“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.

Brain 5α-dihydroprogesterone and allopregnanolone synthesis in a mouse model of protracted social isolation

Allopregnanolone (ALLO), is a brain endogenous neurosteroid that binds with high affinity to γ-aminobutyric acid type A (GABAA) receptors and positively modulates the action of GABA at these receptors. Unlike ALLO, 5α-dihydroprogesterone (5α-DHP) binds with high affinity to intracellular progesterone receptors that regulate DNA transcription. To investigate the physiological roles of ALLO and 5α-DHP synthesized in brain, we have adopted a mouse model involving protracted social isolation. In the frontal cortex of mice, socially isolated for 6 weeks, both neurosteroids were decreased by approximately 50%. After administration of (17β)-17-(bis-1-methyl amino carbonyl) androstane-3,5-diene-3-carboxylic acid (SKF105,111), an inhibitor of the enzyme (5α-reductase Type I and II) that converts progesterone into 5α-DHP, the ALLO and 5α-DHP content of frontal cortex of both group-housed and socially isolated mice decreased exponentially to 10%–20% of control values in about 30 min. The fractional rate constants (k h−1) of ALLO and 5α-DHP decline multiplied by the ALLO and 5α-DHP concentrations at any given steady-state estimate the rate of synthesis required to maintain that steady state. After 6 weeks of social isolation, ALLO and 5α-DHP biosynthesis rates were decreased to 30% of the values calculated in group-housed mice. Moreover, in socially isolated mice, the expression of 5α-reductase Type I mRNA and protein was approximately 50% lower than in group-housed mice whereas 3α-hydroxysteroid oxidoreductase mRNA expression was equal in the two groups. Protracted social isolation in mice may provide a model to investigate whether 5α-DHP by a genomic action, and ALLO by a nongenomic mechanism down-regulate the action of drugs acting as agonists, partial agonists, or positive allosteric modulators of the benzodiazepine recognition sites expressed by GABAA receptors.

Cardiac βARK1 inhibition prolongs survival and augments β blocker therapy in a mouse model of severe heart failure

Chronic human heart failure is characterized by abnormalities in β-adrenergic receptor (βAR) signaling, including increased levels of βAR kinase 1 (βARK1), which seems critical to the pathogenesis of the disease. To determine whether inhibition of βARK1 is sufficient to rescue a model of severe heart failure, we mated transgenic mice overexpressing a peptide inhibitor of βARK1 (βARKct) with transgenic mice overexpressing the sarcoplasmic reticulum Ca2+-binding protein, calsequestrin (CSQ). CSQ mice have a severe cardiomyopathy and markedly shortened survival (9 ± 1 weeks). In contrast, CSQ/βARKct mice exhibited a significant increase in mean survival age (15 ± 1 weeks; P < 0.0001) and showed less cardiac dilation, and cardiac function was significantly improved (CSQ vs. CSQ/βARKct, left ventricular end diastolic dimension 5.60 ± 0.17 mm vs. 4.19 ± 0.09 mm, P < 0.005; % fractional shortening, 15 ± 2 vs. 36 ± 2, P < 0.005). The enhancement of the survival rate in CSQ/βARKct mice was substantially potentiated by chronic treatment with the βAR antagonist metoprolol (CSQ/βARKct nontreated vs. CSQ/βARKct metoprolol treated, 15 ± 1 weeks vs. 25 ± 2 weeks, P < 0.0001). Thus, overexpression of the βARKct resulted in a marked prolongation in survival and improved cardiac function in a mouse model of severe cardiomyopathy that can be potentiated with β-blocker therapy. These data demonstrate a significant synergy between an established heart-failure treatment and the strategy of βARK1 inhibition.