A robust balancing mechanism for spiking neural networks.

Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works also in the absence of strong external currents. Biologically, the mechanism exploits the plasticity of excitatory-excitatory synapses induced by short-term depression. Mathematically, the nonlinear response of the synaptic activity is the key ingredient responsible for the emergence of a stable balanced regime. Our claim is supported by a simple self-consistent analysis accompanied by extensive simulations performed for increasing network sizes. The observed regime is essentially fluctuation driven and characterized by highly irregular spiking dynamics of all neurons.

Mammalian oocytes store proteins for the early embryo on cytoplasmic lattices.

Mammalian oocytes are filled with poorly understood structures called cytoplasmic lattices. First discovered in the 1960s and speculated to correspond to mammalian yolk, ribosomal arrays, or intermediate filaments, their function has remained enigmatic to date. Here, we show that cytoplasmic lattices are sites where oocytes store essential proteins for early embryonic development. Using super-resolution light microscopy and cryoelectron tomography, we show that cytoplasmic lattices are composed of filaments with a high surface area, which contain PADI6 and subcortical maternal complex proteins. The lattices associate with many proteins critical for embryonic development, including proteins that control epigenetic reprogramming of the preimplantation embryo. Loss of cytoplasmic lattices by knocking out PADI6 or the subcortical maternal complex prevents the accumulation of these proteins and results in early embryonic arrest. Our work suggests that cytoplasmic lattices enrich maternally provided proteins to prevent their premature degradation and cellular activity, thereby enabling early mammalian development.

A quantitative map of nuclear pore assembly reveals two distinct mechanisms.

Understanding how the nuclear pore complex (NPC) is assembled is of fundamental importance to grasp the mechanisms behind its essential function and understand its role during the evolution of eukaryotes1-4. There are at least two NPC assembly pathways-one during the exit from mitosis and one during nuclear growth in interphase-but we currently lack a quantitative map of these events. Here we use fluorescence correlation spectroscopy calibrated live imaging of endogenously fluorescently tagged nucleoporins to map the changes in the composition and stoichiometry of seven major modules of the human NPC during its assembly in single dividing cells. This systematic quantitative map reveals that the two assembly pathways have distinct molecular mechanisms, in which the order of addition of two large structural components, the central ring complex and nuclear filaments are inverted. The dynamic stoichiometry data was integrated to create a spatiotemporal model of the NPC assembly pathway and predict the structures of postmitotic NPC assembly intermediates.

Colocalization of different neurotransmitter transporters on synaptic vesicles is sparse except for VGLUT1 and ZnT3.

Vesicular transporters (VTs) define the type of neurotransmitter that synaptic vesicles (SVs) store and release. While certain mammalian neurons release multiple transmitters, it is not clear whether the release occurs from the same or distinct vesicle pools at the synapse. Using quantitative single-vesicle imaging, we show that a vast majority of SVs in the rodent brain contain only one type of VT, indicating specificity for a single neurotransmitter. Interestingly, SVs containing dual transporters are highly diverse (27 types) but small in proportion (2% of all SVs), excluding the largest pool that carries VGLUT1 and ZnT3 (34%). Using VGLUT1-ZnT3 SVs, we demonstrate that the transporter colocalization influences the SV content and synaptic quantal size. Thus, the presence of diverse transporters on the same vesicle is bona fide, and depending on the VT types, this may act to regulate neurotransmitter type, content, and release in space and time.

Coherent oscillations in balanced neural networks driven by endogenous fluctuations.

We present a detailed analysis of the dynamical regimes observed in a balanced network of identical quadratic integrate-and-fire neurons with sparse connectivity for homogeneous and heterogeneous in-degree distributions. Depending on the parameter values, either an asynchronous regime or periodic oscillations spontaneously emerge. Numerical simulations are compared with a mean-field model based on a self-consistent Fokker-Planck equation (FPE). The FPE reproduces quite well the asynchronous dynamics in the homogeneous case by either assuming a Poissonian or renewal distribution for the incoming spike trains. An exact self-consistent solution for the mean firing rate obtained in the limit of infinite in-degree allows identifying balanced regimes that can be either mean- or fluctuation-driven. A low-dimensional reduction of the FPE in terms of circular cumulants is also considered. Two cumulants suffice to reproduce the transition scenario observed in the network. The emergence of periodic collective oscillations is well captured both in the homogeneous and heterogeneous setups by the mean-field models upon tuning either the connectivity or the input DC current. In the heterogeneous situation, we analyze also the role of structural heterogeneity.

Collective dynamics in the presence of finite-width pulses.

The idealization of neuronal pulses as δ-spikes is a convenient approach in neuroscience but can sometimes lead to erroneous conclusions. We investigate the effect of a finite pulse width on the dynamics of balanced neuronal networks. In particular, we study two populations of identical excitatory and inhibitory neurons in a random network of phase oscillators coupled through exponential pulses with different widths. We consider three coupling functions inspired by leaky integrate-and-fire neurons with delay and type I phase-response curves. By exploring the role of the pulse widths for different coupling strengths, we find a robust collective irregular dynamics, which collapses onto a fully synchronous regime if the inhibitory pulses are sufficiently wider than the excitatory ones. The transition to synchrony is accompanied by hysteretic phenomena (i.e., the co-existence of collective irregular and synchronous dynamics). Our numerical results are supported by a detailed scaling and stability analysis of the fully synchronous solution. A conjectured first-order phase transition emerging for δ-spikes is smoothed out for finite-width pulses.

Parental genome unification is highly error-prone in mammalian embryos.

Most human embryos are aneuploid. Aneuploidy frequently arises during the early mitotic divisions of the embryo, but its origin remains elusive. Human zygotes that cluster their nucleoli at the pronuclear interface are thought to be more likely to develop into healthy euploid embryos. Here, we show that the parental genomes cluster with nucleoli in each pronucleus within human and bovine zygotes, and clustering is required for the reliable unification of the parental genomes after fertilization. During migration of intact pronuclei, the parental genomes polarize toward each other in a process driven by centrosomes, dynein, microtubules, and nuclear pore complexes. The maternal and paternal chromosomes eventually cluster at the pronuclear interface, in direct proximity to each other, yet separated. Parental genome clustering ensures the rapid unification of the parental genomes on nuclear envelope breakdown. However, clustering often fails, leading to chromosome segregation errors and micronuclei, incompatible with healthy embryo development.

Permutation Entropy of Weakly Noise-Affected Signals.

We analyze the permutation entropy of deterministic chaotic signals affected by a weak observational noise. We investigate the scaling dependence of the entropy increase on both the noise amplitude and the window length used to encode the time series. In order to shed light on the scenario, we perform a multifractal analysis, which allows highlighting the emergence of many poorly populated symbolic sequences generated by the stochastic fluctuations. We finally make use of this information to reconstruct the noiseless permutation entropy. While this approach works quite well for Hénon and tent maps, it is much less effective in the case of hyperchaos. We argue about the underlying motivations.

Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion.

Energy transport in one-dimensional chains of particles with three conservation laws is generically anomalous and belongs to the Kardar-Parisi-Zhang dynamical universality class. Surprisingly, some examples where an apparent normal heat diffusion is found over a large range of length scales were reported. We propose a novel physical explanation of these intriguing observations. We develop a scaling analysis that explains how this may happen in the vicinity of an integrable limit, such as, but not only, the famous Toda model. In this limit, heat transport is mostly supplied by quasiparticles with a very large mean free path ℓ. Upon increasing the system size L, three different regimes can be observed: a ballistic one, an intermediate diffusive range, and, eventually, the crossover to the anomalous (hydrodynamic) regime. Our theoretical considerations are supported by numerical simulations of a gas of diatomic hard-point particles for almost equal masses and of a weakly perturbed Toda chain. Finally, we discuss the case of the perturbed harmonic chain, which exhibits a yet different scenario.

Heat flux in one-dimensional systems.

Understanding heat transport in one-dimensional systems remains a major challenge in theoretical physics, both from the quantum as well as from the classical point of view. In fact, steady states of one-dimensional systems are commonly characterized by macroscopic inhomogeneities, and by long-range correlations, as well as large fluctuations that are typically absent in standard three-dimensional thermodynamic systems. These effects violate locality-material properties in the bulk may be strongly affected by the boundaries, leading to anomalous energy transport-and they make more problematic the interpretation of mechanical microscopic quantities in terms of thermodynamic observables. Here, we revisit the problem of heat conduction in chains of classical nonlinear oscillators, following a Lagrangian and a Eulerian approach. The Eulerian definition of the flux is composed of a convective and a conductive component. The former component tends to prevail at large temperatures where the system behavior is increasingly gaslike. Finally, we find that the convective component tends to be negative in the presence of a negative pressure.

Blinking chimeras in globally coupled rotators.

In globally coupled ensembles of identical oscillators so-called chimera states can be observed. The chimera state is a symmetry-broken regime, where a subset of oscillators forms a cluster, a synchronized population, while the rest of the system remains a collection of nonsynchronized, scattered units. We describe here a blinking chimera regime in an ensemble of seven globally coupled rotators (Kuramoto oscillators with inertia). It is characterized by a death-birth process, where a long-term stable cluster of four oscillators suddenly dissolves and is very quickly reborn with a new reshuffled configuration. We identify three different kinds of rare blinking events and give a quantitative characterization by applying stability analysis to the long-lived chaotic state and to the short-lived regular regimes that arise when the cluster dissolves.

Between phase and amplitude oscillators.

We analyze an intermediate collective regime where amplitude oscillators distribute themselves along a closed, smooth, time-dependent curve C, thereby maintaining the typical ordering of (identical) phase oscillators. This is achieved by developing a general formalism based on two partial differential equations, which describe the evolution of the probability density along C and of the shape of C itself. The formalism is specifically developed for Stuart-Landau oscillators, but it is general enough to apply to other classes of amplitude oscillators. The main achievements consist in (i) identification and characterization of a transition to self-consistent partial synchrony (SCPS), which confirms the crucial role played by higher Fourier harmonics in the coupling function; (ii) an analytical treatment of SCPS, including a detailed stability analysis; and (iii) the discovery of a different form of collective chaos, which can be seen as a generalization of SCPS and characterized by a multifractal probability density. Finally, we are able to describe given dynamical regimes at both the macroscopic and the microscopic level, thereby shedding additional light on the relationship between the two different levels of description.

Absolute quantification of cohesin, CTCF and their regulators in human cells.

The organisation of mammalian genomes into loops and topologically associating domains (TADs) contributes to chromatin structure, gene expression and recombination. TADs and many loops are formed by cohesin and positioned by CTCF. In proliferating cells, cohesin also mediates sister chromatid cohesion, which is essential for chromosome segregation. Current models of chromatin folding and cohesion are based on assumptions of how many cohesin and CTCF molecules organise the genome. Here we have measured absolute copy numbers and dynamics of cohesin, CTCF, NIPBL, WAPL and sororin by mass spectrometry, fluorescence-correlation spectroscopy and fluorescence recovery after photobleaching in HeLa cells. In G1-phase, there are ~250,000 nuclear cohesin complexes, of which ~ 160,000 are chromatin-bound. Comparison with chromatin immunoprecipitation-sequencing data implies that some genomic cohesin and CTCF enrichment sites are unoccupied in single cells at any one time. We discuss the implications of these findings for how cohesin can contribute to genome organisation and cohesion.

Dynamical Freezing of Relaxation to Equilibrium.

We provide evidence of an extremely slow thermalization occurring in the discrete nonlinear Schrödinger model. At variance with many similar processes encountered in statistical mechanics-typically ascribed to the presence of (free) energy barriers-here the slowness has a purely dynamical origin: it is due to the presence of an adiabatic invariant, which freezes the dynamics of a tall breather. Consequently, relaxation proceeds via rare events, where energy is suddenly released towards the background. We conjecture that this exponentially slow relaxation is a key ingredient contributing to the nonergodic behavior recently observed in the negative-temperature region of the discrete nonlinear Schrödinger equation.

Ubiquity of collective irregular dynamics in balanced networks of spiking neurons.

We revisit the dynamics of a prototypical model of balanced activity in networks of spiking neurons. A detailed investigation of the thermodynamic limit for fixed density of connections (massive coupling) shows that, when inhibition prevails, the asymptotic regime is not asynchronous but rather characterized by a self-sustained irregular, macroscopic (collective) dynamics. So long as the connectivity is massive, this regime is found in many different setups: leaky as well as quadratic integrate-and-fire neurons; large and small coupling strength; and weak and strong external currents.

Experimental and computational framework for a dynamic protein atlas of human cell division.

Essential biological functions, such as mitosis, require tight coordination of hundreds of proteins in space and time. Localization, the timing of interactions and changes in cellular structure are all crucial to ensure the correct assembly, function and regulation of protein complexes1-4. Imaging of live cells can reveal protein distributions and dynamics but experimental and theoretical challenges have prevented the collection of quantitative data, which are necessary for the formulation of a model of mitosis that comprehensively integrates information and enables the analysis of the dynamic interactions between the molecular parts of the mitotic machinery within changing cellular boundaries. Here we generate a canonical model of the morphological changes during the mitotic progression of human cells on the basis of four-dimensional image data. We use this model to integrate dynamic three-dimensional concentration data of many fluorescently knocked-in mitotic proteins, imaged by fluorescence correlation spectroscopy-calibrated microscopy5. The approach taken here to generate a dynamic protein atlas of human cell division is generic; it can be applied to systematically map and mine dynamic protein localization networks that drive cell division in different cell types, and can be conceptually transferred to other cellular functions.

Dual-spindle formation in zygotes keeps parental genomes apart in early mammalian embryos.

At the beginning of mammalian life, the genetic material from each parent meets when the fertilized egg divides. It was previously thought that a single microtubule spindle is responsible for spatially combining the two genomes and then segregating them to create the two-cell embryo. We used light-sheet microscopy to show that two bipolar spindles form in the zygote and then independently congress the maternal and paternal genomes. These two spindles aligned their poles before anaphase but kept the parental genomes apart during the first cleavage. This spindle assembly mechanism provides a potential rationale for erroneous divisions into more than two blastomeric nuclei observed in mammalian zygotes and reveals the mechanism behind the observation that parental genomes occupy separate nuclear compartments in the two-cell embryo.

Quantitative mapping of fluorescently tagged cellular proteins using FCS-calibrated four-dimensional imaging.

The ability to tag a protein at its endogenous locus with a fluorescent protein (FP) enables quantitative understanding of protein dynamics at the physiological level. Genome-editing technology has now made this powerful approach routinely applicable to mammalian cells and many other model systems, thereby opening up the possibility to systematically and quantitatively map the cellular proteome in four dimensions. 3D time-lapse confocal microscopy (4D imaging) is an essential tool for investigating spatial and temporal protein dynamics; however, it lacks the required quantitative power to make the kind of absolute and comparable measurements required for systems analysis. In contrast, fluorescence correlation spectroscopy (FCS) provides quantitative proteomic and biophysical parameters such as protein concentration, hydrodynamic radius, and oligomerization but lacks the capability for high-throughput application in 4D spatial and temporal imaging. Here we present an automated experimental and computational workflow that integrates both methods and delivers quantitative 4D imaging data in high throughput. These data are processed to yield a calibration curve relating the fluorescence intensities (FIs) of image voxels to the absolute protein abundance. The calibration curve allows the conversion of the arbitrary FIs to protein amounts for all voxels of 4D imaging stacks. Using our workflow, users can acquire and analyze hundreds of FCS-calibrated image series to map their proteins of interest in four dimensions. Compared with other protocols, the current protocol does not require additional calibration standards and provides an automated acquisition pipeline for FCS and imaging data. The protocol can be completed in 1 d.

A quantitative map of human Condensins provides new insights into mitotic chromosome architecture.

The two Condensin complexes in human cells are essential for mitotic chromosome structure. We used homozygous genome editing to fluorescently tag Condensin I and II subunits and mapped their absolute abundance, spacing, and dynamic localization during mitosis by fluorescence correlation spectroscopy (FSC)-calibrated live-cell imaging and superresolution microscopy. Although ∼35,000 Condensin II complexes are stably bound to chromosomes throughout mitosis, ∼195,000 Condensin I complexes dynamically bind in two steps: prometaphase and early anaphase. The two Condensins rarely colocalize at the chromatid axis, where Condensin II is centrally confined, but Condensin I reaches ∼50% of the chromatid diameter from its center. Based on our comprehensive quantitative data, we propose a three-step hierarchical loop model of mitotic chromosome compaction: Condensin II initially fixes loops of a maximum size of ∼450 kb at the chromatid axis, whose size is then reduced by Condensin I binding to ∼90 kb in prometaphase and ∼70 kb in anaphase, achieving maximum chromosome compaction upon sister chromatid segregation.

Self-assembly of Mutant Huntingtin Exon-1 Fragments into Large Complex Fibrillar Structures Involves Nucleated Branching.

Huntingtin (HTT) fragments with extended polyglutamine tracts self-assemble into amyloid-like fibrillar aggregates. Elucidating the fibril formation mechanism is critical for understanding Huntington's disease pathology and for developing novel therapeutic strategies. Here, we performed systematic experimental and theoretical studies to examine the self-assembly of an aggregation-prone N-terminal HTT exon-1 fragment with 49 glutamines (Ex1Q49). Using high-resolution imaging techniques such as electron microscopy and atomic force microscopy, we show that Ex1Q49 fragments in cell-free assays spontaneously convert into large, highly complex bundles of amyloid fibrils with multiple ends and fibril branching points. Furthermore, we present experimental evidence that two nucleation mechanisms control spontaneous Ex1Q49 fibrillogenesis: (1) a relatively slow primary fibril-independent nucleation process, which involves the spontaneous formation of aggregation-competent fibrillary structures, and (2) a fast secondary fibril-dependent nucleation process, which involves nucleated branching and promotes the rapid assembly of highly complex fibril bundles with multiple ends. The proposed aggregation mechanism is supported by studies with the small molecule O4, which perturbs early events in the aggregation cascade and delays Ex1Q49 fibril assembly, comprehensive mathematical and computational modeling studies, and seeding experiments with small, preformed fibrillar Ex1Q49 aggregates that promote the assembly of amyloid fibrils. Together, our results suggest that nucleated branching in vitro plays a critical role in the formation of complex fibrillar HTT exon-1 aggregates with multiple ends.