the neuron model and network structure. Results of the simulated experiments assessing map formation using artificial data as well as the Iris and Wisconsin Breast Cancer datasets show that this novel implementation maintains fundamental properties of the conventional SOM, thereby representing a significant step toward further understanding of the self-organizational properties of the brain while providing an additional method for implementing SOMs that can be utilized for future modeling in software or special purpose spiking neuron hardware.