Statistical analysis of channel current from a membrane patch. I. Some stochastic properties of ion channels or molecular systems in equilibrium

The stochastic behavior of single-channel current in a steady-state has been interpreted as the channel's state transitions between several open and shut states, and these transitions have been regarded as a homogeneous Markov process. When a channel is in equilibrium, the principle of detailed balance holds for every step in the state transition scheme. Here we show two stochastic properties of a channel, or any molecule obeying a reversible state transition scheme, under the constraint of detailed balance. First, the distribution functions and the probability density functions of shut or open dwell-time are expressed by the sum of exponential terms with positive coefficients. The same holds for the time-dependent open (or shut) frequency after the shut (or open) transition. Second, the time course of state transition from the state SI to SJ (PI,J(t] is proportional to its reverse transition time course (PJ,I(t], even if SI and SJ are widely separated. The same relation holds also for a transition scheme having transition pathways to the absorbing states. If analysis of a channel current record shows it to be incompatible with either of these two properties, the channel is not in equilibrium but in a steady-state with an energy-consuming cyclic flow. These two properties are also useful for the analysis of any molecular process obeying a homogeneous Markov process or a network of first-order chemical reactions.     

Modeling Age and Nest‐Specific Survival Using a Hierarchical Bayesian Approach

Summary : Recent studies have shown that grassland birds are declining more rapidly than any other group of terrestrial birds. Current methods of estimating avian age‐specific nest survival rates require knowing the ages of nests, assuming homogeneous nests in terms of nest survival rates, or treating the hazard function as a piecewise step function. In this article, we propose a Bayesian hierarchical model with nest‐specific covariates to estimate age‐specific daily survival probabilities without the above requirements. The model provides a smooth estimate of the nest survival curve and identifies the factors that are related to the nest survival. The model can handle irregular visiting schedules and it has the least restrictive assumptions compared to existing methods. Without assuming proportional hazards, we use a multinomial semiparametric logit model to specify a direct relation between age‐specific nest failure probability and nest‐specific covariates. An intrinsic autoregressive prior is employed for the nest age effect. This nonparametric prior provides a more flexible alternative to the parametric assumptions. The Bayesian computation is efficient because the full conditional posterior distributions either have closed forms or are log concave. We use the method to analyze a Missouri dickcissel dataset and find that (1) nest survival is not homogeneous during the nesting period, and it reaches its lowest at the transition from incubation to nestling; and (2) nest survival is related to grass cover and vegetation height in the study area.     

An approximation method for solving the steady-state probability distribution of probabilistic Boolean networks

MOTIVATION: Probabilistic Boolean networks (PBNs) have been proposed to model genetic regulatory interactions. The steady-state probability distribution of a PBN gives important information about the captured genetic network. The computation of the steady-state probability distribution usually includes construction of the transition probability matrix and computation of the steady-state probability distribution. The size of the transition probability matrix is 2(n)-by-2(n) where n is the number of genes in the genetic network. Therefore, the computational costs of these two steps are very expensive and it is essential to develop a fast approximation method. RESULTS: In this article, we propose an approximation method for computing the steady-state probability distribution of a PBN based on neglecting some Boolean networks (BNs) with very small probabilities during the construction of the transition probability matrix. An error analysis of this approximation method is given and theoretical result on the distribution of BNs in a PBN with at most two Boolean functions for one gene is also presented. These give a foundation and support for the approximation method. Numerical experiments based on a genetic network are given to demonstrate the efficiency of the proposed method.     

Mitochondrial Reshaping Accompanies Neural Differentiation in the Developing Spinal Cord

Mitochondria, long known as the cell powerhouses, also regulate redox signaling and arbitrate cell survival. The organelles are now appreciated to exert additional critical roles in cell state transition from a pluripotent to a differentiated state through balancing glycolytic and respiratory metabolism. These metabolic adaptations were recently shown to be concomitant with mitochondrial morphology changes and are thus possibly regulated by contingencies of mitochondrial dynamics. In this context, we examined, for the first time, mitochondrial network plasticity during the transition from proliferating neural progenitors to post-mitotic differentiating neurons. We found that mitochondria underwent morphological reshaping in the developing neural tube of chick and mouse embryos. In the proliferating population, mitochondria in the mitotic cells lying at the apical side were very small and round, while they appeared thick and short in interphase cells. In differentiating neurons, mitochondria were reorganized into a thin, dense network. This reshaping of the mitochondrial network was not specific of a subtype of progenitors or neurons, suggesting that this is a general event accompanying neurogenesis in the spinal cord. Our data shed new light on the various changes occurring in the mitochondrial network during neurogenesis and suggest that mitochondrial dynamics could play a role in the neurogenic process.     

Melting profile and temperature dependent binding constant of an anticancer drug daunomycin-DNA complex

We calculate thermal fluctuational base pair opening probability and the drug binding constant of a daunomycin-bound Poly d(CGTA) · Poly d(TACG) at temperatures from room temperature to its melting temperature. For comparison we also carry out a calculation on a drug-free DNA with the same sequence. Our calculations are carried out by means of a statistical approach using microscopic structures and established force fields and with cooperative effects incorporated into the algorithm. Both hydrogen bond disruption probabilities and drug unstacking probability are determined self-consistently. These probabilities are then used to determine temperature dependent base pair opening probabilities and the drug binding constant. The calculated base pair opening probabilities and drug binding constant are found to be in fair agreement with experiments carried out at room temperature. Our calculation shows cooperative base pair disruption and drug dissociation at certain critical temperatures close to the observed melting temperatures for similar helices. We find that the temperature dependence of the drug binding constant fits well to the van't Hoff relation, in agreement with observations. Our calculation indicates the occurrence of a premelting transition in the drug-bound DNA helix. Some comments are made about this premelting transition.     

Precritical State Transition Dynamics in the Attractor Landscape of a Molecular Interaction Network Underlying Colorectal Tumorigenesis

From the perspective of systems science, tumorigenesis can be hypothesized as a critical transition (an abrupt shift from one state to another) between proliferative and apoptotic attractors on the state space of a molecular interaction network, for which an attractor is defined as a stable state to which all initial states ultimately converge, and the region of convergence is called the basin of attraction. Before the critical transition, a cellular state might transit between the basin of attraction for an apoptotic attractor and that for a proliferative attractor due to the noise induced by the inherent stochasticity in molecular interactions. Such a flickering state transition (state transition between the basins of attraction for alternative attractors from the impact of noise) would become more frequent as the cellular state approaches near the boundary of the basin of attraction, which can increase the variation in the estimate of the respective basin size. To investigate this for colorectal tumorigenesis, we have constructed a stochastic Boolean network model of the molecular interaction network that contains an important set of proteins known to be involved in cancer. In particular, we considered 100 representative sequences of 20 gene mutations that drive colorectal tumorigenesis. We investigated the appearance of cancerous cells by examining the basin size of apoptotic, quiescent, and proliferative attractors along with the sequential accumulation of gene mutations during colorectal tumorigenesis. We introduced a measure to detect the flickering state transition as the variation in the estimate of the basin sizes for three-phenotype attractors from the impact of noise. Interestingly, we found that this measure abruptly increases before a cell becomes cancerous during colorectal tumorigenesis in most of the gene mutation sequences under a certain level of stochastic noise. This suggests that a frequent flickering state transition can be a precritical phenomenon of colorectal tumorigenesis.     

Robustness and evolvability in genetic regulatory networks

Living organisms are robust to a great variety of genetic changes. Gene regulation networks and metabolic pathways self-organize and reaccommodate to make the organism perform with stability and reliability under many point mutations, gene duplications and gene deletions. At the same time, living organisms are evolvable, which means that these kind of genetic perturbations can eventually make the organism acquire new functions and adapt to new environments. It is still an open problem to determine how robustness and evolvability blend together at the genetic level to produce stable organisms that yet can change and evolve. Here we address this problem by studying the robustness and evolvability of the attractor landscape of genetic regulatory network models under the process of gene duplication followed by divergence. We show that an intrinsic property of this kind of networks is that, after the divergence of the parent and duplicate genes, with a high probability the previous phenotypes, encoded in the attractor landscape of the network, are preserved and new ones might appear. The above is true in a variety of network topologies and even for the case of extreme divergence in which the duplicate gene bears almost no relation with its parent. Our results indicate that networks operating close to the so-called "critical regime" exhibit the maximum robustness and evolvability simultaneously.     

Establishment of a new population by a single gravid colonist: implications for Hyalella biogeography and speciation

Establishment of a new population is a significant event in a lineage, one that impacts geographic distribution, community dynamics, and speciation. We examined population establishment in experimental populations of Hyalella, an amphipod crustacean, by introducing a single gravid female into experimental habitats that differed in habitat size and the presence of an interspecific competitor, Physella snails. We found that over the course of 142 days, the length of a typical reproductive season, a single female gave rise to a viable population of descendants in 62 % of experimental habitats, with more than half of these viable populations containing more than 100 descendants. We found no effect of habitat size or interspecific competition on extinction probability or final abundance of descendants. Based on empirical results we estimated the probability that a single female will establish a lasting population, and examined this establishment probability under a broad range of overwinter survival scenarios. We found that establishment probability declines gradually with reductions in overwinter survival, such that establishment probability exceeds 33 % across a broad range of overwinter mortality rates. Our finding that a single female may have a reasonably high probability of establishing a new population helps to resolve the enigmatic biogeographic distribution of Hyalella amphipods, which appear to have very limited overland dispersal, yet are nearly ubiquitous in permanent freshwater habitats of North America.     

Long-range correlations improve understanding of the influence of network structure on contact dynamics

Models of infectious diseases are characterized by a phase transition between extinction and persistence. A challenge in contemporary epidemiology is to understand how the geometry of a host’s interaction network influences disease dynamics close to the critical point of such a transition. Here we address this challenge with the help of moment closures. Traditional moment closures, however, do not provide satisfactory predictions close to such critical points. We therefore introduce a new method for incorporating longer-range correlations into existing closures. Our method is technically simple, remains computationally tractable and significantly improves the approximation’s performance. Our extended closures thus provide an innovative tool for quantifying the influence of interaction networks on spatially or socially structured disease dynamics. In particular, we examine the effects of a network’s clustering coefficient, as well as of new geometrical measures, such as a network’s square clustering coefficients. We compare the relative performance of different closures from the literature, with or without our long-range extension. In this way, we demonstrate that the normalized version of the Bethe approximation-extended to incorporate long-range correlations according to our method-is an especially good candidate for studying influences of network structure. Our numerical results highlight the importance of the clustering coefficient and the square clustering coefficient for predicting disease dynamics at low and intermediate values of transmission rate, and demonstrate the significance of path redundancy for disease persistence.     

One-carbon metabolism and breast cancer: an epidemiological perspective

One-carbon metabolism is a network of biological reactions that plays critical role in DNA methylation and DNA synthesis, and in turn, facilitates the cross-talk between genetic and epigenetic processes. Genetic polymorphisms and supplies of cofactors （e.g. folate, vitamins B） involved in this pathway have been shown to influence cancer risk and even survival. In this review, we summarized the epidemiological evidence for one-carbon metabolism, from both genetics and lifestyle aspects, in relation to breast cancer risk. We also discussed this pathway in relation to breast cancer survival and the modulation of one-carbon polymorphism in chemotherapy. Emerging evidence on modulation of DNA methylation by one-carbon metabolism suggests that disruption of epigenome might have been the underlying mechanism. More results are expected and will be translated to guidance to the general population for disease prevention as well as to clinicians for treatment and management of the disease.     

Thermodynamics and folding kinetics analysis of the SH3 domain form discrete molecular dynamics

We perform a detailed analysis of the thermodynamics and folding kinetics of the SH3 domain fold with discrete molecular dynamic simulations. We propose a protein model that reproduces some of the experimentally observed thermodynamic and folding kinetic properties of proteins. Specifically, we use our model to study the transition state ensemble of the SH3 fold family of proteins, a set of unstable conformations that fold to the protein native state with probability 1/2. We analyze the participation of each secondary structure element formed at the transition state ensemble. We also identify the folding nucleus of the SH3 fold and test extensively its importance for folding kinetics. We predict that a set of amino acid contacts between the RT-loop and the distal hairpin are the critical folding nucleus of the SH3 fold and propose a hypothesis that explains this result.     

The Risk of Disease to Great Apes: Simulating Disease Spread in Orang-Utan (Pongo pygmaeus wurmbii) and Chimpanzee (Pan troglodytes schweinfurthii) Association Networks

All great ape species are endangered, and infectious diseases are thought to pose a particular threat to their survival. As great ape species vary substantially in social organisation and gregariousness, there are likely to be differences in susceptibility to disease types and spread. Understanding the relation between social variables and disease is therefore crucial for implementing effective conservation measures. Here, we simulate the transmission of a range of diseases in a population of orang-utans in Sabangau Forest (Central Kalimantan) and a community of chimpanzees in Budongo Forest (Uganda), by systematically varying transmission likelihood and probability of subsequent recovery. Both species have fission-fusion social systems, but differ considerably in their level of gregariousness. We used long-term behavioural data to create networks of association patterns on which the spread of different diseases was simulated. We found that chimpanzees were generally far more susceptible to the spread of diseases than orang-utans. When simulating different diseases that varied widely in their probability of transmission and recovery, it was found that the chimpanzee community was widely and strongly affected, while in orang-utans even highly infectious diseases had limited spread. Furthermore, when comparing the observed association network with a mean-field network (equal contact probability between group members), we found no major difference in simulated disease spread, suggesting that patterns of social bonding in orang-utans are not an important determinant of susceptibility to disease. In chimpanzees, the predicted size of the epidemic was smaller on the actual association network than on the mean-field network, indicating that patterns of social bonding have important effects on susceptibility to disease. We conclude that social networks are a potentially powerful tool to model the risk of disease transmission in great apes, and that chimpanzees are particularly threatened by infectious disease outbreaks as a result of their social structure.     

Breeding success and nest-site characteristics of Red-breasted Flycatchers Ficedula parva in a primeval forest

Capsule Predation is a major factor influencing the breeding success of Red-breasted Flycatchers under natural conditions.

Aims To examine the breeding success of Red-breasted Flycatchers in relation to nest-site characteristics and time of breeding.

Methods Data were collected during seven breeding seasons under natural conditions in Bia?owie?a National Park. We used survival time analysis to estimate changes in survival probability over time and breeding success in relation to first-egg date and nest-site characteristics.

Results Offspring fledged successfully from 51% of clutches, but the Kaplan–Meier estimate of survival was lower at 0.43. Of the unsuccessful clutches, 82% were lost to predators. The highest probability of loss was during egg-laying and in the second half of incubation. Breeding success was influenced by the height of the nest above the ground, but no relation to other nest-site characteristics was found.

Conclusion To avoid predation Red-breasted Flycatchers build nests in various sites that are more open than most cavity-nesting species. The position of the nest-sites allows the sitting female to observe her surroundings and to escape rapidly from the nest, giving the chance for a replacement clutch.     

Long-Lasting Sparks: Multi-Metastability and Release Competition in the Calcium Release Unit Network

Calcium (Ca) sparks are elementary events of biological Ca signaling. A normal Ca spark has a brief duration in the range of 10 to 100 ms, but long-lasting sparks with durations of several hundred milliseconds to seconds are also widely observed. Experiments have shown that the transition from normal to long-lasting sparks can occur when ryanodine receptor (RyR) open probability is either increased or decreased. Here, we demonstrate theoretically and computationally that long-lasting sparks emerge as a collective dynamical behavior of the network of diffusively coupled Ca release units (CRUs). We show that normal sparks occur when the CRU network is monostable and excitable, while long-lasting sparks occur when the network dynamics possesses multiple metastable attractors, each attractor corresponding to a different spatial firing pattern of sparks. We further highlight the mechanisms and conditions that produce long-lasting sparks, demonstrating the existence of an optimal range of RyR open probability favoring long-lasting sparks. We find that when CRU firings are sparse and sarcoplasmic reticulum (SR) Ca load is high, increasing RyR open probability promotes long-lasting sparks by potentiating Ca-induced Ca release (CICR). In contrast, when CICR is already strong enough to produce frequent firings, decreasing RyR open probability counter-intuitively promotes long-lasting sparks by decreasing spark frequency. The decrease in spark frequency promotes intra-SR Ca diffusion from neighboring non-firing CRUs to the firing CRUs, which helps to maintain the local SR Ca concentration of the firing CRUs above a critical level to sustain firing. In this setting, decreasing RyR open probability further suppresses long-lasting sparks by weakening CICR. Since a long-lasting spark terminates via the Kramers’ escape process over a potential barrier, its duration exhibits an exponential distribution determined by the barrier height and noise strength, which is modulated differently by different ways of altering the Ca release flux strength.     

Modeling survival of experimentally virus-infected laboratory animals--exploration of the survival diagram

In a recent paper (Sühnel & Veckenstedt, 1989, J. theor. Biol. 137, 27) we have proposed a new method of plotting survival data from experimentally virus-infected laboratory animals; the survival diagram. In this diagram two experiments, for which the mean number of virions inoculated is kept fixed but other parameters may vary, are compared. The variations in two basic quantities of survival analysis are simultaneously displayed: the standard mean survival time and the relative mean challenge virus dose, which is via a dose-response relation interrelated with the fraction of animals dying. It is analyzed in which manner variations in the kinetic parameters and the critical virus level necessary to produce a particular effect influence the location of the points of comparison in the survival diagram. The analysis presented is a prerequisite for further applications of this diagram and of the underlying mathematical model.     

Transition between two regimes describing internal fluctuation of DNA in a nanochannel

We measure the thermal fluctuation of the internal segments of a piece of DNA confined in a nanochannel about 50-100 nm wide. This local thermodynamic property is key to accurate measurement of distances in genomic analysis. For DNA in ~100 nm channels, we observe a critical length scale ~10 m for the mean extension of internal segments, below which the de Gennes' theory describes the fluctuations with no fitting parameters, and above which the fluctuation data falls into Odijk's deflection theory regime. By analyzing the probability distributions of the extensions of the internal segments, we infer that folded structures of length 150-250 nm, separated by ~10 m exist in the confined DNA during the transition between the two regimes. For ~50 nm channels we find that the fluctuation is significantly reduced since the Odijk regime appears earlier. This is critical for genomic analysis. We further propose a more detailed theory based on small fluctuations and incorporating the effects of confinement to explicitly calculate the statistical properties of the internal fluctuations. Our theory is applicable to polymers with heterogeneous mechanical properties confined in non-uniform channels. We show that existing theories for the end-to-end extension/fluctuation of polymers can be used to study the internal fluctuations only when the contour length of the polymer is many times larger than its persistence length. Finally, our results suggest that introducing nicks in the DNA will not change its fluctuation behavior when the nick density is below 1 nick per kbp DNA.     

Hematological health state indices predict local survival in a small passerine bird, the great tit (Parus major)

In birds, it has been shown that reproductive effort may impair parental condition, while the relation of different condition indices to subsequent survival is still poorly understood. In this study, we measured body mass and various hematological condition indices in breeding great tits in relation to local survival. Number and quality of nestlings and the occurrence of second broods, potentially reflecting parents' breeding effort, were also considered in analyses. The great tits, both male and female, that returned the following year had had a higher albumin/globulin ratio, lower plasma globulin concentration, and a lower heterophile/lymphocyte ratio during breeding in the preceding year, compared to those who did not return. Surviving males (but not females) also had had a higher level of circulating lymphocytes, compared to nonsurvivors. There was no correlation between breeding effort and survival. We conclude that better immunological state and lower stress in great tits during breeding were positively related to their survival probability.     

Conditional heteroscedasticity as a leading indicator of ecological regime shifts

Regime shifts are massive, often irreversible, rearrangements of nonlinear ecological processes that occur when systems pass critical transition points. Ecological regime shifts sometimes have severe consequences for human well-being, including eutrophication in lakes, desertification, and species extinctions. Theoretical and laboratory evidence suggests that statistical anomalies may be detectable leading indicators of regime shifts in ecological time series, making it possible to foresee and potentially avert incipient regime shifts. Conditional heteroscedasticity is persistent variance characteristic of time series with clustered volatility. Here, we analyze conditional heteroscedasticity as a potential leading indicator of regime shifts in ecological time series. We evaluate conditional heteroscedasticity by using ecological models with and without four types of critical transition. On approaching transition points, all time series contain significant conditional heteroscedasticity. This signal is detected hundreds of time steps in advance of the regime shift. Time series without regime shifts do not have significant conditional heteroscedasticity. Because probability values are easily associated with tests for conditional heteroscedasticity, detection of false positives in time series without regime shifts is minimized. This property reduces the need for a reference system to compare with the perturbed system.     

Social networks predict patch discovery in a wild population of songbirds

Animals use social information in a wide variety of contexts. Its extensive use by individuals to locate food patches has been documented in a number of species, and various mechanisms of discovery have been identified. However, less is known about whether individuals differ in their access to, and use of, social information to find food. We measured the social network of a wild population of three sympatric tit species (family Paridae) and then recorded individual discovery of novel food patches. By using recently developed methods for network-based diffusion analysis, we show that order of arrival at new food patches was predicted by social associations. Models based only on group searching did not explain this relationship. Furthermore, network position was correlated with likelihood of patch discovery, with central individuals more likely to locate and use novel foraging patches than those with limited social connections. These results demonstrate the utility of social network analysis as a method to investigate social information use, and suggest that the greater probability of receiving social information about new foraging patches confers a benefit on more socially connected individuals.