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Ensemble-averaged randomly scaled radar or sonar pulses are considered and the statistical theory for the corresponding phase and amplitude modulations are developed. Random scaling expresses varying radar cross-sections for scattering objects or varying antenna gain of a sweeping emitter. The noise variance of the modulations depends on the distribution function of the scaling, and how to minimise the variance by rejecting pulses below a certain amplitude threshold is shown. The theory is asymptotic in the sense that it is more accurate for increasing signal-to-noise ratios (SNRs). In a test case with uniformly distributed scaling, sufficient accuracy is reached for an average SNR larger than ∼5 for the phase average and ∼15 for the amplitude average. [ABSTRACT FROM AUTHOR]

Abstract Background Carotenoids 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. Results The 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. Conclusion The 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.

When potassium in the extracellular space separating neurons and glia reaches sufficient levels, neurons may fire spontaneous action potentials or even become inactivated due to membrane depolarisation, which, in turn, may lead to increased extracellular potassium levels. Under certain circumstances, this chain of events may trigger periodic bursts of neuronal activity. In the present study, reduced neuron-glia models are applied to explore the relationship between bursting behaviour and ion concentration dynamics. These reduced models are built based on a previously developed neuron-glia model, in which channel-mediated neuronal sodium and potassium currents are replaced by a function of neuronal sodium and extracellular potassium concentrations. Simulated dynamics of the resulting two reduced models display features that are qualitatively similar to those of the existing neuron-glia model. Bifurcation analyses of the reduced models show rich and interesting dynamics that include the existence of Hopf bifurcations between which the models exhibit slow ion concentration oscillations for a wide range of parameter values. The study demonstrates that even very simple models can provide insights of possible relevance to complex phenomena., Competing Interests: The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Øyehaug.)

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.

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., (Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Cardiomyocyte contraction and relaxation are controlled by Ca(2+) 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 Ca(2+) fluxes. Here we investigate whether altered Ca(2+) 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(+)/Ca(2+)-exchanger proximal to ryanodine receptors in the SR but did not contain Ca(2+)-channels. Ca(2+) measurements demonstrated a switch from SR-driven to Ca(2+) influx-driven Ca(2+) transients in KO. Still, SR Ca(2+) release constituted 20% of the Ca(2+) transient in KO. Mathematical modeling suggested that Ca(2+) influx via Na(+)/Ca(2+)-exchange in longitudinal T-tubules triggers release from apposing ryanodine receptors in KO, partially compensating for reduced SERCA by allowing for local Ca(2+) 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.

Exposed to a sufficiently high extracellular potassium concentration ([K( + )]₀), 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( + )]₀ 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( + )]₀-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.

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.

Neuronal stimulation causes approximately 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(+)/HCO(3) (-) (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.

A stochastic model of cancer initiation is considered. The model is used to evaluate whether a bystander effect may be important in the pre-malignant and malignant stages of carcinogenesis, and furthermore, on the basis of epidemiological data, to estimate the mutation rates of genes involved in the development of oral leukoplakias. The bystander effect is defined here as the capability of oncogenic mutations to increase the mutation probability of neighbouring (bystander) cells, thus leading potentially to a cascade of neighbouring mutated and neoplastic cells as a pre-stage in the development to leukoplakias and cancer. We find that incidence data for oral cancer are indeed in accordance with a significant bystander effect, operating either alone or in combination with genomic instability in the early stages of carcinogenesis, i.e. the development of neoplasia. Simulations performed gave a picture of how mutations and neoplasia may spread in a tissue, to form characteristic leukoplakias with a core of neoplastic cells. The model also showed that the probability of finding at least one neoplastic cell in the tissue after a given number of years is more sensitive to changes in genomic instability within the cell itself than to changes in a bystander effect. Based on epidemiological data we also calculate the maximum number of oncogenic genes that may be involved in the bystander effect and development of genomic instability. Even if capable of explaining the initial development of oncogenic mutations towards neoplastic cells, the bystander model could not reproduce the observed incidence rates of leukoplakia without assuming a carcinogen mutation probability per cell per year of neoplastic cells practically equal to one. This means that the bystander effect, to be of substantial importance in the final development of neoplastic cells towards leukoplakias, requires a very significant increase in mutation probabilities for bystanders to neoplastic cells. Alternatively, additional mechanisms such as abnormal cell differentiation and uncontrolled proliferation and apoptotis in the neoplastic stage may be of major importance during the development to cancerization.

Background: Carotenoids 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., Results: The 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., Conclusion: The 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.

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.

Melanin produced in follicular melanocytes is the major basis for pigmentation of hair and wool in mammals. Two major types of melanin may be synthesized, the black/brown eumelanin and the reddish/yellow pheomelanin. Based on available cell biological evidence and reasonable assumptions, a mathematical model is developed to improve our understanding of melanogenic switching, i.e. the switching between eumelanin and pheomelanin production depending on the extracellular signalling context. In 1993, Ito proposed that melanogenic switching is due to the covalent binding of the intermediate DOPAquinone to the enzyme glutathione reductase. We were only able to obtain a good fit to available experimental data on the relation between pheomelanin levels and the activity of the key enzyme tyrosinase by taking Ito's hypothesis into account. Thus, our results support Ito's hypothesis, and suggest that melanogenic switching may be due to a jump between two stable production pattern states when the tyrosinase activity varies between two bifurcation levels. This implies that small changes in the levels of external regulatory factors may cause an accentuated change in the proportion of the produced colour pigments and may explain the fact that mammalian coat patterns often exhibit sharply delimited patches of either black or reddish colour., (Copyright 2002 Elsevier Science Ltd. All rights reserved.)