Leiv Øyehaug

Astrocytic Mechanisms Explaining Neural-Activity-Induced Shrinkage of Extraneuronal Space

Neuronal stimulation causes ∼30% shrinkage of the extracellular space (ECS) between neurons and surrounding astrocytes in grey and white matter under experimental conditions. Despite its possible implications for a proper understanding of basic aspects of potassium clearance and astrocyte function, the phenomenon remains unexplained. Here we present a dynamic model that accounts for current experimental data related to the shrinkage phenomenon in wild-type as well as in gene knockout individuals. We find that neuronal release of potassium and uptake of sodium during stimulation, astrocyte uptake of potassium, sodium, and chloride in passive channels, action of the Na/K/ATPase pump, and osmotically driven transport of water through the astrocyte membrane together seem sufficient for generating ECS shrinkage as such. However, when taking into account ECS and astrocyte ion concentrations observed in connection with neuronal stimulation, the actions of the Na+/K+/Cl− (NKCC1) and the Na+/HCO3 − (NBC) cotransporters appear to be critical determinants for achieving observed quantitative levels of ECS shrinkage. Considering the current state of knowledge, the model framework appears sufficiently detailed and constrained to guide future key experiments and pave the way for more comprehensive astroglia–neuron interaction models for normal as well as pathophysiological situations.

Extreme sarcoplasmic reticulum volume loss and compensatory T-tubule remodeling after Serca2 knockout

Cardiomyocyte contraction and relaxation are controlled by Ca2+ handling, which can be regulated to meet demand. Indeed, major reduction in sarcoplasmic reticulum (SR) function in mice with Serca2 knockout (KO) is compensated by enhanced plasmalemmal Ca2+ fluxes. Here we investigate whether altered Ca2+ fluxes are facilitated by reorganization of cardiomyocyte ultrastructure. Hearts were fixed for electron microscopy and enzymatically dissociated for confocal microscopy and electrophysiology. SR relative surface area and volume densities were reduced by 63% and 76%, indicating marked loss and collapse of the free SR in KO. Although overall cardiomyocyte dimensions were unaltered, total surface area was increased. This resulted from increased T-tubule density, as revealed by confocal images. Fourier analysis indicated a maintained organization of transverse T-tubules but an increased presence of longitudinal T-tubules. This demonstrates a remarkable plasticity of the tubular system in the adult myocardium. Immunocytochemical data showed that the newly grown longitudinal T-tubules contained Na+/Ca2+-exchanger proximal to ryanodine receptors in the SR but did not contain Ca2+-channels. Ca2+ measurements demonstrated a switch from SR-driven to Ca2+ influx-driven Ca2+ transients in KO. Still, SR Ca2+ release constituted 20% of the Ca2+ transient in KO. Mathematical modeling suggested that Ca2+ influx via Na+/Ca2+-exchange in longitudinal T-tubules triggers release from apposing ryanodine receptors in KO, partially compensating for reduced SERCA by allowing for local Ca2+ release near the myofilaments. T-tubule proliferation occurs without loss of the original ordered transverse orientation and thus constitutes the basis for compensation of the declining SR function without structural disarrangement.

Carotenoid dynamics in Atlantic salmon

BackgroundCarotenoids are pigment molecules produced mainly in plants and heavily exploited by a wide range of organisms higher up in the food-chain. The fundamental processes regulating how carotenoids are absorbed and metabolized in vertebrates are still not fully understood. We try to further this understanding here by presenting a dynamic ODE (ordinary differential equation) model to describe and analyse the uptake, deposition, and utilization of a carotenoid at the whole-organism level. The model focuses on the pigment astaxanthin in Atlantic salmon because of the commercial importance of understanding carotenoid dynamics in this species, and because deposition of carotenoids in the flesh is likely to play an important life history role in anadromous salmonids.ResultsThe model is capable of mimicking feed experiments analyzing astaxanthin uptake and retention over short and long time periods (hours, days and years) under various conditions. A sensitivity analysis of the model provides information on where to look for possible genetic determinants underlying the observed phenotypic variation in muscle carotenoid retention. Finally, the model framework is used to predict that a specific regulatory system controlling the release of astaxanthin from the muscle is not likely to exist, and that the release of the pigment into the blood is instead caused by the androgen-initiated autolytic degradation of the muscle in the sexually mature salmon.ConclusionThe results show that a dynamic model describing a complex trait can be instrumental in the early stages of a project trying to uncover underlying determinants. The model provides a heuristic basis for an experimental research programme, as well as defining a scaffold for modelling carotenoid dynamics in mammalian systems.

Ca2+ wave probability is determined by the balance between SERCA2-dependent Ca2+ reuptake and threshold SR Ca2+ content

AIMS In this manuscript, we determined the roles of the sarcoendoplasmic reticulum Ca(2+) ATPase 2 (SERCA2) and the ryanodine receptor (RyR) in Ca(2+) wave development during β-adrenergic stimulation. METHODS AND RESULTS SERCA2 knockout mice (KO) were used 6 days after cardio-specific gene deletion, with left ventricular SERCA2a abundance reduced by 54 ± 9% compared with SERCA2(flox/flox) controls (FF) (P < 0.05). Ca(2+) waves occurred in fewer KO than FF myocytes (40 vs. 68%, P < 0.05), whereas the addition of isoproterenol (ISO) induced waves in an equal percentage of myocytes (82 vs. 64%). SERCA2-dependent Ca(2+) reuptake was slower in KO (-ISO, KO vs. FF: 15.4 ± 1.2 vs. 21.1 ± 1.4 s(-1), P < 0.05), but equal during ISO (+ISO, KO vs. FF: 21.9 ± 3.3 vs. 27.7 ± 2.7 s(-1)). Threshold SR Ca(2+) content for wave development was lower in KO (-ISO, KO vs. FF: 126.6 ± 10.3 vs. 159.3 ± 7.1 µmol/L, P < 0.05) and was increased by ISO only in FF (+ISO, KO vs. FF: 131.7 ± 8.7 vs. 205.5 ± 20.4 µmol/L, P < 0.05). During ISO, Ca(2+)/calmodulin-dependent kinase II (CaMKII)-dependent phosphorylation of RyR in KO was 217 ± 21% of FF (P < 0.05), and SR Ca(2+) leak indicated higher RyR open probability in KO. CaMKII inhibition decreased Ca(2+) spark frequency in KO by 44% (P < 0.05) but not in FF. Mathematical modelling predicted that increased Ca(2+) sensitivity of RyR in KO could account for increased Ca(2+) wave probability during ISO. CONCLUSIONS In ventricular cardiomyocytes with reduced SERCA2 abundance, Ca(2+) wave development following β-adrenergic stimulation is potentiated. We suggest that this is caused by a CaMKII-dependent shift in the balance between SERCA2-dependent Ca(2+) reuptake and threshold SR Ca(2+) content.

Dependence of spontaneous neuronal firing and depolarisation block on astroglial membrane transport mechanisms

Exposed to a sufficiently high extracellular potassium concentration ([K + ]o), the neuron can fire spontaneous discharges or even become inactivated due to membrane depolarisation (‘depolarisation block’). Since these phenomena likely are related to the maintenance and propagation of seizure discharges, it is of considerable importance to understand the conditions under which excess [K + ]o causes them. To address the putative effect of glial buffering on neuronal activity under elevated [K + ]o conditions, we combined a recently developed dynamical model of glial membrane ion and water transport with a Hodgkin–Huxley type neuron model. In this interconnected glia-neuron model we investigated the effects of natural heterogeneity or pathological changes in glial membrane transporter density by considering a large set of models with different, yet empirically plausible, sets of model parameters. We observed both the high [K + ]o-induced duration of spontaneous neuronal firing and the prevalence of depolarisation block to increase when reducing the magnitudes of the glial transport mechanisms. Further, in some parameter regions an oscillatory bursting spiking pattern due to the dynamical coupling of neurons and glia was observed. Bifurcation analyses of the neuron model and of a simplified version of the neuron-glia model revealed further insights about the underlying mechanism behind these phenomena. The above insights emphasise the importance of combining neuron models with detailed astroglial models when addressing phenomena suspected to be influenced by the astroglia-neuron interaction. To facilitate the use of our neuron-glia model, a CellML version of it is made publicly available.

Synchrony of Cardiomyocyte Ca2+ Release is Controlled by t-tubule Organization, SR Ca2+ Content, and Ryanodine Receptor Ca2+ Sensitivity

Recent work has demonstrated that cardiomyocyte Ca(2+)release is desynchronized in several pathological conditions. Loss of Ca(2+) release synchrony has been attributed to t-tubule disruption, but it is unknown if other factors also contribute. We investigated this issue in normal and failing myocytes by integrating experimental data with a mathematical model describing spatiotemporal dynamics of Ca(2+) in the cytosol and sarcoplasmic reticulum (SR). Heart failure development in postinfarction mice was associated with progressive t-tubule disorganization, as quantified by fast-Fourier transforms. Data from fast-Fourier transforms were then incorporated in the model as a dyadic organization index, reflecting the proportion of ryanodine receptors located in dyads. With decreasing dyadic-organization index, the model predicted greater dyssynchrony of Ca(2+) release, which exceeded that observed in experimental line-scan images. Model and experiment were reconciled by reducing the threshold for Ca(2+) release in the model, suggesting that increased RyR sensitivity partially offsets the desynchronizing effects of t-tubule disruption in heart failure. Reducing the magnitude of SR Ca(2+) content and release, whether experimentally by thapsigargin treatment, or in the model, desynchronized the Ca(2+) transient. However, in cardiomyocytes isolated from SERCA2 knockout mice, RyR sensitization offset such effects. A similar interplay between RyR sensitivity and SR content was observed during treatment of myocytes with low-dose caffeine. Initial synchronization of Ca(2+) release during caffeine was reversed as SR content declined due to enhanced RyR leak. Thus, synchrony of cardiomyocyte Ca(2+) release is not only determined by t-tubule organization but also by the interplay between RyR sensitivity and SR Ca(2+) content.

Targeted reduction of complex models with time scale hierarchy--a case study.

With the increasing flow of biological data there is a growing demand for mathematical tools whereby essential aspects of complex causal dynamic models can be captured and detected by simpler mathematical models without sacrificing too much of the realism provided by the original ones. Given the presence of a time scale hierarchy, singular perturbation techniques represent an elegant method for making such minimised mathematical representations. Any reduction of a complex model by singular perturbation methods is a targeted reduction by the fact that one has to pick certain mechanisms, processes or aspects thought to be essential in a given explanatory context. Here we illustrate how such a targeted reduction of a complex model of melanogenesis in mammals recently developed by the authors provides a way to improve the understanding of how the melanogenic system may behave in a switch-like manner between production of the two major types of melanins. The reduced model is shown by numerical means to be in good quantitative agreement with the original model. Furthermore, it is shown how the reduced model discloses hidden robustness features of the full model, and how the making of a reduced model represents an efficient analytical sensitivity analysis. In addition to yielding new insights concerning the melanogenic system, the paper provides an illustration of a protocol that could be followed to make validated simplifications of complex biological models possessing time scale hierarchies.

ICaL inhibition prevents arrhythmogenic Ca2+ waves caused by abnormal Ca2+ sensitivity of RyR or SR Ca2+ accumulation

AIMS Arrhythmogenic Ca(2+) waves result from uncontrolled Ca(2+) release from the sarcoplasmic reticulum (SR) that occurs with increased Ca(2+) sensitivity of the ryanodine receptor (RyR) or excessive Ca(2+) accumulation during β-adrenergic stimulation. We hypothesized that inhibition of the L-type Ca(2+) current (I(CaL)) could prevent such Ca(2+) waves in both situations. METHODS AND RESULTS Ca(2+) waves were induced in mouse left ventricular cardiomyocytes by isoproterenol combined with caffeine to increase RyR Ca(2+) sensitivity. I(CaL) inhibition by verapamil (0.5 µM) reduced Ca(2+) wave probability in cardiomyocytes during electrostimulation, and during a 10 s rest period after ceasing stimulation. A separate type of Ca(2+) release events occurred during the decay phase of the Ca(2+) transient and was not prevented by verapamil. Verapamil decreased Ca(2+) spark frequency, but not in permeabilized cells, indicating that this was not due to direct effects on RyR. The antiarrhythmic effect of verapamil was due to reduced SR Ca(2+) content following I(CaL) inhibition. Computational modelling supported that the level of I(CaL) inhibition obtained experimentally was sufficient to reduce the SR Ca(2+) content. Ca(2+) wave prevention through reduced SR Ca(2+) content was also effective in heterozygous ankyrin B knockout mice with excessive SR Ca(2+) accumulation during β-adrenergic stimulation. CONCLUSION I(CaL) inhibition prevents diastolic Ca(2+) waves caused by increased Ca(2+) sensitivity of RyR or excessive SR Ca(2+) accumulation during β-adrenergic stimulation. In contrast, unstimulated early Ca(2+) release during the decay of the Ca(2+) transient is not prevented, and merits further study to understand the full antiarrhythmic potential of I(CaL) inhibition.

The mathematics of tanning

BackgroundThe pigment melanin is produced by specialized cells, called melanocytes. In healthy skin, melanocytes are sparsely spread among the other cell types in the basal layer of the epidermis. Sun tanning results from an UV-induced increase in the release of melanin to neighbouring keratinocytes, the major cell type component of the epidermis as well as redistribution of melanin among these cells. Here we provide a mathematical conceptualization of our current knowledge of the tanning response, in terms of a dynamic model. The resolution level of the model is tuned to available data, and its primary focus is to describe the tanning response following UV exposure.ResultsThe model appears capable of accounting for available experimental data on the tanning response in different skin and photo types. It predicts that the thickness of the epidermal layer and how far the melanocyte dendrites grow out in the epidermal layers after UV exposure influence the tanning response substantially.ConclusionDespite the paucity of experimental validation data the model is constrained enough to serve as a foundation for the establishment of a theoretical-experimental research programme aimed at elucidating the more fine-grained regulatory anatomy underlying the tanning response.

Travelling Waves as a Mechanism of Pattern Generation in Discrete Cell Lattices

This year marks the fiftieth anniversary of Turing’s famous paper [10] where he predicted that instabilities could result in otherwise stable two-species systems when diffusion was added to the system, so-called diffusion-driven instabilities. This idea has later been investigated more profoundly by Meinhardt and Gierer [3]. They proposed that diffusion with long-range inhibition and local self-activation represents a basic mechanism for pattern formation in biology. Do the ideas originating in Turing’s paper and further developed by Meinhardt and others apply to discrete models as well? If this is not the case, what kind of mechanisms cause pattern formation in discrete models?