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.