A mathematical model for persistent post-CSD vasoconstriction.

Cortical spreading depression (CSD) is the propagation of a relatively slow wave in cortical brain tissue that is linked to a number of pathological conditions such as stroke and migraine. Most of the existing literature investigates the dynamics of short term phenomena such as the depolarization and repolarization of membrane potentials or large ion shifts. Here, we focus on the clinically-relevant hour-long state of neurovascular malfunction in the wake of CSDs. This dysfunctional state involves widespread vasoconstriction and a general disruption of neurovascular coupling. We demonstrate, using a mathematical model, that dissolution of calcium that has aggregated within the mitochondria of vascular smooth muscle cells can drive an hour-long disruption. We model the rate of calcium clearance as well as the dynamical implications on overall blood flow. Based on reaction stoichiometry, we quantify a possible impact of calcium phosphate dissolution on the maintenance of F0F1-ATP synthase activity.

Dissecting transcriptional amplification by MYC.

Supraphysiological MYC levels are oncogenic. Originally considered a typical transcription factor recruited to E-boxes (CACGTG), another theory posits MYC a global amplifier increasing output at all active promoters. Both models rest on large-scale genome-wide "-omics'. Because the assumptions, statistical parameter and model choice dictates the '-omic' results, whether MYC is a general or specific transcription factor remains controversial. Therefore, an orthogonal series of experiments interrogated MYC's effect on the expression of synthetic reporters. Dose-dependently, MYC increased output at minimal promoters with or without an E-box. Driving minimal promoters with exogenous (glucocorticoid receptor) or synthetic transcription factors made expression more MYC-responsive, effectively increasing MYC-amplifier gain. Mutations of conserved MYC-Box regions I and II impaired amplification, whereas MYC-box III mutations delivered higher reporter output indicating that MBIII limits over-amplification. Kinetic theory and experiments indicate that MYC activates at least two steps in the transcription-cycle to explain the non-linear amplification of transcription that is essential for global, supraphysiological transcription in cancer.

Intrinsic Dynamics of a Human Gene Reveal the Basis of Expression Heterogeneity.

Transcriptional regulation in metazoans occurs through long-range genomic contacts between enhancers and promoters, and most genes are transcribed in episodic "bursts" of RNA synthesis. To understand the relationship between these two phenomena and the dynamic regulation of genes in response to upstream signals, we describe the use of live-cell RNA imaging coupled with Hi-C measurements and dissect the endogenous regulation of the estrogen-responsive TFF1 gene. Although TFF1 is highly induced, we observe short active periods and variable inactive periods ranging from minutes to days. The heterogeneity in inactive times gives rise to the widely observed "noise" in human gene expression and explains the distribution of protein levels in human tissue. We derive a mathematical model of regulation that relates transcription, chromosome structure, and the cell's ability to sense changes in estrogen and predicts that hypervariability is largely dynamic and does not reflect a stable biological state.

Kinetic competition during the transcription cycle results in stochastic RNA processing.

Synthesis of mRNA in eukaryotes involves the coordinated action of many enzymatic processes, including initiation, elongation, splicing, and cleavage. Kinetic competition between these processes has been proposed to determine RNA fate, yet such coupling has never been observed in vivo on single transcripts. In this study, we use dual-color single-molecule RNA imaging in living human cells to construct a complete kinetic profile of transcription and splicing of the ß-globin gene. We find that kinetic competition results in multiple competing pathways for pre-mRNA splicing. Splicing of the terminal intron occurs stochastically both before and after transcript release, indicating there is not a strict quality control checkpoint. The majority of pre-mRNAs are spliced after release, while diffusing away from the site of transcription. A single missense point mutation (S34F) in the essential splicing factor U2AF1 which occurs in human cancers perturbs this kinetic balance and defers splicing to occur entirely post-release.

A conserved protein motif is required for full modulatory activity of negative elongation factor subunits NELF-A and NELF-B in modifying glucocorticoid receptor-regulated gene induction properties.

NELF-B is a BRCA1-interacting protein and subunit (with NELF-A, -C/D, and -E) of the human negative elongation factor (NELF) complex, which participates in RNA polymerase II pausing shortly after transcription initiation, especially for synchronized gene expression. We now report new activities of NELF-B and other NELF complex subunits, which are to attenuate glucocorticoid receptor (GR)-mediated gene induction, reduce the partial agonist activity of an antagonist, and increase the EC50 of an agonist during nonsynchronized expression of exogenous and endogenous reporters. Stable knockdown of endogenous NELF-B has the opposite effects on an exogenous gene. The GR ligand-binding domain suffices for these biological responses. ChIP assays reveal that NELF-B diminishes GR recruitment to promoter regions of two endogenous genes. Using a new competition assay, NELF-A and NELF-B are each shown to act independently as competitive decelerators at two steps after the site of GR action and before or at the site of reporter gene activity. A common motif in each NELF was identified that is required for full activity of both NELF-A and NELF-B. These studies allow us to position the actions of two new modulators of GR-regulated transactivation, NELF-A and NELF-B, relative to other factors in the overall gene induction sequence.

PA1 protein, a new competitive decelerator acting at more than one step to impede glucocorticoid receptor-mediated transactivation.

Numerous cofactors modulate the gene regulatory activity of glucocorticoid receptors (GRs) by affecting one or more of the following three major transcriptional properties: the maximal activity of agonists (A(max)), the potency of agonists (EC(50)), and the partial agonist activity of antisteroids (PAA). Here, we report that the recently described nuclear protein, Pax2 transactivation domain interaction protein (PTIP)-associated protein 1 (PA1), is a new inhibitor of GR transactivation. PA1 suppresses A(max), increases the EC(50), and reduces the PAA of an exogenous reporter gene in a manner that is independent of associated PTIP. PA1 is fully active with, and strongly binds to, the C-terminal half of GR. PA1 reverses the effects of the coactivator TIF2 on GR-mediated gene induction but is unable to augment the actions of the corepressor SMRT. Analysis of competition assays between PA1 and TIF2 with an exogenous reporter indicates that the kinetic definition of PA1 action is a competitive decelerator at two sites upstream from where TIF2 acts. With the endogenous genes IGFBP1 and IP6K3, PA1 also represses GR induction, increases the EC(50), and decreases the PAA. ChIP and re-ChIP experiments indicate that PA1 accomplishes this inhibition of the two genes via different mechanisms as follows: PA1 appears to increase GR dissociation from and reduce GR transactivation at the IGFBP1 promoter regions but blocks GR binding to the IP6K3 promoter. We conclude that PA1 is a new competitive decelerator of GR transactivation and can act at more than one molecularly defined step in a manner that depends upon the specific gene.

Identification of location and kinetically defined mechanism of cofactors and reporter genes in the cascade of steroid-regulated transactivation.

A currently obscure area of steroid hormone action is where the component factors, including receptor and reporter gene, act. The DNA binding of factors can be precisely defined, but the location and timing of factor binding and action are usually not equivalent. These questions are addressed for several factors (e.g. glucocorticoid receptor (GR), reporter, TIF2, NCoR, NELF-A, sSMRT, and STAMP) using our recently developed competition assay. This assay reveals both the kinetically defined mechanism of factor action and where the above factors act relative to both each other and the equilibrium equivalent to the rate-limiting step, which we call the concentration limiting step (CLS). The utility of this competition assay would be greatly increased if the position of the CLS is invariant and if the factor acting at the CLS is known. Here we report that the exogenous GREtkLUC reporter acts at the CLS as an accelerator for gene induction by GRs in U2OS cells. This mechanism of reporter function at the CLS persists with different reporters, factors, receptors, and cell types. We, therefore, propose that the reporter gene always acts at the CLS during gene induction and constitutes a landmark around which one can order the actions of all other factors. Current data suggest that how and where GR and the short form of SMRT act is also constant. These results validate a novel and rational methodology for identifying distally acting factors that would be attractive targets for pharmaceutical intervention in the treatment of diseases involving GR-regulated genes.

Deducing the temporal order of cofactor function in ligand-regulated gene transcription: theory and experimental verification.

Cofactors are intimately involved in steroid-regulated gene expression. Two critical questions are (1) the steps at which cofactors exert their biological activities and (2) the nature of that activity. Here we show that a new mathematical theory of steroid hormone action can be used to deduce the kinetic properties and reaction sequence position for the functioning of any two cofactors relative to a concentration limiting step (CLS) and to each other. The predictions of the theory, which can be applied using graphical methods similar to those of enzyme kinetics, are validated by obtaining internally consistent data for pair-wise analyses of three cofactors (TIF2, sSMRT, and NCoR) in U2OS cells. The analysis of TIF2 and sSMRT actions on GR-induction of an endogenous gene gave results identical to those with an exogenous reporter. Thus new tools to determine previously unobtainable information about the nature and position of cofactor action in any process displaying first-order Hill plot kinetics are now available.

In silico models of acute inflammation in animals.

Trauma and hemorrhagic shock elicit an acute inflammatory response, predisposing patients to sepsis, organ dysfunction, and death. Few approved therapies exist for these acute inflammatory states, mainly due to the complex interplay of interacting inflammatory and physiological elements working at multiple levels. Various animal models have been used to simulate these phenomena, but these models often do not replicate the clinical setting of multiple overlapping insults. Mathematical modeling of complex systems is an approach for understanding the interplay among biological interactions. We constructed a mathematical model using ordinary differential equations that encompass the dynamics of cells and cytokines of the acute inflammatory response, as well as global tissue dysfunction. The model was calibrated in C57Bl/6 mice subjected to (1) various doses of lipopolysaccharide (LPS) alone, (2) surgical trauma, and (3) surgery + hemorrhagic shock. We tested the model's predictive ability in scenarios on which it had not been trained, namely, (1) surgery +/- hemorrhagic shock + LPS given at times after the beginning of surgical instrumentation, and (2) surgery + hemorrhagic shock + bilateral femoral fracture. Software was created that facilitated fitting of the mathematical model to experimental data, as well as for simulation of experiments with various inflammatory challenges and associated variations (gene knockouts, inhibition of specific cytokines, etc.). Using this software, the C57Bl/6-specific model was recalibrated for inflammatory analyte data in CD14-/- mice and was used to elucidate altered features of inflammation in these animals. In other experiments, rats were subjected to surgical trauma +/- LPS or to bacterial infection via fibrin clots impregnated with various inocula of Escherichia coli. Mathematical modeling may provide insights into the complex dynamics of acute inflammation in a manner that can be tested in vivo using many fewer animals than has been possible previously.

A spiking neuron model for binocular rivalry.

We present a biologically plausible model of binocular rivalry consisting of a network of Hodgkin-Huxley type neurons. Our model accounts for the experimentally and psychophysically observed phenomena: (1) it reproduces the distribution of dominance durations seen in both humans and primates, (2) it exhibits a lack of correlation between lengths of successive dominance durations, (3) variation of stimulus strength to one eye influences only the mean dominance duration of the contralateral eye, not the mean dominance duration of the ipsilateral eye, (4) increasing both stimuli strengths in parallel decreases the mean dominance durations. We have also derived a reduced population rate model from our spiking model from which explicit expressions for the dependence of the dominance durations on input strengths are analytically calculated. We also use this reduced model to derive an expression for the distribution of dominance durations seen within an individual.