The last five years have witnessed a remarkable renaissance in vitamin D research and a complete re-evaluation of its benefits to human health. Two key factors have catalyzed these changes. First, it now seems likely that localized, tissue-specific, conversion of 25-hydroxyvitamin D (25OHD) to 1,25-dihydroxyvitamin D (1,25(OH)2D) drives many of the newly recognized effects of vitamin D on human health. The second key factor concerns the ongoing discussion as to what constitutes adequate or optimal serum vitamin D (25OHD) status, with the possibility that vitamin D-deficiency is common to communities across the globe. These two concepts appear to be directly linked when low serum concentrations of 25OHD compromise intracrine generation of 1,25(OH)2D within target tissues. But, is this an over-simplification? Pro-hormone 25OHD is a lipophilic molecule that is transported in the circulation bound primarily to vitamin D binding protein (DBP). While the association between 25OHD and DBP is pivotal for renal handling of 25OHD and endocrine synthesis of 1,25(OH)2D, what is the role of DBP for extra-renal synthesis of 1,25(OH)2D? We hypothesize that binding to DBP impairs delivery of 25OHD to the vitamin D-activating enzyme 1α-hydroxylase in some target cells. Specifically, it is unbound, ‘free’ 25OHD that drives many of the non-classical actions of vitamin D. Levels of ‘free’ 25OHD are dependent on the concentration of DBP and alternative serum binding proteins such as albumin, but will also be influenced by variations in DBP binding affinity for specific vitamin D metabolites. The aim of this review will be to discuss the merits of ‘free 25OHD’ as an alternative marker of vitamin D status, particularly in the context of non-classical responses to vitamin D.

H app determined in that experiment (using the diffusional model) for experiments in the absence (open circles) or presence (filled circles) of 1 mM amiloride.

Vitamin D binding protein (DBP) plays a key role in the bioavailability of active 1,25-dihydroxyvitamin D (1,25(OH)2D) and its precursor 25-hydroxyvitamin D (25OHD), but accurate analysis of DBP-bound and free 25OHD and 1,25(OH)2D is difficult. To address this, two new mathematical models were developed to estimate: 1) serum levels of free 25OHD/1,25(OH)2D based on DBP concentration and genotype; 2) the impact of DBP on the biological activity of 25OHD/1,25(OH)2D in vivo. The initial extracellular steady state (eSS) model predicted that 50 nM 25OHD and 100 pM 1,25(OH)2D), <0.1% 25OHD and <1.5% 1,25(OH)2D are ‘free’ in vivo. However, for any given concentration of total 25OHD, levels of free 25OHD are higher for low affinity versus high affinity forms of DBP. The eSS model was then combined with an intracellular (iSS) model that incorporated conversion of 25OHD to 1,25(OH)2D via the enzyme CYP27B1, as well as binding of 1,25(OH)2D to the vitamin D receptor (VDR). The iSS model was optimized to 25OHD/1,25(OH)2D-mediated in vitro dose-responsive induction of the vitamin D target gene cathelicidin (CAMP) in human monocytes. The iSS model was then used to predict vitamin D activity in vivo (100% serum). The predicted induction of CAMP in vivo was minimal at basal settings but increased with enhanced expression of VDR (5-fold) and CYP27B1 (10-fold). Consistent with the eSS model, the iSS model predicted stronger responses to 25OHD for low affinity forms of DBP. Finally, the iSS model was used to compare the efficiency of endogenously synthesized versus exogenously added 1,25(OH)2D. Data strongly support the endogenous model as the most viable mode for CAMP induction by vitamin D in vivo. These novel mathematical models underline the importance of DBP as a determinant of vitamin D ‘status’ in vivo, with future implications for clinical studies of vitamin D status and supplementation.

Intracellular H+ mobility was estimated in the rabbit isolated ventricular myocyte by diffusing HCl into the cell from a patch pipette, while imaging pHi confocally using intracellular ratiometric SNARF fluorescence. The delay for acid diffusion between two downstream regions ≈40 μm apart was reduced from ≈25 s to ≈6 s by replacing Hepes buffer in the extracellular superfusate with a 5 % CO2/HCO3− buffer system (at constant pHo of 7.40). Thus CO2/HCO3− (carbonic) buffer facilitates apparent H+i mobility. The delay with carbonic buffer was increased again by adding acetazolamide (ATZ), a membrane permeant carbonic anhydrase (CA) inhibitor. Thus facilitation of apparent H+i mobility by CO2/HCO3− relies on the activity of intracellular CA. By using a mathematical model of diffusion, the apparent intracellular H+ equivalent diffusion coefficient (DHapp) in CO2/HCO3−‐buffered conditions was estimated to be 21.9 × 10−7 cm2 s−1, 5.8 times faster than in the absence of carbonic buffer. Facilitation of H+i mobility is discussed in terms of an intracellular carbonic buffer shuttle, catalysed by intracellular CA. Turnover of this shuttle is postulated to be faster than that of the intrinsic buffer shuttle. By regulating the carbonic shuttle, CA regulates effective H+i mobility which, in turn, regulates the spatiotemporal uniformity of pHi. This is postulated to be a major function of CA in heart.

Individual mouse pancreatic islets exhibit oscillations in [Ca 21 ] i and insulin secretion in response to glucose in vitro, but how the oscillations of a million islets are coordinated within the human pancreas in vivo is unclear. Islet to islet synchronization is necessary, however, for the pancreas to produce regular pulses of insulin. To determine whether neurohormone release within the pancreas might play a role in coordinating islet activity, [Ca 21 ] i changes in 4-6 isolated mouse islets were simultaneously monitored before and after a transient pulse of a putative synchronizing agent. The degree of synchronicity was quantified using a novel analytical approach that yields a parameter that we call the ''Synchronization Index''. Individual islets exhibited [Ca 21 ] i oscillations with periods of 3-6 min, but were not synchronized under control conditions. However, raising islet [Ca 21 ] i with a brief application of the cholinergic agonist carbachol (25 mM) or elevated KCl in glucose-containing saline rapidly synchronized islet [Ca 21 ] i oscillations for $30 min, long after the synchronizing agent was removed. In contrast, the adrenergic agonists clonidine or norepinephrine, and the K ATP channel inhibitor tolbutamide, failed to synchronize islets. Partial synchronization was observed, however, with the K ATP channel opener diazoxide. The synchronizing action of carbachol depended on the glucose concentration used, suggesting that glucose metabolism was necessary for synchronization to occur. To understand how transiently perturbing islet [Ca 21 ] i produced sustained synchronization, we used a mathematical model of islet oscillations in which complex oscillatory behavior results from the interaction between a fast electrical subsystem and a slower metabolic oscillator. Transient synchronization simulated by the model was mediated by resetting of the islet oscillators to a similar initial phase followed by transient ''ringing'' behavior, during which the model islets oscillated with a similar frequency. These results suggest that neurohormone release from intrapancreatic neurons could help synchronize islets in situ. Defects in this coordinating mechanism could contribute to the disrupted insulin secretion observed in Type 2 diabetes.

Wimmer RJ, Liu Y, Schachter TN, Stonko DP, Peercy BE, Schneider MF. Mathematical modeling reveals modulation of both nuclear influx and efflux of Foxo1 by the IGF-I/PI3K/Akt pathway in skeletal muscle fibers. Am J Physiol Cell Physiol 306: C570-C584, 2014. First published January 22, 2014; doi:10.1152/ajpcell.00338.2013.-Foxo family transcription factors contribute to muscle atrophy by promoting transcription of the ubiquitin ligases muscle-specific RING finger protein and muscle atrophy F-box/atrogin-1. Foxo transcriptional effectiveness is largely determined by its nuclear-cytoplasmic distribution, with unphosphorylated Foxo1 transported into nuclei and phosphorylated Foxo1 transported out of nuclei. We expressed the fluorescent fusion protein Foxo1-green fluorescent protein (GFP) in cultured adult mouse flexor digitorum brevis muscle fibers and tracked the time course of the nuclear-to-cytoplasmic Foxo1-GFP mean pixel fluorescence ratio (N/C) in living fibers by confocal imaging. We previously showed that IGF-I, which activates the Foxo kinase Akt/PKB, caused a rapid marked decline in N/C, whereas inhibition of Akt caused a modest increase in N/C. Here we develop a two-state mathematical model for Foxo1 nuclear-cytoplasmic redistribution, where Foxo phosphorylation/dephosphorylation is assumed to be fast compared with nuclear influx and efflux. Cytoplasmic Foxo1-GFP mean pixel fluorescence is constant due to the much larger cytoplasmic than nuclear volume. Analysis of N/C time courses reveals that IGF-I strongly increased unidirectional nuclear efflux, indicating similarly increased fractional phosphorylation of Foxo1 within nuclei, and decreased unidirectional nuclear influx, indicating increased cytoplasmic fractional phosphorylation of Foxo1. Inhibition of Akt increased Foxo1 unidirectional nuclear influx, consistent with block of Foxo1 cytoplasmic phosphorylation, but did not decrease Foxo1 unidirectional nuclear efflux, indicating that Akt may not be involved in Foxo1 nuclear efflux under control conditions. New media change experiments show that cultured fibers release IGF-I-like factors, which maintain low nuclear Foxo1 in the medium. This study demonstrates the power of quantitative modeling of observed nuclear fluxes.Akt1; Foxo1; IGF-I; skeletal muscle TRANSCRIPTION OF A GIVEN GENE is controlled by numerous regulatory proteins, including transcription factors, which are primary activators of transcription, as well as numerous other activators, coactivators, repressors, and corepressors (12, 15a). These factors combine to form macromolecular transcriptional regulatory complexes assembled on the promoter regions of the gene in question (16). To participate in such regulatory complexes, the regulatory molecules must be resident in the nucleus. Thus an important aspect of transcriptional regulation is control of the nuclear-cytoplasmic distribution of these regulatory molecules, and the mechanisms controlling nuclearcytoplasmic movements of transcriptional regulatory molecules can thus be important dete...

Heart disease is the leading cause of mortality in the United States. One cause of heart arrhythmia is calcium (Ca 2+) mishandling in cardiac muscle cells. We adapt Izu's et al. mathematical reaction-diffusion model of calcium in cardiac muscle cells, or cardiomyocytes, [14], implemented by Gobbert [12], and analyzed in Coulibaly et al. [8] to include calcium being released from the sarcoplasmic reticulum (SR), the effects of buffers in the SR, particularly calsequestrin, and the effects of Ca 2+ influx due to voltage across the cell membrane. Based on simulations of the model implemented in parallel using MPI, our findings aligned with known biological models and principles, giving us a thorough understanding of several factors that influence Ca 2+ dynamics in cardiac myocytes. Specifically, dynamic calcium store will cap previous calcium blow-up seen in the model. Calcium channels located in spatial opposition of calcium release units produce more predictable intracellular calcium propagation. And we used multi-parametric calcium dynamics tables, which act as a multidimensional bifurcation diagram, to visualize parameter boundaries between different biophysical dynamics.

Cell migration is essential in animal development, homeostasis, and disease progression, but many questions remain unanswered about how this process is controlled. While many kinds of individual cell movements have been characterized, less effort has been directed towards understanding how clusters of cells migrate collectively through heterogeneous, cellular environments. To explore this, we have focused on the migration of the border cells during Drosophila egg development. In this case, a cluster of different cell types coalesce and traverse as a group between large cells, called nurse cells, in the center of the egg chamber. We have developed a new model for this collective cell migration based on the forces of adhesion, repulsion, migration and stochastic fluctuation to generate the movement of discrete cells. We implement the model using Identical Math Cells, or IMCs. IMCs can each represent one biological cell of the system, or can be aggregated using increased adhesion forces to model the dynamics of larger biological cells. The domain of interest is filled with IMCs, each assigned specific biophysical properties to mimic a diversity of cell types. Using this system, we have successfully simulated the migration of the border cell cluster through an environment filled with larger cells, which represent nurse cells. Interestingly, our simulations suggest that the forces utilized in this model are sufficient to produce behaviors of the cluster that are observed in vivo, such as rotation. Our framework was developed to capture a heterogeneous cell population, and our implementation strategy allows for diverse, but precise, initial position specification over a three- dimensional domain. Therefore, we believe that this model will be useful for not only examining aspects of Drosophila oogenesis, but also for modeling other two or three-dimensional systems that have multiple cell types and where investigating the forces between cells is of interest.