Irregular dynamics in up and down cortical states

Complex coherent dynamics is present in a wide variety of neural systems. A typical example is the voltage transitions between up and down states observed in cortical areas in the brain. In this work, we study this phenomenon via a biologically motivated stochastic model of up and down transitions. The model is constituted by a simple bistable rate dynamics, where the synaptic current is modulated by short-term synaptic processes which introduce stochasticity and temporal correlations. A complete analysis of our model, both with mean-field approaches and numerical simulations, shows the appearance of complex transitions between high (up) and low (down) neural activity states, driven by the synaptic noise, with permanence times in the up state distributed according to a power-law. We show that the experimentally observed large fluctuation in up and down permanence times can be explained as the result of sufficiently noisy dynamical synapses with sufficiently large recovery times. Static synapses cannot account for this behavior, nor can dynamical synapses in the absence of noise.     

Dense Percolation in Large-Scale Mean-Field Random Networks Is Provably “Explosive”

Recent reports suggest that evolving large-scale networks exhibit “explosive percolation”: a large fraction of nodes suddenly becomes connected when sufficiently many links have formed in a network. This phase transition has been shown to be continuous (second-order) for most random network formation processes, including classical mean-field random networks and their modifications. We study a related yet different phenomenon referred to as dense percolation, which occurs when a network is already connected, but a large group of nodes must be dense enough, i.e., have at least a certain minimum required percentage of possible links, to form a “highly connected” cluster. Such clusters have been considered in various contexts, including the recently introduced network modularity principle in biological networks. We prove that, contrary to the traditionally defined percolation transition, dense percolation transition is discontinuous (first-order) under the classical mean-field network formation process (with no modifications); therefore, there is not only quantitative, but also qualitative difference between regular and dense percolation transitions. Moreover, the size of the largest dense (highly connected) cluster in a mean-field random network is explicitly characterized by rigorously proven tight asymptotic bounds, which turn out to naturally extend the previously derived formula for the size of the largest clique (a cluster with all possible links) in such a network. We also briefly discuss possible implications of the obtained mathematical results on studying first-order phase transitions in real-world linked systems.     

Enzyme dynamics and activity: time-scale dependence of dynamical transitions in glutamate dehydrogenase solution.

We have examined the temperature dependence of motions in a cryosolution of the enzyme glutamate dehydrogenase (GDH) and compared these with activity. Dynamic neutron scattering was performed with two instruments of different energy resolution, permitting the separate determination of the average dynamical mean square displacements on the sub-approximately 100 ps and sub-approximately 5 ns time scales. The results demonstrate a marked dependence on the time scale of the temperature profile of the mean square displacement. The lowest temperature at which anharmonic motion is observed is heavily dependent on the time window of the instrument used to observe the dynamics. Several dynamical transitions (inflexions of the mean squared displacement) are observed in the slower dynamics. Comparison with the temperature profile of the activity of the enzyme in the same solvent reveals dynamical transitions that have no effect on GDH function.     

Perspectives on the neuroscience of cognition and consciousness

The origin and current use of the concepts of computation, representation and information in Neuroscience are examined and conceptual flaws are identified which vitiate their usefulness for addressing the problem of the neural basis of Cognition and Consciousness. In contrast, a convergence of views is presented to support the characterization of the Nervous System as a complex dynamical system operating in a metastable regime, and capable of evolving to configurations and transitions in phase space with potential relevance for Cognition and Consciousness.     

Methods for imaging labeled neurons together with neuropil features in Drosophila.

We describe staining protocols for serial semithin sections of Drosophila central ganglia that allow visualization of gene expression in particular neurons with counterstaining to display the ganglion architecture. Green fluorescent protein (GFP), expressed in a subset of sensory neurons from a selected enhancer trap line, is visualized by conventional immunohistochemistry with a peroxidase-linked antibody, and neural architecture is revealed by reduced silver staining. This makes visible in histological sections the same GFP-labeled cells seen with confocal microscopy, but with the especial advantage that neuropil structures are also revealed at the level of individual cells and neuron processes. Not only does this allow the physical relationships among intracellularly labeled neurons to be determined by reference to specific features in the neuropil but it also enables a function to be ascribed provisionally to particular regions of neuropil. These methods have particular utility for mapping morphological information on specific neurons in the context of central nervous system architecture, both in adult Drosophila and during development.     

A generalized Flory-Stockmayer kinetic theory of connectivity percolation and rigidity percolation of cytoskeletal networks

Actin networks are essential for living cells to move, reproduce, and sense their environments. The dynamic and rheological behavior of actin networks is modulated by actin-binding proteins such as α-actinin, Arp2/3, and myosin. There is experimental evidence that actin-binding proteins modulate the cooperation of myosin motors by connecting the actin network. In this work, we present an analytical mean field model, using the Flory-Stockmayer theory of gelation, to understand how different actin-binding proteins change the connectivity of the actin filaments as the networks are formed. We follow the kinetics of the networks and estimate the concentrations of actin-binding proteins that are needed to reach connectivity percolation as well as to reach rigidity percolation. We find that Arp2/3 increases the actomyosin connectivity in the network in a non-monotonic way. We also describe how changing the connectivity of actomyosin networks modulates the ability of motors to exert forces, leading to three possible phases of the networks with distinctive dynamical characteristics: a sol phase, a gel phase, and an active phase. Thus, changes in the concentration and activity of actin-binding proteins in cells lead to a phase transition of the actin network, allowing the cells to perform active contraction and change their rheological properties.     

Developments in describing equilibrium phase transitions of multivalent associative macromolecules

Biomolecular condensates are distinct cellular bodies that form and dissolve reversibly to organize cellular matter and biochemical reactions in space and time. Condensates are thought to form and dissolve under the influence of spontaneous and driven phase transitions of multivalent associative macromolecules. These include phase separation, which is defined by segregation of macromolecules from the solvent or from one another, and percolation or gelation, which is an inclusive networking transition driven by reversible associations among multivalent macromolecules. Considerable progress has been made to model sequence-specific phase transitions, especially for intrinsically disordered proteins. Here, we summarize the state-of-the-art of theories and computations aimed at understanding and modeling sequence-specific, thermodynamically controlled, coupled associative and segregative phase transitions of archetypal multivalent macromolecules.     

Geometric properties of a class of piecewise affine biological network models

The purpose of this report is to investigate some dynamical properties common to several biological systems. A model is chosen, which consists of a system of piecewise affine differential equations. Such a model has been previously studied in the context of gene regulation and neural networks, as well as biochemical kinetics. Unlike most of these studies, nonuniform decay rates and several thresholds per variable are assumed, thus considering a more realistic model. This model is investigated with the aid of a geometric formalism. We first provide an analysis of a continuous-space, discrete-time dynamical system equivalent to the initial one, by the way of a transition map. This is similar to former studies. Especially, the analysis of periodic trajectories is carried out in the case of multiple thresholds, thus extending previous results, which all concerned the restricted case of binary systems. The piecewise affine structure of such models is then used to provide a partition of the phase space, in terms of explicit cells. Allowed transitions between these cells define a language on a finite alphabet. Some words are proved to be forbidden in this language, thus improving the knowledge on such systems in terms of symbolic dynamics. More precisely, we show that taking these forbidden words into account leads to a dynamical system with strictly lower topological entropy. This holds for a class of systems, characterized by the presence of a splitting box, with additional conditions. We conclude after an illustrative three-dimensional example.     

Msps governs acentrosomal microtubule assembly and reactivation of quiescent neural stem cells

The ability of stem cells to switch between quiescence and proliferation is crucial for tissue homeostasis and regeneration. Drosophila quiescent neural stem cells (NSCs) extend a primary cellular protrusion from the cell body prior to their reactivation. However, the structure and function of this protrusion are not well established. Here, we show that in the protrusion of quiescent NSCs, microtubules are predominantly acentrosomal and oriented plus‐end‐out toward the tip of the primary protrusion. We have identified Mini Spindles (Msps)/XMAP215 as a key microtubule regulator in quiescent NSCs that governs NSC reactivation via regulating acentrosomal microtubule growth and orientation. We show that quiescent NSCs form membrane contact with the neuropil and E‐cadherin, a cell adhesion molecule, localizes to these NSC‐neuropil junctions. Msps and a plus‐end directed motor protein Kinesin‐2 promote NSC cell cycle re‐entry and target E‐cadherin to NSC‐neuropil contact during NSC reactivation. Together, this work establishes acentrosomal microtubule organization in the primary protrusion of quiescent NSCs and the Msps‐Kinesin‐2 pathway that governs NSC reactivation, in part, by targeting E‐cad to NSC‐neuropil contact sites.     

The emergence of Up and Down states in cortical networks

The cerebral cortex is continuously active in the absence of external stimuli. An example of this spontaneous activity is the voltage transition between an Up and a Down state, observed simultaneously at individual neurons. Since this phenomenon could be of critical importance for working memory and attention, its explanation could reveal some fundamental properties of cortical organization. To identify a possible scenario for the dynamics of Up–Down states, we analyze a reduced stochastic dynamical system that models an interconnected network of excitatory neurons with activity-dependent synaptic depression. The model reveals that when the total synaptic connection strength exceeds a certain threshold, the phase space of the dynamical system contains two attractors, interpreted as Up and Down states. In that case, synaptic noise causes transitions between the states. Moreover, an external stimulation producing a depolarization increases the time spent in the Up state, as observed experimentally. We therefore propose that the existence of Up–Down states is a fundamental and inherent property of a noisy neural ensemble with sufficiently strong synaptic connections.     

Inference of Boolean Networks Using Sensitivity Regularization

The inference of genetic regulatory networks from global measurements of gene expressions is an important problem in computational biology. Recent studies suggest that such dynamical molecular systems are poised at a critical phase transition between an ordered and a disordered phase, affording the ability to balance stability and adaptability while coordinating complex macroscopic behavior. We investigate whether incorporating this dynamical system-wide property as an assumption in the inference process is beneficial in terms of reducing the inference error of the designed network. Using Boolean networks, for which there are well-defined notions of ordered, critical, and chaotic dynamical regimes as well as well-studied inference procedures, we analyze the expected inference error relative to deviations in the networks'' dynamical regimes from the assumption of criticality. We demonstrate that taking criticality into account via a penalty term in the inference procedure improves the accuracy of prediction both in terms of state transitions and network wiring, particularly for small sample sizes.     

Exploring local and non-local interactions for protein stability by structural motif engineering

In order to probe the relative contribution of local and non-local interactions to the thermodynamic stability of proteins, we have devised an experimental approach based on a combination of motif engineering and sequence shuffling. Candidate chain segments in an immunoglobulin V(L) domain were identified whose conformation is proposed to be dominated by non-local interactions. Locally interacting structural motifs of a different conformation were then constructed as replacements, by introducing motif consensus sequences. We find that all nine replacements we constructed systematically reduce the folding cooperativity. By comparing this destabilising effect with the folding transitions of shuffled sequences for three of these motifs, we estimate the contribution of local, native interactions to the free energy of folding. Our results suggest that local and non-local interactions contribute to stability by an approximately equal amount, but that local interactions stabilise by increasing the resistance to denaturation while non-local interactions increase folding cooperativity. The systematic loss of stability by sequence shuffling in these host-guest experiments suggests that the designed interactions indeed are present in the native state, thus consensus sequence engineering may be a useful tool in structure design, but non-local interactions must be taken into account for global stability engineering. Statistical approaches are powerful tools for engineering protein structure and stability, but an analysis based on local sequence propensities alone does not adequately represent the balance of sequence and context in protein structures.     

Pattern recognition in neural networks with competing dynamics: coexistence of fixed-point and cyclic attractors

We study the properties of the dynamical phase transition occurring in neural network models in which a competition between associative memory and sequential pattern recognition exists. This competition occurs through a weighted mixture of the symmetric and asymmetric parts of the synaptic matrix. Through a generating functional formalism, we determine the structure of the parameter space at non-zero temperature and near saturation (i.e., when the number of stored patterns scales with the size of the network), identifying the regions of high and weak pattern correlations, the spin-glass solutions, and the order-disorder transition between these regions. This analysis reveals that, when associative memory is dominant, smooth transitions appear between high correlated regions and spurious states. In contrast when sequential pattern recognition is stronger than associative memory, the transitions are always discontinuous. Additionally, when the symmetric and asymmetric parts of the synaptic matrix are defined in terms of the same set of patterns, there is a discontinuous transition between associative memory and sequential pattern recognition. In contrast, when the symmetric and asymmetric parts of the synaptic matrix are defined in terms of independent sets of patterns, the network is able to perform both associative memory and sequential pattern recognition for a wide range of parameter values.     

Dynamics of hydrocephalus: a physical approach

As brain ventricles lose their ability to regulate the cerebrospinal fluid (CSF) pressure, serious brain conditions collectively named hydrocephalus can appear. By modelling ventricular dynamics with the laws of physics, dynamical instabilities are evidenced, caused by either CSF transport dysregulations or abnormal properties of the elasticity of the ependyma. We show that these instabilities would lead, in most cases, to dilation of the ventricles, establishing a close connection to hydrocephalus, or in some other cases to a ventricular contraction as observed in the slit ventricle syndrome. Signs seem to indicate the possibility of phase transitions occurring as a result of these instabilities, which might have important clinical consequences, such as the inability to recover a healthy state. Even so, our dynamical approach could allow the development of a unified view of these complex intracranial conditions along with a classification that might be clinically relevant.     

On a New Method to Study Drastic Change in Ecosystems

We describe a novel method to study drastic change in ecosystems, based on generic functions used in the study of phase transitions and related physical phenomena. We illustrate its use by applying it to the problem of shallow lake eutrophication, and express our results in terms of an interplay between phosphorus content in the water column and fluxes of this substance between the lake and both its biological community and its surroundings. We contrast our solution to this problem with a previous one based on the concept of resilience, and on bifurcation analysis of a dynamical equation that also involves phosphorus concentration and fluxes. We then suggest a generalized dynamical scheme incorporating the generic functions above, that reduces to our original method in the stationary condition, and allows in addition dealing with cyclic and chaotic regimes, as illustrated through a particular example.     

On ecosystems dynamics

We show how a dynamical system given by a t-score function for some class of monotonic data transformations generates consistent extreme value estimators. The variation of their values increases the uncertainty of proper assessment of climate change. Two important examples illustrate the methodology: mass balance measurements on Guanaco glacier, Chile, and extreme snow loads in Slovakia. We experience singular learning of the transitions in ecosystems.     

Evolutionarily Conserved Repulsive Guidance Role of Slit in the Silkworm Bombyx mori

Axon guidance molecule Slit is critical for the axon repulsion in neural tissues, which is evolutionarily conserved from planarians to humans. However, the function of Slit in the silkworm Bombyx mori was unknown. Here we showed that the structure of Bombyx mori Slit (BmSlit) was different from that in most other species in its C-terminal sequence. BmSlit was localized in the midline glial cell, the neuropil, the tendon cell, the muscle and the silk gland and colocalized with BmRobo1 in the neuropil, the muscle and the silk gland. Knock-down of Bmslit by RNA interference (RNAi) resulted in abnormal development of axons and muscles. Our results suggest that BmSlit has a repulsive role in axon guidance and muscle migration. Moreover, the localization of BmSlit in the silk gland argues for its important function in the development of the silk gland.     

Consciousness related neural events viewed as brain state space transitions

This theoretical and speculative essay addresses a categorical distinction between neural events of sensory-motor cognition and those presumably associated with consciousness. It proposes to view this distinction in the framework of the branch of Statistical Physics currently referred to as Modern Critical Theory (Stanley, Introduction to phase transitions and critical phenomena, 1987; Marro and Dickman, Nonequilibrium phase transitions in lattice, 1999). Based on established landmarks of brain dynamics, network configurations and their role for conveying oscillatory activity of certain frequencies bands, the question is examined: what kind of state space transitions can systems with these properties undergo, and could the relation between neural processes of sensory-motor cognition and those of events in consciousness be of the same category as is characterized by state transitions in non-equilibrium physical systems? Approaches for empirical validation of this view by suitably designed brain imaging studies, and for computational simulations of the proposed principle are discussed.     

Fitting of dynamic recurrent neural network models to sensory stimulus-response data

We present a theoretical study aiming at model fitting for sensory neurons. Conventional neural network training approaches are not applicable to this problem due to lack of continuous data. Although the stimulus can be considered as a smooth time-dependent variable, the associated response will be a set of neural spike timings (roughly the instants of successive action potential peaks) that have no amplitude information. A recurrent neural network model can be fitted to such a stimulus-response data pair by using the maximum likelihood estimation method where the likelihood function is derived from Poisson statistics of neural spiking. The universal approximation feature of the recurrent dynamical neuron network models allows us to describe excitatory-inhibitory characteristics of an actual sensory neural network with any desired number of neurons. The stimulus data are generated by a phased cosine Fourier series having a fixed amplitude and frequency but a randomly shot phase. Various values of amplitude, stimulus component size, and sample size are applied in order to examine the effect of the stimulus to the identification process. Results are presented in tabular and graphical forms at the end of this text. In addition, to demonstrate the success of this research, a study involving the same model, nominal parameters and stimulus structure, and another study that works on different models are compared to that of this research.