Structure and Dynamics of ER: Minimal Networks and Biophysical Constraints

The endoplasmic reticulum (ER) in live cells is a highly mobile network whose structure dynamically changes on a number of timescales. The role of such drastic changes in any system is unclear, although there are correlations with ER function. A better understanding of the fundamental biophysical constraints on the system will allow biologists to determine the effects of molecular factors on ER dynamics. Previous studies have identified potential static elements that the ER may remodel around. Here, we use these structural elements to assess biophysical principles behind the network dynamics. By analyzing imaging data of tobacco leaf epidermal cells under two different conditions, i.e., native state (control) and latrunculin B (treated), we show that the geometric structure and dynamics of ER networks can be understood in terms of minimal networks. Our results show that the ER network is well modeled as a locally minimal-length network between the static elements that potentially anchor the ER to the cell cortex over longer timescales; this network is perturbed by a mixture of random and deterministic forces. The network need not have globally minimum length; we observe cases where the local topology may change dynamically between different Euclidean Steiner network topologies. The networks in the treated cells are easier to quantify, because they are less dynamic (the treatment suppresses actin dynamics), but the same general features are found in control cells. Using a Langevin approach, we model the dynamics of the nonpersistent nodes and use this to show that the images can be used to estimate both local viscoelastic behavior of the cytoplasm and filament tension in the ER network. This means we can explain several aspects of the ER geometry in terms of biophysical principles.     

Robustness in phenotypic plasticity and heterogeneity patterns enabled by EMT networks

Epithelial-mesenchymal plasticity (EMP) is a key arm of cancer metastasis and is observed across many contexts. Cells undergoing EMP can reversibly switch between three classes of phenotypes: epithelial (E), mesenchymal (M), and hybrid E/M. While a large number of multistable regulatory networks have been identified to be driving EMP in various contexts, the exact mechanisms and design principles that enable robustness in driving EMP across contexts are not yet fully understood. Here, we investigated dynamic and structural robustness in EMP networks with regard to phenotypic heterogeneity and plasticity. We use two different approaches to simulate these networks: a computationally inexpensive, parameter-independent continuous state space Boolean model, and an ODE-based parameter-agnostic framework (RACIPE), both of which yielded similar phenotypic distributions. While the latter approach is useful for measurements of plasticity, the former model enabled us to extensively investigate robustness in phenotypic heterogeneity. Using perturbations to network topology and by varying network parameters, we show that multistable EMP networks are structurally and dynamically more robust compared with their randomized counterparts, thereby highlighting their topological hallmarks. These features of robustness are governed by a balance of positive and negative feedback loops embedded in these networks. Using a combination of the number of negative and positive feedback loops weighted by their lengths, we identified a metric that can explain the structural and dynamical robustness of these networks. This metric enabled us to compare networks across multiple sizes, and the network principles thus obtained can be used to identify fragilities in large networks without simulating their dynamics. Our analysis highlights a network topology-based approach to quantify robustness in the phenotypic heterogeneity and plasticity emergent from EMP networks.     

Intrinsic Neuronal Properties Switch the Mode of Information Transmission in Networks

Diverse ion channels and their dynamics endow single neurons with complex biophysical properties. These properties determine the heterogeneity of cell types that make up the brain, as constituents of neural circuits tuned to perform highly specific computations. How do biophysical properties of single neurons impact network function? We study a set of biophysical properties that emerge in cortical neurons during the first week of development, eventually allowing these neurons to adaptively scale the gain of their response to the amplitude of the fluctuations they encounter. During the same time period, these same neurons participate in large-scale waves of spontaneously generated electrical activity. We investigate the potential role of experimentally observed changes in intrinsic neuronal properties in determining the ability of cortical networks to propagate waves of activity. We show that such changes can strongly affect the ability of multi-layered feedforward networks to represent and transmit information on multiple timescales. With properties modeled on those observed at early stages of development, neurons are relatively insensitive to rapid fluctuations and tend to fire synchronously in response to wave-like events of large amplitude. Following developmental changes in voltage-dependent conductances, these same neurons become efficient encoders of fast input fluctuations over few layers, but lose the ability to transmit slower, population-wide input variations across many layers. Depending on the neurons'' intrinsic properties, noise plays different roles in modulating neuronal input-output curves, which can dramatically impact network transmission. The developmental change in intrinsic properties supports a transformation of a networks function from the propagation of network-wide information to one in which computations are scaled to local activity. This work underscores the significance of simple changes in conductance parameters in governing how neurons represent and propagate information, and suggests a role for background synaptic noise in switching the mode of information transmission.     

Stochasticity,Bistability and the Wisdom of Crowds: A Model for Associative Learning in Genetic Regulatory Networks

It is generally believed that associative memory in the brain depends on multistable synaptic dynamics, which enable the synapses to maintain their value for extended periods of time. However, multistable dynamics are not restricted to synapses. In particular, the dynamics of some genetic regulatory networks are multistable, raising the possibility that even single cells, in the absence of a nervous system, are capable of learning associations. Here we study a standard genetic regulatory network model with bistable elements and stochastic dynamics. We demonstrate that such a genetic regulatory network model is capable of learning multiple, general, overlapping associations. The capacity of the network, defined as the number of associations that can be simultaneously stored and retrieved, is proportional to the square root of the number of bistable elements in the genetic regulatory network. Moreover, we compute the capacity of a clonal population of cells, such as in a colony of bacteria or a tissue, to store associations. We show that even if the cells do not interact, the capacity of the population to store associations substantially exceeds that of a single cell and is proportional to the number of bistable elements. Thus, we show that even single cells are endowed with the computational power to learn associations, a power that is substantially enhanced when these cells form a population.     

Actin network growth under load

Many processes in eukaryotic cells, including the crawling motion of the whole cell, rely on the growth of branched actin networks from surfaces. In addition to their well-known role in generating propulsive forces, actin networks can also sustain substantial pulling loads thanks to their persistent attachment to the surface from which they grow. The simultaneous network elongation and surface attachment inevitably generate a force that opposes network growth. Here, we study the local dynamics of a growing actin network, accounting for simultaneous network elongation and surface attachment, and show that there exist several dynamical regimes that depend on both network elasticity and the kinetic parameters of actin polymerization. We characterize this in terms of a phase diagram and provide a connection between mesoscopic theories and the microscopic dynamics of an actin network at a surface. Our framework predicts the onset of instabilities that lead to the local detachment of the network and translate to oscillatory behavior and waves, as observed in many cellular phenomena and in vitro systems involving actin network growth, such as the saltatory dynamics of actin-propelled oil drops.     

Population networks: a large-scale framework for modelling cortical neural networks

Artificial neural networks are usually built on rather few elements such as activation functions, learning rules, and the network topology. When modelling the more complex properties of realistic networks, however, a number of higher-level structural principles become important. In this paper we present a theoretical framework for modelling cortical networks at a high level of abstraction. Based on the notion of a population of neurons, this framework can accommodate the common features of cortical architecture, such as lamination, multiple areas and topographic maps, input segregation, and local variations of the frequency of different cell types (e.g., cytochrome oxidase blobs). The framework is meant primarily for the simulation of activation dynamics; it can also be used to model the neural environment of single cells in a multiscale approach. Received: 9 January 1996 / Accepted in revised form: 24 July 1996     

Functional Connectivity in MRI Is Driven by Spontaneous BOLD Events

Functional brain signals are frequently decomposed into a relatively small set of large scale, distributed cortical networks that are associated with different cognitive functions. It is generally assumed that the connectivity of these networks is static in time and constant over the whole network, although there is increasing evidence that this view is too simplistic. This work proposes novel techniques to investigate the contribution of spontaneous BOLD events to the temporal dynamics of functional connectivity as assessed by ultra-high field functional magnetic resonance imaging (fMRI). The results show that: 1) spontaneous events in recognised brain networks contribute significantly to network connectivity estimates; 2) these spontaneous events do not necessarily involve whole networks or nodes, but clusters of voxels which act in concert, forming transiently synchronising sub-networks and 3) a task can significantly alter the number of localised spontaneous events that are detected within a single network. These findings support the notion that spontaneous events are the main driver of the large scale networks that are commonly detected by seed-based correlation and ICA. Furthermore, we found that large scale networks are manifestations of smaller, transiently synchronising sub-networks acting dynamically in concert, corresponding to spontaneous events, and which do not necessarily involve all voxels within the network nodes oscillating in unison.     

Neuro-robotics study on integrative learning of proactive visual attention and motor behaviors

The current paper proposes a novel model for integrative learning of proactive visual attention and sensory-motor control as inspired by the premotor theory of visual attention. The model is characterized by coupling a slow dynamics network with a fast dynamics network and by inheriting our prior proposed multiple timescales recurrent neural networks model (MTRNN) that may correspond to the fronto-parietal networks in the cortical brains. The neuro-robotics experiments in a task of manipulating multiple objects utilizing the proposed model demonstrated that some degrees of generalization in terms of position and object size variation can be achieved by organizing seamless integration of the proactive object-related visual attention and the related sensory-motor control into a set of action primitives in the distributed neural activities appearing in the fast dynamics network. It was also shown that such action primitives can be combined in compositional ways in acquiring novel actions in the slow dynamics network. The experimental results presented substantiate the premotor theory of visual attention.     

Membrane and Actin Tethering Transitions Help IQGAP1 Coordinate GTPase and Lipid Messenger Signaling

The coordination of lipid messenger signaling with cytoskeletal regulation is central to many organelle-specific regulatory processes. This coupling often depends on the function of multidomain scaffolds that orchestrate transient interactions among multiple signaling intermediates and regulatory proteins on organelles. The number of possible scaffold interaction partners and the ability for these interactions to occur at different timescales makes investigations of scaffold functions challenging. This work employs live cell imaging to probe how the multidomain scaffold IQ motif containing GTPase activating protein 1 (IQGAP1) coordinates the activities of proteins affecting local actin polymerization, membrane processing, and phosphoinositide signaling. Using endosomes that are confined by a local actin network as a model system, we demonstrate that IQGAP1 can transition between different actin and endosomal membrane tethered states. Fast scaffold binding/disassociation transitions are shown to be driven by interactions between C-terminal scaffold domains and Rho GTPases at the membrane. Fluctuations in these binding modes are linked to negative regulation of actin polymerization. Although this control governs core elements of IQGAP1 dynamics, actin binding by the N-terminal calponin homology domain of the scaffold is shown to help the scaffold track the temporal development of endosome membrane markers, implying actin associations bolster membrane and actin coordination. Importantly, these effects are not easily distilled purely through standard (static) co-localization analyses or traditional pathway perturbations methods and were resolved by performing dynamic correlation and multiple regression analyses of IQGAP1 scaffold mutants. Using these capabilities with pharmacological inhibition, we provide evidence that membrane tethering is dependent on the activities of the lipid kinase phosphoinositide 3-kinase in addition to the Rho GTPases Rac1 and Cdc42. Overall, these methods and results point to a scaffold tethering mechanism that allows IQGAP1 to help control the amplitude of phosphoinositide lipid messenger signaling by coordinating signaling intermediate activities with the development and disassembly of local actin cytoskeletal networks.     

Emergence of Slow-Switching Assemblies in Structured Neuronal Networks

Unraveling the interplay between connectivity and spatio-temporal dynamics in neuronal networks is a key step to advance our understanding of neuronal information processing. Here we investigate how particular features of network connectivity underpin the propensity of neural networks to generate slow-switching assembly (SSA) dynamics, i.e., sustained epochs of increased firing within assemblies of neurons which transition slowly between different assemblies throughout the network. We show that the emergence of SSA activity is linked to spectral properties of the asymmetric synaptic weight matrix. In particular, the leading eigenvalues that dictate the slow dynamics exhibit a gap with respect to the bulk of the spectrum, and the associated Schur vectors exhibit a measure of block-localization on groups of neurons, thus resulting in coherent dynamical activity on those groups. Through simple rate models, we gain analytical understanding of the origin and importance of the spectral gap, and use these insights to develop new network topologies with alternative connectivity paradigms which also display SSA activity. Specifically, SSA dynamics involving excitatory and inhibitory neurons can be achieved by modifying the connectivity patterns between both types of neurons. We also show that SSA activity can occur at multiple timescales reflecting a hierarchy in the connectivity, and demonstrate the emergence of SSA in small-world like networks. Our work provides a step towards understanding how network structure (uncovered through advancements in neuroanatomy and connectomics) can impact on spatio-temporal neural activity and constrain the resulting dynamics.     

Probing Cellular Mechanoadaptation Using Cell-Substrate De-Adhesion Dynamics: Experiments and Model

Physical properties of the extracellular matrix (ECM) are known to regulate cellular processes ranging from spreading to differentiation, with alterations in cell phenotype closely associated with changes in physical properties of cells themselves. When plated on substrates of varying stiffness, fibroblasts have been shown to exhibit stiffness matching property, wherein cell cortical stiffness increases in proportion to substrate stiffness up to 5 kPa, and subsequently saturates. Similar mechanoadaptation responses have also been observed in other cell types. Trypsin de-adhesion represents a simple experimental framework for probing the contractile mechanics of adherent cells, with de-adhesion timescales shown to scale inversely with cortical stiffness values. In this study, we combine experiments and computation in deciphering the influence of substrate properties in regulating de-adhesion dynamics of adherent cells. We first show that NIH 3T3 fibroblasts cultured on collagen-coated polyacrylamide hydrogels de-adhere faster on stiffer substrates. Using a simple computational model, we qualitatively show how substrate stiffness and cell-substrate bond breakage rate collectively influence de-adhesion timescales, and also obtain analytical expressions of de-adhesion timescales in certain regimes of the parameter space. Finally, by comparing stiffness-dependent experimental and computational de-adhesion responses, we show that faster de-adhesion on stiffer substrates arises due to force-dependent breakage of cell-matrix adhesions. In addition to illustrating the utility of employing trypsin de-adhesion as a biophysical tool for probing mechanoadaptation, our computational results highlight the collective interplay of substrate properties and bond breakage rate in setting de-adhesion timescales.     

Transient dynamics of genetic regulatory networks

We present an approximation scheme for deriving reaction rate equations of genetic regulatory networks. This scheme predicts the timescales of transient dynamics of such networks more accurately than does standard quasi-steady state analysis by introducing prefactors to the ODEs that govern the dynamics of the protein concentrations. These prefactors render the ODE systems slower than their quasi-steady state approximation counterparts. We introduce the method by examining a positive feedback gene regulatory network, and show how the transient dynamics of this network are more accurately modeled when the prefactor is included. Next, we examine the repressilator, a genetic oscillator, and show that the period, amplitude, and bifurcation diagram defining the onset of the oscillations are better estimated by the prefactor method. Finally, we examine the consequences of the method to the dynamics of reduced models of the phage lambda switch, and show that the switching times between the two states is slowed by the presence of the prefactor that arises from protein multimerization and DNA binding.     

Two-Cell to N-Cell Heterogeneous,Inhibitory Networks: Precise Linking of Multistable and Coherent Properties

Inhibitory networks are now recognized as being the controllers of several brain rhythms. However, experimental work with inhibitory cells is technically difficult not only because of their smaller percentage of the neuronal population, but also because of their diverse properties. As such, inhibitory network models with tight links to the experimental data are needed to understand their contributions to population rhythms. However, mathematical analyses of network models with more than two cells is challenging when the cellular models involve biophysical details. We use bifurcation analyses and simulations to show that two-cell analyses can quantitatively predict N-cell (N = 20, 50, 100) network dynamics for heterogeneous, inhibitory networks. Interestingly, multistable states in the two-cell system are manifest as different and distinct coherent network patterns in the N-cell networks for the same parameter sets.     

Transitions between asynchronous and synchronous states: a theory of correlations in small neural circuits

The study of correlations in neural circuits of different size, from the small size of cortical microcolumns to the large-scale organization of distributed networks studied with functional imaging, is a topic of central importance to systems neuroscience. However, a theory that explains how the parameters of mesoscopic networks composed of a few tens of neurons affect the underlying correlation structure is still missing. Here we consider a theory that can be applied to networks of arbitrary size with multiple populations of homogeneous fully-connected neurons, and we focus its analysis to a case of two populations of small size. We combine the analysis of local bifurcations of the dynamics of these networks with the analytical calculation of their cross-correlations. We study the correlation structure in different regimes, showing that a variation of the external stimuli causes the network to switch from asynchronous states, characterized by weak correlation and low variability, to synchronous states characterized by strong correlations and wide temporal fluctuations. We show that asynchronous states are generated by strong stimuli, while synchronous states occur through critical slowing down when the stimulus moves the network close to a local bifurcation. In particular, strongly positive correlations occur at the saddle-node and Andronov-Hopf bifurcations of the network, while strongly negative correlations occur when the network undergoes a spontaneous symmetry-breaking at the branching-point bifurcations. These results show how the correlation structure of firing-rate network models is strongly modulated by the external stimuli, even keeping the anatomical connections fixed. These results also suggest an effective mechanism through which biological networks may dynamically modulate the encoding and integration of sensory information.     

Bistable responses in bacterial genetic networks: designs and dynamical consequences

A key property of living cells is their ability to react to stimuli with specific biochemical responses. These responses can be understood through the dynamics of underlying biochemical and genetic networks. Evolutionary design principles have been well studied in networks that display graded responses, with a continuous relationship between input signal and system output. Alternatively, biochemical networks can exhibit bistable responses so that over a range of signals the network possesses two stable steady states. In this review, we discuss several conceptual examples illustrating network designs that can result in a bistable response of the biochemical network. Next, we examine manifestations of these designs in bacterial master-regulatory genetic circuits. In particular, we discuss mechanisms and dynamic consequences of bistability in three circuits: two-component systems, sigma-factor networks, and a multistep phosphorelay. Analyzing these examples allows us to expand our knowledge of evolutionary design principles networks with bistable responses.     

Modelling the modulation of cortical Up-Down state switching by astrocytes

Up-Down synchronization in neuronal networks refers to spontaneous switches between periods of high collective firing activity (Up state) and periods of silence (Down state). Recent experimental reports have shown that astrocytes can control the emergence of such Up-Down regimes in neural networks, although the molecular or cellular mechanisms that are involved are still uncertain. Here we propose neural network models made of three populations of cells: excitatory neurons, inhibitory neurons and astrocytes, interconnected by synaptic and gliotransmission events, to explore how astrocytes can control this phenomenon. The presence of astrocytes in the models is indeed observed to promote the emergence of Up-Down regimes with realistic characteristics. Our models show that the difference of signalling timescales between astrocytes and neurons (seconds versus milliseconds) can induce a regime where the frequency of gliotransmission events released by the astrocytes does not synchronize with the Up and Down phases of the neurons, but remains essentially stable. However, these gliotransmission events are found to change the localization of the bifurcations in the parameter space so that with the addition of astrocytes, the network enters a bistability region of the dynamics that corresponds to Up-Down synchronization. Taken together, our work provides a theoretical framework to test scenarios and hypotheses on the modulation of Up-Down dynamics by gliotransmission from astrocytes.     

Consistent dynamics suggests tight regulation of biophysical parameters in a small network of bursting neurons

The neuronal firing patterns in the pyloric network of crustaceans are remarkably consistent among animals. Although this characteristic of the pyloric network is well-known, the biophysical mechanisms underlying the regulation of the systems output are receiving renewed attention. Computer simulations of the pyloric network recently demonstrated that consistent motor output can be achieved from neurons with disparate biophysical parameters among animals. Here we address this hypothesis by pharmacologically manipulating the pyloric network and analyzing the emerging voltage oscillations and firing patterns. Our results show that the pyloric network of the lobster stomatogastric ganglion maintains consistent and regular firing patterns even when entire populations of specific voltage-gated channels and synaptic receptors are blocked. The variations of temporal parameters used to characterize the burst patterns of the neurons as well as their intraburst spike dynamics do not display statistically significant increase after blocking the transient K-currents (with 4-aminopyridine), the glutamatergic inhibitory synapses (with picrotoxin), or the cholinergic synapses (with atropine) in pyloric networks from different animals. These data suggest that in this very compact circuit, the biophysical parameters are cell-specific and tightly regulated.     

Modeling,analysis and simulation of ant-based network routing protocols

Using the metaphor of swarm intelligence, ant-based routing protocols deploy control packets that behave like ants to discover and optimize routes between pairs of nodes. These ant-based routing protocols provide an elegant, scalable solution to the routing problem for both wired and mobile ad hoc networks. The routing problem is highly nonlinear because the control packets alter the local routing tables as they are routed through the network. We mathematically map the local rules by which the routing tables are altered to the dynamics of the entire networks. Using dynamical systems theory, we map local protocol rules to full network performance, which helps us understand the impact of protocol parameters on network performance. In this paper, we systematically derive and analyze global models for simple ant-based routing protocols using both pheromone deposition and evaporation. In particular, we develop a stochastic model by modeling the probability density of ants over the network. The model is validated by comparing equilibrium pheromone levels produced by the global analysis to results obtained from simulation studies. We use both a Matlab simulation with ideal communications and a QualNet simulation with realistic communication models. Using these analytic and computational methods, we map out a complete phase diagram of network behavior over a small multipath network. We show the existence of both stable and unstable (inaccessible) routing solutions having varying properties of efficiency and redundancy depending upon the routing parameters. Finally, we apply these techniques to a larger 50-node network and show that the design principles acquired from studying the small model network extend to larger networks.     

A new approach for extracting information from protein dynamics

Increased ability to predict protein structures is moving research focus towards understanding protein dynamics. A promising approach is to represent protein dynamics through networks and take advantage of well-developed methods from network science. Most studies build protein dynamics networks from correlation measures, an approach that only works under very specific conditions, instead of the more robust inverse approach. Thus, we apply the inverse approach to the dynamics of protein dihedral angles, a system of internal coordinates, to avoid structural alignment. Using the well-characterized adhesion protein, FimH, we show that our method identifies networks that are physically interpretable, robust, and relevant to the allosteric pathway sites. We further use our approach to detect dynamical differences, despite structural similarity, for Siglec-8 in the immune system, and the SARS-CoV-2 spike protein. Our study demonstrates that using the inverse approach to extract a network from protein dynamics yields important biophysical insights.