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.

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.

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.

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.

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.

Ki-67 acts as a biological surfactant to disperse mitotic chromosomes.

Eukaryotic genomes are partitioned into chromosomes that form compact and spatially well-separated mechanical bodies during mitosis. This enables chromosomes to move independently of each other for segregation of precisely one copy of the genome to each of the nascent daughter cells. Despite insights into the spatial organization of mitotic chromosomes and the discovery of proteins at the chromosome surface, the molecular and biophysical bases of mitotic chromosome structural individuality have remained unclear. Here we report that the proliferation marker protein Ki-67 (encoded by the MKI67 gene), a component of the mitotic chromosome periphery, prevents chromosomes from collapsing into a single chromatin mass after nuclear envelope disassembly, thus enabling independent chromosome motility and efficient interactions with the mitotic spindle. The chromosome separation function of human Ki-67 is not confined within a specific protein domain, but correlates with size and net charge of truncation mutants that apparently lack secondary structure. This suggests that Ki-67 forms a steric and electrostatic charge barrier, similar to surface-active agents (surfactants) that disperse particles or phase-separated liquid droplets in solvents. Fluorescence correlation spectroscopy showed a high surface density of Ki-67 and dual-colour labelling of both protein termini revealed an extended molecular conformation, indicating brush-like arrangements that are characteristic of polymeric surfactants. Our study thus elucidates a biomechanical role of the mitotic chromosome periphery in mammalian cells and suggests that natural proteins can function as surfactants in intracellular compartmentalization.

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.

Spindle pole body-anchored Kar3 drives the nucleus along microtubules from another nucleus in preparation for nuclear fusion during yeast karyogamy.

Nuclear migration during yeast karyogamy, termed nuclear congression, is required to initiate nuclear fusion. Congression involves a specific regulation of the microtubule minus end-directed kinesin-14 motor Kar3 and a rearrangement of the cytoplasmic microtubule attachment sites at the spindle pole bodies (SPBs). However, how these elements interact to produce the forces necessary for nuclear migration is less clear. We used electron tomography, molecular genetics, quantitative imaging, and first principles modeling to investigate how cytoplasmic microtubules are organized during nuclear congression. We found that Kar3, with the help of its light chain, Cik1, is anchored during mating to the SPB component Spc72 that also serves as a nucleator and anchor for microtubules via their minus ends. Moreover, we show that no direct microtubule-microtubule interactions are required for nuclear migration. Instead, SPB-anchored Kar3 exerts the necessary pulling forces laterally on microtubules emanating from the SPB of the mating partner nucleus. Therefore, a twofold symmetrical application of the core principle that drives nuclear migration in higher cells is used in yeast to drive nuclei toward each other before nuclear fusion.

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.

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.

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.

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.

Real-Time Imaging of a Single Gene Reveals Transcription-Initiated Local Confinement.

Genome dynamics are intimately linked to the regulation of gene expression, the most fundamental mechanism in biology, yet we still do not know whether the very process of transcription drives spatial organization at specific gene loci. Here, we have optimized the ANCHOR/ParB DNA-labeling system for real-time imaging of a single-copy, estrogen-inducible transgene in human cells. Motion of an ANCHOR3-tagged DNA locus was recorded in the same cell before and during the appearance of nascent MS2-labeled mRNA. We found that transcription initiation by RNA polymerase 2 resulted in confinement of the mRNA-producing gene domain within minutes. Transcription-induced confinement occurred in each single cell independently of initial, highly heterogeneous mobility. Constrained mobility was maintained even when inhibiting polymerase elongation. Chromatin motion at constant step size within a largely confined area hence leads to increased collisions that are compatible with the formation of gene-specific chromatin domains, and reflect the assembly of functional protein hubs and DNA processing during the rate-limiting steps of transcription.

Quantifying the Dynamical Complexity of Chaotic Time Series.

A powerful approach is proposed for the characterization of chaotic signals. It is based on the combined use of two classes of indicators: (i) the probability of suitable symbolic sequences (obtained from the ordinal patterns of the corresponding time series); (ii) the width of the corresponding cylinder sets. This way, much information can be extracted and used to quantify the complexity of a given signal. As an example of the potentiality of the method, I introduce a modified permutation entropy which allows for quantitative estimates of the Kolmogorov-Sinai entropy in hyperchaotic models, where other methods would be unpractical. As a by-product, estimates of the fractal dimension of the underlying attractors are possible as well.

Feedback, Mass Conservation and Reaction Kinetics Impact the Robustness of Cellular Oscillations.

Oscillations occur in a wide variety of cellular processes, for example in calcium and p53 signaling responses, in metabolic pathways or within gene-regulatory networks, e.g. the circadian system. Since it is of central importance to understand the influence of perturbations on the dynamics of these systems a number of experimental and theoretical studies have examined their robustness. The period of circadian oscillations has been found to be very robust and to provide reliable timing. For intracellular calcium oscillations the period has been shown to be very sensitive and to allow for frequency-encoded signaling. We here apply a comprehensive computational approach to study the robustness of period and amplitude of oscillatory systems. We employ different prototype oscillator models and a large number of parameter sets obtained by random sampling. This framework is used to examine the effect of three design principles on the sensitivities towards perturbations of the kinetic parameters. We find that a prototype oscillator with negative feedback has lower period sensitivities than a prototype oscillator relying on positive feedback, but on average higher amplitude sensitivities. For both oscillator types, the use of Michaelis-Menten instead of mass action kinetics in all degradation and conversion reactions leads to an increase in period as well as amplitude sensitivities. We observe moderate changes in sensitivities if replacing mass conversion reactions by purely regulatory reactions. These insights are validated for a set of established models of various cellular rhythms. Overall, our work highlights the importance of reaction kinetics and feedback type for the variability of period and amplitude and therefore for the establishment of predictive models.

Immunization and Targeted Destruction of Networks using Explosive Percolation.

A new method ("explosive immunization") is proposed for immunization and targeted destruction of networks. It combines the explosive percolation (EP) paradigm with the idea of maintaining a fragmented distribution of clusters. The ability of each node to block the spread of an infection (or to prevent the existence of a large cluster of connected nodes) is estimated by a score. The algorithm proceeds by first identifying low score nodes that should not be vaccinated or destroyed, analogously to the links selected in EP if they do not lead to large clusters. As in EP, this is done by selecting the worst node (weakest blocker) from a finite set of randomly chosen "candidates." Tests on several real-world and model networks suggest that the method is more efficient and faster than any existing immunization strategy. Because of the latter property it can deal with very large networks.

Diverging Fluctuations of the Lyapunov Exponents.

We show that in generic one-dimensional Hamiltonian lattices the diffusion coefficient of the maximum Lyapunov exponent diverges in the thermodynamic limit. We trace this back to the long-range correlations associated with the evolution of the hydrodynamic modes. In the case of normal heat transport, the divergence is even stronger, leading to the breakdown of the usual single-function Family-Vicsek scaling ansatz. A similar scenario is expected to arise in the evolution of rough interfaces in the presence of suitably correlated background noise.

Geometrical and mechanical properties control actin filament organization.

The different actin structures governing eukaryotic cell shape and movement are not only determined by the properties of the actin filaments and associated proteins, but also by geometrical constraints. We recently demonstrated that limiting nucleation to specific regions was sufficient to obtain actin networks with different organization. To further investigate how spatially constrained actin nucleation determines the emergent actin organization, we performed detailed simulations of the actin filament system using Cytosim. We first calibrated the steric interaction between filaments, by matching, in simulations and experiments, the bundled actin organization observed with a rectangular bar of nucleating factor. We then studied the overall organization of actin filaments generated by more complex pattern geometries used experimentally. We found that the fraction of parallel versus antiparallel bundles is determined by the mechanical properties of actin filament or bundles and the efficiency of nucleation. Thus nucleation geometry, actin filaments local interactions, bundle rigidity, and nucleation efficiency are the key parameters controlling the emergent actin architecture. We finally simulated more complex nucleation patterns and performed the corresponding experiments to confirm the predictive capabilities of the model.