Brain-wide dendrites in a near-optimal performance of dynamic range and information transmission.

Dendrites receive and process signals from other neurons. The range of signal intensities that can be robustly distinguished by dendrites is quantified by the dynamic range. We investigate the dynamic range and information transmission efficiency of dendrites in relation to dendritic morphology. We model dendrites in a neuron as multiple excitable binary trees connected to the soma where each node in a tree can be excited by external stimulus or by receiving signals transmitted from adjacent excited nodes. It has been known that larger dendritic trees have a higher dynamic range. We show that for dendritic tress of the same number of nodes, the dynamic range increases with the number of somatic branches and decreases with the asymmetry of dendrites, and the information transmission is more efficient for dendrites with more somatic branches. Moreover, our simulated data suggest that there is an exponential association (decay resp.) of overall relative energy consumption (dynamic range resp.) in relation to the number of somatic branches. This indicates that further increasing the number of somatic branches (e.g. beyond 10 somatic branches) has limited ability to improve the transmission efficiency. With brain-wide neuron digital reconstructions of the pyramidal cells, 90% of neurons have no more than 10 dendrites. These suggest that actual brain-wide dendritic morphology is near optimal in terms of both dynamic range and information transmission.

Synchronization stability of power-grid-tied converters.

Synchronization stability is one of central problems in power systems, and it is becoming much more complicated with the high penetration of renewable energy and power electronics devices. In this paper, we review recent work by several nonlinear models for renewable-dominated power systems in terms of multiple timescales, in particular, grid-tied converters within the DC voltage timescale. For the simplest model, a second-order differential equations called the generalized swing equation by considering only the phase-locked loop (PLL) is obtained, which shows a similar form with the well-known swing equation for a synchronous generator in the traditional power systems. With more outer controllers included, fourth-order and fifth-order models can be obtained. The fourth-order model is called the extended generalized swing equation, exhibiting the combined function of grid synchronization and active power balance on the DC capacitor. In addition, a nonlinear model for a two coupled converter system is given. Based on these studies, we find that the PLL plays a key role in synchronization stability. In summary, the value of this paper is to clarify the key concept of the synchronization stability in renewable-dominated power systems based on different nonlinear models, which still lacks systematic studies and is controversial in the field of electrical power engineering. Meanwhile, it clearly uncovers that the synchronization stability of converters has its root in the phase synchronization concept in nonlinear sciences.

Bursting hierarchy in an adaptive exponential integrate-and-fire network synchronization.

Neuronal network synchronization has received wide interest. In the present manuscript, we study the influence of initial membrane potentials together with network topology on bursting synchronization, in particular the sequential order of stabilized bursting among neurons. We find a hierarchical phenomenon on their bursting order. With a focus on situations where network coupling advances spiking times of neurons, we grade neurons into different layers. Together with the neuronal network structure, we construct directed graphs to indicate bursting propagation between different layers. More explicitly, neurons in upper layers burst earlier than those in lower layers. More interestingly, we find that among the same layer, bursting order of neurons is mainly associated with the number of neurons they connected to the upper layer; more stimuli lead to earlier bursting. Receiving effectively the same stimuli from the upper layer, we observe neurons with fewer connections would burst earlier.

Asynchronous changes of normal lung lobes during respiration based on quantitative computed tomography (CT).

Background: This study aimed to explore the coordinated and independent actions of lung lobes during respiration using quantitative computed tomography (CT) in order to increase our in vivo understanding of pulmonary anatomy. Methods: Cases for whom test results showed normal pulmonary function tests (PFTs) results, and normal paired inspiratory-expiratory chest CT findings, as assessed by 2 radiologists, were retrospectively included in this study. From the chest CT results, we measured quantitative indices of lung volume (LV) and mean lung density (MLD) for the total lung (TL), left lung (LL), right lung (RL), and 5 lobes in inspiratory and expiratory phases. The differences of these measures between bilateral lungs and among the lobes were evaluated to study whether they were consistent or different during respiration. Results: A total of 70 cases were included {median age of 49.5 [interquartile range (IQR), 38.0 to 60.3] years; 32 males; 38 females}. Overall, the inspiratory and expiratory volumes of the LL were smaller than those of the RL (both P<0.001). For the ventilation workload (λ, which indicates the ratio of lobar volume to total LV), the end-expiratory volume ratio (λex ) of the LL was 0.44 (IQR, 0.43 to 0.46), while the end-inspiratory volume ratio (λin ) had risen to 0.46 (IQR, 0.45 to 0.47) (P<0.001). Comparing the 5 lobes, not all lobes shared the same LV. However, the left lower lobe (LLL) and right lower lobe (RLL) showed some similarities. The λin-LLL and λin-RLL was higher than λex-LLL and λex-RLL , respectively (both P<0.001), while the ratios of the other lobes reduced. The pairwise mean absolute difference (PMAD) on λin and λex of the bilateral lower lobes was low in inspiration (0.0288) and expiration (0.0346). The MLD of bilateral lower lobes showed consistency in inspiration or in expiration (inspiration: P>0.999; expiration: P=0.975). In addition, the PMADs between the right middle lobe (RML) and other lobes were significantly larger than the PMAD between other pairs of lobes in both inspiration and expiration. Beyond that, the expiratory MLD of RML [-789.6 (IQR, -814 to -762.05) HU] was the lowest among the 5 lobes. Conclusions: We found that the LL assumes a higher workload during ventilation than it does during respiration. The 5 normal lobes were non-synchronous during respiration and contributed differently to ventilation. The bilateral lower lobes showed similarities and had a high-ventilation function, while and the LV and MLD of the RML showed the least changes within a respiration cycle.

Modelling the motion of organelles in an elongated cell via the coordination of heterogeneous drift-diffusion and long-range transport.

 Cellular distribution of organelles in living cells is achieved via a variety of transport mechanisms, including directed motion, mediated by molecular motors along microtubules (MTs), and diffusion which is predominantly heterogeneous in space. In this paper, we introduce a model for particle transport in elongated cells that couples poleward drift, long-range bidirectional transport and diffusion with spatial heterogeneity in a three-dimensional space. Using stochastic simulations and analysis of a related population model, we find parameter regions where the three-dimensional model can be reduced to a coupled one-dimensional model or even a one-dimensional scalar model. We explore the efficiency with which individual model components can overcome drift towards one of the cell poles to reach an approximately even distribution. In particular, we find that if lateral movement is well mixed, then increasing the binding ability of particles to MTs is an efficient way to overcome a poleward drift, whereas if lateral motion is not well mixed, then increasing the axial diffusivity away from MTs becomes an efficient way to overcome the poleward drift. Our three-dimensional model provides a new tool that will help to understand the mechanisms by which eukaryotic cells organize their organelles in an elongated cell, and in particular when the one-dimensional models are applicable.

Domino-like transient dynamics at seizure onset in epilepsy.

The International League Against Epilepsy (ILAE) groups seizures into "focal", "generalized" and "unknown" based on whether the seizure onset is confined to a brain region in one hemisphere, arises in several brain region simultaneously, or is not known, respectively. This separation fails to account for the rich diversity of clinically and experimentally observed spatiotemporal patterns of seizure onset and even less so for the properties of the brain networks generating them. We consider three different patterns of domino-like seizure onset in Idiopathic Generalized Epilepsy (IGE) and present a novel approach to classification of seizures. To understand how these patterns are generated on networks requires understanding of the relationship between intrinsic node dynamics and coupling between nodes in the presence of noise, which currently is unknown. We investigate this interplay here in the framework of domino-like recruitment across a network. In particular, we use a phenomenological model of seizure onset with heterogeneous coupling and node properties, and show that in combination they generate a range of domino-like onset patterns observed in the IGE seizures. We further explore the individual contribution of heterogeneous node dynamics and coupling by interpreting in-vitro experimental data in which the speed of onset can be chemically modulated. This work contributes to a better understanding of possible drivers for the spatiotemporal patterns observed at seizure onset and may ultimately contribute to a more personalized approach to classification of seizure types in clinical practice.

Miro2 tethers the ER to mitochondria to promote mitochondrial fusion in tobacco leaf epidermal cells.

Mitochondria are highly pleomorphic, undergoing rounds of fission and fusion. Mitochondria are essential for energy conversion, with fusion favouring higher energy demand. Unlike fission, the molecular components involved in mitochondrial fusion in plants are unknown. Here, we show a role for the GTPase Miro2 in mitochondria interaction with the ER and its impacts on mitochondria fusion and motility. Mutations in AtMiro2's GTPase domain indicate that the active variant results in larger, fewer mitochondria which are attached more readily to the ER when compared with the inactive variant. These results are contrary to those in metazoans where Miro predominantly controls mitochondrial motility, with additional GTPases affecting fusion. Synthetically controlling mitochondrial fusion rates could fundamentally change plant physiology by altering the energy status of the cell. Furthermore, altering tethering to the ER could have profound effects on subcellular communication through altering the exchange required for pathogen defence.

Modelling brain-wide neuronal morphology via rooted Cayley trees.

Neuronal morphology is an essential element for brain activity and function. We take advantage of current availability of brain-wide neuron digital reconstructions of the Pyramidal cells from a mouse brain, and analyze several emergent features of brain-wide neuronal morphology. We observe that axonal trees are self-affine while dendritic trees are self-similar. We also show that tree size appear to be random, independent of the number of dendrites within single neurons. Moreover, we consider inhomogeneous branching model which stochastically generates rooted 3-Cayley trees for the brain-wide neuron topology. Based on estimated order-dependent branching probability from actual axonal and dendritic trees, our inhomogeneous model quantitatively captures a number of topological features including size and shape of both axons and dendrites. This sheds lights on a universal mechanism behind the topological formation of brain-wide axonal and dendritic trees.

Modeling the Geometry and Dynamics of the Endoplasmic Reticulum Network.

The endoplasmic reticulum (ER) is an intricate network that pervades the entire cortex of plant cells and its geometric shape undergoes drastic changes. This paper proposes a mathematical model to reconstruct geometric network dynamics by combining the node movements within the network and topological changes engendered by these nodes. The network topology in the model is determined by a modified optimization procedure from the work (Lemarchand, et al. 2014) which minimizes the total length taking into account both degree and angle constraints, beyond the conditions of connectedness and planarity. A novel feature for solving our optimization problem is the use of "lifted" angle constraints, which allows one to considerably reduce the solution runtimes. Using this optimization technique and a Langevin approach for the branching node movement, the simulated network dynamics represent the ER network dynamics observed under latrunculin B treated condition and recaptures features such as the appearance/disappearance of loops within the ER under the native condition. The proposed modeling approach allows quantitative comparison of networks between the model and experimental data based on topological changes induced by node dynamics. An increased temporal resolution of experimental data will allow a more detailed comparison of network dynamics using this modeling approach.

Modeling Endoplasmic Reticulum Network Maintenance in a Plant Cell.

The endoplasmic reticulum (ER) in plant cells forms a highly dynamic network of complex geometry. ER network morphology and dynamics are influenced by a number of biophysical processes, including filament/tubule tension, viscous forces, Brownian diffusion, and interactions with many other organelles and cytoskeletal elements. Previous studies have indicated that ER networks can be thought of as constrained minimal-length networks acted on by a variety of forces that perturb and/or remodel the network. Here, we study two specific biophysical processes involved in remodeling. One is the dynamic relaxation process involving a combination of tubule tension and viscous forces. The other is the rapid creation of cross-connection tubules by direct or indirect interactions with cytoskeletal elements. These processes are able to remodel the ER network: the first reduces network length and complexity whereas the second increases both. Using live cell imaging of ER network dynamics in tobacco leaf epidermal cells, we examine these processes on ER network dynamics. Away from regions of cytoplasmic streaming, we suggest that the dynamic network structure is a balance between the two processes, and we build an integrative model of the two processes for network remodeling. This model produces quantitatively similar ER networks to those observed in experiments. We use the model to explore the effect of parameter variation on statistical properties of the ER network.

Spatial organization of organelles in fungi: Insights from mathematical modelling.

Mathematical modelling in cellular systems aims to describe biological processes in a quantitative manner. Most accurate modelling is based on robust experimental data. Here we review recent progress in the theoretical description of motor behaviour, early endosome motility, ribosome distribution and peroxisome transport in the fungal model system Ustilago maydis and illustrate the power of modelling in our quest to understand molecular details and cellular roles of membrane trafficking in filamentous fungi.

Plant ER geometry and dynamics: biophysical and cytoskeletal control during growth and biotic response.

The endoplasmic reticulum (ER) is an intricate and dynamic network of membrane tubules and cisternae. In plant cells, the ER 'web' pervades the cortex and endoplasm and is continuous with adjacent cells as it passes through plasmodesmata. It is therefore the largest membranous organelle in plant cells. It performs essential functions including protein and lipid synthesis, and its morphology and movement are linked to cellular function. An emerging trend is that organelles can no longer be seen as discrete membrane-bound compartments, since they can physically interact and 'communicate' with one another. The ER may form a connecting central role in this process. This review tackles our current understanding and quantification of ER dynamics and how these change under a variety of biotic and developmental cues.

Active diffusion and microtubule-based transport oppose myosin forces to position organelles in cells.

Even distribution of peroxisomes (POs) and lipid droplets (LDs) is critical to their role in lipid and reactive oxygen species homeostasis. How even distribution is achieved remains elusive, but diffusive motion and directed motility may play a role. Here we show that in the fungus Ustilago maydis ∼95% of POs and LDs undergo diffusive motions. These movements require ATP and involve bidirectional early endosome motility, indicating that microtubule-associated membrane trafficking enhances diffusion of organelles. When early endosome transport is abolished, POs and LDs drift slowly towards the growing cell end. This pole-ward drift is facilitated by anterograde delivery of secretory cargo to the cell tip by myosin-5. Modelling reveals that microtubule-based directed transport and active diffusion support distribution, mobility and mixing of POs. In mammalian COS-7 cells, microtubules and F-actin also counteract each other to distribute POs. This highlights the importance of opposing cytoskeletal forces in organelle positioning in eukaryotes.

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.

Motor-mediated bidirectional transport along an antipolar microtubule bundle: a mathematical model.

Long-distance bidirectional transport of organelles depends on the coordinated motion of various motor proteins on the cytoskeleton. Recent quantitative live cell imaging in the elongated hyphal cells of Ustilago maydis has demonstrated that long-range motility of motors and their endosomal cargo occurs on unipolar microtubules (MTs) near the extremities of the cell. These MTs are bundled into antipolar bundles within the central part of the cell. Dynein and kinesin-3 motors coordinate their activity to move early endosomes (EEs) in a bidirectional fashion where dynein drives motility towards MT minus ends and kinesin towards MT plus ends. Although this means that one can easily assign the drivers of bidirectional motion in the unipolar section, the bipolar orientations in the bundle mean that it is possible for either motor to drive motion in either direction. In this paper we use a multilane asymmetric simple exclusion process modeling approach to simulate and investigate phases of bidirectional motility in a minimal model of an antipolar MT bundle. In our model, EE cargos (particles) change direction on each MT with a turning rate Ω and there is switching between MTs in the bundle at the minus ends. At these ends, particles can hop between MTs with rate q(1) on passing from a unipolar to a bipolar section (the obstacle-induced switching rate) or q(2) on passing in the other direction (the end-induced switching rate). By a combination of numerical simulations and mean-field approximations, we investigate the distribution of particles along the MTs for different values of these parameters and of Θ, the overall density of particles within this closed system. We find that even if Θ is low, the system can exhibit a variety of phases with shocks in the density profiles near plus and minus ends caused by queuing of particles. We discuss how the parameters influence the type of particle that dominates active transport in the bundle.

Controlled and stochastic retention concentrates dynein at microtubule ends to keep endosomes on track.

Bidirectional transport of early endosomes (EEs) involves microtubules (MTs) and associated motors. In fungi, the dynein/dynactin motor complex concentrates in a comet-like accumulation at MT plus-ends to receive kinesin-3-delivered EEs for retrograde transport. Here, we analyse the loading of endosomes onto dynein by combining live imaging of photoactivated endosomes and fluorescent dynein with mathematical modelling. Using nuclear pores as an internal calibration standard, we show that the dynein comet consists of ∼55 dynein motors. About half of the motors are slowly turned over (T(1/2): ∼98 s) and they are kept at the plus-ends by an active retention mechanism involving an interaction between dynactin and EB1. The other half is more dynamic (T(1/2): ∼10 s) and mathematical modelling suggests that they concentrate at MT ends because of stochastic motor behaviour. When the active retention is impaired by inhibitory peptides, dynein numbers in the comet are reduced to half and ∼10% of the EEs fall off the MT plus-ends. Thus, a combination of stochastic accumulation and active retention forms the dynein comet to ensure capturing of arriving organelles by retrograde motors.

Queueing induced by bidirectional motor motion near the end of a microtubule.

Recent live observations of motors in long-range microtubule (MT) dependent transport in the fungus Ustilago maydis have reported bidirectional motion of dynein and an accumulation of the motors at the polymerization-active (the plus-end) of the microtubule. Quantitative data derived from in vivo observation of dynein has enabled us to develop an accurate, quantitatively-valid asymmetric simple exclusion process (ASEP) model that describes the coordinated motion of anterograde and retrograde motors sharing a single oriented microtubule. We give approximate expressions for the size and distribution of the accumulation, and discuss queueing properties for motors entering this accumulation. We show for this ASEP model, that the mean accumulation can be modeled as an M/M/∞ queue that is Poisson distributed with mean F(arr)/p(d), where F(arr) is the flux of motors that arrives at the tip and p(d) is the rate at which individual motors change direction from anterograde to retrograde motion. Deviations from this can in principle be used to gain information about other processes at work in the accumulation. Furthermore, our work is a significant step toward a mathematical description of the complex interactions of motors in cellular long-range transport of organelles.