Switching Dynamics in Reaction Networks Induced by Molecular Discreteness

To study the fluctuations and dynamics in chemical reaction processes, stochastic differential equations based on the rate equation involving chemical concentrations are often adopted. When the number of molecules is very small, however, the discreteness in the number of molecules cannot be neglected since the number of molecules must be an integer. This discreteness can be important in biochemical reactions, where the total number of molecules is not significantly larger than the number of chemical species. To elucidate the effects of such discreteness, we study autocatalytic reaction systems comprising several chemical species through stochastic particle simulations. The generation of novel states is observed; it is caused by the extinction of some molecular species due to the discreteness in their number. We demonstrate that the reaction dynamics are switched by a single molecule, which leads to the reconstruction of the acting network structure. We also show the strong dependence of the chemical concentrations on the system size, which is caused by transitions to discreteness-induced novel states.Comment: 11 pages, 5 figure

Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics

We present a bidomain threshold model of intracellular calcium (Ca²⁺) dynamics in which, as suggested by recent experiments, the cytosolic threshold for Ca²⁺ liberation is modulated by the Ca²⁺ concentration in the releasing compartment. We explicitly construct stationary fronts and determine their stability using an Evans function approach. Our results show that a biologically motivated choice of a dynamic threshold, as opposed to a constant threshold, can pin stationary fronts that would otherwise be unstable. This illustrates a novel mechanism to stabilise pinned interfaces in continuous excitable systems. Our framework also allows us to compute travelling pulse solutions in closed form and systematically probe the wave speed as a function of physiologically important parameters. We find that the existence of travelling wave solutions depends on the time scale of the threshold dynamics, and that facilitating release by lowering the cytosolic threshold increases the wave speed. The construction of the Evans function for a travelling pulse shows that of the co-existing fast and slow solutions the slow one is always unstable

Cardiac cell modelling: Observations from the heart of the cardiac physiome project

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field

Arsenic hyperaccumulation efficiency depends on time and tissue in Pteris vittata

The metalloid arsenic is a toxic environmental pollutant. Arsenic pollution becomes serious due to mining, mineral, smelting and tannery industry. Leaching of naturally occurring arsenic into drinking water aquifers, has been reported in many countries including India and Bangladesh. Available engineering methods for remediation is costly and difficult. Many plant species reported to accumulate arsenic. Pteris vittata has been reported as arsenic hyperaccumulator. An Indian eco-type of P. vittata has been used to study the arsenic accumulation. The plants were grown in arsenic containing soil along with soil without arsenic (control). The ferns were separated into two portions, i.e., above ground (fronds), stage specific as well as tissues from different position of pinnae and below ground (roots and rhizomes). Futher, it was also harvested at different time interval. Dried fern samples (0.1 g) were digested with mixture of concentrated nitric acid and perchloric acid. Heavy metal measurement in foliar and root samples was performed with ICP-OES. Tissue specific arsenic accumulation indicates that juvenile leaf contains highest arsenic than mature leaf. Middle pinnae of mature leaf show high arsenic content compared to upper and lower pinnae. Among the underground parts of the plant, rhizome contains high arsenic than roots. Further, time dependent arsenic accumulation study indicates that active accumulation of arsenic starts from day 7 to day 30 in leaf tissue, while in roots, day 3 to 7 show sudden increase and no much drastic change in accumulation from day 7 onwards

Phytochemical Diversity in Essential Oil of Vitex negundo L. Populations from India

Vitex negundo L., commonly known as the ‘Nirgundi’ has a long history of medicinal use in traditional and folk medicines for various diseases. To explore the diversity of the essential oil yield and composition of V. negundo, 23 populations were collected during spring season from the western Himalayan region. The essential oil yields varied from 0.06 to 0.10% in different populations of V. negundo. GC-FID, GC-MS, and statistical analysis of the leaf volatile oils showed significant phytochemical diversity. The volatiles of V. negundo were complex mixtures of 61 constituents, with sabinene (2.8-40.8%), viridiflorol (10.7%-23.8%), β-caryophyllene (5.3-21.4%), terpinen-4-ol (0.1-7.2%), epi-laurenene (2.2-5.9%), humulene epoxide II (0.5-4.6%), and abietadiene (0.1%-4.3%) as major constituents. Based on the distribution of major constituents, four groups were noticed by the multidimensional scaling and hierarchical average linkage cluster analyses. In conclusion, the yield and composition of the essential oils isolated from V. negundo varied considerably, depending on the origin

Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games

Biodiversity is essential to the viability of ecological systems. Species diversity in ecosystems is promoted by cyclic, non-hierarchical interactions among competing populations. Such non-transitive relations lead to an evolution with central features represented by the `rock-paper-scissors' game, where rock crushes scissors, scissors cut paper, and paper wraps rock. In combination with spatial dispersal of static populations, this type of competition results in the stable coexistence of all species and the long-term maintenance of biodiversity. However, population mobility is a central feature of real ecosystems: animals migrate, bacteria run and tumble. Here, we observe a critical influence of mobility on species diversity. When mobility exceeds a certain value, biodiversity is jeopardized and lost. In contrast, below this critical threshold all subpopulations coexist and an entanglement of travelling spiral waves forms in the course of temporal evolution. We establish that this phenomenon is robust, it does not depend on the details of cyclic competition or spatial environment. These findings have important implications for maintenance and evolution of ecological systems and are relevant for the formation and propagation of patterns in excitable media, such as chemical kinetics or epidemic outbreaks.Comment: Final submitted version; the printed version can be found at http://dx.doi.org/10.1038/nature06095 Supplementary movies are available at http://www.theorie.physik.uni-muenchen.de/lsfrey/images_content/movie1.AVI and http://www.theorie.physik.uni-muenchen.de/lsfrey/images_content/movie2.AV

Waiting time distributions for clusters of complex molecules

Waiting time distributions are in the core of theories for a large variety of subjects ranging from the analysis of patch clamp records to stochastic excitable systems. Here, we present a novel exact method for the calculation of waiting time distributions for state transitions of complex molecules with independent subunit dynamics. The absorbing state is a specific set of subunit states, i.e. is defined on the molecule level. Consequently, we formulate the problem as a random walk in the molecule state space. The subunits can possess an arbitrary number of states and any topology of transitions between them. The method circumvents problems arising from combinatorial explosion due to subunit coupling and requires solutions of the subunit master equation only