The what and where of adding channel noise to the Hodgkin-Huxley equations

One of the most celebrated successes in computational biology is the Hodgkin-Huxley framework for modeling electrically active cells. This framework, expressed through a set of differential equations, synthesizes the impact of ionic currents on a cell's voltage -- and the highly nonlinear impact of that voltage back on the currents themselves -- into the rapid push and pull of the action potential. Latter studies confirmed that these cellular dynamics are orchestrated by individual ion channels, whose conformational changes regulate the conductance of each ionic current. Thus, kinetic equations familiar from physical chemistry are the natural setting for describing conductances; for small-to-moderate numbers of channels, these will predict fluctuations in conductances and stochasticity in the resulting action potentials. At first glance, the kinetic equations provide a far more complex (and higher-dimensional) description than the original Hodgkin-Huxley equations. This has prompted more than a decade of efforts to capture channel fluctuations with noise terms added to the Hodgkin-Huxley equations. Many of these approaches, while intuitively appealing, produce quantitative errors when compared to kinetic equations; others, as only very recently demonstrated, are both accurate and relatively simple. We review what works, what doesn't, and why, seeking to build a bridge to well-established results for the deterministic Hodgkin-Huxley equations. As such, we hope that this review will speed emerging studies of how channel noise modulates electrophysiological dynamics and function. We supply user-friendly Matlab simulation code of these stochastic versions of the Hodgkin-Huxley equations on the ModelDB website (accession number 138950) and http://www.amath.washington.edu/~etsb/tutorials.html.Comment: 14 pages, 3 figures, review articl

MFA15 (MFA 2015)

Catalogue of a culminating student exhibition held at the Mildred Lane Kemper Art Museum, May 1 - August 2, 2015 . Introduction / Heather Corcoran and Patricia Olynyk -- Diana Casanova / Emily J. Hanson -- Andrea M. Coates : in the operating theater / Stephanie Dering -- Margaux Crump -- Brandon Daniels -- Addoley Dzegede : do you prefer answers or truth? / Aaron Coleman -- Vita Eruhimovitz -- Carling Hale -- Amanda Helman -- Mike Helms / Ming Ying Hong -- Ming Ying Hong / Emily J. Hanson -- Sea A Joung / Ervin Malakaj -- Stephanie Kang / Jeremy Shipley -- Dayna Jean Kriz / Andrew Johnson -- Thomas Moore : you should move to the city / Nathaniel Rosenthalis -- Jacob Muldowney -- Laurel Panella / Garrett Clough -- Caitlin Penny -- On the bridge, between Juarez and El Paso / Eric Lyle Schultz -- Jeremy Shipley -- Emmeline Solomon -- Kellie Spano / Margaux Crump -- Michael Aaron Williams -- Austin R. Wolf : monumental labor / Adam Turl.https://openscholarship.wustl.edu/books/1015/thumbnail.jp

Protein supplementation in strength and conditioning adepts: knowledge, dietary behaviour and practice in Palermo, Italy

Background: It is known that supplement use is a widespread and accepted practice by athletes and people who attend commercial gyms. Little is known about protein supplement amongst people undertaking strength training in commercial gyms in Italy when compared to the US. Objective: The purpose of this study was to examine the use of protein supplementation, alone or in association with other supplements, and dietary behavior amongst regular fitness center attendees in Palermo, Italy. Design: Resistance training information have been collected from 800 regular fitness center attendees for the initial analysis. A specific questionnaire was generated for the experimentation. Data were collected using a face-to-face interview method. Supplement users were then compared to the non users and analyzed using a one-way ANOVA, Kruskall-Wallis, chi-square test or exact test of Fisher when appropriate. Results: 30.1% of the respondents use dietary supplements during their training as a believe it is the "way to gain muscles and strength". Whey protein shakes (50.0%) mixed with creatine and amino-acids (48.3%) were the most frequent choices amongst the users. A majority of the subjects (34.0%) appeared to rely on their gym instructors' advice for their intake; a lower proportion (13.0%) consulted physicians, while none of them consulted nutritionists. A high consumption of milk has been noticed in both users (67,7%) and non-users (52,8%); supplement non-users consumed significantly more snacks and bakery products than users per week (P < 0.001), while users consumed significantly more protein-rich foods (P < 0.01) with a particular preference for meat (48.0%). Conclusions: A considerable number of regular strength training adepts consume protein supplements mixed with other products (mainly creatine and amino-acids). Limited numbers consult "dietary specialists" and rely mainly on their instructors. We emphasize on the importance of the dissemination of scientifically based information about supplementation in this environment and the promotion of updated educational programs for the instructors

Accurate and Fast Simulation of Channel Noise in Conductance-Based Model Neurons by Diffusion Approximation

Stochastic channel gating is the major source of intrinsic neuronal noise whose functional consequences at the microcircuit- and network-levels have been only partly explored. A systematic study of this channel noise in large ensembles of biophysically detailed model neurons calls for the availability of fast numerical methods. In fact, exact techniques employ the microscopic simulation of the random opening and closing of individual ion channels, usually based on Markov models, whose computational loads are prohibitive for next generation massive computer models of the brain. In this work, we operatively define a procedure for translating any Markov model describing voltage- or ligand-gated membrane ion-conductances into an effective stochastic version, whose computer simulation is efficient, without compromising accuracy. Our approximation is based on an improved Langevin-like approach, which employs stochastic differential equations and no Montecarlo methods. As opposed to an earlier proposal recently debated in the literature, our approximation reproduces accurately the statistical properties of the exact microscopic simulations, under a variety of conditions, from spontaneous to evoked response features. In addition, our method is not restricted to the Hodgkin-Huxley sodium and potassium currents and is general for a variety of voltage- and ligand-gated ion currents. As a by-product, the analysis of the properties emerging in exact Markov schemes by standard probability calculus enables us for the first time to analytically identify the sources of inaccuracy of the previous proposal, while providing solid ground for its modification and improvement we present here

Hundreds of variants clustered in genomic loci and biological pathways affect human height

Most common human traits and diseases have a polygenic pattern of inheritance: DNA sequence variants at many genetic loci influence the phenotype. Genome-wide association (GWA) studies have identified more than 600 variants associated with human traits, but these typically explain small fractions of phenotypic variation, raising questions about the use of further studies. Here, using 183,727 individuals, we show that hundreds of genetic variants, in at least 180 loci, influence adult height, a highly heritable and classic polygenic trait. The large number of loci reveals patterns with important implications for genetic studies of common human diseases and traits. First, the 180 loci are not random, but instead are enriched for genes that are connected in biological pathways (P = 0.016) and that underlie skeletal growth defects (P < 0.001). Second, the likely causal gene is often located near the most strongly associated variant: in 13 of 21 loci containing a known skeletal growth gene, that gene was closest to the associated variant. Third, at least 19 loci have multiple independently associated variants, suggesting that allelic heterogeneity is a frequent feature of polygenic traits, that comprehensive explorations of already-discovered loci should discover additional variants and that an appreciable fraction of associated loci may have been identified. Fourth, associated variants are enriched for likely functional effects on genes, being over-represented among variants that alter amino-acid structure of proteins and expression levels of nearby genes. Our data explain approximately 10% of the phenotypic variation in height, and we estimate that unidentified common variants of similar effect sizes would increase this figure to approximately 16% of phenotypic variation (approximately 20% of heritable variation). Although additional approaches are needed to dissect the genetic architecture of polygenic human traits fully, our findings indicate that GWA studies can identify large numbers of loci that implicate biologically relevant genes and pathways.

New genetic loci implicated in fasting glucose homeostasis and their impact on type 2 diabetes risk.

Levels of circulating glucose are tightly regulated. To identify new loci influencing glycemic traits, we performed meta-analyses of 21 genome-wide association studies informative for fasting glucose, fasting insulin and indices of beta-cell function (HOMA-B) and insulin resistance (HOMA-IR) in up to 46,186 nondiabetic participants. Follow-up of 25 loci in up to 76,558 additional subjects identified 16 loci associated with fasting glucose and HOMA-B and two loci associated with fasting insulin and HOMA-IR. These include nine loci newly associated with fasting glucose (in or near ADCY5, MADD, ADRA2A, CRY2, FADS1, GLIS3, SLC2A2, PROX1 and C2CD4B) and one influencing fasting insulin and HOMA-IR (near IGF1). We also demonstrated association of ADCY5, PROX1, GCK, GCKR and DGKB-TMEM195 with type 2 diabetes. Within these loci, likely biological candidate genes influence signal transduction, cell proliferation, development, glucose-sensing and circadian regulation. Our results demonstrate that genetic studies of glycemic traits can identify type 2 diabetes risk loci, as well as loci containing gene variants that are associated with a modest elevation in glucose levels but are not associated with overt diabetes

Stochastic Ion Channel Gating in Dendritic Neurons: Morphology Dependence and Probabilistic Synaptic Activation of Dendritic Spikes

Neuronal activity is mediated through changes in the probability of stochastic transitions between open and closed states of ion channels. While differences in morphology define neuronal cell types and may underlie neurological disorders, very little is known about influences of stochastic ion channel gating in neurons with complex morphology. We introduce and validate new computational tools that enable efficient generation and simulation of models containing stochastic ion channels distributed across dendritic and axonal membranes. Comparison of five morphologically distinct neuronal cell types reveals that when all simulated neurons contain identical densities of stochastic ion channels, the amplitude of stochastic membrane potential fluctuations differs between cell types and depends on sub-cellular location. For typical neurons, the amplitude of membrane potential fluctuations depends on channel kinetics as well as open probability. Using a detailed model of a hippocampal CA1 pyramidal neuron, we show that when intrinsic ion channels gate stochastically, the probability of initiation of dendritic or somatic spikes by dendritic synaptic input varies continuously between zero and one, whereas when ion channels gate deterministically, the probability is either zero or one. At physiological firing rates, stochastic gating of dendritic ion channels almost completely accounts for probabilistic somatic and dendritic spikes generated by the fully stochastic model. These results suggest that the consequences of stochastic ion channel gating differ globally between neuronal cell-types and locally between neuronal compartments. Whereas dendritic neurons are often assumed to behave deterministically, our simulations suggest that a direct consequence of stochastic gating of intrinsic ion channels is that spike output may instead be a probabilistic function of patterns of synaptic input to dendrites

Cell type-specific over-expression of chromosome 21 genes in fibroblasts and fetal hearts with trisomy 21

BACKGROUND: Down syndrome (DS) is caused by trisomy 21 (+21), but the aberrations in gene expression resulting from this chromosomal aneuploidy are not yet completely understood. METHODS: We used oligonucleotide microarrays to survey mRNA expression in early- and late-passage control and +21 fibroblasts and mid-gestation fetal hearts. We supplemented this analysis with northern blotting, western blotting, real-time RT-PCR, and immunohistochemistry. RESULTS: We found chromosome 21 genes consistently over-represented among the genes over-expressed in the +21 samples. However, these sets of over-expressed genes differed across the three cell/tissue types. The chromosome 21 gene MX1 was strongly over-expressed (mean 16-fold) in senescent +21 fibroblasts, a result verified by northern and western blotting. MX1 is an interferon target gene, and its mRNA was induced by interferons present in +21 fibroblast conditioned medium, suggesting an autocrine loop for its over-expression. By immunohistochemistry the p78(MX1 )protein was induced in lesional tissue of alopecia areata, an autoimmune disorder associated with DS. We found strong over-expression of the purine biosynthesis gene GART (mean 3-fold) in fetal hearts with +21 and verified this result by northern blotting and real-time RT-PCR. CONCLUSION: Different subsets of chromosome 21 genes are over-expressed in different cell types with +21, and for some genes this over-expression is non-linear (>1.5X). Hyperactive interferon signaling is a candidate pathway for cell senescence and autoimmune disorders in DS, and abnormal purine metabolism should be investigated for a potential role in cardiac defects

A Threshold Equation for Action Potential Initiation

In central neurons, the threshold for spike initiation can depend on the stimulus and varies between cells and between recording sites in a given cell, but it is unclear what mechanisms underlie this variability. Properties of ionic channels are likely to play a role in threshold modulation. We examined in models the influence of Na channel activation, inactivation, slow voltage-gated channels and synaptic conductances on spike threshold. We propose a threshold equation which quantifies the contribution of all these mechanisms. It provides an instantaneous time-varying value of the threshold, which applies to neurons with fluctuating inputs. We deduce a differential equation for the threshold, similar to the equations of gating variables in the Hodgkin-Huxley formalism, which describes how the spike threshold varies with the membrane potential, depending on channel properties. We find that spike threshold depends logarithmically on Na channel density, and that Na channel inactivation and K channels can dynamically modulate it in an adaptive way: the threshold increases with membrane potential and after every action potential. Our equation was validated with simulations of a previously published multicompartemental model of spike initiation. Finally, we observed that threshold variability in models depends crucially on the shape of the Na activation function near spike initiation (about −55 mV), while its parameters are adjusted near half-activation voltage (about −30 mV), which might explain why many models exhibit little threshold variability, contrary to experimental observations. We conclude that ionic channels can account for large variations in spike threshold