Altered cyclic nucleotide binding and pore opening in a diseased human HCN4 channel.

A growing number of nonsynonymous mutations in the human HCN4 channel gene, the major component of the funny channel of the sinoatrial node, are associated with disease but how they impact channel structure and function, and, thus, how they result in disease, is not clear for any of them. Here, we study the S672R mutation, in the cyclic nucleotide-binding domain of the channel, which has been associated with an inherited bradycardia in an Italian family. This may be the best studied of all known mutations, yet the underlying molecular and atomistic mechanisms remain unclear and controversial. We combine measurements of binding by isothermal titration calorimetry to a naturally occurring tetramer of the HCN4 C-terminal region with a mathematical model to show that weaker binding of cAMP to the mutant channel contributes to a lower level of facilitation of channel opening at submicromolar ligand concentrations but that, in general, facilitation occurs over a range that is similar between the mutant and wild-type because of enhanced opening of the mutant channel when liganded. We also show that the binding affinity for cGMP, which produces the same maximum facilitation of HCN4 opening as cAMP, is weaker in the mutant HCN4 channel but that, for both wild-type and mutant, high-affinity binding of cGMP occurs in a range of concentrations below 1 µM. Thus, binding of cGMP to the HCN4 channel may be relevant normally in vivo and reduced binding of cGMP, as well as cAMP, to the mutant channel may contribute to the reduced resting heart rate observed in the affected family.

Inferring individual rules from collective behavior.

Social organisms form striking aggregation patterns, displaying cohesion, polarization, and collective intelligence. Determining how they do so in nature is challenging; a plethora of simulation studies displaying life-like swarm behavior lack rigorous comparison with actual data because collecting field data of sufficient quality has been a bottleneck. Here, we bridge this gap by gathering and analyzing a high-quality dataset of flocking surf scoters, forming well-spaced groups of hundreds of individuals on the water surface. By reconstructing each individual's position, velocity, and trajectory, we generate spatial and angular neighbor-distribution plots, revealing distinct concentric structure in positioning, a preference for neighbors directly in front, and strong alignment with neighbors on each side. We fit data to zonal interaction models and characterize which individual interaction forces suffice to explain observed spatial patterns. Results point to strong short-range repulsion, intermediate-range alignment, and longer-range attraction (with circular zones), as well as a weak but significant frontal-sector interaction with one neighbor. A best-fit model with such interactions accounts well for observed group structure, whereas absence or alteration in any one of these rules fails to do so. We find that important features of observed flocking surf scoters can be accounted for by zonal models with specific, well-defined rules of interaction.

Characterizing mixed mode oscillations shaped by noise and bifurcation structure.

Many neuronal systems and models display a certain class of mixed mode oscillations (MMOs) consisting of periods of small amplitude oscillations interspersed with spikes. Various models with different underlying mechanisms have been proposed to generate this type of behavior. Stochastic versions of these models can produce similarly looking time series, often with noise-driven mechanisms different from those of the deterministic models. We present a suite of measures which, when applied to the time series, serves to distinguish models and classify routes to producing MMOs, such as noise-induced oscillations or delay bifurcation. By focusing on the subthreshold oscillations, we analyze the interspike interval density, trends in the amplitude, and a coherence measure. We develop these measures on a biophysical model for stellate cells and a phenomenological FitzHugh-Nagumo-type model and apply them on related models. The analysis highlights the influence of model parameters and resets and return mechanisms in the context of a novel approach using noise level to distinguish model types and MMO mechanisms. Ultimately, we indicate how the suite of measures can be applied to experimental time series to reveal the underlying dynamical structure, while exploiting either the intrinsic noise of the system or tunable extrinsic noise.

An integrated model of electrical spiking, bursting, and calcium oscillations in GnRH neurons.

The plasma membrane electrical activities of neurons that secrete gonadotropin-releasing hormone (GnRH) have been studied extensively. A couple of mathematical models have been developed previously to explain different aspects of these activities. The goal of this article is to develop a single model that accounts for the previously modeled experimental results and some more recent results that have not been accounted for. The latter includes two types of membrane potential bursting mechanisms and their associated cytosolic calcium oscillations. One bursting mechanism has not been reported in experiments and is thus regarded as a model prediction. Although the model is mainly based on data collected in immortalized GnRH cell lines, it is capable of explaining some properties of GnRH neurons observed in several other preparations including mature GnRH neurons in hypothalamic slices. We present a spatial model that incorporates a detailed description of calcium dynamics in a three-dimensional cell body with the ion channels evenly distributed on the cell surface. A phenomenological reduction of the spatial model into a simplified form is also presented. The simplified model will facilitate the study of the roles of plasma membrane electrical activities in the pulsatile release of GnRH.

A conceptual model for milling formations in biological aggregates.

Collective behavior of swarms and flocks has been studied from several perspectives, including continuous (Eulerian) and individual-based (Lagrangian) models. Here, we use the latter approach to examine a minimal model for the formation and maintenance of group structure, with specific emphasis on a simple milling pattern in which particles follow one another around a closed circular path.We explore how rules and interactions at the level of the individuals lead to this pattern at the level of the group. In contrast to many studies based on simulation results, our model is sufficiently simple that we can obtain analytical predictions. We consider a Newtonian framework with distance-dependent pairwise interaction-force. Unlike some other studies, our mill formations do not depend on domain boundaries, nor on centrally attracting force-fields or rotor chemotaxis.By focusing on a simple geometry and simple distant-dependent interactions, we characterize mill formations and derive existence conditions in terms of model parameters. An eigenvalue equation specifies stability regions based on properties of the interaction function. We explore this equation numerically, and validate the stability conclusions via simulation, showing distinct behavior inside, outside, and on the boundary of stability regions. Moving mill formations are then investigated, showing the effect of individual autonomous self-propulsion on group-level motion. The simplified framework allows us to clearly relate individual properties (via model parameters) to group-level structure. These relationships provide insight into the more complicated milling formations observed in nature, and suggest design properties of artificial schools where such rotational motion is desired.

Binding and structural asymmetry governs ligand sensitivity in a cyclic nucleotide-gated ion channel.

Hyperpolarization-activated cyclic nucleotide-gated (HCN) channels open more easily when cAMP or cGMP bind to a domain in the intracellular C-terminus in each of four identical subunits. How sensitivity of the channels to these ligands is determined is not well understood. Here, we apply a mathematical model, which incorporates negative cooperativity, to gating and mutagenesis data available in the literature and combine the results with binding data collected using isothermal titration calorimetry. This model recapitulates the concentration-response data for the effects of cAMP and cGMP on wild-type HCN2 channel opening and, remarkably, predicts the concentration-response data for a subset of mutants with single-point amino acid substitutions in the binding site. Our results suggest that ligand sensitivity is determined by negative cooperativity and asymmetric effects on structure and channel opening, which are tuned by ligand-specific interactions and residues within the binding site.

A mathematical model for the actions of activin, inhibin, and follistatin on pituitary gonadotrophs.

The timed secretion of the luteinizing hormone (LH) and follicle stimulating hormone (FSH) from pituitary gonadotrophs during the estrous cycle is crucial for normal reproductive functioning. The release of LH and FSH is stimulated by gonadotropin releasing hormone (GnRH) secreted by hypothalamic GnRH neurons. It is controlled by the frequency of the GnRH signal that varies during the estrous cycle. Curiously, the secretion of LH and FSH is differentially regulated by the frequency of GnRH pulses. LH secretion increases as the frequency increases within a physiological range, and FSH secretion shows a biphasic response, with a peak at a lower frequency. There is considerable experimental evidence that one key factor in these differential responses is the autocrine/paracrine actions of the pituitary polypeptides activin and follistatin. Based on these data, we develop a mathematical model that incorporates the dynamics of these polypeptides. We show that a model that incorporates the actions of activin and follistatin is sufficient to generate the differential responses of LH and FSH secretion to changes in the frequency of GnRH pulses. In addition, it shows that the actions of these polypeptides, along with the ovarian polypeptide inhibin and the estrogen-mediated variations in the frequency of GnRH pulses, are sufficient to account for the time courses of LH and FSH plasma levels during the rat estrous cycle. That is, a single peak of LH on the afternoon of proestrus and a double peak of FSH on proestrus and early estrus. We also use the model to identify which regulation pathways are indispensable for the differential regulation of LH and FSH and their time courses during the estrous cycle. We conclude that the actions of activin, inhibin, and follistatin are consistent with LH/FSH secretion patterns, and likely complement other factors in the production of the characteristic secretion patterns in female rats.

Robust synchrony and rhythmogenesis in endocrine neurons via autocrine regulations in vitro and in vivo.

Episodic pulses of gonadotropin-releasing hormone (GnRH) are essential for maintaining reproductive functions in mammals. An explanation for the origin of this rhythm remains an ultimate goal for researchers in this field. Some plausible mechanisms have been proposed among which the autocrine-regulation mechanism has been implicated by numerous experiments. GnRH binding to its receptors in cultured GnRH neurons activates three types of G-proteins that selectively promote or inhibit GnRH secretion (Krsmanovic et al. in Proc. Natl. Acad. Sci. 100:2969-2974, 2003). This mechanism appears to be consistent with most data collected so far from both in vitro and in vivo experiments. Based on this mechanism, a mathematical model has been developed (Khadra and Li in Biophys. J. 91:74-83, 2006) in which GnRH in the extracellular space plays the roles of a feedback regulator and a synchronizing agent. In the present study, we show that synchrony between different neurons through sharing a common pool of GnRH is extremely robust. In a diversely heterogeneous population of neurons, the pulsatile rhythm is often maintained when only a small fraction of the neurons are active oscillators (AOs). These AOs are capable of recruiting nonoscillatory neurons into a group of recruited oscillators while forcing the nonrecruitable neurons to oscillate along. By pointing out the existence of the key elements of this model in vivo, we predict that the same mechanism revealed by experiments in vitro may also operate in vivo. This model provides one plausible explanation for the apparently controversial conclusions based on experiments on the effects of the ultra-short feedback loop of GnRH on its own release in vivo.

Relevance between GerdQ score and the severity of reflux esophagitis in Uygur and Han Chinese.

Gastroesophageal reflux disease questionnaire (GerdQ) was used to investigate the inpatients with typical reflux related symptoms in Gastroenterology. According to heartburn, regurgitation, abdominal pain, nausea, sleep disorders, whether taking over the counter (OTC) drugs 6 points to score. Using endoscopy as the gold standard for the diagnosis of reflux esophagitis (RE), and the results were compared with GerdQ score to determine the threshold value for RE, to analyze the distribution of GerdQ score for patients with RE, to assess the relationship between the GerdQ score and the severity of RE. A total of 1233 patients were enrolled in this study, including 538 patients had RE and 695 had not. There was statistical significance in the GerdQ score of RE group and non-RE group (P <0.05), showing that significant correlation between the score and the occurrence of RE. GerdQ score and the severity of RE were positively correlated. Further research also showed that there was a direct correlation between GerdQ score and the severity of RE in the Uygur and Han. GerdQ seems to be an useful screening tool in initial diagnosis of RE, and positively correlated with the severity of RE.

Association of HLA-DRB1 alleles and anti-neutrophil cytoplasmic antibodies in Han and Uyghur patients with ulcerative colitis in China.

OBJECTIVE: We aimed to study the association between HLA-DRB1 alleles and anti-neutrophil cytoplasmic antibodies (ANCA) among Uyghur and Han patients with ulcerative colitis (UC) in China. METHODS: Altogether 160 UC patients and 466 healthy controls of Uyghur and Han groups residing in the Xinjiang Uyghur Autonomous Region of China were included. HLA-DRB1 variants were identified from genomic DNA using polymerase chain reaction and gene sequencing. Serum ANCA were determined by indirect immunofluorescence assay. RESULTS: Among the Uyghur populations, the HLA-DRB1*08 gene frequency was lower in the UC patients than in the control group (P = 0.012, OR 0.12, 95% CI 0.02-0.91); however, that of HLA-DRB1*13 was much higher in the UC patients than in the controls (P = 0.001, OR 4.32, 95% CI 1.92-9.74). In Han patients with UC, there was no significant difference in HLA-DRB1 frequency between UC patients and healthy controls. The positive rate of ANCA in Uyghur patients with UC was significantly higher than in Han UC patients (P = 0.026), and ANCA positivity was associated with an increased frequency of HLA-DRB1*13 in Uyghur UC patients, but no such difference was observed in the Han patients. CONCLUSIONS: Genetic polymorphisms of the HLA-DRB1*08 and *13 may contribute to the clinical heterogeneity of UC between Uyghur and Han UC patients in China. In Uyghur UC patients, HLA-DRB1*13 may be correlated with ANCA positivity.

A computational study of spike time reliability in two types of threshold dynamics.

Spike time reliability (STR) refers to the phenomenon in which repetitive applications of a frozen copy of one stochastic signal to a neuron trigger spikes with reliable timing while a constant signal fails to do so. Observed and explored in numerous experimental and theoretical studies, STR is a complex dynamic phenomenon depending on the nature of external inputs as well as intrinsic properties of a neuron. The neuron under consideration could be either quiescent or spontaneously spiking in the absence of the external stimulus. Focusing on the situation in which the unstimulated neuron is quiescent but close to a switching point to oscillations, we numerically analyze STR treating each spike occurrence as a time localized event in a model neuron. We study both the averaged properties as well as individual features of spike-evoking epochs (SEEs). The effects of interactions between spikes is minimized by selecting signals that generate spikes with relatively long interspike intervals (ISIs). Under these conditions, the frequency content of the input signal has little impact on STR. We study two distinct cases, Type I in which the f-I relation (f for frequency, I for applied current) is continuous and Type II where the f-I relation exhibits a jump. STR in the two types shows a number of similar features and differ in some others. SEEs that are capable of triggering spikes show great variety in amplitude and time profile. On average, reliable spike timing is associated with an accelerated increase in the "action" of the signal as a threshold for spike generation is approached. Here, "action" is defined as the average amount of current delivered during a fixed time interval. When individual SEEs are studied, however, their time profiles are found important for triggering more precisely timed spikes. The SEEs that have a more favorable time profile are capable of triggering spikes with higher precision even at lower action levels.

Difference in DRB1* gene polymorphisms between Han and Uyghur ulcerative colitis patients in China.

AIM: To evaluate the association between HLA-DRB1 alleles and Han and Uyghur ulcerative colitis (UC) patients residing in the Xinjiang Uyghur Autonomous Region of China. METHODS: In this study, 102 UC patients (53 Han including 22 men and 31 women, and 49 Uyghur patients including 25 men and 24 women; aged 48.07 ± 15.83 years) and 310 age- and sex-matched healthy controls were enrolled in the Department of Gastroenterology, Xinjiang People's Hospital of China from January 2010 to May 2011. UC was diagnosed based on the clinical, endoscopic and histological findings following Lennard-Jones criteria. Blood samples were collected and genomic DNA was extracted by routine laboratory methods, and both polymerase chain reaction and gene sequencing were used to identify HLA-DRB1 allele variants. The potential association between genetic variation and UC in Han and Uyghur patients was examined. There were no statistical differences in HLA-DRB1 allele frequencies in Han UC patients. RESULTS: There was no significant difference in the sex ratio between the controls and UC patients (P = 0.740). In Han patients with UC (n = 53), HLA-DRB1 *03, *13 allele frequencies were lower than in healthy controls (n = 161), but not statistically significant, and HLA-DRB1*04*11*14 allele frequencies were higher than in healthy controls, but without statistical significance. Differences between Uyghur UC patients and the control group were observed for HLA-DRB1*04 and HLA-DRB1*13, both showed a greater frequency in UC patients (10.21% vs 2.69%, P = 0.043; 14.29% vs 4.03%, P = 0.019). HLA-DRB1*14 also showed a greater frequency in UC patients (14.29% vs 2.69%, P = 0.006). The frequencies of DRB1*04, *13*14 alleles were increased in Uyghur UC patients compared with normal controls. The frequency of DRB1 * 08 was decreased in Uyghur UC patients compared with normal controls. HLA-DRB1 alleles showed no association with UC in Han patients. There were no statistical differences in HLA-DRB1 allele frequencies in Han UC patients. The frequencies of DRB1*04, *13*14 alleles were increased in Uyghur UC patients compared with normal controls. The frequency of DRB1*08 was decreased in Uyghur UC patients compared with normal controls. Polymorphism of the HLA-DRB1 gene may contribute to the clinical heterogeneity of UC between Han and Uyghur UC patients in China. CONCLUSION: HLA-DRB1*04*13*14 and DRB1*08 may contribute to the clinical heterogeneity of UC between Han and Uyghur UC patients.

Simple models for quorum sensing: nonlinear dynamical analysis.

Quorum sensing refers to the change in the cooperative behavior of a collection of elements in response to the change in their population size or density. This behavior can be observed in chemical and biological systems. These elements or cells are coupled via chemicals in the surrounding environment. Here we focus on the change of dynamical behavior, in particular from quiescent to oscillatory, as the cell population changes. For instance, the silent behavior of the elements can become oscillatory as the system concentration or population increases. In this work, two simple models are constructed that can produce the essential representative properties in quorum sensing. The first is an excitable or oscillatory phase model, which is probably the simplest model one can construct to describe quorum sensing. Using the mean-field approximation, the parameter regime for quorum sensing behavior can be identified, and analytical results for the detailed dynamical properties, including the phase diagrams, are obtained and verified numerically. The second model consists of FitzHugh-Nagumo elements coupled to the signaling chemicals in the environment. Nonlinear dynamical analysis of this mean-field model exhibits rich dynamical behaviors, such as infinite period bifurcation, supercritical Hopf, fold bifurcation, and subcritical Hopf bifurcations as the population parameter changes for different coupling strengths. Analytical result is obtained for the Hopf bifurcation phase boundary. Furthermore, two elements coupled via the environment and their synchronization behavior for these two models are also investigated. For both models, it is found that the onset of oscillations is accompanied by the synchronized dynamics of the two elements. Possible applications and extension of these models are also discussed.

Stochastic phase dynamics and noise-induced mixed-mode oscillations in coupled oscillators.

Synaptically coupled neurons show in-phase or antiphase synchrony depending on the chemical and dynamical nature of the synapse. Deterministic theory helps predict the phase differences between two phase-locked oscillators when the coupling is weak. In the presence of noise, however, deterministic theory faces difficulty when the coexistence of multiple stable oscillatory solutions occurs. We analyze the solution structure of two coupled neuronal oscillators for parameter values between a subcritical Hopf bifurcation point and a saddle node point of the periodic branch that bifurcates from the Hopf point, where a rich variety of coexisting solutions including asymmetric localized oscillations occurs. We construct these solutions via a multiscale analysis and explore the general bifurcation scenario using the lambda-omega model. We show for both excitatory and inhibitory synapses that noise causes important changes in the phase and amplitude dynamics of such coupled neuronal oscillators when multiple oscillatory solutions coexist. Mixed-mode oscillations occur when distinct bistable solutions are randomly visited. The phase difference between the coupled oscillators in the localized solution, coexisting with in-phase or antiphase solutions, is clearly represented in the stochastic phase dynamics.

A model for the pulsatile secretion of gonadotropin-releasing hormone from synchronized hypothalamic neurons.

Cultured gonadotropin-releasing hormone (GnRH) neurons have been shown to express GnRH receptors. GnRH binding to its receptors activates three types of G-proteins at increasing doses. These G-proteins selectively activate or inhibit GnRH secretion by regulating the intracellular levels of Ca2+ and cAMP. Based on these recent observations, we build a model in which GnRH plays the roles of a feedback regulator and a diffusible synchronizing agent. We show that this GnRH-regulated GnRH-release mechanism is sufficient for generating pulsatile GnRH release. The model reproduces the observed effects of some key drugs that disturb the GnRH pulse generator in specific ways. Simulations of 100 heterogeneous neurons revealed that the synchronization mediated by a common pool of diffusible GnRH is robust. The population can generate synchronized pulsatile signals even when all the individual GnRH neurons oscillate at different amplitudes and peak at different times. These results suggest that the positive and negative effects of the autocrine regulation by GnRH on GnRH neurons are sufficient and robust in generating GnRH pulses.

Noise-induced coherence and network oscillations in a reduced bursting model.

The dynamics of the Hindmarsh-Rose (HR) model of bursting thalamic neurons is reduced to a system of two linear differential equations that retains the subthreshold resonance properties of the HR model. Introducing a reset mechanism after a threshold crossing, we turn this system into a resonant integrate-and-fire (RIF) model. Using Monte-Carlo simulations and mathematical analysis, we examine the effects of noise and the subthreshold dynamic properties of the RIF model on the occurrence of coherence resonance (CR). Synchronized burst firing occurs in a network of such model neurons with excitatory pulse-coupling. The coherence level of the network oscillations shows a stochastic resonance-like dependence on the noise level. Stochastic analysis of the equations shows that the slow recovery from the spike-induced inhibition is crucial in determining the frequencies of the CR and the subthreshold resonance in the original HR model. In this particular type of CR, the oscillation frequency strongly depends on the intrinsic time scales but changes little with the noise intensity. We give analytical quantities to describe this CR mechanism and illustrate its influence on the emerging network oscillations. We discuss the profound physiological roles this kind of CR may have in information processing in neurons possessing a subthreshold resonant frequency and in generating synchronized network oscillations with a frequency that is determined by intrinsic properties of the neurons.

Clustering in small networks of excitatory neurons with heterogeneous coupling strengths.

Excitatory coupling with a slow rise time destabilizes synchrony between coupled neurons. Thus, the fully synchronous state is usually unstable in networks of excitatory neurons. Phase-clustered states, in which neurons are divided into multiple synchronized clusters, have also been found unstable in numerical studies of excitatory networks in the presence of noise. The question arises as to whether synchrony is possible in networks of neurons coupled through slow, excitatory synapses. In this paper, we show that robust, synchronous clustered states can occur in such networks. The effects of non-uniform distributions of coupling strengths are explored. Conditions for the existence and stability of clustered states are derived analytically. The analysis shows that a multi-cluster state can be stable in excitatory networks if the overall interactions between neurons in different clusters are stabilizing and strong enough to counter-act the destabilizing interactions between neurons within each cluster. When heterogeneity in the coupling strengths strengthens the stabilizing inter-cluster interactions and/or weakens the destabilizing in-cluster interactions, robust clustered states can occur in excitatory networks of all known model neurons. Numerical simulations were carried out to support the analytical results.

The influences of Ih on temporal summation in hippocampal CA1 pyramidal neurons: a modeling study.

Recent experimental and theoretical studies have found that active dendritic ionic currents can compensate for the effects of electrotonic attenuation. In particular, temporal summation, the percentage increase in peak somatic voltage responses invoked by a synaptic input train, is independent of location of the synaptic input in hippocampal CA1 pyramidal neurons under normal conditions. This independence, known as normalization of temporal summation, is destroyed when the hyperpolarization-activated current, Ih, is blocked [Magee JC (1999a), Nature Neurosci. 2: 508-514]. Using a compartmental model derived from morphological recordings of hippocampal CA1 pyramidal neurons, we examined the hypothesis that Ih was primarily responsible for normalization of temporal summation. We concluded that this hypothesis was incomplete. With a model that included Ih, the persistent Na(+) current (INaP), and the transient A-type K+ current (IA), however, we observed normalization of temporal summation across a wide range of synaptic input frequencies, in keeping with experimental observations.