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

Interaction of Aspirin (Acetylsalicylic Acid) with Lipid Membranes

We studied the interaction of Aspirin (acetylsalicylic acid) with lipid membranes using x-ray diffraction for bilayers containing up to 50 mol% of aspirin. From 2D x-ray intensity maps that cover large areas of reciprocal space we determined the position of the ASA molecules in the phospholipid bilayers and the molecular arrangement of the molecules in the plane of the membranes. We present direct experimental evidence that ASA molecules participate in saturated lipid bilayers of DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine) and preferably reside in the head group region of the membrane. Up to 50 mol% ASA molecules can be dissolved in this type of bilayer before the lateral membrane organization is disturbed and the membranes are found to form an ordered, 2D crystal-like structure. Furthermore, ASA and cholesterol were found to co-exist in saturated lipid bilayers, with the ASA molecules residing in the head group region and the cholesterol molecules participating in the hydrophobic membrane core

Multiway modeling and analysis in stem cell systems biology

<p>Abstract</p> <p>Background</p> <p>Systems biology refers to multidisciplinary approaches designed to uncover emergent properties of biological systems. Stem cells are an attractive target for this analysis, due to their broad therapeutic potential. A central theme of systems biology is the use of computational modeling to reconstruct complex systems from a wealth of reductionist, molecular data (e.g., gene/protein expression, signal transduction activity, metabolic activity, etc.). A number of deterministic, probabilistic, and statistical learning models are used to understand sophisticated cellular behaviors such as protein expression during cellular differentiation and the activity of signaling networks. However, many of these models are bimodal i.e., they only consider row-column relationships. In contrast, multiway modeling techniques (also known as tensor models) can analyze multimodal data, which capture much more information about complex behaviors such as cell differentiation. In particular, tensors can be very powerful tools for modeling the dynamic activity of biological networks over time. Here, we review the application of systems biology to stem cells and illustrate application of tensor analysis to model collagen-induced osteogenic differentiation of human mesenchymal stem cells.</p> <p>Results</p> <p>We applied Tucker1, Tucker3, and Parallel Factor Analysis (PARAFAC) models to identify protein/gene expression patterns during extracellular matrix-induced osteogenic differentiation of human mesenchymal stem cells. In one case, we organized our data into a tensor of type protein/gene locus link × gene ontology category × osteogenic stimulant, and found that our cells expressed two distinct, stimulus-dependent sets of functionally related genes as they underwent osteogenic differentiation. In a second case, we organized DNA microarray data in a three-way tensor of gene IDs × osteogenic stimulus × replicates, and found that application of tensile strain to a collagen I substrate accelerated the osteogenic differentiation induced by a static collagen I substrate.</p> <p>Conclusion</p> <p>Our results suggest gene- and protein-level models whereby stem cells undergo transdifferentiation to osteoblasts, and lay the foundation for mechanistic, hypothesis-driven studies. Our analysis methods are applicable to a wide range of stem cell differentiation models.</p

Antibody Repertoires in Humanized NOD-scid-IL2Rγnull Mice and Human B Cells Reveals Human-Like Diversification and Tolerance Checkpoints in the Mouse

Immunodeficient mice reconstituted with human hematopoietic stem cells enable the in vivo study of human hematopoiesis. In particular, NOD-scid-IL2Rγnull engrafted mice have been shown to have reasonable levels of T and B cell repopulation and can mount T-cell dependent responses; however, antigen-specific B-cell responses in this model are generally poor. We explored whether developmental defects in the immunoglobulin gene repertoire might be partly responsible for the low level of antibody responses in this model. Roche 454 sequencing was used to obtain over 685,000 reads from cDNA encoding immunoglobulin heavy (IGH) and light (IGK and IGL) genes isolated from immature, naïve, or total splenic B cells in engrafted NOD-scid-IL2Rγnull mice, and compared with over 940,000 reads from peripheral B cells of two healthy volunteers. We find that while naïve B-cell repertoires in humanized mice are chiefly indistinguishable from those in human blood B cells, and display highly correlated patterns of immunoglobulin gene segment use, the complementarity-determining region H3 (CDR-H3) repertoires are nevertheless extremely diverse and are specific for each individual. Despite this diversity, preferential DH-JH pairings repeatedly occur within the CDR-H3 interval that are strikingly similar across all repertoires examined, implying a genetic constraint imposed on repertoire generation. Moreover, CDR-H3 length, charged amino-acid content, and hydropathy are indistinguishable between humans and humanized mice, with no evidence of global autoimmune signatures. Importantly, however, a statistically greater usage of the inherently autoreactive IGHV4-34 and IGKV4-1 genes was observed in the newly formed immature B cells relative to naïve B or total splenic B cells in the humanized mice, a finding consistent with the deletion of autoreactive B cells in humans. Overall, our results provide evidence that key features of the primary repertoire are shaped by genetic factors intrinsic to human B cells and are principally unaltered by differences between mouse and human stromal microenvironments