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

Using GAMMs to model trial-by-trial fluctuations in experimental data: more risks but hardly any benefit

Data from each subject in a repeated-measures experiment form a time series, which may include trial-by-trial fluctuations arising from human factors such as practice or fatigue. Concerns about the statistical implications of such effects have increased the popularity of Generalized Additive Mixed Models (GAMMs), a powerful technique for modeling wiggly patterns. We question these statistical concerns and investigate the costs and benefits of using GAMMs relative to linear mixed-effects models (LMEMs). In two sets of Monte Carlo simulations, LMEMs that ignored time-varying effects were no more prone to false positives than GAMMs. Although GAMMs generally boosted power for within-subject effects, they reduced power for between-subject effects, sometimes to a severe degree. Our results signal the importance of proper subject-level randomization as the main defense against statistical artifacts due to by-trial fluctuations

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

On the phase space structure of IP3 induced Ca2+ signalling and concepts for predictive modeling

The correspondence between mathematical structures and experimental systems is the basis of the generalizability of results found with specific systems, and is the basis of the predictive power of theoretical physics. While physicists have confidence in this correspondence, it is less recognized in cellular biophysics. On the one hand, the complex organization of cellular dynamics involving a plethora of interacting molecules and the basic observation of cell variability seem to question its possibility. The practical difficulties of deriving the equations describing cellular behaviour from first principles support these doubts. On the other hand, ignoring such a correspondence would severely limit the possibility of predictive quantitative theory in biophysics. Additionally, the existence of functional modules (like pathways) across cell types suggests also the existence of mathematical structures with comparable universality. Only a few cellular systems have been sufficiently investigated in a variety of cell types to follow up these basic questions. IP3 induced Ca2+ signalling is one of them, and the mathematical structure corresponding to it is subject of ongoing discussion. We review the system’s general properties observed in a variety of cell types. They are captured by a reaction diffusion system. We discuss the phase space structure of its local dynamics. The spiking regime corresponds to noisy excitability. Models focussing on different aspects can be derived starting from this phase space structure. We discuss how the initial assumptions on the set of stochastic variables and phase space structure shape the predictions of parameter dependencies of the mathematical models resulting from the derivation

cDNA cloning and characterization of tryptophan synthase alpha subunit from Polygonum tinctorium

Polygonum tinctorium is a cultivated plant that produces indigo, a natural blue dye. Its leaves contain a large amount of indican (indoxyl-beta-D-glucoside), a colorless precursor of indigo. The enzyme beta-glucosidase, which degrades indican, is present in leaf cells. If the leaves ar e scratched because of some external factors, indican is enzymatically degraded into indoxyl and glucose. Because of the chemical instability of indoxyl, it is immediately oxidized to indigo by atmospheric oxygen. Beta-glucosidase is located in chloroplasts, whereas the substrate indican is stored in vacuoles. Therefore, indigo is only produced if leaf cells are physically broken. The insoluble indigo may have a negative effect on infectious fungi and bacteria as well as on invasive insects and other animals. We hypothesize that the physiological role of indican as a secondary metabolite is of a defense system against predators. In a previous study, we have shown that indican is synthesized from indoxyl and UDP-glucose by the catalysis of UDP-glucosyltransferase. The substrate indoxyl is probably produced by the hydroxylation of indole catalyzed by cytochrome P450. Indole is an intermediate product in tryptophan syn thesis, which is the final step of the shikimic acid pathway, a primary metabolic pathway. The tryptophan synthase consists of four subunits: two alpha subunits (TSA) and two beta subunits (TSB). Only TSA catalyzes the synthetic reaction of indole. Subsequently, indole is converted to tryptophan by the action of TSB. The purpose of this study is to uncover the complete indican synthetic pathway and to provide insight into the switching mechanism from primary to secondary metabolism. Here, we report on the cDNA cloning, expression, and characterization of TSA from P. tinctorium. Transcriptome analysis using mRNA from P. tinctorium leaf tissue resulted in a one-fragment sequence that has homology with sequences from other plant TSAs. Based on this sequence, the RACE method was used to get the complete length of the TSA cDNA. The obtained cDNA consisted of 1,469 bp encoding a polypeptide of 315 amino acids. The primary structure contained the consensus sequences of TSAs and the regions for interaction with beta subunits. P. tinctorium TSA, which we named as ptTSA1, showed high homology to some enzymes from plants; this was the case particularly with TSA from Isatis tinctoria, another indigo plant, which showed 95.7% homology to ptTSA1. To analyze the properties and functions of ptTSA1, the recombinant protein was expressed in Escherichia coli. In addition, the ptTSA1 cDNA was used to examine whether ptTSA1 could complement a TSA deletion in E. coli. ptTSA1 protein expression and mRNA levels in various tissues of P. tinctorium were examined by the Western blot analysis and semi-quantitative RT-PCR. These expression patterns were also compared with those of TSBs. Here, we will further discuss regarding the analysis of ptTSA1 and the interaction between TSA and TSB

A Bayesian approach to modelling heterogeneous calcium responses in cell populations

Calcium responses have been observed as spikes of the whole-cell calcium concentration in numerous cell types and are essential for translating extracellular stimuli into cellular responses. While there are several suggestions for how this encoding is achieved, we still lack a comprehensive theory. To achieve this goal it is necessary to reliably predict the temporal evolution of calcium spike sequences for a given stimulus. Here, we propose a modelling framework that allows us to quantitatively describe the timing of calcium spikes. Using a Bayesian approach, we show that Gaussian processes model calcium spike rates with high fidelity and perform better than standard tools such as peri-stimulus time histograms and kernel smoothing. We employ our modelling concept to analyse calcium spike sequences from dynamically-stimulated HEK293T cells. Under these conditions, different cells often experience diverse stimuli time courses, which is a situation likely to occur in vivo. This single cell variability and the concomitant small number of calcium spikes per cell pose a significant modelling challenge, but we demonstrate that Gaussian processes can successfully describe calcium spike rates in these circumstances. Our results therefore pave the way towards a statistical description of heterogeneous calcium oscillations in a dynamic environmen

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