Synapsin 2a tetramerisation selectively controls the presynaptic nanoscale organisation of reserve synaptic vesicles

Neurotransmitter release relies on the regulated fusion of synaptic vesicles (SVs) that are tightly packed within the presynaptic bouton of neurons. The mechanism by which SVs are clustered at the presynapse, while preserving their ability to dynamically recycle to support neuronal communication, remains unknown. Synapsin 2a (Syn2a) tetramerization has been suggested as a potential clustering mechanism. Here, we used Dual-pulse sub-diffractional Tracking of Internalised Molecules (DsdTIM) to simultaneously track single SVs from the recycling and the reserve pools, in live hippocampal neurons. The reserve pool displays a lower presynaptic mobility compared to the recycling pool and is also present in the axons. Triple knockout of Synapsin 1-3 genes (SynTKO) increased the mobility of reserve pool SVs. Re-expression of wild-type Syn2a (Syn2aWT), but not the tetramerization-deficient mutant K337Q (Syn2aK337Q), fully rescued these effects. Single-particle tracking revealed that Syn2aK337QmEos3.1 exhibited altered activity-dependent presynaptic translocation and nanoclustering. Therefore, Syn2a tetramerization controls its own presynaptic nanoclustering and thereby contributes to the dynamic immobilisation of the SV reserve pool.

Chromatin phase separated nanoregions explored by polymer cross-linker models and reconstructed from single particle trajectories

Phase separated domains (PSDs) are ubiquitous in cell biology, representing nanoregions of high molecular concentration. PSDs appear at diverse cellular domains, such as neuronal synapses but also in eukaryotic cell nucleus, limiting the access of transcription factors and thus preventing gene expression. We develop a generalized cross-linker polymer model, to study PSDs: we show that increasing the number of cross-linkers induces a polymer condensation, preventing access of diffusing molecules. To investigate how the PSDs restrict the motion of diffusing molecules, we compute the mean residence and first escaping times. Finally, we develop a method based on mean-square-displacement of single particle trajectories to reconstruct the properties of PSDs from the continuum range of anomalous exponents. We also show here that PSD generated by polymers do not induces a long-range attracting field (potential well), in contrast with nanodomains at neuronal synapses. To conclude, PSDs can result from condensed chromatin organization, where the number of cross-linkers controls molecular access.

Mapping general anesthesia states based on electro-encephalogram transition phases

Cortical electro-encephalography (EEG) served as the clinical reference for monitoring unconsciousness during general anesthesia. The existing EEG-based monitors classified general anesthesia states as underdosed, adequate, or overdosed, lacking predictive power due to the absence of transition phases among these states. In response to this limitation, we undertook an analysis of the EEG signal during isoflurane-induced general anesthesia in mice. Adopting a data-driven approach, we applied signal processing techniques to track θ- and δ-band dynamics, along with iso-electric suppressions. Combining this approach with machine learning, we successfully developed an automated algorithm. The findings of our study revealed that the dampening of the δ-band occurred several minutes before the onset of significant iso-electric suppression episodes. Furthermore, a distinct γ-frequency oscillation was observed, persisting for several minutes during the recovery phase subsequent to isoflurane-induced overdose. As a result of our research, we generated a map summarizing multiple brain states and their transitions, offering a tool for predicting and preventing overdose during general anesthesia. The transition phases identified, along with the developed algorithm, have the potential to be generalized, enabling clinicians to prevent inadequate anesthesia and, consequently, tailor anesthetic regimens to individual patients.

Analyzing Photoactivation with Diffusion Models to Study Transport in the Endoplasmic Reticulum Network

Photoactivation is a paradigm consisting in local molecular fluorescent activation by laser illumination in a chosen region (source) while measuring the concentration at a target region. Data-driven modeling is concerned with the following questions: how from the measurement in these two regions is it possible to infer the properties of molecular propagation? How is it possible to use such responses to infer motions occurring in networks such as the endoplasmic reticulum? In this book chapter, we shall review the data-driven analysis based on diffusion-transport models and numerical simulations to interpret the photoactivation dynamics and extract biophysical parameters. We will discuss modeling approaches to reconstruct local network properties from photoactivation transients.

Live-cell three-dimensional single-molecule tracking reveals modulation of enhancer dynamics by NuRD

To understand how the nucleosome remodeling and deacetylase (NuRD) complex regulates enhancers and enhancer-promoter interactions, we have developed an approach to segment and extract key biophysical parameters from live-cell three-dimensional single-molecule trajectories. Unexpectedly, this has revealed that NuRD binds to chromatin for minutes, decompacts chromatin structure and increases enhancer dynamics. We also uncovered a rare fast-diffusing state of enhancers and found that NuRD restricts the time spent in this state. Hi-C and Cut&Run experiments revealed that NuRD modulates enhancer-promoter interactions in active chromatin, allowing them to contact each other over longer distances. Furthermore, NuRD leads to a marked redistribution of CTCF and, in particular, cohesin. We propose that NuRD promotes a decondensed chromatin environment, where enhancers and promoters can contact each other over longer distances, and where the resetting of enhancer-promoter interactions brought about by the fast decondensed chromatin motions is reduced, leading to more stable, long-lived enhancer-promoter relationships.

Multi-feature clustering of CTCF binding creates robustness for loop extrusion blocking and Topologically Associating Domain boundaries

Topologically Associating Domains (TADs) separate vertebrate genomes into insulated regulatory neighborhoods that focus genome-associated processes. TADs are formed by Cohesin-mediated loop extrusion, with many TAD boundaries consisting of clustered binding sites of the CTCF insulator protein. Here we determine how this clustering of CTCF binding contributes to the blocking of loop extrusion and the insulation between TADs. We identify enrichment of three features of CTCF binding at strong TAD boundaries, consisting of strongly bound and closely spaced CTCF binding peaks, with a further enrichment of DNA-binding motifs within these peaks. Using multi-contact Nano-C analysis in cells with normal and perturbed CTCF binding, we establish that individual CTCF binding sites contribute to the blocking of loop extrusion, but in an incomplete manner. When clustered, individual CTCF binding sites thus create a stepwise insulation between neighboring TADs. Based on these results, we propose a model whereby multiple instances of temporal loop extrusion blocking create strong insulation between TADs.

Diversity of dynamic voltage patterns in neuronal dendrites revealed by nanopipette electrophysiology

Dendrites and dendritic spines are the essential cellular compartments in neuronal communication, conveying information through transient voltage signals. Our understanding of these compartmentalized voltage dynamics in fine, distal neuronal dendrites remains poor due to the difficulties inherent to accessing and stably recording from such small, nanoscale cellular compartments for a sustained time. To overcome these challenges, we use nanopipettes that permit long and stable recordings directly from fine neuronal dendrites. We reveal a diversity of voltage dynamics present locally in dendrites, such as spontaneous voltage transients, bursting events and oscillating periods of silence and firing activity, all of which we characterized using segmentation analysis. Remarkably, we find that neuronal dendrites can display spontaneous hyperpolarisation events, and sustain transient hyperpolarised states. The voltage patterns were activity-dependent, with a stronger dependency on synaptic activity than on action potentials. Long-time recordings of fine dendritic protrusions show complex voltage dynamics that may represent a previously unexplored contribution to dendritic computations.

Interactive nanocluster compaction of the ELKS scaffold and Cacophony Ca2+ channels drives sustained active zone potentiation

At presynaptic active zones (AZs), conserved scaffold protein architectures control synaptic vesicle (SV) release by defining the nanoscale distribution and density of voltage-gated Ca²⁺ channels (VGCCs). While AZs can potentiate SV release in the minutes range, we lack an understanding of how AZ scaffold components and VGCCs engage into potentiation. We here establish dynamic, intravital single-molecule imaging of endogenously tagged proteins at Drosophila AZs undergoing presynaptic homeostatic potentiation. During potentiation, the numbers of α1 VGCC subunit Cacophony (Cac) increased per AZ, while their mobility decreased and nanoscale distribution compacted. These dynamic Cac changes depended on the interaction between Cac channel's intracellular carboxyl terminus and the membrane-close amino-terminal region of the ELKS-family protein Bruchpilot, whose distribution compacted drastically. The Cac-ELKS/Bruchpilot interaction was also needed for sustained AZ potentiation. Our single-molecule analysis illustrates how the AZ scaffold couples to VGCC nanoscale distribution and dynamics to establish a state of sustained potentiation.

Predicting neurological outcome after cardiac arrest by combining computational parameters extracted from standard and deviant responses from auditory evoked potentials

Background

Despite multimodal assessment (clinical examination, biology, brain MRI, electroencephalography, somatosensory evoked potentials, mismatch negativity at auditory evoked potentials), coma prognostic evaluation remains challenging.

Methods

We present here a method to predict the return to consciousness and good neurological outcome based on classification of auditory evoked potentials obtained during an oddball paradigm. Data from event-related potentials (ERPs) were recorded noninvasively using four surface electroencephalography (EEG) electrodes in a cohort of 29 post-cardiac arrest comatose patients (between day 3 and day 6 following admission). We extracted retrospectively several EEG features (standard deviation and similarity for standard auditory stimulations and number of extrema and oscillations for deviant auditory stimulations) from the time responses in a window of few hundreds of milliseconds. The responses to the standard and the deviant auditory stimulations were thus considered independently. By combining these features, based on machine learning, we built a two-dimensional map to evaluate possible group clustering.

Results

Analysis in two-dimensions of the present data revealed two separated clusters of patients with good versus bad neurological outcome. When favoring the highest specificity of our mathematical algorithms (0.91), we found a sensitivity of 0.83 and an accuracy of 0.90, maintained when calculation was performed using data from only one central electrode. Using Gaussian, K-neighborhood and SVM classifiers, we could predict the neurological outcome of post-anoxic comatose patients, the validity of the method being tested by a cross-validation procedure. Moreover, the same results were obtained with one single electrode (Cz).

Conclusion

statistics of standard and deviant responses considered separately provide complementary and confirmatory predictions of the outcome of anoxic comatose patients, better assessed when combining these features on a two-dimensional statistical map. The benefit of this method compared to classical EEG and ERP predictors should be tested in a large prospective cohort. If validated, this method could provide an alternative tool to intensivists, to better evaluate neurological outcome and improve patient management, without neurophysiologist assistance.

Spectral EEG correlations from the different phases of general anesthesia

Introduction

Electroencephalography (EEG) signals contain transient oscillation patterns commonly used to classify brain states in responses to action, sleep, coma or anesthesia.

Methods

Using a time-frequency analysis of the EEG, we search for possible causal correlations between the successive phases of general anesthesia. We hypothesize that it could be possible to anticipate recovery patterns from the induction or maintenance phases. For that goal, we track the maximum power of the α-band and follow its time course.

Results and discussion

We quantify the frequency shift of the α-band during the recovery phase and the associated duration. Using Pearson coefficient and Bayes factor, we report non-significant linear correlation between the α-band frequency and duration shifts during recovery and the presence of the δ or the α rhythms during the maintenance phase. We also found no correlations between the α-band emergence trajectory and the total duration of the flat EEG epochs (iso-electric suppressions) induced by a propofol bolus injected during induction. Finally, we quantify the instability of the α-band using the mathematical total variation that measures possible deviations from a flat line. To conclude, the present correlative analysis shows that EEG dynamics extracted from the initial and maintenance phases of general anesthesia cannot anticipate both the emergence trajectory and the extubation time.

How large the number of redundant copies should be to make a rare event probable

The redundancy principle provides a framework to study how rare events are made possible with probability 1 in accelerated time, by making many copies of similar random searchers. However, what is a large n? To estimate large n with respect to the geometrical properties of a domain and the dynamics, we present here a criterion based on splitting probabilities between a small fraction of the exploration space associated with an activation process and other absorbing regions where trajectories can be terminated. We obtain explicit computations especially when there is a killing region located inside the domain that we compare with stochastic simulations. We also present examples of extreme trajectories with killing in dimension 2. For a large n, the optimal trajectories avoid penetrating inside the killing region. Finally, we discuss some applications to cell biology.

Dynamic Regulation of Mitochondrial [Ca2+] in Hippocampal Neurons

While neuronal mitochondria have been studied extensively in their role in health and disease, the rules that govern calcium regulation in mitochondria remain somewhat vague. In the present study using cultured rat hippocampal neurons transfected with the mtRCaMP mitochondrial calcium sensor, we investigated the effects of cytosolic calcium surges on the dynamics of mitochondrial calcium ([Ca²⁺]m). Cytosolic calcium ([Ca²⁺]c) was measured using the high affinity sensor Fluo-2. We recorded two types of calcium events: local and global ones. Local events were limited to a small, 2–5 µm section of the dendrite, presumably caused by local synaptic activity, while global events were associated with network bursts and extended throughout the imaged dendrite. In both cases, cytosolic surges were followed by a delayed rise in [Ca²⁺]m. In global events, the rise lasted longer and was observed in all mitochondrial clusters. At the end of the descending part of the global event, [Ca²⁺]m was still high. Global events were accompanied by short and rather high [Ca²⁺]m surges which we called spikelets, and were present until the complete decay of the cytosolic event. In the case of local events, selective short-term responses were limited to the part of the mitochondrial cluster that was located directly in the center of [Ca²⁺]c activity, and faded quickly, while responses in the neighboring regions were rarely observed. Caffeine (which recruits ryanodine receptors to supply calcium to the mitochondria), and carbonyl cyanide m-chlorophenyl hydrazine (CCCP, a mitochondrial uncoupler) could affect [Ca²⁺]m in both global and local events. We constructed a computational model to simulate the fundamental role of mitochondria in restricting calcium signals within a narrow range under synapses, preventing diffusion into adjacent regions of the dendrite. Our results indicate that local cytoplasmic and mitochondrial calcium concentrations are highly correlated. This reflects a key role of signaling pathways that connect the postsynaptic membrane to local mitochondrial clusters.

Computational methods and diffusion theory in triangulation sensing to model neuronal navigation

Computational methods are now recognized as powerful and complementary approaches in various applied sciences such as biology. These computing methods are used to explore the gap between scales such as the one between molecular and cellular. Here we present recent progress in the development of computational approaches involving diffusion modeling, asymptotic analysis of the model partial differential equations, hybrid methods and simulations in the generic context of cell sensing and guidance via external gradients. Specifically, we highlight the reconstruction of the location of a point source in two and three dimensions from the steady-state diffusion fluxes arriving to narrow windows located on the cell. We discuss cases in which these windows are located on the boundary of a two-dimensional plane or three-dimensional half-space, on a disk in free space or inside a two-dimensional corridor, or a ball in three dimensions. The basis of this computational approach is explicit solutions of the Neumann-Green's function for the mentioned geometry. This analysis can be used to design hybrid simulations where Brownian paths are generated only in small regions in which the local spatial organization is relevant. Particle trajectories outside of this region are only implicitly treated by generating exit points at the boundary of this domain of interest. This greatly accelerates the simulation time by avoiding the explicit computation of Brownian paths in an infinite domain and serves to generate statistics, without following all trajectories at the same time, a process that can become numerically expensive quickly. Moreover, these computational approaches are used to reconstruct a point source and estimating the uncertainty in the source reconstruction due to an additive noise perturbation present in the fluxes. We also discuss the influence of various window configurations (cluster vs uniform distributions) on recovering the source position. Finally, the applications in developmental biology are formulated into computational principles that could underly neuronal navigation in the brain.

High-throughput super-resolution single-particle trajectory analysis reconstructs organelle dynamics and membrane reorganization

Super-resolution imaging can generate thousands of single-particle trajectories. These data can potentially reconstruct subcellular organization and dynamics, as well as measure disease-linked changes. However, computational methods that can derive quantitative information from such massive datasets are currently lacking. We present data analysis and algorithms that are broadly applicable to reveal local binding and trafficking interactions and organization of dynamic subcellular sites. We applied this analysis to the endoplasmic reticulum and neuronal membrane. The method is based on spatiotemporal segmentation that explores data at multiple levels and detects the architecture and boundaries of high-density regions in areas measuring hundreds of nanometers. By connecting dense regions, we reconstructed the network topology of the endoplasmic reticulum (ER), as well as molecular flow redistribution and the local space explored by trajectories. The presented methods are available as an ImageJ plugin that can be applied to large datasets of overlapping trajectories offering a standard of single-particle trajectory (SPT) metrics.

Adaptive single-channel EEG artifact removal for real-time clinical monitoring

OBJECTIVE

Electroencephalography (EEG) has become very common in clinical practice due to its relatively low cost, ease of installation, non-invasiveness, and good temporal resolution. Portable EEG devices are increasingly popular in clinical monitoring applications such as sleep scoring or anesthesia monitoring. In these situations, for reasons of speed and simplicity only few electrodes are used and contamination of the EEG signal by artifacts is inevitable. Visual inspection and manual removal of artifacts is often not possible, especially in real-time applications. Our goal is to develop a flexible technique to remove EEG artifacts in these contexts with minimal supervision.

METHODS

We propose here a new wavelet-based method which allows to remove artifacts from single-channel EEGs. The method is based on a data-driven renormalization of the wavelet components and is capable of adaptively attenuate artifacts of different nature. We benchmark our method against alternative artifact removal techniques.

RESULTS

We assessed the performance of the proposed method on publicly available datasets comprising ocular, muscular, and movement artifacts. The proposed method shows superior performances on different kinds of artifacts and signal-to-noise levels. Finally, we present an application of our method to the monitoring of general anesthesia.

CONCLUSIONS

We show that our method can successfully attenuate various types of artifacts in single-channel EEG.

SIGNIFICANCE

Thanks to its data-driven approach and low computational cost, the proposed method provides a valuable tool to remove artifacts in real-time EEG applications with few electrodes, such as monitoring in special care units.

Studying the Dynamics of Chromatin-Binding Proteins in Mammalian Cells Using Single-Molecule Localization Microscopy

Single-molecule localization microscopy (SMLM) allows the super-resolved imaging of proteins within mammalian nuclei at spatial resolutions comparable to that of a nucleosome itself (~20 nm). The technique is therefore well suited to the study of chromatin structure. Fixed-cell SMLM has already allowed temporal "snapshots" of how proteins are arranged on chromatin within mammalian nuclei. In this chapter, we focus on how recent developments, for example in selective plane illumination, 3D SMLM, and protein labeling, have led to a range of live-cell SMLM studies. We describe how to carry out single-particle tracking (SPT) of single proteins and, by analyzing their diffusion parameters, how to determine whether proteins interact with chromatin, diffuse freely, or do both. We can study the numbers of proteins that interact with chromatin and also determine their residence time on chromatin. We can determine whether these proteins form functional clusters within the nucleus as well as whether they form specific nuclear structures.

Modelling and asymptotic analysis of the concentration difference in a nanoregion between an influx andoutflux diffusion acrossnarrow windows

When a flux of Brownian particles is injected in a narrow window located on the surface of a bounded domain, these particles diffuse and can eventually escape through a cluster of narrow windows. At steady state, we compute asymptotically the distribution of concentration between the different windows. The solution is obtained by solving Laplace’s equation using Green’s function techniques and second-order asymptotic analysis, and depends on the influx amplitude, the diffusion properties, as well as the geometrical organization of all the windows, such as their distances and the mean curvature. We explore the range of validity of the present asymptotic expansions using numerical simulations of the mixed boundary value problem. Finally, we introduce a length scale to estimate how deep inside a domain a local diffusion current can spread.

Nanoscale molecular architecture controls calcium diffusion and ER replenishment in dendritic spines

Dendritic spines are critical components of neuronal synapses as they receive and transform synaptic inputs into a succession of calcium-regulated biochemical events. The spine apparatus (SA), an extension of smooth endoplasmic reticulum, regulates slow and fast calcium dynamics in spines. Calcium release events deplete SA calcium ion reservoir rapidly, yet the next cycle of signaling requires its replenishment. How spines achieve this replenishment without triggering calcium release remains unclear. Using computational modeling, calcium and STED superresolution imaging, we show that the SA replenishment involves the store-operated calcium entry pathway during spontaneous calcium transients. We identified two main conditions for SA replenishment without depletion: a small amplitude and a slow timescale for calcium influx, and a close proximity between SA and plasma membranes. Thereby, spine’s nanoscale organization separates SA replenishment from depletion. We further conclude that spine’s receptor organization also determines the calcium dynamics during the induction of long-term synaptic changes.

Reconstructing a point source from diffusion fluxes to narrow windows in three dimensions

We develop a computational approach to locate the source of a steady-state gradient of diffusing particles from the fluxes through narrow windows distributed either on the boundary of a three-dimensional half-space or on a sphere. This approach is based on solving the mixed boundary stationary diffusion equation with Neumann–Green’s function. The method of matched asymptotic expansions enables the computation of the probability fluxes. To explore the range of validity of this expansion, we develop a fast analytical-Brownian numerical scheme. This scheme accelerates the simulation time by avoiding the explicit computation of Brownian trajectories in the infinite domain. The results obtained from our derived analytical formulae and the fast numerical simulation scheme agree on a large range of parameters. Using the analytical representation of the particle fluxes, we show how to reconstruct the location of the point source. Furthermore, we investigate the uncertainty in the source reconstruction due to additive fluctuations present in the fluxes. We also study the influence of various window configurations: clustered versus uniform distributions on recovering the source position. Finally, we discuss possible applications for cell navigation in biology.

Physics meets biology: The joining of two forces to further our understanding of cellular function

Some biological questions are tough to solve through standard molecular and cell biological methods and naturally lend themselves to investigation by physical approaches. Below, a group of formally trained physicists discuss, among other things, how they apply physics to address biological questions and how physical approaches complement conventional biological approaches.

Chromatin stability generated by stochastic binding and unbinding of cross-linkers at looping sites revealed by Markov models

Chromatin loops inside the nucleus can be stable for a very long time, which remains poorly understood. Such a time is crucial for chromatin organization maintenance and stability. We explore here several physical scenarios, where loop maintenance is due to diffusing cross-linkers (cohesin stabilized by two CTCF molecules) that can bind and unbind at the base of chromatin loops. Using a Markov chain approach to coarse-grain the binding and unbinding, we consider that a stable loop disappears when the last cross-linker is unbound. We derive expressions for this last passage time that we use to quantify the loop stability for various parameters, such as the chemical rate constant or the number of cross-linkers. The present analysis suggests that the balance between binding and unbinding events regulates the number of cross-linkers in place, based on a positive feed-back mechanism that stabilizes the loop over long-time. To conclude, we found that short- and long-lasting stable loops can vary from minutes to the entire cell cycle lifetime, when the number of cross-linkers increases from 1 to 10. This result suggests that a large spectrum of loop time scales is expected with such a few numbers of cross-linkers per local binding sites.

Modeling the voltage distribution in a non-locally but globally electroneutral confined electrolyte medium: applications for nanophysiology

The distribution of voltage in sub-micron cellular domains remains poorly understood. In neurons, the voltage results from the difference in ionic concentrations which are continuously maintained by pumps and exchangers. However, it not clear how electro-neutrality could be maintained by an excess of fast moving positive ions that should be counter balanced by slow diffusing negatively charged proteins. Using the theory of electro-diffusion, we study here the voltage distribution in a generic domain, which consists of two concentric disks (resp. ball) in two (resp. three) dimensions, where a negative charge is fixed in the inner domain. When global but not local electro-neutrality is maintained, we solve the Poisson-Nernst-Planck equation both analytically and numerically in dimension 1 (flat) and 2 (cylindrical) and found that the voltage changes considerably on a spatial scale which is much larger than the Debye screening length, which assumes electro-neutrality. The present result suggests that long-range voltage drop changes are expected in neuronal microcompartments, probably relevant to explain the activation of far away voltage-gated channels located on the surface membrane.

The structure and global distribution of the endoplasmic reticulum network are actively regulated by lysosomes

The endoplasmic reticulum (ER) comprises morphologically and functionally distinct domains: sheets and interconnected tubules. These domains undergo dynamic reshaping in response to changes in the cellular environment. However, the mechanisms behind this rapid remodeling are largely unknown. Here, we report that ER remodeling is actively driven by lysosomes, following lysosome repositioning in response to changes in nutritional status: The anchorage of lysosomes to ER growth tips is critical for ER tubule elongation and connection. We validate this causal link via the chemo- and optogenetically driven repositioning of lysosomes, which leads to both a redistribution of the ER tubules and a change of its global morphology. Therefore, lysosomes sense metabolic change in the cell and regulate ER tubule distribution accordingly. Dysfunction in this mechanism during axonal extension may lead to axonal growth defects. Our results demonstrate a critical role of lysosome-regulated ER dynamics and reshaping in nutrient responses and neuronal development.

Triangulation Sensing to Determine the Gradient Source from Diffusing Particles to Small Cell Receptors

How does a cell locate the source of molecular guidance cues from within a concentration gradient? We present a computational approach to recover the source from the absorbed fluxes at narrow receptor windows located on the surface of the cell. In the limit of fast binding, we solve the steady-state diffusion equation using an asymptotic approach and hybrid stochastic-analytical simulations. We show that the sensitivity to the gradient direction decays too rapidly to enable long-distance sensing. We illustrate how this constraint can be alleviated when triangulating the source with an increasing number of receptor windows and quantify the susceptibility of this process to flux perturbations.

Active flow network generates molecular transport by packets: case of the endoplasmic reticulum

Biological networks are characterized by their connectivity and topology but also by their ability to transport materials. In the case of random transportation, the efficacy is measured by the time it takes to travel between two nodes of the network. We study here the consequences of a unidirectional transport mechanism occurring in the endoplasmic reticulum (ER) network, a structure present in the cell cytoplasm. This unidirectional transport mechanism is an active-waiting transportation, where molecules have to wait a random time before being transported from one node to the next one. We develop here a general theory of transport in an active network and find an unusual network transportation, where molecules group together in redundant packets instead of being disperse. Finally, the mean time to travel between two nodes of the ER is of the order of 20 min, but is reduced to 30 s when we consider the fastest particles because it uses optimal paths. To conclude, the present theory shows that unidirectional transport is an efficient and robust mechanism for fast molecular redistribution inside the ER.

Biophysics of high density nanometer regions extracted from super-resolution single particle trajectories: application to voltage-gated calcium channels and phospholipids

The cellular membrane is very heterogenous and enriched with high-density regions forming microdomains, as revealed by single particle tracking experiments. However the organization of these regions remain unexplained. We determine here the biophysical properties of these regions, when described as a basin of attraction. We develop two methods to recover the dynamics and local potential wells (field of force and boundary). The first method is based on the local density of points distribution of trajectories, which differs inside and outside the wells. The second method focuses on recovering the drift field that is convergent inside wells and uses the transient field to determine the boundary. Finally, we apply these two methods to the distribution of trajectories recorded from voltage gated calcium channels and phospholipid anchored GFP in the cell membrane of hippocampal neurons and obtain the size and energy of high-density regions with a nanometer precision.

Alpha rhythm collapse predicts iso-electric suppressions during anesthesia

Could an overly deep sedation be anticipated from ElectroEncephaloGram (EEG) patterns? We report here motifs hidden in the EEG signal that predict the appearance of Iso-Electric Suppressions (IES), observed during epileptic encephalopathies, drug intoxications, comatose, brain death or during anesthetic over-dosage that are considered to be detrimental. To show that IES occurrences can be predicted from EEG traces dynamics, we focus on transient suppression of the alpha rhythm (8-14 Hz) recorded for 80 patients, that had a Propofol target controlled infusion of 5 μg/ml during a general anesthesia. We found that the first time of appearance as well as changes in duration of these Alpha-Suppressions (αS) are two parameters that anticipate the appearance of IES. Using machine learning, we predicted IES appearance from the first 10 min of EEG (AUC of 0.93). To conclude, transient motifs in the alpha rhythm predict IES during anesthesia and can be used to identify patients, with higher risks of post-operative complications.

Advances Using Single-Particle Trajectories to Reconstruct Chromatin Organization and Dynamics

Chromatin organization remains complex and far from understood. In this article, we review recent statistical methods of extracting biophysical parameters from in vivo single-particle trajectories of loci to reconstruct chromatin reorganization in response to cellular stress such as DNA damage. We look at methods for analyzing both single locus and multiple loci tracked simultaneously and explain how to quantify and describe chromatin motion using a combination of extractable parameters. These parameters can be converted into information about chromatin dynamics and function. Furthermore, we discuss how the timescale of recurrent encounter between loci can be extracted and interpreted. We also discuss the effect of sampling rate on the estimated parameters. Finally, we review a polymer method to reconstruct chromatin structure using crosslinkers between chromatin sites. We list and refer to some software packages that are now publicly available to simulate polymer motion. To conclude, chromatin organization and dynamics can be reconstructed from locus trajectories and predicted based on polymer models.

Fast calcium transients in dendritic spines driven by extreme statistics

Fast calcium transients (<10 ms) remain difficult to analyse in cellular microdomains, yet they can modulate key cellular events such as trafficking, local ATP production by endoplasmic reticulum-mitochondria complex (ER-mitochondria complex), or spontaneous activity in astrocytes. In dendritic spines receiving synaptic inputs, we show here that in the presence of a spine apparatus (SA), which is an extension of the smooth ER, a calcium-induced calcium release (CICR) is triggered at the base of the spine by the fastest calcium ions arriving at a Ryanodyne receptor (RyR). The mechanism relies on the asymmetric distributions of RyRs and sarco/ER calcium-ATPase (SERCA) pumps that we predict using a computational model and further confirm experimentally in culture and slice hippocampal neurons. The present mechanism for which the statistics of the fastest particles arriving at a small target, followed by an amplification, is likely to be generic in molecular transduction across cellular microcompartments, such as thin neuronal processes, astrocytes, endfeets, or protrusions.

Electrical transient laws in neuronal microdomains based on electro-diffusion

The current-voltage (I-V) conversion characterizes the physiology of cellular microdomains and reflects cellular communication, excitability, and electrical transduction. Yet deriving such I-V laws remains a major challenge in most cellular microdomains due to their small sizes and the difficulty in assessing voltage with high nanometer precision. We present here novel analytical relations derived for different numbers of ionic species inside neuronal micro/nano-domains, such as dendritic spines. When a steady-state current is injected, we find a large deviation from the classical Ohm's law, showing that the spine neck resistance is insufficient to characterize electrical properties. For a constricted spine neck, modeled by a hyperboloid, we obtain a new I-V law that illustrates the consequences of narrow passages on electrical conduction. Finally, during a fast current transient, the local voltage is modulated by the distance between activated voltage-gated channels. To conclude, electro-diffusion laws can now be used to interpret voltage distribution in neuronal microdomains.

Transient Confinement of CaV2.1 Ca2+-Channel Splice Variants Shapes Synaptic Short-Term Plasticity

The precision and reliability of synaptic information transfer depend on the molecular organization of voltage-gated calcium channels (VGCCs) within the presynaptic membrane. Alternative splicing of exon 47 affects the C-terminal structure of VGCCs and their affinity to intracellular partners and synaptic vesicles (SVs). We show that hippocampal synapses expressing VGCCs either with exon 47 (Ca_V2.1₊₄₇) or without (Ca_V2.1_Δ47) differ in release probability and short-term plasticity. Tracking single channels revealed transient visits (∼100 ms) of presynaptic VGCCs in nanodomains (∼80 nm) that were controlled by neuronal network activity. Surprisingly, despite harboring prominent binding sites to scaffold proteins, Ca_V2.1₊₄₇ persistently displayed higher mobility within nanodomains. Synaptic accumulation of Ca_V2.1 was accomplished by optogenetic clustering, but only Ca_V2.1₊₄₇ increased transmitter release and enhanced synaptic short-term depression. We propose that exon 47-related alternative splicing of Ca_V2.1 channels controls synapse-specific release properties at the level of channel mobility-dependent coupling between VGCCs and SVs.

Redundancy principle and the role of extreme statistics in molecular and cellular biology

The paradigm of chemical activation rates in cellular biology has been shifted from the mean arrival time of a single particle to the mean of the first among many particles to arrive at a small activation site. The activation rate is set by extremely rare events, which have drastically different time scales from the mean times between activations, and depends on different structural parameters. This shift calls for reconsideration of physical processes used in deterministic and stochastic modeling of chemical reactions that are based on the traditional forward rate, especially for fast activation processes in living cells. Consequently, the biological activation time is not necessarily exponentially distributed. We review here the physical models, the mathematical analysis and the new paradigm of setting the scale to be the shortest time for activation that clarifies the role of population redundancy in selecting and accelerating transient cellular search processes. We provide examples in cellular transduction, gene activation, cell senescence activation or spermatozoa selection during fertilization, where the rate depends on numbers. We conclude that the statistics of the minimal time to activation set kinetic laws in biology, which can be very different from the ones associated to average times.

Encounter times of chromatin loci influenced by polymer decondensation

The time for a DNA sequence to find its homologous counterpart depends on a long random search inside the cell nucleus. Using polymer models, we compute here the mean first encounter time (MFET) between two sites located on two different polymer chains and confined locally by potential wells. We find that reducing tethering forces acting on the polymers results in local decondensation, and numerical simulations of the polymer model show that these changes are associated with a reduction of the MFET by several orders of magnitude. We derive here new asymptotic formula for the MFET, confirmed by Brownian simulations. We conclude from the present modeling approach that the fast search for homology is mediated by a local chromatin decondensation due to the release of multiple chromatin tethering forces. The present scenario could explain how the homologous recombination pathway for double-stranded DNA repair is controlled by its random search step.

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.

Mixed analytical-stochastic simulation method for the recovery of a Brownian gradient source from probability fluxes to small windows

Is it possible to recover the position of a source from the steady-state fluxes of Brownian particles to small absorbing windows located on the boundary of a domain? To address this question, we develop a numerical procedure to avoid tracking Brownian trajectories in the entire infinite space. Instead, we generate particles near the absorbing windows, computed from the analytical expression of the exit probability. When the Brownian particles are generated by a steady-state gradient at a single point, we compute asymptotically the fluxes to small absorbing holes distributed on the boundary of half-space and on a disk in two dimensions, which agree with stochastic simulations. We also derive an expression for the splitting probability between small windows using the matched asymptotic method. Finally, when there are more than two small absorbing windows, we show how to reconstruct the position of the source from the diffusion fluxes. The present approach provides a computational first principle for the mechanism of sensing a gradient of diffusing particles, a ubiquitous problem in cell biology.

Deconvolution of Voltage Sensor Time Series and Electro-diffusion Modeling Reveal the Role of Spine Geometry in Controlling Synaptic Strength

Most synaptic excitatory connections are made on dendritic spines. But how the voltage in spines is modulated by its geometry remains unclear. To investigate the electrical properties of spines, we combine voltage imaging data with electro-diffusion modeling. We first present a temporal deconvolution procedure for the genetically encoded voltage sensor expressed in hippocampal cultured neurons and then use electro-diffusion theory to compute the electric field and the current-voltage conversion. We extract a range for the neck resistances of 〈R〉=100±35MΩ. When a significant current is injected in a spine, the neck resistance can be inversely proportional to its radius, but not to the radius square, as predicted by Ohm's law. We conclude that the postsynaptic voltage cannot only be modulated by changing the number of receptors, but also by the spine geometry. Thus, spine morphology could be a key component in determining synaptic transduction and plasticity.

Reconstructing the gradient source position from steady-state fluxes to small receptors

Recovering the position of a source from the fluxes of diffusing particles through small receptors allows a biological cell to determine its relative position, spatial localization and guide it to a final target. However, how a source can be recovered from point fluxes remains unclear. Using the Narrow Escape approach for an open domain, we compute the diffusion fluxes of Brownian particles generated by a steady-state gradient from a single source through small holes distributed on a surface in two dimensions. We find that the location of a source can be recovered when there are at least 3 receptors and the source is positioned no further than 10 cell radii away, but this condition is not necessary in a narrow strip. The present approach provides a computational basis for the first step of direction sensing of a gradient at a single cell level.

Visualization of Chromatin Decompaction and Break Site Extrusion as Predicted by Statistical Polymer Modeling of Single-Locus Trajectories

Chromatin moves with subdiffusive and spatially constrained dynamics within the cell nucleus. Here, we use single-locus tracking by time-lapse fluorescence microscopy to uncover information regarding the forces that influence chromatin movement following the induction of a persistent DNA double-strand break (DSB). Using improved time-lapse imaging regimens, we monitor trajectories of tagged DNA loci at a high temporal resolution, which allows us to extract biophysical parameters through robust statistical analysis. Polymer modeling based on these parameters predicts chromatin domain expansion near a DSB and damage extrusion from the domain. Both phenomena are confirmed by live imaging in budding yeast. Calculation of the anomalous exponent of locus movement allows us to differentiate forces imposed on the nucleus through the actin cytoskeleton from those that arise from INO80 remodeler-dependent changes in nucleosome organization. Our analytical approach can be applied to high-density single-locus trajectories obtained in any cell type.

Electrostatics of non-neutral biological microdomains

Voltage and charge distributions in cellular microdomains regulate communications, excitability, and signal transduction. We report here new electrical laws in a biological cell, which follow from a nonlinear electro-diffusion model. These newly discovered laws derive from the geometrical cell-membrane properties, such as membrane curvature, volume, and surface area. The electro-diffusion laws can now be used to predict and interpret voltage distribution in cellular microdomains such as synapses, dendritic spine, cilia and more.