The existence of global-in-time weak solutions to reaction-cross-diffusion systems for an arbitrary number of competing population species is proved. The equations can be derived from an on-lattice random-walk model with general transition rates. In the case of linear transition rates, it extends the two-species population model of Shigesada, Kawasaki, and Teramoto. The equations are considered in a bounded domain with homogeneous Neumann boundary conditions. The existence proof is based on a refined entropy method and a new approximation scheme. Global existence follows under a detailed balance or weak cross-diffusion condition. The detailed balance condition is related to the symmetry of the mobility matrix, which mirrors Onsager's principle in thermodynamics. Under detailed balance (and without reaction) the entropy is nonincreasing in time, but counter-examples show that the entropy may increase initially if detailed balance does not hold. Mathematics Subject Classification

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Strong compactness results for families of functions in seminormed nonnegative cones in the spirit of the Aubin-Lions-Dubinskiȋ lemma are proven, refining some recent results in the literature. The first theorem sharpens slightly a result of Dubinskiȋ (1965) for seminormed cones. The second theorem applies to piecewise constant functions in time and sharpens slightly the results of Dreher and Jüngel (2012) and Chen and Liu (2012). An application is given, which is useful in the study of porous-medium or fast-diffusion type equations.

The weak-strong uniqueness for solutions to reaction-cross-diffusion systems in a bounded domain with no-flux boundary conditions is proved. The system generalizes the Shigesada-Kawasaki-Teramoto population model to an arbitrary number of species. The diffusion matrix is neither symmetric nor positive definite, but the system possesses a formal gradient-flow or entropy structure. No growth conditions on the source terms are imposed. It is shown that any renormalized solution coincides with a strong solution with the same initial data, as long as the strong solution exists. The proof is based on the evolution of the relative entropy modified by suitable cutoff functions.

In this study, we investigated the role of peroxisome proliferator-activated receptor γ (PPARγ) on store-operated calcium entry (SOCE) and expression of the main store-operated calcium channels (SOCCs) components, canonical transient receptor potential (TRPC) in chronic hypoxia (CH) and monocrotaline (MCT)-induced PH rat models. siRNA knockdown and adenoviral overexpression strategies were constructed for both loss-of-function and gain-of-function experiments. PPARγ agonist rosiglitazone attenuates the pathogenesis of both CHPH and MCT-PH, suppresses Hif-1α, TRPC1, TRPC6 expression in the distal pulmonary artery (PA) and SOCE in freshly isolated rat distal pulmonary arterial smooth muscle cells (PASMCs). By comprehensive use of knockdown and overexpression studies, bioinformatically analysis of the TRPC gene promoter and luciferase reporter assay, we demonstrated that PPARγ exerts roles of anti-proliferation, anti-migration, and pro-apoptosis in PASMCs, likely by inhibiting the elevated SOCE and TRPC expression. These effects were inhibited under the conditions of hypoxia or Hif-1α accumulation. We also found that under hypoxia, accumulated Hif-1α protein acts as upstream of suppressed PPARγ level, however, targeted PPARγ rescue acts negative feedback on suppressing Hif-1α level and Hif-1α mediated signaling pathway. PPARγ inhibits PH by targeting SOCE and TRPC via inhibiting Hif-1α expression and signaling transduction.

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Abstract. The uniqueness of bounded weak solutions to strongly coupled parabolic equations in a bounded domain with no-flux boundary conditions is shown. The equations include cross-diffusion and drift terms and are coupled self-consistently to the Poisson equation. The model class contains special cases of the Maxwell-Stefan equations for gas mixtures, generalized Shigesada-Kawasaki-Teramoto equations for population dynamics, and volume-filling models for ion transport. The uniqueness proof is based on a combination of the H −1 technique and the entropy method of Gajewski.

Background and Purpose: Tetramethylpyrazine (TMP) was originally isolated from the traditional Chinese herb ligusticum and the fermented Japanese food natto and has since been synthesized. TMP has a long history of beneficial effects in the treatment of many cardiovascular diseases. Here we have evaluated the therapeutic effects of TMP on pulmonary hypertension (PH) in animal models and in patients with pulmonary arterial hypertension (PAH) or chronic thromboembolic pulmonary hypertension (CTEPH).Experimental Approach: Three well-defined models of PH -chronic hypoxia (10% O 2 )-induced PH (HPH), monocrotaline-induced PH (MCT-PH) and Sugen 5416/hypoxia-induced PH (SuHx-PH) -were used in Sprague-Dawley rats, and assessed by echocardiography, along with haemodynamic and histological techniques. Primary cultures of rat distal pulmonary arterial smooth muscle cells (PASMCs) were used to study intracellular calcium levels. Western blots and RT-qPCR assays were also used.In the clinical cohort, patients with PAH or CTEPH were recruited. The effects of TMP were evaluated in all systems.Key Results: TMP (100 mgÁkg −1 Áday −1 ) prevented rats from developing experimental PH and ameliorated three models of established PH: HPH, MCT-PH and SuHx-PH.The therapeutic effects of TMP were accompanied by inhibition of intracellular calcium homeostasis in PASMCs. In a small cohort of patients with PAH or CTEPH, oral Abbreviations: 2D, 2-dimensional; 6MWD, 6-min walking distance; Ccr, creatinine clearance; CTEPH, chronic thromboembolic pulmonary hypertension; EIP, End-inspiratory plateau pressure; FAC, Fractional area change; H&E, haematoxylin and eosin; HPH, hypoxia-induced pulmonary hypertension; HRR1, heart rate recovery at 1 min of rest; IPAH, idiopathic pulmonary arterial hypertension; KRBS, Krebs Ringer bicarbonate solution; LV, left ventricle; LVEF, left ventricular ejection fraction; LVFS, left ventricular fractional shortening; MCT, monocrotaline; mPAP, mean pulmonary arterial pressure; PA, pulmonary artery; PAD, pulmonary arterial diameter; PAH, pulmonary arterial hypertension; PAP, pulmonary arterial pressure; PASMC, pulmonary arterial smooth muscle cells; PAT, pulmonary arterial acceleration time; PET, pulmonary arterial ejection time; PH, pulmonary hypertension; PVR, pulmonary vascular resistance; RAD, right atrium diameter; RHC, right heart catheterization; ROCC, receptor-operated Ca 2+ channels; ROCE, receptor-operated Ca 2+ entry; RV, right ventricle; RVEDD, Right ventricular end diastolic diameter; RVEDWT, right ventricular end-diastolic free-wall thickness; RVSP, right ventricular systolic pressure; S, septum; SOCC, store-operated Ca 2+ channels; SOCE, store-operated Ca 2+ entry; SuHx-PH, Sugen/hypoxia-induced pulmonary hypertension; TAPSE, tricuspid annular plane systolic excursion; TMP, tetramethylpyrazine; VDCC, voltage-dependent Ca 2+ channels. administration of TMP (100 mg, t.i.d. for 16 weeks) increased the 6-min walk distance and improved the 1-min heart rate recovery.Conclusion and Implications: Our results s...