Identification of novel prognostic indicators for triple-negative breast cancer patients through integrative analysis of cancer genomics data and protein interactome data.

Triple negative breast cancers (TNBCs) are highly heterogeneous and aggressive without targeted treatment. Here, we aim to systematically dissect TNBCs from a prognosis point of view by building a subnetwork atlas for TNBC prognosis through integrating multi-dimensional cancer genomics data from The Cancer Genome Atlas (TCGA) project and the interactome data from three different interaction networks. The subnetworks are represented as the protein-protein interaction modules perturbed by multiple genetic and epigenetic interacting mechanisms contributing to patient survival. Predictive power of these subnetwork-derived prognostic models is evaluated using Monte Carlo cross-validation and the concordance index (C-index). We uncover subnetwork biomarkers of low oncogenic GTPase activity, low ubiquitin/proteasome degradation, effective protection from oxidative damage, and tightly immune response are linked to better prognosis. Such a systematic approach to integrate massive amount of cancer genomics data into clinical practice for TNBC prognosis can effectively dissect the molecular mechanisms underlying TNBC patient outcomes and provide potential opportunities to optimize treatment and develop therapeutics.

Calcium homeostasis in a local/global whole cell model of permeabilized ventricular myocytes with a Langevin description of stochastic calcium release.

Population density approaches to modeling local control of Ca(2+)-induced Ca(2+) release in cardiac myocytes can be used to construct minimal whole cell models that accurately represent heterogeneous local Ca(2+) signals. Unfortunately, the computational complexity of such "local/global" whole cell models scales with the number of Ca(2+) release unit (CaRU) states, which is a rapidly increasing function of the number of ryanodine receptors (RyRs) per CaRU. Here we present an alternative approach based on a Langevin description of the collective gating of RyRs coupled by local Ca(2+) concentration ([Ca(2+)]). The computational efficiency of this approach no longer depends on the number of RyRs per CaRU. When the RyR model is minimal, Langevin equations may be replaced by a single Fokker-Planck equation, yielding an extremely compact and efficient local/global whole cell model that reproduces and helps interpret recent experiments that investigate Ca(2+) homeostasis in permeabilized ventricular myocytes. Our calculations show that elevated myoplasmic [Ca(2+)] promotes elevated network sarcoplasmic reticulum (SR) [Ca(2+)] via SR Ca(2+)-ATPase-mediated Ca(2+) uptake. However, elevated myoplasmic [Ca(2+)] may also activate RyRs and promote stochastic SR Ca(2+) release, which can in turn decrease SR [Ca(2+)]. Increasing myoplasmic [Ca(2+)] results in an exponential increase in spark-mediated release and a linear increase in nonspark-mediated release, consistent with recent experiments. The model exhibits two steady-state release fluxes for the same network SR [Ca(2+)] depending on whether myoplasmic [Ca(2+)] is low or high. In the later case, spontaneous release decreases SR [Ca(2+)] in a manner that maintains robust Ca(2+) sparks.

Computer simulation of voltage sensitive calcium ion channels in a dendritic spine.

Membrane current through voltage-sensitive calcium ion channels at the postsynaptic density of a dendritic spine is investigated. To simulate the ion channels that carry such current and the resulting temporal and spatial distribution of concentration, current, and voltage within the dendritic spine, the immersed boundary method with electrodiffusion is applied. In this simulation method a spatially continuous chemical potential barrier is used to simulate the influence of the membrane on each species of ion. The amplitudes of these barriers can be regulated to simulate channel gating. Here we introduce this methodology in a one-dimensional setting. First, we study the current-voltage relationship obtained with fixed chemical potential barriers. Next, we simulate stochastic ion-channel gating in a calcium channel with multiple subunits, and observe the diffusive wave of calcium entry within the dendritic spine that follows channel opening. This work lays the foundation for future three-dimensional studies of electrodiffusion and advection electrodiffusion in dendritic spines.

Spontaneous Ca2+ sparks and Ca2+ homeostasis in a minimal model of permeabilized ventricular myocytes.

Many issues remain unresolved concerning how local, subcellular Ca(2+) signals interact with bulk cellular concentrations to maintain homeostasis in health and disease. To aid in the interpretation of data obtained in quiescent ventricular myocytes, we present here a minimal whole cell model that accounts for both localized (subcellular) and global (cellular) aspects of Ca(2+) signaling. Using a minimal formulation of the distribution of local [Ca(2+)] associated with a large number of Ca(2+)-release sites, the model simulates both random spontaneous Ca(2+) sparks and the changes in myoplasmic and sarcoplasmic reticulum (SR) [Ca(2+)] that result from the balance between stochastic release and reuptake into the SR. Ca(2+)-release sites are composed of clusters of two-state ryanodine receptors (RyRs) that exhibit activation by local cytosolic [Ca(2+)] but no inactivation or regulation by luminal Ca(2+). Decreasing RyR open probability in the model causes a decrease in aggregate release flux and an increase in SR [Ca(2+)], regardless of whether RyR inhibition is mediated by a decrease in RyR open dwell time or an increase in RyR closed dwell time. The same balance of stochastic release and reuptake can be achieved, however, by either high-frequency/short-duration or low-frequency/long-duration Ca(2+) sparks. The results are well correlated with recent experimental observations using pharmacological RyR inhibitors and clarify those aspects of the release-reuptake balance that are inherent to the coupling between local and global Ca(2+) signals and those aspects that depend on molecular-level details. The model of Ca(2+) sparks and homeostasis presented here can be a useful tool for understanding changes in cardiac Ca(2+ )release resulting from drugs, mutations, or acquired diseases.

Models of cardiac excitation-contraction coupling in ventricular myocytes.

Mathematical and computational modeling of cardiac excitation-contraction coupling has produced considerable insights into how the heart muscle contracts. With the increase in biophysical and physiological data available, the modeling has become more sophisticated with investigations spanning in scale from molecular components to whole cells. These modeling efforts have provided insight into cardiac excitation-contraction coupling that advanced and complemented experimental studies. One goal is to extend these detailed cellular models to model the whole heart. While this has been done with mechanical and electrophysiological models, the complexity and fast time course of calcium dynamics have made inclusion of detailed calcium dynamics in whole heart models impractical. Novel methods such as the probability density approach and moment closure technique which increase computational efficiency might make this tractable.

Teaching resources. Using web-based discussion forums as a model of the peer-review process and a tool for assessment.

This Teaching Resource describes how to use an online asynchronous discussion as a mechanism to introduce students to the peer-review process, as well as to assess student performance and understanding. This method was applied to a graduate course on signal transduction and the Teaching Resource includes a syllabus, detailed plan for incorporating the online discussion, sample journal club questions, and sample student responses to the discussion forum, faculty responses, and student revisions.

Termination of cardiac Ca(2+) sparks: an investigative mathematical model of calcium-induced calcium release.

A Ca(2+) spark arises when a cluster of sarcoplasmic reticulum (SR) channels (ryanodine receptors or RyRs) opens to release calcium in a locally regenerative manner. Normally triggered by Ca(2+) influx across the sarcolemmal or transverse tubule membrane neighboring the cluster, the Ca(2+) spark has been shown to be the elementary Ca(2+) signaling event of excitation-contraction coupling in heart muscle. However, the question of how the Ca(2+) spark terminates remains a central, unresolved issue. Here we present a new model, "sticky cluster," of SR Ca(2+) release that simulates Ca(2+) spark behavior and enables robust Ca(2+) spark termination. Two newly documented features of RyR behavior have been incorporated in this otherwise simple model: "coupled gating" and an opening rate that depends on SR lumenal [Ca(2+)]. Using a Monte Carlo method, local Ca(2+)-induced Ca(2+) release from clusters containing between 10 and 100 RyRs is modeled. After release is triggered, Ca(2+) flux from RyRs diffuses into the cytosol and binds to intracellular buffers and the fluorescent Ca(2+) indicator fluo-3 to produce the model Ca(2+) spark. Ca(2+) sparks generated by the sticky cluster model resemble those observed experimentally, and Ca(2+) spark duration and amplitude are largely insensitive to the number of RyRs in a cluster. As expected from heart cell investigation, the spontaneous Ca(2+) spark rate in the model increases with elevated cytosolic or SR lumenal [Ca(2+)]. Furthermore, reduction of RyR coupling leads to prolonged model Ca(2+) sparks just as treatment with FK506 lengthens Ca(2+) sparks in heart cells. This new model of Ca(2+) spark behavior provides a "proof of principle" test of a new hypothesis for Ca(2+) spark termination and reproduces critical features of Ca(2+) sparks observed experimentally.