An Algorithm Based on a Cable-Nernst Planck Model Predicting Synaptic Activity throughout the Dendritic Arbor with Micron Specificity.

Recent technological advances have enabled the recording of neurons in intact circuits with a high spatial and temporal resolution, creating the need for modeling with the same precision. In particular, the development of ultra-fast two-photon microscopy combined with fluorescence-based genetically-encoded Ca2+-indicators allows capture of full-dendritic arbor and somatic responses associated with synaptic input and action potential output. The complexity of dendritic arbor structures and distributed patterns of activity over time results in the generation of incredibly rich 4D datasets that are challenging to analyze (Sakaki et al. in Frontiers in Neural Circuits 14:33, 2020). Interpreting neural activity from fluorescence-based Ca2+ biosensors is challenging due to non-linear interactions between several factors influencing intracellular calcium ion concentration and its binding to sensors, including the ionic dynamics driven by diffusion, electrical gradients and voltage-gated conductances. To investigate those dynamics, we designed a model based on a Cable-like equation coupled to the Nernst-Planck equations for ionic fluxes in electrolytes. We employ this model to simulate signal propagation and ionic electrodiffusion across a dendritic arbor. Using these simulation results, we then designed an algorithm to detect synapses from Ca2+ imaging datasets. We finally apply this algorithm to experimental Ca2+-indicator datasets from neurons expressing jGCaMP7s (Dana et al. in Nature Methods 16:649-657, 2019), using full-dendritic arbor sampling in vivo in the Xenopus laevis optic tectum using fast random-access two-photon microscopy. Our model reproduces the dynamics of visual stimulus-evoked jGCaMP7s-mediated calcium signals observed experimentally, and the resulting algorithm allows prediction of the location of synapses across the dendritic arbor. Our study provides a way to predict synaptic activity and location on dendritic arbors, from fluorescence data in the full dendritic arbor of a neuron recorded in the intact and awake developing vertebrate brain.

Automating Event-detection of Brain Neuron Synaptic Activity and Action Potential Firing in vivo using a Random-access Multiphoton Laser Scanning Microscope for Real-time Analysis.

Determining how a neuron computes requires an understanding of the complex spatiotemporal relationship between its input (e.g. synaptic input as a result of external stimuli) and action potential output. Recent advances in in vivo, laser-scanning multiphoton technology, known as random-access microscopy (RAM), can capture this relationship by imaging fluorescent light, emitted from calcium-sensitive biosensors responding to synaptic and action potential firing in a neuron's full dendritic arbor and cell body. Ideally, a continuous output of fluorescent intensities from the neuron would be converted to a binary output (`event', 'or no-event'). These binary events can be used to correlate temporal and spatial associations between the input and output. However, neurons contain hundreds-to-thousands of synapses on the dendritic arbors generating an enormous quantity of data composed of physiological signals, which vary greatly in shape and size. Thus, automating data-processing tasks is essential to support high-throughput analysis for real-time/post-processing operations and to improve operators' comprehension of the data used to decipher neuron computations. Here, we describe an automated software algorithm to detect brain neuron events in real-time using an acousto-optic, multiphoton, laser scanning RAM developed in our laboratory. The fluorescent light intensities, from a genetically encoded, calcium biosensor (GCAMP 6m), are measured by our RAM system and are input to our 'event-detector', which converts them to a binary output meant for real-time applications. We evaluate three algorithms for this purpose: exponentially weighted moving average, cumulative sum, and template matching; present each algorithm's performance; and discuss user-feasibility of each. We validated our system in vivo, using the visual circuit of the Xenopus laevis.

The First 100 nm Inside the Pre-synaptic Terminal Where Calcium Diffusion Triggers Vesicular Release.

Calcium diffusion in the thin 100 nm layer located between the plasma membrane and docked vesicles in the pre-synaptic terminal of neuronal cells mediates vesicular fusion and synaptic transmission. Accounting for the narrow-cusp geometry located underneath the vesicle is a key ingredient that defines the probability and the time scale of calcium diffusion to bind calcium sensors for the initiation of vesicular release. We review here the time scale, the calcium binding dynamics and the consequences for asynchronous versus synchronous release. To conclude, three-dimensional modeling approaches and the associated coarse-grained simulations can now account efficiently for the precise co-organization of vesicles and Voltage-Gated-Calcium-Channel (VGCC). This co-organization is a key determinant of short-term plasticity and it shapes asynchronous release. Moreover, changing the location of VGCC from few nanometers underneath the vesicle modifies significantly the release probability. Finally, by modifying the calcium buffer concentration, a single synapse can switch from facilitation to depression.

Hybrid Markov-mass action law model for cell activation by rare binding events: Application to calcium induced vesicular release at neuronal synapses.

Binding of molecules, ions or proteins to small target sites is a generic step of cell activation. This process relies on rare stochastic events where a particle located in a large bulk has to find small and often hidden targets. We present here a hybrid discrete-continuum model that takes into account a stochastic regime governed by rare events and a continuous regime in the bulk. The rare discrete binding events are modeled by a Markov chain for the encounter of small targets by few Brownian particles, for which the arrival time is Poissonian. The large ensemble of particles is described by mass action laws. We use this novel model to predict the time distribution of vesicular release at neuronal synapses. Vesicular release is triggered by the binding of few calcium ions that can originate either from the synaptic bulk or from the entry through calcium channels. We report here that the distribution of release time is bimodal although it is triggered by a single fast action potential. While the first peak follows a stimulation, the second corresponds to the random arrival over much longer time of ions located in the synaptic terminal to small binding vesicular targets. To conclude, the present multiscale stochastic modeling approach allows studying cellular events based on integrating discrete molecular events over several time scales.

Robust network oscillations during mammalian respiratory rhythm generation driven by synaptic dynamics.

How might synaptic dynamics generate synchronous oscillations in neuronal networks? We address this question in the preBötzinger complex (preBötC), a brainstem neural network that paces robust, yet labile, inspiration in mammals. The preBötC is composed of a few hundred neurons that alternate bursting activity with silent periods, but the mechanism underlying this vital rhythm remains elusive. Using a computational approach to model a randomly connected neuronal network that relies on short-term synaptic facilitation (SF) and depression (SD), we show that synaptic fluctuations can initiate population activities through recurrent excitation. We also show that a two-step SD process allows activity in the network to synchronize (bursts) and generate a population refractory period (silence). The model was validated against an array of experimental conditions, which recapitulate several processes the preBötC may experience. Consistent with the modeling assumptions, we reveal, by electrophysiological recordings, that SF/SD can occur at preBötC synapses on timescales that influence rhythmic population activity. We conclude that nondeterministic neuronal spiking and dynamic synaptic strengths in a randomly connected network are sufficient to give rise to regular respiratory-like rhythmic network activity and lability, which may play an important role in generating the rhythm for breathing and other coordinated motor activities in mammals.