Selection of Multiarmed Spiral Waves in a Regular Network of Neurons

Formation and selection of multiarmed spiral wave due to spontaneous symmetry breaking are investigated in a regular network of Hodgkin-Huxley neuron by changing the excitability and imposing spatial forcing currents on the neurons in the network. The arm number of the multiarmed spiral wave is dependent on the distribution of spatial forcing currents and excitability diversity in the network, and the selection criterion for supporting multiarmed spiral waves is discussed. A broken spiral segment is measured by a short polygonal line connected by three adjacent points (controlled nodes), and a double-spiral wave can be developed from the spiral segment. Multiarmed spiral wave is formed when a group of double-spiral waves rotate in the same direction in the network. In the numerical studies, a group of controlled nodes are selected and spatial forcing currents are imposed on these nodes, and our results show that l-arm stable spiral wave (l = 2, 3, 4,...8) can be induced to occupy the network completely. It is also confirmed that low excitability is critical to induce multiarmed spiral waves while high excitability is important to propagate the multiarmed spiral wave outside so that distinct multiarmed spiral wave can occupy the network completely. Our results confirm that symmetry breaking of target wave in the media accounts for emergence of multiarmed spiral wave, which can be developed from a group of spiral waves with single arm under appropriate condition, thus the potential formation mechanism of multiarmed spiral wave in the media is explained.     

A Cayley tree immune network model with antibody dynamics

A Cayley tree model of idiotypic networks that includes both B cell and antibody dynamics is formulated and analysed. As in models with B cells only, localized states exist in the network with limited numbers of activated clones surrounded by virgin or near-virgin clones. The existence and stability of these localized network states are explored as a function of model parameters. As in previous models that have included antibody, the stability of immune and tolerant localized states are shown to depend on the ratio of antibody to B cell lifetimes as well as the rate of antibody complex removal. As model parameters are varied, localized steady-states can break down via two routes: dynamically, into chaotic attractors, or structurally into percolation attractors. For a given set of parameters percolation and chaotic attractors can coexist with localized attractors, and thus there do not exist clear cut boundaries in parameter space that separate regions of localized attractors from regions of percolation and chaotic attractors. Stable limit cycles, which are frequent in the two-clone antibody B cell (AB) model, are only observed in highly connected networks. Also found in highly connected networks are localized chaotic attractors. As in experiments by Lundkvistet al. (1989.Proc. natn. Acad. Sci. U.S.A. 86, 5074–5078), injection ofAb ₁ antibodies into a system operating in the chaotic regime can cause a cessation of fluctuations ofAb ₁ andAb ₂ antibodies, a phenomenon already observed in the two-clone AB model. Interestingly, chaotic fluctuations continue at higher levels of the tree, a phenomenon observed by Lundkvistet al. but not accounted for previously.     

An in silico target identification using Boolean network attractors: Avoiding pathological phenotypes

Target identification aims at identifying biomolecules whose function should be therapeutically altered to cure the considered pathology. An algorithm for in silico target identification using Boolean network attractors is proposed. It assumes that attractors correspond to phenotypes produced by the modeled biological network. It identifies target combinations which allow disturbed networks to avoid attractors associated with pathological phenotypes. The algorithm is tested on a Boolean model of the mammalian cell cycle and its applications are illustrated on a Boolean model of Fanconi anemia. Results show that the algorithm returns target combinations able to remove attractors associated with pathological phenotypes and then succeeds in performing the proposed in silico target identification. However, as with any in silico evidence, there is a bridge to cross between theory and practice. Nevertheless, it is expected that the algorithm is of interest for target identification.     

An Efficient Algorithm for Computing Attractors of Synchronous And Asynchronous Boolean Networks

Biological networks, such as genetic regulatory networks, often contain positive and negative feedback loops that settle down to dynamically stable patterns. Identifying these patterns, the so-called attractors, can provide important insights for biologists to understand the molecular mechanisms underlying many coordinated cellular processes such as cellular division, differentiation, and homeostasis. Both synchronous and asynchronous Boolean networks have been used to simulate genetic regulatory networks and identify their attractors. The common methods of computing attractors are that start with a randomly selected initial state and finish with exhaustive search of the state space of a network. However, the time complexity of these methods grows exponentially with respect to the number and length of attractors. Here, we build two algorithms to achieve the computation of attractors in synchronous and asynchronous Boolean networks. For the synchronous scenario, combing with iterative methods and reduced order binary decision diagrams (ROBDD), we propose an improved algorithm to compute attractors. For another algorithm, the attractors of synchronous Boolean networks are utilized in asynchronous Boolean translation functions to derive attractors of asynchronous scenario. The proposed algorithms are implemented in a procedure called geneFAtt. Compared to existing tools such as genYsis, geneFAtt is significantly faster in computing attractors for empirical experimental systems.

Availability

The software package is available at https://sites.google.com/site/desheng619/download.     

Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons

We are interested in noise-induced firings of subthreshold neurons which may be used for encoding environmental stimuli. Noise-induced population synchronization was previously studied only for the case of global coupling, unlike the case of subthreshold spiking neurons. Hence, we investigate the effect of complex network architecture on noise-induced synchronization in an inhibitory population of subthreshold bursting Hindmarsh–Rose neurons. For modeling complex synaptic connectivity, we consider the Watts–Strogatz small-world network which interpolates between regular lattice and random network via rewiring, and investigate the effect of small-world connectivity on emergence of noise-induced population synchronization. Thus, noise-induced burst synchronization (synchrony on the slow bursting time scale) and spike synchronization (synchrony on the fast spike time scale) are found to appear in a synchronized region of the J–D plane (J: synaptic inhibition strength and D: noise intensity). As the rewiring probability p is decreased from 1 (random network) to 0 (regular lattice), the region of spike synchronization shrinks rapidly in the J–D plane, while the region of the burst synchronization decreases slowly. We separate the slow bursting and the fast spiking time scales via frequency filtering, and characterize the noise-induced burst and spike synchronizations by employing realistic order parameters and statistical-mechanical measures introduced in our recent work. Thus, the bursting and spiking thresholds for the burst and spike synchronization transitions are determined in terms of the bursting and spiking order parameters, respectively. Furthermore, we also measure the degrees of burst and spike synchronizations in terms of the statistical-mechanical bursting and spiking measures, respectively.     

Determination of wave speed and wave separation in the arteries using diameter and velocity

The determination of arterial wave speed and the separation of the forward and backward waves have been established using simultaneous measurements of pressure (P) and velocity (U). In this work, we present a novel algorithm for the determination of local wave speed and the separation of waves using the simultaneous measurements of diameter (D) and U. The theoretical basis of this work is the solution of the 1D equations of flow in elastic tubes. A relationship between D and U is derived, from which, local wave speed can be determined; C=±0.5(dU_±/d ln D_±). When only unidirectional waves are present, this relationship describes a linear relationship between ln D and U. Therefore, constructing a ln DU-loop should result in a straight line in the early part of the cycle when it is most probable that waves are running in the forward direction. Using this knowledge of wave speed, it is also possible to derive a set of equations to separate the forward and backward waves from the measured D and U waveforms. Once the forward and backward waveforms of D and U are established, we can calculate the energy carried by the forward and backward waves, in a similar way to that of wave intensity analysis. In this paper, we test the new algorithm in vitro and present results from data measured in the carotid artery of human and the ascending aorta of canine. We conclude that the new technique can be reproduced in vitro, and in different vessels of different species, in vivo. The new algorithm is easy to use to determine wave speed and separate D and U waveforms into their forward and backward directions. Using this technique has the merits of utilising noninvasive measurements, which would be useful in the clinical setting.     

Noise-induced spatiotemporal patterns in Hodgkin–Huxley neuronal network

The effect of noise on the pattern selection in a regular network of Hodgkin–Huxley neurons is investigated, and the transition of pattern in the network is measured from subexcitable to excitable media. Extensive numerical results confirm that kinds of travelling wave such as spiral wave, circle wave and target wave could be developed and kept alive in the subexcitable network due to the noise. In the case of excitable media under noise, the developed spiral wave and target wave could coexist and new target-like wave is induced near to the border of media. The averaged membrane potentials over all neurons in the network are calculated to detect the periodicity of the time series and the generated traveling wave. Furthermore, the firing probabilities of neurons in networks are also calculated to analyze the collective behavior of networks.     

Effects of fatigue on inter-cycle variability in cross-country skiing

The aim of the study was to examine the inter-cycle variability in cross-country skiing gait and its evolution with fatigue. Both issues were investigated to understand the flexibility capabilities of the neuromuscular system. Four women and four men skied on a treadmill, up to exhaustion. The angular displacements of the arms and legs movements were obtained for 40 s period at the beginning and end of the skiing test. Mean inter-cycle standard deviation (SD_c), largest Lyapunov exponent (λ₁) and correlation dimension (D_c) were computed for each time series and surrogate counterpart to evaluate the magnitude and nature of the variability. For any experimental time series, λ₁ was positive, D_c greater than 1 and both were found to be different from their surrogate counterparts, confirming that the temporal variations of the data had a deterministic origin. More, larger SD_c, D_c and λ₁ values were observed at the end of the test, indicating more variability, noise and local dynamic instability in the data with fatigue. Hence, the fluctuations of limb angular displacements displayed a chaotic behavior, which reflected flexibility of the neuromuscular system to adapt to possible perturbations during skiing. However, such chaotic behavior degraded with fatigue, making the neuromuscular system less adaptable and more unstable.     

Receptor,Ligand and Transducer Contributions to Dopamine D2 Receptor Functional Selectivity

Functional selectivity (or biased agonism) is a property exhibited by some G protein-coupled receptor (GPCR) ligands, which results in the modulation of a subset of a receptor’s signaling capabilities and more precise control over complex biological processes. The dopamine D2 receptor (D₂R) exhibits pleiotropic responses to the biogenic amine dopamine (DA) to mediate complex central nervous system functions through activation of G proteins and β-arrestins. D₂R is a prominent therapeutic target for psychological and neurological disorders in which DA biology is dysregulated and targeting D₂R with functionally selective drugs could provide a means by which pharmacotherapies could be developed. However, factors that determine GPCR functional selectivity in vivo may be multiple with receptors, ligands and transducers contributing to the process. We have recently described a mutagenesis approach to engineer biased D₂R mutants in which G protein-dependent (^[Gprot]D₂R) and β-arrestin-dependent signaling (^[βarr]D₂R) were successfully separated (Peterson, et al. PNAS, 2015). Here, permutations of these mutants were used to identify critical determinants of the D₂R signaling complex that impart signaling bias in response to the natural or synthetic ligands. Critical residues identified in generating ^[Gprot]D₂R and ^[βarr]D₂R conferred control of partial agonism at G protein and/or β-arrestin activity. Another set of mutations that result in G protein bias was identified that demonstrated that full agonists can impart unique activation patterns, and provided further credence to the concept of ligand texture. Finally, the contributions and interplay between different transducers indicated that G proteins are not aberrantly activated, and that receptor kinase and β-arrestin activities are inextricably linked. These data provide a thorough elucidation of the feasibility and malleability of D₂R functional selectivity and point to means by which novel in vivo therapies could be modeled.     

Segmental flexibility of ribosomal protein S1 bound to ribosomes and Q beta-replicase

The protonization pattern of the endogenous donor component D₁ which feeds electrons directly into chl-a⁺_II has been analyzed in Tris-washed inside-out thylakoids with the aid of appropriate pH-indicators. It was found that under repetitive flash excitation the amount of protons released is proportional to the extent of D₁-oxidation, depending on the time between the flashes. The kinetics of D₁-oxidation (being practically the same as in normal Tris-washed chloroplasts) are faster than the proton release by two orders of magnitude. The results lead to the conclusion that D₁ is protonized in the reduced state with pK(D^ox₁) < 5 and becomes deprotonized in the oxidized state with pK(D^red₁) ? 8. The proton release is kinetically limited by a transport barrier. Implications on the interpretation of the proton release pattern in preparation with intact water oxidation are discussed.     

PvD1 defensin,a plant antimicrobial peptide with inhibitory activity against Leishmania amazonensis

Plant defensins are small cysteine-rich peptides and exhibit antimicrobial activity against a variety of both plant and human pathogens. Despite the broad inhibitory activity that plant defensins exhibit against different micro-organisms, little is known about their activity against protozoa. In a previous study, we isolated a plant defensin named PvD₁ from Phaseolus vulgaris (cv. Pérola) seeds, which was seen to be deleterious against different yeast cells and filamentous fungi. It exerted its effects by causing an increase in the endogenous production of ROS (reactive oxygen species) and NO (nitric oxide), plasma membrane permeabilization and the inhibition of medium acidification. In the present study, we investigated whether PvD₁ could act against the protozoan Leishmania amazonensis. Our results show that, besides inhibiting the proliferation of L. amazonensis promastigotes, the PvD₁ defensin was able to cause cytoplasmic fragmentation, formation of multiple cytoplasmic vacuoles and membrane permeabilization in the cells of this organism. Furthermore, we show, for the first time, that PvD₁ defensin was located within the L. amazonensis cells, suggesting the existence of a possible intracellular target.     

Ca2+-mobility in the sarcoplasmic reticulum of ventricular myocytes is low

The sarcoplasmic reticulum (SR) in ventricular myocytes contains releasable Ca²⁺ for activating cellular contraction. Recent measurements of intra-SR (luminal) Ca²⁺ suggest a high diffusive Ca²⁺-mobility constant (D_CaSR). This could help spatially to unify SR Ca²⁺-content ([Ca²⁺]_SRT) and standardize Ca²⁺-release throughout the cell. But measurements of localized depletions of luminal Ca²⁺ (Ca²⁺-blinks), associated with local Ca²⁺-release (Ca²⁺-sparks), suggest D_CaSR may actually be low. Here we describe a novel method for measuring D_CaSR. Using a cytoplasmic Ca²⁺-fluorophore, we estimate regional [Ca²⁺]_SRT from localized, caffeine-induced SR Ca²⁺-release. Caffeine microperfusion of one end of a guinea pig or rat myocyte diffusively empties the whole SR at a rate indicating D_CaSR is 8-9 μm²/s, up to tenfold lower than previous estimates. Ignoring background SR Ca²⁺-leakage in our measurement protocol produces an artifactually high D_CaSR (>40 μm²/s), which may also explain the previous high values. Diffusion-reaction modeling suggests that a low D_CaSR would be sufficient to support local SR Ca²⁺-signaling within sarcomeres during excitation-contraction coupling. Low D_CaSR also implies that [Ca²⁺]_SRT may readily become spatially nonuniform, particularly under pathological conditions of spatially nonuniform Ca²⁺-release. Local control of luminal Ca²⁺, imposed by low D_CaSR, may complement the well-established local control of SR Ca²⁺-release by Ca²⁺-channel/ryanodine receptor couplons.     

Studies on mixing in horizontal rotating tubular bioreactor

Mixing studies in the horizontal rotating tubular bioreactor (HRTB) were done to explore the influences of the liquid level (H _M =0.050.08 m) and the distance between the partition walls (D _S =0.020.07 m) on the mixing performance in the bioreactor described by the “spiral flow” model. The optimised adjustable parameters of the model were correlated with the process parameters of the bioreactor expressed as dimensionless numbers: Reynolds rotation number (Re _N ) and Reynolds axial flow number (Re _D ). The polynomial coefficients of the correlations were correlated further with the liquid level in the bioreactor (H _M ) and the distance between the partition walls (D _S ). In that way, three modified prediction systems (SC-2A, SC-6A and SC-9A) were established. The analysis based on different criteria selected the prediction system SC-9A as the most suitable to describe the mixing performance of HRTB.     

Predicting Local SR Ca Dynamics during Ca Wave Propagation in Ventricular Myocytes

Of the many ongoing controversies regarding the workings of the sarcoplasmic reticulum (SR) in cardiac myocytes, two unresolved and interconnected topics are 1), mechanisms of calcium (Ca²⁺) wave propagation, and 2), speed of Ca²⁺ diffusion within the SR. Ca²⁺ waves are initiated when a spontaneous local SR Ca²⁺ release event triggers additional release from neighboring clusters of SR release channels (ryanodine receptors (RyRs)). A lack of consensus regarding the effective Ca²⁺ diffusion constant in the SR (D_Ca,SR) severely complicates our understanding of whether dynamic local changes in SR [Ca²⁺] can influence wave propagation. To address this problem, we have implemented a computational model of cytosolic and SR [Ca²⁺] during Ca²⁺ waves. Simulations have investigated how dynamic local changes in SR [Ca²⁺] are influenced by 1), D_Ca,SR; 2), the distance between RyR clusters; 3), partial inhibition or stimulation of SR Ca²⁺ pumps; 4), SR Ca²⁺ pump dependence on cytosolic [Ca²⁺]; and 5), the rate of transfer between network and junctional SR. Of these factors, D_Ca,SR is the primary determinant of how release from one RyR cluster alters SR [Ca²⁺] in nearby regions. Specifically, our results show that local increases in SR [Ca²⁺] ahead of the wave can potentially facilitate Ca²⁺ wave propagation, but only if SR diffusion is relatively slow. These simulations help to delineate what changes in [Ca²⁺] are possible during SR Ca²⁺release, and they broaden our understanding of the regulatory role played by dynamic changes in [Ca²⁺]_SR.     

Chaotic neural network applied to two-dimensional motion control

Chaotic dynamics generated in a chaotic neural network model are applied to 2-dimensional (2-D) motion control. The change of position of a moving object in each control time step is determined by a motion function which is calculated from the firing activity of the chaotic neural network. Prototype attractors which correspond to simple motions of the object toward four directions in 2-D space are embedded in the neural network model by designing synaptic connection strengths. Chaotic dynamics introduced by changing system parameters sample intermediate points in the high-dimensional state space between the embedded attractors, resulting in motion in various directions. By means of adaptive switching of the system parameters between a chaotic regime and an attractor regime, the object is able to reach a target in a 2-D maze. In computer experiments, the success rate of this method over many trials not only shows better performance than that of stochastic random pattern generators but also shows that chaotic dynamics can be useful for realizing robust, adaptive and complex control function with simple rules.     

Measurements of transmembrane potential and magnetic field at the apex of the heart

We studied the transmembrane potential and magnetic fields from electrical activity at the apex of the isolated rabbit heart experimentally using optical mapping and superconducting quantum interference device microscopy, and theoretically using monodomain and bidomain models. The cardiac apex has a complex spiral fiber architecture that plays an important role in the development and propagation of action currents during stimulation at the apex. This spiral fiber orientation contains both radial electric currents that contribute to the electrocardiogram and electrically silent circular currents that cannot be detected by the electrocardiogram but are detectable by their magnetic field, B_z. In our experiments, the transmembrane potential, V_m, was first measured optically and then B_z was measured with a superconducting quantum interference device microscope. Based on a simple model of the spiral structure of the apex, V_m was expected to exhibit circular wave front patterns and B_z to reflect the circular component of the action currents. Although the circular V_m wave fronts were detected, the B_z maps were not as simple as expected. However, we observed a pattern consistent with a tilted axis for the apex spiral fiber geometry. We were able to simulate similar patterns in both a monodomain model of a tilted stack of rings of dipole current and a bidomain model of a tilted stack of spiraled cardiac tissue that was stimulated at the apex. The fact that the spatial pattern of the magnetic data was more complex than the simple circles observed for V_m suggests that the magnetic data contain information that cannot be found electrically.     

Analysis of the primary structure of collagen for the origins of molecular packing

The amino acid sequence in the triplet region of the α1 chain of collagen was analyzed for complementary relationships that would explain the stagger of multiples of 670 Å between the rod-like molecules in the fibril. The analysis was done by moving the sequence of 1011 amino acids past itself and scoring for complementarity between opposing amino acids allowing a range of ±2 to 3 residues. It was found that interactions between amino acids of opposite charge and between large hydrophobic amino acids in the overlapping region between two chains are maximal when the chains are staggered by 0D, 1D, 2D, 3D and 4D, where D = 234 ± 1 residues. The residue repeat derived from this value is 2.86 ± 0.02 Å. The existence of a D separation between interacting residues was shown to be reflected in the actual distribution of large hydrophobic amino acids. Surprisingly, the distribution approximates the pattern ($\text{2D}\text{11}$)₅($\text{D}\text{11}$) repeated over 4.4D intervals. The regularity may arise from structural constraints imposed by super-coiling. The distribution of charged residues is less regular and does not show a well-defined periodicity. However, positively-charged residues tend to be near negatively-charged residues, allowing intramolecular charge neutralization as well as strong intermolecular charge interactions at 0D.