A quantitative synchronization model for smooth pursuit target tracking

We propose a quantitative model for human smooth pursuit tracking of a continuously moving visual target which is based on synchronization of an internal expectancy model of the target position coupled to the retinal target signal. The model predictions are tested in a smooth circular pursuit eye tracking experiment with transient target blanking of variable duration. In subjects with a high tracking accuracy, the model accounts for smooth pursuit and repeatedly reproduces quantitatively characteristic patterns of the eye dynamics during target blanking. In its simplest form, the model has only one free parameter, a coupling constant. An extended model with a second parameter, a time delay or memory term, accounts for predictive smooth pursuit eye movements which advance the target. The model constitutes an example of synchronization of a complex biological system with perceived sensory signals. Cognitive and Neurobiological Research Consortium in Traumatic Brain Injury (CNRC-TBI).     

Global stability for cholera epidemic models

Cholera is a water and food borne infectious disease caused by the gram-negative bacterium, Vibrio cholerae. Its dynamics are highly complex owing to the coupling among multiple transmission pathways and different factors in pathogen ecology. Although various mathematical models and clinical studies published in recent years have made important contribution to cholera epidemiology, our knowledge of the disease mechanism remains incomplete at present, largely due to the limited understanding of the dynamics of cholera. In this paper, we conduct global stability analysis for several deterministic cholera epidemic models. These models, incorporating both human population and pathogen V. cholerae concentration, constitute four-dimensional non-linear autonomous systems where the classical Poincaré-Bendixson theory is not applicable. We employ three different techniques, including the monotone dynamical systems, the geometric approach, and Lyapunov functions, to investigate the endemic global stability for several biologically important cases. The analysis and results presented in this paper make building blocks towards a comprehensive study and deeper understanding of the fundamental mechanism in cholera dynamics.     

A linear model for characterization of synchronization frequencies of neural networks

The synchronization frequency of neural networks and its dynamics have important roles in deciphering the working mechanisms of the brain. It has been widely recognized that the properties of functional network synchronization and its dynamics are jointly determined by network topology, network connection strength, i.e., the connection strength of different edges in the network, and external input signals, among other factors. However, mathematical and computational characterization of the relationships between network synchronization frequency and these three important factors are still lacking. This paper presents a novel computational simulation framework to quantitatively characterize the relationships between neural network synchronization frequency and network attributes and input signals. Specifically, we constructed a series of neural networks including simulated small-world networks, real functional working memory network derived from functional magnetic resonance imaging, and real large-scale structural brain networks derived from diffusion tensor imaging, and performed synchronization simulations on these networks via the Izhikevich neuron spiking model. Our experiments demonstrate that both of the network synchronization strength and synchronization frequency change according to the combination of input signal frequency and network self-synchronization frequency. In particular, our extensive experiments show that the network synchronization frequency can be represented via a linear combination of the network self-synchronization frequency and the input signal frequency. This finding could be attributed to an intrinsically-preserved principle in different types of neural systems, offering novel insights into the working mechanism of neural systems.     

Visual perception of ambiguous figures: synchronization based neural models

We develop and study two neural network models of perceptual alternations. Both models have a star-like architecture of connections with a central element connected to a set of peripheral elements. A particular perception is simulated in terms of partial synchronization between the central element and some sub-group of peripheral elements. The first model is constructed from phase oscillators and the mechanism of perceptual alternations is based on chaotic intermittency under fixed parameter values. Similar to experimental evidence, the distribution of times between perceptual alternations is represented by the gamma distribution. The second model is built of spiking neurons of the Hodgkin–Huxley type. The mechanism of perceptual alternations is based on plasticity of inhibitory synapses which increases the inhibition from the central unit to the neural assembly representing the current percept. As a result another perception is formed. Simulations show that the second model is in good agreement with behavioural data on switching times between percepts of ambiguous figures and with experimental results on binocular rivalry of two and four percepts. This article is part of a special issue on Neuronal Dynamics of Sensory Coding. This special issue is in honour of Professor Pepe Segundo who is one of the pioneers in the study of neural coding. Pepe has been an active participant in many Neural Coding Workshops sharing his great knowledge and experience of research in this field. I (R. Borisyuk) was very happy to meet Pepe for the first time in Prague when attending the first Neural Coding Workshop in 1995. From that time we regularly met at Neural Coding Workshops and these meetings have always been very stimulating and fruitful for my research. Remarkably, the first paper I studied at the beginning of my scientific career was a seminal paper by Moore et al. (1970). For me, this paper provided a great opportunity to learn the basic statistical techniques for the analysis of multiple spike trains and neural coding. According to the Institute of Scientific Information, this paper has been cited 380 times! This exciting paper has inspired my research into the synaptic and functional connectivity of neural circuits derived from spike-train recordings (Borisyuk et al. 1985; Stuart et al. 2005) and guided my search for new ideas on neural coding.     

An alternative method for Plasmodium culture synchronization

Since the synchronization of Plasmodium falciparum has become an essential tool in research, we have investigated the use of a commercial gelatine solution, Plasmion, to replace Plasmagel, which is now difficult to obtain. This method also avoids the use of techniques based on Percoll-glucose gradients. The Plasmion-based technique proved to be a good method and could become an alternative to Plasmagel.     

Coupling-induced synchronization in multicellular circadian oscillators of mammals

In mammals, circadian rhythms are controlled by the neurons located in the suprachiasmatic nucleus (SCN) of the hypothalamus. Each neuron in the SCN contains an autonomous molecular clock. The fundamental question is how the individual cellular oscillators, expressing a wide range of periods, interact and assemble to achieve phase synchronization. Most of the studies carried out so far emphasize the crucial role of the periodicity imposed by the light-dark cycle in neuronal synchronization. However, in natural conditions, the interaction between the SCN neurons is non-negligible and coupling between cells in the SCN is achieved partly by neurotransmitters. In this paper, we use a model of nonidentical, globally coupled cellular clocks considered as Goodwin oscillators. We mainly study the synchronization induced by coupling from an analytical way. Our results show that the role of the coupling is to enhance the synchronization to the external forcing. The conclusion of this paper can help us better understand the mechanism of circadian rhythm.     

Firing synchronization and temporal order in noisy neuronal networks

Noise-induced complete synchronization and frequency synchronization in coupled spiking and bursting neurons are studied firstly. The effects of noise and coupling are discussed. It is found that bursting neurons are easier to achieve firing synchronization than spiking ones, which means that bursting activities are more important for information transfer in neuronal networks. Secondly, the effects of noise on firing synchronization in a noisy map neuronal network are presented. Noise-induced synchronization and temporal order are investigated by means of the firing rate function and the order index. Firing synchronization and temporal order of excitatory neurons can be greatly enhanced by subthreshold stimuli with resonance frequency. Finally, it is concluded that random perturbations play an important role in firing activities and temporal order in neuronal networks.     

Pairwise curve synchronization for functional data

Data collected by scientists are increasingly in the form oftrajectories or curves. Often these can be viewed as realizationsof a composite process driven by both amplitude and time variation.We consider the situation in which functional variation is dominatedby time variation, and develop a curve-synchronization methodthat uses every trajectory in the sample as a reference to obtainpairwise warping functions in the first step. These initialpairwise warping functions are then used to create improvedestimators of the underlying individual warping functions inthe second step. A truncated averaging process is used to obtainrobust estimation of individual warping functions. The methodcompares well with other available time-synchronization approachesand is illustrated with Berkeley growth data and gene expressiondata for multiple sclerosis.     

On synchronization in semelparous populations

Synchronization, i.e., convergence towards a dynamical state where the whole population is in one age class, is a characteristic feature of some population models with semelparity. We prove some rigorous results on this, for a simple class of nonlinear one- population models with age structure and semelparity: (i) the survival probabilities are assumed constant, and (ii) only the last age class is reproducing (semelparity), with fecundity decreasing with total population. For this model we prove: (a) The synchronized, or Single Year Class (SYC), dynamical state is always attracting. (b) The coexistence equilibrium is often unstable; we state and prove simple results on this. (c) We describe dynamical states with some, but not all, age classes populated, which we call Multiple Year Class (MYC) patterns, and we prove results extending (a) and (b) into these patterns.Acknowledgement Boris Kruglikov contributed the nonlinear part of the formulation as well as the proof of Theorem 1. The authors are grateful for critical and constructive comments by N. Davydova and O. Diekmann. E.M. is also grateful for discussions with Marius Overholt concerning problems of proving Theorem 2.     

Hopf bifurcation and bursting synchronization in an excitable systems with chemical delayed coupling

In this paper we consider the Hopf bifurcation and synchronization in the two coupled Hindmarsh–Rose excitable systems with chemical coupling and time-delay. We surveyed the conditions for Hopf bifurcations by means of dynamical bifurcation analysis and numerical simulation. The results show that the coupled excitable systems with no delay have supercritical Hopf bifurcation, while the delayed system undergoes Hopf bifurcations at critical time delays when coupling strength lies in a particular region. We also investigated the effect of the delay on the transition of bursting synchronization in the coupled system. The results are helpful for us to better understand the dynamical properties of excitable systems and the biological mechanism of information encoding and cognitive activity.     

Firing pattern and synchronization property analysis in a network model of the olfactory bulb

In the olfactory system, both the temporal spike structure and spatial distribution of neuronal activity are important for processing odor information. In this paper, a biophysically-detailed, spiking neuronal model is used to simulate the activity of olfactory bulb. It is shown that by varying some key parameters such as maximal conductances of Ks and Nap the spike train of single neuron can exhibit various firing patterns. Synchronization in coupled neurons is also investigated as the coupling strength varying in the situation of two neurons and network. It is illustrated that the coupled neurons can exhibit different types of pattern when the coupling strength varies. These results may be instructive to understand information transmission in olfactory system.     

Movement curvature planning through force field internal models

Human motion studies have focused primarily on modeling straight point-to-point reaching movements. However, many goal-directed reaching movements, such as movements directed towards oneself, are not straight but rather follow highly curved trajectories. These movements are particularly interesting to study since they are essential in our everyday life, appear early in development and are routinely used to assess movement deficits following brain lesions. We argue that curved and straight-line reaching movements are generated by a unique neural controller and that the observed curvature of the movement is the result of an active control strategy that follows the geometry of one’s body, for instance to avoid trajectories that would hit the body or yield postures close to the joint limits. We present a mathematical model that accounts for such an active control strategy and show that the model reproduces with high accuracy the kinematic features of human data during unconstrained reaching movements directed toward the head. The model consists of a nonlinear dynamical system with a single stable attractor at the target. Embodiment-related task constraints are expressed as a force field that acts on the dynamical system. Finally, we discuss the biological plausibility and neural correlates of the model’s parameters and suggest that embodiment should be considered as a main cause for movement trajectory curvature.     

Efficacy of four synchronization protocols on the estrus behavior and conception in native Korean cattle (Hanwoo)

Ineffective estrus detection is the foremost limiting factor in the fertility of farmed cattle worldwide. Failure to detect estrus or erroneous diagnosis of estrus results in great economic losses in Korea each year. This study was carried out in order to comprehensively describe the estrus behaviors and conception rates of different estrus synchronization protocols applied to 40 cycling native Korean cattle (Hanwoo). The cows were grouped into four (n = 10) and treated with the following protocols: (1) Day -15: controlled intravaginal drug-releasing device (CIDR) for 12 days; Day -5: prostaglandin F_2α (PGF_2α), (2) ovulation synchronization (OVS): Day -15: GnRH; Day -6: PGF_2α; Day -4: GnRH, (3) Day -15: progesterone-releasing intravaginal device for 12 days; Day -5: PGF_2α; and (4) Day -15: PGF_2α; Day -4: PGF_2α. Artificial insemination was performed 12 hours after the detection of estrus using frozen-thawed semen. Estrus signs were compared using a charge-coupled device camera (CCDC) and a control method (direct visual observation). The pregnancy of the cows was determined by transrectal ultrasonography at Days 25 to 30 postinsemination. The results indicated that the day of estrus return was significantly earlier using the CCDC method compared with direct visualization (P < 0.05). Mounting of other cows was the most predominant sign of estrus among the flock (P < 0.05), as analyzed using the CCDC. In the OVS group, a lower rate of mounting was observed than in the other three groups. Moreover, significantly fewer estrus behaviors were noticed in the OVS protocol group (P < 0.05). Both first service conception and overall conception rates were significantly higher (P < 0.05) in the CIDR and OVS treatment groups. In conclusion, the CIDR and OVS protocols appear to be the best practice for the synchronization of estrus for reproductive competence through the CCDC in Hanwoo cows. However, CIDR has a practical advantage over OVS with respect to estrus detection.     

Optimizing conditions for tobacco BY-2 cell cycle synchronization

Summary Tobacco BY-2 cells have become a major tool in plant cell biological research, in part due to the availability of a cell cycle synchronization protocol. This method, pioneered by Nagata and coworkers, involves sequential treatments with aphidicolin (a DNA synthesis inhibitor) and propyzamide (a microtubule inhibitor which arrests mitosis). The effects of these inhibitors are reversible, allowing the cell culture to progress into M phase synchronously. However, attempts to reproduce high levels of synchrony with published protocols have not been uniformly successful. This paper describes critical parameters for cell cycle synchronization and documents the kinetics and variation typically found in using this protocol.     

In vitro regulatory models for systems biology

The reductionist approach has revolutionized biology in the past 50 years. Yet its limits are being felt as the complexity of cellular interactions is gradually revealed by high-throughput technology. In order to make sense of the deluge of “omic data”, a hypothesis-driven view is needed to understand how biomolecular interactions shape cellular networks. We review recent efforts aimed at building in vitro biochemical networks that reproduce the flow of genetic regulation. We highlight how those efforts have culminated in the rational construction of biochemical oscillators and bistable memories in test tubes. We also recapitulate the lessons learned about in vivo biochemical circuits such as the importance of delays and competition, the links between topology and kinetics, as well as the intriguing resemblance between cellular reaction networks and ecosystems.     

Nocodazole does not synchronize cells: implications for cell-cycle control and whole-culture synchronization

It has been predicted that nocodazole-inhibited cells are not synchronized because nocodazole-arrested cells with a G2-phase amount of DNA would not have a narrow cell-size range reflecting the cell size of some specific, presumably G2-phase, cell-cycle age. Size measurements of nocodazole-inhibited cells now fully confirm this prediction. Further, release from nocodazole inhibition does not produce cells that move through the cell cycle mimicking the passage of normal unperturbed cells through the cell cycle. Nocodazole, an archetypal whole-culture synchronization method, can inhibit growth to produce cells with a G2-phase amount of DNA, but such cells are not synchronized. Cells produced by a selective (i.e., non-whole-culture) method not only have a specific DNA content, but also have a narrow size distribution. The current view of cell-cycle control that is based on methods that are not suitable for cell-cycle analysis must therefore be reconsidered when results are based on whole-culture synchronization.This work was supported by the National Science Foundation (grant MCB–0323346) and (in part) by the National Institutes of Health (University of Michigan’s Cancer Center, support grant 5 P30 CA46592). G.I., M.T., and P. B. are associated with the Undergraduate Research Opportunity Program of the University of Michigan, which also supported this research.     

Hydroxyurea-induced mitotic synchronization in Allium sativum root meristems

The synchronized divisions following a treatment with hydroxyurea (HU) — an inhibitor of DNA synthesis — were studied in root meristems of Allium sativum using two methods: autoradiography of median sections and morphological labeling with a cytokinesis inhibitor. It is shown that the second wave of mitoses is heterogeneous: it is composed mostly of cells which have been synchronized in the S phase by the HU treatment, of cells coming from the quiescent center stimulated to enter DNA synthesis and of cells which were not blocked by the 23 h HU treatment (slow cycling cells). It is also shown that the cell cycle following the first synchronized division is considerably shortened by the synchronization procedure.Abbreviations QC quiescent center - HU hydroxyurea - MHQD methyl-3 hydroxy-6 quinazoline dione 2–4     

Numerical investigations of rib fracture failure models in different dynamic loading conditions

Rib fracture is one of the most common thoracic injuries in vehicle traffic accidents that can result in fatalities associated with seriously injured internal organs. A failure model is critical when modelling rib fracture to predict such injuries. Different rib failure models have been proposed in prediction of thorax injuries. However, the biofidelity of the fracture failure models when varying the loading conditions and the effects of a rib fracture failure model on prediction of thoracic injuries have been studied only to a limited extent. Therefore, this study aimed to investigate the effects of three rib failure models on prediction of thoracic injuries using a previously validated finite element model of the human thorax. The performance and biofidelity of each rib failure model were first evaluated by modelling rib responses to different loading conditions in two experimental configurations: (1) the three-point bending on the specimen taken from rib and (2) the anterior–posterior dynamic loading to an entire bony part of the rib. Furthermore, the simulation of the rib failure behaviour in the frontal impact to an entire thorax was conducted at varying velocities and the effects of the failure models were analysed with respect to the severity of rib cage damages. Simulation results demonstrated that the responses of the thorax model are similar to the general trends of the rib fracture responses reported in the experimental literature. However, they also indicated that the accuracy of the rib fracture prediction using a given failure model varies for different loading conditions.     

When to go with the crowd: Modelling synchronization of all-or-nothing activity transitions in grouped animals

For groups of animals to keep together, the group members have to perform switches between staying in one place and moving to another place in synchrony. However, synchronization imposes a cost on individual animals, because they have to switch from one to the other behaviour at a communal time rather than at their ideal times. Here we model this situation analytically for groups in which the ideal times vary quasinormally and grouping benefit increases linearly with group size. Across the parameter space consisting of variation in the grouping benefit/cost ratio and variation in how costly it is to act too early and too late, the most common optimal solutions are full synchronization with the group staying together and zero synchronization with immediate dissolution of the group, if the group is too small for the given benefit/cost ratio. Partial synchronization, with animals at the tails of the distribution switching individually and the central core of the group in synchrony, occurs only at a narrow stripe of the space. Synchronization cost never causes splitting of the group into two as either zero, partial or full synchronization is always more advantageous. Stable solutions dictate lower degree of synchrony and lower net benefits than optimal solutions for a large range of the parameter values. If groups undergo repeated synchronization challenges, they stay together or quickly dissolve, unless the animals assort themselves into a smaller group with less variation in the ideal times. We conclude with arguing that synchronization cost is different from other types of grouping costs since it does not increase much with increasing group size. As a result, larger groups may be more stable than smaller groups. This results in the paradoxical prediction that when the grouping benefit/grouping cost ratio increases, the average group sizes might decrease, since smaller groups will be able to withstand synchronization challenges.