Simultaneous Bayesian Estimation of Excitatory and Inhibitory Synaptic Conductances by Exploiting Multiple Recorded Trials

Adaptive unscented Kalman filter for neuronal state and parameter estimation

Data assimilation techniques for state and parameter estimation are frequently applied in the context of computational neuroscience. In this work, we show how an adaptive variant of the unscented Kalman filter (UKF) performs on the tracking of a conductance-based neuron model. Unlike standard recursive filter implementations, the robust adaptive unscented Kalman filter (RAUKF) jointly estimates the states and parameters of the neuronal model while adjusting noise covariance matrices online based on innovation and residual information. We benchmark the adaptive filter's performance against existing nonlinear Kalman filters and explore the sensitivity of the filter parameters to the system being modelled. To evaluate the robustness of the proposed solution, we simulate practical settings that challenge tracking performance, such as a model mismatch and measurement faults. Compared to standard variants of the Kalman filter the adaptive variant implemented here is more accurate and robust to faults.

A novel theoretical framework for simultaneous measurement of excitatory and inhibitory conductances

The firing of neurons throughout the brain is determined by the precise relations between excitatory and inhibitory inputs, and disruption of their balance underlies many psychiatric diseases. Whether or not these inputs covary over time or between repeated stimuli remains unclear due to the lack of experimental methods for measuring both inputs simultaneously. We developed a new analytical framework for instantaneous and simultaneous measurements of both the excitatory and inhibitory neuronal inputs during a single trial under current clamp recording. This can be achieved by injecting a current composed of two high frequency sinusoidal components followed by analytical extraction of the conductances. We demonstrate the ability of this method to measure both inputs in a single trial under realistic recording constraints and from morphologically realistic CA1 pyramidal model cells. Future experimental implementation of our new method will facilitate the understanding of fundamental questions about the health and disease of the nervous system.

Most neurons in the brain receive synaptic inputs from both excitatory and inhibitory neurons. Together, these inputs determine neuronal activity: excitatory synapses shift the electrical potential across the membrane towards the threshold for generation of action potentials, whereas inhibitory synapses lower this potential away from the threshold. Action potentials are the rapid electrochemical signals that transmit information to other neurons and they are critical for the information processing abilities of the brain.

Although there are many ways to measure either excitatory or inhibitory inputs, these methods have been unable to measure both at the same time. Measuring both inputs together is essential towards understanding how neurons integrate information. We developed a new analytical method to measure excitatory and inhibitory inputs at the same time from the voltage response to injection of an alternating current into a neuron. We describe the foundation of this new method and find that it works in biologically realistic simulations of neurons. By using this technique in real neurons, scientists could investigate basic principles of information processing in the healthy and diseased brain.

What is the dynamical regime of cerebral cortex?

Many studies have shown that the excitation and inhibition received by cortical neurons remain roughly balanced across many conditions. A key question for understanding the dynamical regime of cortex is the nature of this balancing. Theorists have shown that network dynamics can yield systematic cancellation of most of a neuron's excitatory input by inhibition. We review a wide range of evidence pointing to this cancellation occurring in a regime in which the balance is loose, meaning that the net input remaining after cancellation of excitation and inhibition is comparable in size with the factors that cancel, rather than tight, meaning that the net input is very small relative to the canceling factors. This choice of regime has important implications for cortical functional responses, as we describe: loose balance, but not tight balance, can yield many nonlinear population behaviors seen in sensory cortical neurons, allow the presence of correlated variability, and yield decrease of that variability with increasing external stimulus drive as observed across multiple cortical areas.

Inferring synaptic inputs from spikes with a conductance-based neural encoding model

Descriptive statistical models of neural responses generally aim to characterize the mapping from stimuli to spike responses while ignoring biophysical details of the encoding process. Here, we introduce an alternative approach, the conductance-based encoding model (CBEM), which describes a mapping from stimuli to excitatory and inhibitory synaptic conductances governing the dynamics of sub-threshold membrane potential. Remarkably, we show that the CBEM can be fit to extracellular spike train data and then used to predict excitatory and inhibitory synaptic currents. We validate these predictions with intracellular recordings from macaque retinal ganglion cells. Moreover, we offer a novel quasi-biophysical interpretation of the Poisson generalized linear model (GLM) as a special case of the CBEM in which excitation and inhibition are perfectly balanced. This work forges a new link between statistical and biophysical models of neural encoding and sheds new light on the biophysical variables that underlie spiking in the early visual pathway.

Determination of effective synaptic conductances using somatic voltage clamp

The interplay between excitatory and inhibitory neurons imparts rich functions of the brain. To understand the synaptic mechanisms underlying neuronal computations, a fundamental approach is to study the dynamics of excitatory and inhibitory synaptic inputs of each neuron. The traditional method of determining input conductance, which has been applied for decades, employs the synaptic current-voltage (I-V) relation obtained via voltage clamp. Due to the space clamp effect, the measured conductance is different from the local conductance on the dendrites. Therefore, the interpretation of the measured conductance remains to be clarified. Using theoretical analysis, electrophysiological experiments, and realistic neuron simulations, here we demonstrate that there does not exist a transform between the local conductance and the conductance measured by the traditional method, due to the neglect of a nonlinear interaction between the clamp current and the synaptic current in the traditional method. Consequently, the conductance determined by the traditional method may not correlate with the local conductance on the dendrites, and its value could be unphysically negative as observed in experiment. To circumvent the challenge of the space clamp effect and elucidate synaptic impact on neuronal information processing, we propose the concept of effective conductance which is proportional to the local conductance on the dendrite and reflects directly the functional influence of synaptic inputs on somatic membrane potential dynamics, and we further develop a framework to determine the effective conductance accurately. Our work suggests re-examination of previous studies involving conductance measurement and provides a reliable approach to assess synaptic influence on neuronal computation.

To understand synaptic mechanisms underlying neuronal computations, a fundamental approach is to use voltage clamp to measure the dynamics of excitatory and inhibitory input conductances. Due to the space clamp effect, the measured conductance in general deviates from the local input conductance on the dendrites, hence its biological interpretation is questionable, as we demonstrate in this work. We further propose the concept of effective conductance that is proportional to the local input conductance on the dendrites and reflects directly the synaptic impact on spike generation, and develop a framework to determine the effective conductance reliably. Our work provides a biologically plausible metric for elucidating synaptic influence on neuronal computation under the constraint of the space clamp effect.

Opportunities for model-based precision dosing in the treatment of sickle cell anemia

Hydroxyurea is the primary pharmacotherapy to prevent complications of sickle cell anemia (SCA). Accumulated clinical experience across multiple age ranges has suggested that the use of an individualized maximum tolerated dose (MTD) will achieve optimal benefit of hydroxyurea treatment. However, the current empirical and trial-and-error approach for dose escalation often results in a lengthy titration process and is not strictly implemented in many clinics. Opportunities exist for pharmacokinetics model-based precision dosing of hydroxyurea to quickly achieve individual MTD. This review intends to introduce the use of a quantitative modeling approach including a Bayesian adaptive control strategy for the precision dosing of hydroxyurea. The rationale and practical considerations for the implementation of this approach are discussed. Future research directions with a focus on integrating specific safety and other clinical outcome endpoints into dose selection decision making are also discussed.

A single spike deteriorates synaptic conductance estimation

We investigated the estimation accuracy of synaptic conductances by analyzing simulated voltage traces generated by a Hodgkin-Huxley type model. We show that even a single spike substantially deteriorates the estimation. We also demonstrate that two approaches, namely, negative current injection and spike removal, can ameliorate this deterioration.

Estimation of Synaptic Conductances in Presence of Nonlinear Effects Caused by Subthreshold Ionic Currents

Subthreshold fluctuations in neuronal membrane potential traces contain nonlinear components, and employing nonlinear models might improve the statistical inference. We propose a new strategy to estimate synaptic conductances, which has been tested using in silico data and applied to in vivo recordings. The model is constructed to capture the nonlinearities caused by subthreshold activated currents, and the estimation procedure can discern between excitatory and inhibitory conductances using only one membrane potential trace. More precisely, we perform second order approximations of biophysical models to capture the subthreshold nonlinearities, resulting in quadratic integrate-and-fire models, and apply approximate maximum likelihood estimation where we only suppose that conductances are stationary in a 50–100 ms time window. The results show an improvement compared to existent procedures for the models tested here.