Localization of polymers in a finite medium with fixed random obstacles

In this paper we investigate the conformation statistics of a Gaussian chain embedded in a medium of finite size, in the presence of quenched random obstacles. The similarities and differences between the case of random obstacles and the case of a Gaussian random potential are elucidated. The connection with the density of states of electrons in a metal with random repulsive impurities of finite range is discussed. We also interpret the results obtained in some previous numerical simulations.Comment: 23 pages, 3 figures, revte

Polymers with self-avoiding interaction in random media: a localization-delocalization transition

In this paper we investigate the problem of a long self-avoiding polymer chain immersed in a random medium. We find that in the limit of a very long chain and when the self-avoiding interaction is weak, the conformation of the chain consists of many ``blobs'' with connecting segments. The blobs are sections of the molecule curled up in regions of low potential in the case of a Gaussian distributed random potential or in regions of relatively low density of obstacles in the case of randomly distributed hard obstacles. We find that as the strength of the self-avoiding interaction is increased the chain undergoes a delocalization transition in the sense that the appropriate free energy per monomer is no longer negative. The chain is then no longer bound to a particular location in the medium but can easily wander around under the influence of a small perturbation. For a localized chain we estimate quantitatively the expected number of monomers in the ``blobs'' and in the connecting segments.Comment: 20 pages, 2 figures, revtex

Nonlinear signaling on biological networks: the role of stochasticity and spectral clustering

Signal transduction within biological cells is governed by networks of interacting proteins. Communication between these proteins is mediated by signaling molecules which bind to receptors and induce stochastic transitions between different conformational states. Signaling is typically a cooperative process which requires the occurrence of multiple binding events so that reaction rates have a nonlinear dependence on the amount of signaling molecule. It is this nonlinearity that endows biological signaling networks with robust switch-like properties which are critical to their biological function. In this study, we investigate how the properties of these signaling systems depend on the network architecture. Our main result is that these nonlinear networks exhibit bistability where the network activity can switch between states that correspond to a low and high activity level. We show that this bistable regime emerges at a critical coupling strength that is determined by the spectral structure of the network. In particular, the set of nodes that correspond to large components of the leading eigenvector of the adjacency matrix determines the onset of bistability. Above this transition, the eigenvectors of the adjacency matrix determine a hierarchy of clusters, defined by its spectral properties, which are activated sequentially with increasing network activity. We argue further that the onset of bistability occurs either continuously or discontinuously depending upon whether the leading eigenvector is localized or delocalized. Finally, we show that at low network coupling stochastic transitions to the active branch are also driven by the set of nodes that contribute more strongly to the leading eigenvector.Comment: 30 pages, 12 figure

Cardiac Cellular Coupling and the Spread of Early Instabilities in Intracellular Ca2+

AbstractRecent experimental and modeling studies demonstrate the fine spatial scale, complex nature, and independent contribution of Ca2+ dynamics as a proarrhythmic factor in the heart. The mechanism of progression of cell-level Ca2+ instabilities, known as alternans, to tissue-level arrhythmias is not well understood. Because gap junction coupling dictates cardiac syncytial properties, we set out to elucidate its role in the spatiotemporal evolution of Ca2+ instabilities. We experimentally perturbed cellular coupling in cardiac syncytium in vitro. Coupling was quantified by fluorescence recovery after photobleaching, and related to function, including subtle fine-scale Ca2+ alternans, captured by optical mapping. Conduction velocity and threshold for alternans monotonically increased with coupling. Lower coupling enhanced Ca2+ alternans amplitude, but the spatial spread of early (<2 Hz) alternation was the greatest under intermediate (not low) coupling. This nonmonotonic relationship was closely matched by the percent of samples exhibiting large-scale alternans at higher pacing rates. Computer modeling corroborated these experimental findings for strong but not weak electromechanical (voltage-Ca2+) coupling, and offered mechanistic insight. In conclusion, using experimental and modeling approaches, we reveal a general mechanism for the spatial spread of subtle cellular Ca2+ alternans that relies on a combination of gap-junctional and voltage-Ca2+ coupling

Stochastic coupled map model of subcellular calcium cycling in cardiac cells

In this study, we analyze a nonlinear map model of intracellular calcium (Ca) and voltage in cardiac cells. In this model, Ca release from the sarcoplasmic reticulum (SR) occurs at spatially distributed dyadic junctions that are diffusively coupled. At these junctions, release occurs with a probability that depends on key variables such as the SR load and the diastolic interval. Using this model, we explore how nonlinearity and stochasticity determine the spatial distribution of Ca release events within a cardiac cell. In particular, we identify a novel synchronization transition, which occurs at rapid pacing rates, in which the global Ca transient transitions from a period 2 response to a period 1 response. In the global period 2 response dyadic junctions fire in unison, on average, on alternate beats, while in the period 1 regime, Ca release at individual dyads is highly irregular. A close examination of the spatial distribution of Ca reveals that in the period 1 regime, the system coarsens into spatially out-of-phase regions with a length scale much smaller than the system size, but larger than the spacing between dyads.We have also explored in detail the coupling to membrane voltage. We study first the case of positive coupling, where a large Ca transient promotes a long action potential duration (APD). Here, the coupling to voltage synchronizes Ca release so that the system exhibits a robust period 2 response that is independent of initial conditions. On the other hand, in the case of negative coupling, where a large Ca transient tends to shorten the APD, we find a multitude of metastable states which consist of complex spatially discordant alternans patterns. Using an analogy to equilibrium statistical mechanics, we show that the spatial patterns observed can be explained by a mapping to the Potts model, with an additional term that accounts for a global coupling of spin states. Using this analogy, we argue that Ca cycling in cardiac cells exhibits complex spatiotemporal patterns that emerge via first or second order phase transitions. These results show that voltage and Ca can interact in order to induce complex subcellular responses, which can potentially lead to heart rhythm disorders.Peer ReviewedPostprint (published version

Major reproductive disorders on Jersey breed dairy cattle at Adea Berga dairy farm, West Shewa Zone, Oromia Region, Ethiopia

Reproductive efficiency of dairy cows is influenced by different factors including gene, season, age, production system, nutrition, management, environment anddisease. This study was conducted with the objectives of determining the   prevalence of reproductive disorders and evaluates reproductive performances of Jersey dairy cattle maintained at Adea berga dairy farm. The retrospective and longitudinal studies were employed through document revision; clinical and laboratory examination from 1996 to 2010 and from 2010 to 2014, respectively. All 97 cows from first to 10th parity which were kept under semi intensive management system in the farm were included in this study. The overall prevalence of reproductive health problems was 54.6% (n=53) and the major ones were found to be prolonged anoestrus, abortion, still birth and retained fetal membrane accounting for 48.5%, 28.9%, 14.4% and 5.2% prevalence, respectively. Of the considered risk factors, age, parity and body condition didn’t show significant (P&gt;0.05) effect on abortion and prolonged anestrous while found to significantly (P&lt;0.05) affect still birth. However, season had a significant (P&lt;0.05) effect on all disorders (abortion, prolonged anestrous and still birth). Pluriparus animal with no statistically significant difference (P&gt;0.05) showed higher prevalence of abortion (29%), still birth (15.1%) and retained fetal membrane (5.4%) than uniparus ones which represented 25%, o%, o% prevalence for abortion, still birth and retained fetal membrane respectively. In contrast uniparus animals showed higher  prevalence (50%) of prolonged anoestrus as compared to the pluriparus ones  (48.4%) and no statistical significant difference was observed (P&gt;0.05) among them. The parasitological, serological and bacteriological test results in this study showed a negative result, where all animals tested were found to be free from brucellosis, trichomonoiasis and other bacterial infections. In this study a mean value for AFS (age at first service), AFCA (age at first calving), ALS (age at last service), ALCA (age at last calving) and CI (calving interval) were found to be (25.8 + 0.76), (35.5 + 0.71), (66.6 + 3.2), (77.1 + 2.6) and (17.7 + 0.4) months respectively. While the mean value for parity, LN (lactation number), NSPC (number of service per conception) and days open were (4.16 + 0.19), (3.09 + 0.2), (2.25 + 0.14) and (270.47 + 14.17), respectively. From this study, it was concluded that the major reproductive disorders responsible for the altered reproductive performance of jersey dairy cows were prolonged anoestrus, abortion, still birth and retained fetal membrane. Routine and periodical examination of cows during postpartum period, awareness creation to farm attendants and employing improved dairy herd management should be implemented. Moreover associated economic losses in this dairy farm and cause of abortion should be exclusively investigatedwith other test methodologies for other entities. Keywords: Adea berga, Jersey breed, Oromia region, Reproductive disorder, West Shewa

The Statistics of Calcium-Mediated Focal Excitations on a One-Dimensional Cable

ABSTRACT It is well known that various cardiac arrhythmias are initiated by an ill-timed excitation that originates from a focal region of the heart. However, up to now, it is not known what governs the timing, location, and morphology of these focal excitations. Recent studies have shown that these excitations can be caused by abnormalities in the calcium (Ca) cycling system. However, the cause-and-effect relationships linking subcellular Ca dynamics and focal activity in cardiac tissue is not completely understood. In this article, we present a minimal model of Ca-mediated focal excitations in cardiac tissue. This model accounts for the stochastic nature of spontaneous Ca release on a one-dimensional cable of cardiac cells. Using this model, we show that the timing of focal excitations is equivalent to a first passage time problem in a spatially extended system. In particular, we find that for a short cable the mean first passage time increases exponentially with the number of cells in tissue, and is critically dependent on the ratio of inward to outward currents near the threshold for an action potential. For long cables excitations occurs due to ectopic foci that occur on a length scale determined by the minimum length of tissue that can induce an action potential. Furthermore, we find that for long cables the mean first passage time decreases as a power law in the number cells. These results provide precise criteria for the occurrence of focal excitations in cardiac tissue, and will serve as a guide to determine the propensity of Ca-mediated triggered arrhythmias in the heart

Calcium alternans is a global order-disorder phase transition: robustness on ryanodine receptor release dynamics

Electromechanical alternans is a beat-to-beat alterna- tion in the strength of contraction of a cardiac cell which appears often due to an instability of calcium cycling. The global calcium signal in cardiomyocytes is the result of the combined effect of several thousand micron scale domains called Calcium Release Units (CaRU), coupled through diffusion, where the flow of calcium among different cell compartments is regulated by stochastic signaling involv- ing the ryanodine receptor (RyR). Recently, numerical sim- ulations have suggested that the transition from regular Ca cycling to alternans is an order-disorder phase transition consistent with the Ising universality class. Inside the cell, groups of CaRU form transient areas within the cell where alternans appear. However, global alternans appears only as a result of the synchronization of the oscillation phase among different subunits. We show here that this transi- tion is indeed robust and universal upon changes in the behavior of the RyR. Using three different set of parame- ters for the transition rates among open, closed and inacti- vated states in the RyR, we show that different RyR behav- ior leads to the same type of order-disorder transition.Postprint (published version

Solvable model of a polymer in random media with long ranged disorder correlations

We present an exactly solvable model of a Gaussian (flexible) polymer chain in a quenched random medium. This is the case when the random medium obeys very long range quadratic correlations. The model is solved in $d$ spatial dimensions using the replica method, and practically all the physical properties of the chain can be found. In particular the difference between the behavior of a chain that is free to move and a chain with one end fixed is elucidated. The interesting finding is that a chain that is free to move in a quadratically correlated random potential behaves like a free chain with $R^2 \sim L$, where $R$ is the end to end distance and $L$ is the length of the chain, whereas for a chain anchored at one end $R^2 \sim L^4$. The exact results are found to agree with an alternative numerical solution in $d=1$ dimensions. The crossover from long ranged to short ranged correlations of the disorder is also explored.Comment: REVTeX, 28 pages, 12 figures in eps forma