Computational Assessment of Transport Distances in Living Skeletal Muscle Fibers Studied In Situ.

Transport distances in skeletal muscle fibers are mitigated by these cells having multiple nuclei. We have studied mouse living slow (soleus) and fast (extensor digitorum longus) muscle fibers in situ and determined cellular dimensions and the positions of all the nuclei within fiber segments. We modeled the effect of placing nuclei optimally and randomly using the nuclei as the origin of a transportation network. It appeared that an equidistant positioning of nuclei minimizes transport distances along the surface for both muscles. In the soleus muscle, however, which were richer in nuclei, positioning of nuclei to reduce transport distances to the cytoplasm were of less importance, and these fibers exhibit a pattern not statistically different from a random positioning of nuclei. We also simulated transport times for myoglobin and found that they were remarkably similar between the two muscles despite differences in nuclear patterning and distances. Together, these results highlight the importance of spatially distributed nuclei to minimize transport distances to the surface when nuclear density is low, whereas it appears that the distribution are of less importance at higher nuclear densities.

Spatially resolved estimation of metabolic oxygen consumption from optical measurements in cortex.

Significance: The cerebral metabolic rate of oxygen ( CMRO 2 ) is an important indicator of brain function and pathology. Knowledge about its magnitude is also required for proper interpretation of the blood oxygenation level-dependent (BOLD) signal measured with functional MRI. Despite the need for estimating CMRO 2 , no gold standard exists. Traditionally, the estimation of CMRO 2 has been pursued with somewhat indirect approaches combining several different types of measurements with mathematical modeling of the underlying physiological processes. The recent ability to measure the level of oxygen ( pO 2 ) in cortex with two-photon resolution in in vivo conditions has provided a more direct way for estimating CMRO 2 , but has so far only been used to estimate the average CMRO 2 close to cortical penetrating arterioles in rats. Aim: The aim of this study was to propose a method to provide spatial maps of CMRO 2 based on two-photon pO 2 measurements. Approach: The method has two key steps. First, the pO 2 maps are spatially smoothed to reduce the effects of noise in the measurements. Next, the Laplace operator (a double spatial derivative) in two spatial dimensions is applied on the smoothed pO 2 maps to obtain spatially resolved CMRO 2 estimates. Result: The smoothing introduces a bias, and a balance must be found where the effects of the noise are sufficiently reduced without introducing too much bias. In this model-based study, we explored this balance using synthetic model-based data, that is, data where the spatial maps of CMRO 2 were preset and thus known. The corresponding pO 2 maps were found by solving the Poisson equation, which relates CMRO 2 and pO 2 . MATLAB code for using the method is provided. Conclusion: Through this model-based study, we propose a method for estimating CMRO 2 with high spatial resolution based on measurements of pO 2 in cerebral cortex.

Finite Element Simulation of Ionic Electrodiffusion in Cellular Geometries.

Mathematical models for excitable cells are commonly based on cable theory, which considers a homogenized domain and spatially constant ionic concentrations. Although such models provide valuable insight, the effect of altered ion concentrations or detailed cell morphology on the electrical potentials cannot be captured. In this paper, we discuss an alternative approach to detailed modeling of electrodiffusion in neural tissue. The mathematical model describes the distribution and evolution of ion concentrations in a geometrically-explicit representation of the intra- and extracellular domains. As a combination of the electroneutral Kirchhoff-Nernst-Planck (KNP) model and the Extracellular-Membrane-Intracellular (EMI) framework, we refer to this model as the KNP-EMI model. Here, we introduce and numerically evaluate a new, finite element-based numerical scheme for the KNP-EMI model, capable of efficiently and flexibly handling geometries of arbitrary dimension and arbitrary polynomial degree. Moreover, we compare the electrical potentials predicted by the KNP-EMI and EMI models. Finally, we study ephaptic coupling induced in an unmyelinated axon bundle and demonstrate how the KNP-EMI framework can give new insights in this setting.

Cachexia does not induce loss of myonuclei or muscle fibres during xenografted prostate cancer in mice.

AIM: Cachexia is a severe wasting disorder involving loss of body- and muscle mass reducing survival and quality of life in cancer patients. We aim at determining if cachexia is a mere perturbation of the protein balance or if the condition also involves a degenerative loss of myonuclei within the fibre syncytia or loss of whole muscle fibres. METHODS: We induced cachexia by xenografting PC3 prostate cancer cells in nu/nu mice. Six weeks later, we counted myonuclei by in vivo microscopic imaging of single live fibres in the extensor digitorum longus muscle (EDL), and the EDL, soleus and tibialis anterior muscles were also harvested for ex vivo histology. RESULTS: The mice lost on average 15% of the whole-body wt. The muscle wet weight of the glycolytic, fast EDL was reduced by 14%, the tibialis anterior by 17%, and the slow, oxidative soleus by 6%. The fibre cross-sectional area in the EDL was reduced by 21% with no loss of myonuclei or any significant reduction in the number of muscle fibres. TUNEL-positive nuclei or fibres with embryonic myosin were rare both in cachectic and control muscles, and haematoxylin-eosin staining revealed no clear signs of muscle pathology. CONCLUSION: The data suggest that the cachexia induced by xenografted prostate tumours induces a pronounced atrophy not accompanied by a loss of myonuclei or a loss of muscle fibres. Thus, stem cell related treatment might be redundant, and the quest for treatment options should rather focus on intervening with intracellular pathways regulating muscle fibre size.

A Kirchhoff-Nernst-Planck framework for modeling large scale extracellular electrodiffusion surrounding morphologically detailed neurons.

Many pathological conditions, such as seizures, stroke, and spreading depression, are associated with substantial changes in ion concentrations in the extracellular space (ECS) of the brain. An understanding of the mechanisms that govern ECS concentration dynamics may be a prerequisite for understanding such pathologies. To estimate the transport of ions due to electrodiffusive effects, one must keep track of both the ion concentrations and the electric potential simultaneously in the relevant regions of the brain. Although this is currently unfeasible experimentally, it is in principle achievable with computational models based on biophysical principles and constraints. Previous computational models of extracellular ion-concentration dynamics have required extensive computing power, and therefore have been limited to either phenomena on very small spatiotemporal scales (micrometers and milliseconds), or simplified and idealized 1-dimensional (1-D) transport processes on a larger scale. Here, we present the 3-D Kirchhoff-Nernst-Planck (KNP) framework, tailored to explore electrodiffusive effects on large spatiotemporal scales. By assuming electroneutrality, the KNP-framework circumvents charge-relaxation processes on the spatiotemporal scales of nanometers and nanoseconds, and makes it feasible to run simulations on the spatiotemporal scales of millimeters and seconds on a standard desktop computer. In the present work, we use the 3-D KNP framework to simulate the dynamics of ion concentrations and the electrical potential surrounding a morphologically detailed pyramidal cell. In addition to elucidating the single neuron contribution to electrodiffusive effects in the ECS, the simulation demonstrates the efficiency of the 3-D KNP framework. We envision that future applications of the framework to more complex and biologically realistic systems will be useful in exploring pathological conditions associated with large concentration variations in the ECS.

Neuronify: An Educational Simulator for Neural Circuits.

Educational software (apps) can improve science education by providing an interactive way of learning about complicated topics that are hard to explain with text and static illustrations. However, few educational apps are available for simulation of neural networks. Here, we describe an educational app, Neuronify, allowing the user to easily create and explore neural networks in a plug-and-play simulation environment. The user can pick network elements with adjustable parameters from a menu, i.e., synaptically connected neurons modelled as integrate-and-fire neurons and various stimulators (current sources, spike generators, visual, and touch) and recording devices (voltmeter, spike detector, and loudspeaker). We aim to provide a low entry point to simulation-based neuroscience by allowing students with no programming experience to create and simulate neural networks. To facilitate the use of Neuronify in teaching, a set of premade common network motifs is provided, performing functions such as input summation, gain control by inhibition, and detection of direction of stimulus movement. Neuronify is developed in C++ and QML using the cross-platform application framework Qt and runs on smart phones (Android, iOS) and tablet computers as well personal computers (Windows, Mac, Linux).

Enhanced exercise and regenerative capacity in a mouse model that violates size constraints of oxidative muscle fibres.

A central tenet of skeletal muscle biology is the existence of an inverse relationship between the oxidative fibre capacity and its size. However, robustness of this relationship is unknown. We show that superimposition of Estrogen-related receptor gamma (Errγ) on the myostatin (Mtn) mouse null background (Mtn(-/-)/Errγ(Tg/+)) results in hypertrophic muscle with a high oxidative capacity thus violating the inverse relationship between fibre size and oxidative capacity. We also examined the canonical view that oxidative muscle phenotype positively correlate with Satellite cell number, the resident stem cells of skeletal muscle. Surprisingly, hypertrophic fibres from Mtn(-/-)/Errγ(Tg/+) mouse showed satellite cell deficit which unexpectedly did not affect muscle regeneration. These observations 1) challenge the concept of a constraint between fibre size and oxidative capacity and 2) indicate the important role of the microcirculation in the regenerative capacity of a muscle even when satellite cell numbers are reduced.