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Journal articles on the topic 'Control of PDEs'

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Published: 7 July 2024

Last updated: 7 July 2024

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1

Reid, Ian A. "Role of Phosphodiesterase Isoenzymes in the Control of Renin Secretion: Effects of Selective Enzyme Inhibitors." Current Pharmaceutical Design 5, no. 9 (January 1999): 725–35. http://dx.doi.org/10.2174/1381612805666230111201536.

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<p>In most cells, the steady-state level of cAMP ultimately depends on the rate of cAMP synthesis by adenylyl cyclase and the rate of cAMP hydrolysis by cyclic nucleotide phosphodiesterases (PDEs). PDEs exist in multiple forms that have been grouped into seven families based on their substrate specificity, mode of regulation and kinetic properties. Selective inhibitors of many PDE families are now available. Examples are milrinone and trequinsin (PDE3); rolipram and Ro 20-1724 (PDE4); and zaprinast, sildenafil and didyridamole (PDE5). These inhibitors have proven to be valuable tools to investigate the role of PDEs in cell function.</p> <p> Representatives of most PDE families are present in the kidneys, and recent studies in this and other laboratories have provided evidence that some of them participate in the regulation of renin secretion. In particular, administration of selective PDE inhibitors has marked effects on renin secretion. For example, the PDE3 inhibitors milrinone and trequinsin increase resting renin in conscious rabbits and enhance the renin secretory response to beta-adrenergic stimulation. Milrinone also increases renin secretion in human subjects. The PDE4 inhibitors rolipram and Ro 20-1724 both increase renin secretion in rabbits and also enhance the renin response to beta-adrenergic stimulation. Studies in other laboratories have implicated other PDE families in the control of renin secretion. The aim of this review is to present current concepts concerning the PDEs and to discuss their role in the control of renin secretion by the kidneys.</p>

2

Lugnier, Claire. "The Complexity and Multiplicity of the Specific cAMP Phosphodiesterase Family: PDE4, Open New Adapted Therapeutic Approaches." International Journal of Molecular Sciences 23, no. 18 (September 13, 2022): 10616. http://dx.doi.org/10.3390/ijms231810616.

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Cyclic nucleotides (cAMP, cGMP) play a major role in normal and pathologic signaling. Beyond receptors, cyclic nucleotide phosphodiesterases; (PDEs) rapidly convert the cyclic nucleotide in its respective 5′-nucleotide to control intracellular cAMP and/or cGMP levels to maintain a normal physiological state. However, in many pathologies, dysregulations of various PDEs (PDE1-PDE11) contribute mainly to organs and tissue failures related to uncontrolled phosphorylation cascade. Among these, PDE4 represents the greatest family, since it is constituted by 4 genes with multiple variants differently distributed at tissue, cellular and subcellular levels, allowing different fine-tuned regulations. Since the 1980s, pharmaceutical companies have developed PDE4 inhibitors (PDE4-I) to overcome cardiovascular diseases. Since, they have encountered many undesired problems, (emesis), they focused their research on other PDEs. Today, increases in the knowledge of complex PDE4 regulations in various tissues and pathologies, and the evolution in drug design, resulted in a renewal of PDE4-I development. The present review describes the recent PDE4-I development targeting cardiovascular diseases, obesity, diabetes, ulcerative colitis, and Crohn’s disease, malignancies, fatty liver disease, osteoporosis, depression, as well as COVID-19. Today, the direct therapeutic approach of PDE4 is extended by developing allosteric inhibitors and protein/protein interactions allowing to act on the PDE interactome.

3

Cai, Ying-Lan, Mo-Han Zhang, Xu Huang, Jing-Zhi Jiang, Li-Hua Piao, Zheng Jin, and Wen-Xie Xu. "CNP-pGC-cGMP-PDE3-cAMP Signal Pathway Upregulated in Gastric Smooth Muscle of Diabetic Rats." Gastroenterology Research and Practice 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/305258.

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Our previous studies have shown that CNP-NPR-B/pGC-cGMP is upregulated in the diabetic rats. The present study was designed to determine whether the upregulation of CNP-NPR-B/pGC-cGMP signal pathway affects cGMP-PDE3-cAMP signal pathway in diabetic gastric smooth muscle. The gastric smooth muscle motility was observed by using isometric measurement. PDEs expressions in diabetic gastric smooth muscle tissue were observed by using immunohistochemistry, Western blotting, and RT-PCR methods. The results demonstrated that the inhibitory effect of CNP on the spontaneous contraction of gastric antral circular smooth muscle was potentiated in STZ-induced diabetic rat. CNP-induced increase of cGMP and cAMP was much higher in diabetic gastric smooth muscle tissue than in controls. The expression of PDE3 is downregulated while the levels of gene expression of PDE1, PDE2, PDE4, and PDE5 were not altered in the diabetic gastric smooth muscle tissue. The results suggest that the sensitivity of gastric smooth muscle to CNP is potentiated via activation of CNP-pGC-cGMP-PDE3-cAMP signal pathway in STZ-induced diabetic rats, which may be associated with diabetes-induced gastric motility disorder.

4

Krstic, Miroslav, and Andrey Smyshlyaev. "ADAPTIVE CONTROL OF PDES." IFAC Proceedings Volumes 40, no. 13 (2007): 20–31. http://dx.doi.org/10.3182/20070829-3-ru-4911.00004.

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5

Krstic, Miroslav, and Andrey Smyshlyaev. "ADAPTIVE CONTROL OF PDES." IFAC Proceedings Volumes 40, no. 14 (2007): 20–31. http://dx.doi.org/10.3182/20070829-3-ru-4912.00004.

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6

Krstic, Miroslav, and Andrey Smyshlyaev. "Adaptive control of PDEs." Annual Reviews in Control 32, no. 2 (December 2008): 149–60. http://dx.doi.org/10.1016/j.arcontrol.2008.05.001.

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7

Hengge, Regine. "Trigger phosphodiesterases as a novel class of c-di-GMP effector proteins." Philosophical Transactions of the Royal Society B: Biological Sciences 371, no. 1707 (November 5, 2016): 20150498. http://dx.doi.org/10.1098/rstb.2015.0498.

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The bacterial second messenger c-di-GMP controls bacterial biofilm formation, motility, cell cycle progression, development and virulence. It is synthesized by diguanylate cyclases (with GGDEF domains), degraded by specific phosphodiesterases (PDEs, with EAL of HD-GYP domains) and sensed by a wide variety of c-di-GMP-binding effectors that control diverse targets. c-di-GMP-binding effectors can be riboswitches as well as proteins with highly diverse structures and functions. The latter include ‘degenerate’ GGDEF/EAL domain proteins that are enzymatically inactive but still able to bind c-di-GMP. Surprisingly, two enzymatically active ‘trigger PDEs’, the Escherichia coli proteins PdeR and PdeL, have recently been added to this list of c-di-GMP-sensing effectors. Mechanistically, trigger PDEs are multifunctional. They directly and specifically interact with a macromolecular target (e.g. with a transcription factor or directly with a promoter region), whose activity they control by their binding and degradation of c-di-GMP—their PDE activity thus represents the c-di-GMP sensor or effector function. In this process, c-di-GMP serves as a regulatory ligand, but in contrast to classical allosteric control, this ligand is also degraded. The resulting kinetics and circuitry of control are ideally suited for trigger PDEs to serve as key components in regulatory switches. This article is part of the themed issue ‘The new bacteriology’.

8

Idres, Sarah, Germain Perrin, Valérie Domergue, Florence Lefebvre, Susana Gomez, Audrey Varin, Rodolphe Fischmeister, Véronique Leblais, and Boris Manoury. "Contribution of BKCa channels to vascular tone regulation by PDE3 and PDE4 is lost in heart failure." Cardiovascular Research 115, no. 1 (June 23, 2018): 130–44. http://dx.doi.org/10.1093/cvr/cvy161.

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Abstract Aims Regulation of vascular tone by 3′,5′-cyclic adenosine monophosphate (cAMP) involves many effectors including the large conductance, Ca2+-activated, K+ (BKCa) channels. In arteries, cAMP is mainly hydrolyzed by type 3 and 4 phosphodiesterases (PDE3, PDE4). Here, we examined the specific contribution of BKCa channels to tone regulation by these PDEs in rat coronary arteries, and how this is altered in heart failure (HF). Methods and results Concomitant application of PDE3 (cilostamide) and PDE4 (Ro-20-1724) inhibitors increased BKCa unitary channel activity in isolated myocytes from rat coronary arteries. Myography was conducted in isolated, U46619-contracted coronary arteries. Cilostamide (Cil) or Ro-20-1724 induced a vasorelaxation that was greatly reduced by iberiotoxin (IBTX), a BKCa channel blocker. Ro-20-1724 and Cil potentiated the relaxation induced by the β-adrenergic agonist isoprenaline (ISO) or the adenylyl cyclase activator L-858051 (L85). IBTX abolished the effect of PDE inhibitors on ISO but did not on L85. In coronary arteries from rats with HF induced by aortic stenosis, contractility and response to acetylcholine were dramatically reduced compared with arteries from sham rats, but relaxation to PDE inhibitors was retained. Interestingly, however, IBTX had no effect on Ro-20-1724- and Cil-induced vasorelaxations in HF. Expression of the BKCa channel α-subunit, of a 98 kDa PDE3A and of a 80 kDa PDE4D were lower in HF compared with sham coronary arteries, while that of a 70 kDa PDE4B was increased. Proximity ligation assays demonstrated that PDE3 and PDE4 were localized in the vicinity of the channel. Conclusion BKCa channels mediate the relaxation of coronary artery induced by PDE3 and PDE4 inhibition. This is achieved by co-localization of both PDEs with BKCa channels, enabling tight control of cAMP available for channel opening. Contribution of the channel is prominent at rest and on β-adrenergic stimulation. This coupling is lost in HF.

9

Vinogradova, Tatiana M., and Edward G. Lakatta. "Dual Activation of Phosphodiesterase 3 and 4 Regulates Basal Cardiac Pacemaker Function and Beyond." International Journal of Molecular Sciences 22, no. 16 (August 5, 2021): 8414. http://dx.doi.org/10.3390/ijms22168414.

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The sinoatrial (SA) node is the physiological pacemaker of the heart, and resting heart rate in humans is a well-known risk factor for cardiovascular disease and mortality. Consequently, the mechanisms of initiating and regulating the normal spontaneous SA node beating rate are of vital importance. Spontaneous firing of the SA node is generated within sinoatrial nodal cells (SANC), which is regulated by the coupled-clock pacemaker system. Normal spontaneous beating of SANC is driven by a high level of cAMP-mediated PKA-dependent protein phosphorylation, which rely on the balance between high basal cAMP production by adenylyl cyclases and high basal cAMP degradation by cyclic nucleotide phosphodiesterases (PDEs). This diverse class of enzymes includes 11 families and PDE3 and PDE4 families dominate in both the SA node and cardiac myocardium, degrading cAMP and, consequently, regulating basal cardiac pacemaker function and excitation-contraction coupling. In this review, we will demonstrate similarities between expression, distribution, and colocalization of various PDE subtypes in SANC and cardiac myocytes of different species, including humans, focusing on PDE3 and PDE4. Here, we will describe specific targets of the coupled-clock pacemaker system modulated by dual PDE3 + PDE4 activation and provide evidence that concurrent activation of PDE3 + PDE4, operating in a synergistic manner, regulates the basal cardiac pacemaker function and provides control over normal spontaneous beating of SANCs through (PDE3 + PDE4)-dependent modulation of local subsarcolemmal Ca2+ releases (LCRs).

10

Murray, Fiona, Hemal H. Patel, Ryan Y. S. Suda, Shen Zhang, Patricia A. Thistlethwaite, Jason X. J. Yuan, and Paul A. Insel. "Expression and activity of cAMP phosphodiesterase isoforms in pulmonary artery smooth muscle cells from patients with pulmonary hypertension: role for PDE1." American Journal of Physiology-Lung Cellular and Molecular Physiology 292, no. 1 (January 2007): L294—L303. http://dx.doi.org/10.1152/ajplung.00190.2006.

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Pulmonary hypertension (PHT) is associated with increased vascular resistance due to sustained contraction and enhanced proliferation of pulmonary arterial smooth muscle cells (PASMC); the abnormal tone and remodeling in the pulmonary vasculature may relate, at least in part, to decreased cyclic nucleotide levels. Cyclic nucleotide phosphodiesterases (PDEs), of which 11 families have been identified, catalyze the hydrolysis of cAMP and cGMP. We tested the hypothesis that PASMC isolated from patients with PHT, either idiopathic pulmonary arterial hypertension (IPAH) or secondary pulmonary hypertension (SPH), have increased expression and activity of PDE isoforms that reduce the responsiveness of agents that raise cellular cAMP. Real-time PCR and immunoblotting demonstrated that the expression of PDE1A, PDE1C, PDE3B, and PDE5A was enhanced in PASMC from both IPAH and SPH patients compared with control PASMC. Consistent with this enhanced expression of PDEs, agonist-stimulated cAMP levels were significantly reduced in IPAH and SPH PASMC unless a PDE inhibitor was present. The use of specific PDE inhibitors revealed that an increase in PDE1 and PDE3 activity largely accounted for reduced agonist-induced cAMP levels and increased proliferation in IPAH and SPH PASMC. Treatment with PDE1C-targeted small interference RNA enhanced cAMP accumulation and inhibited cellular proliferation to a greater extent in PHT PASMC than controls. The results imply that an increase in PDE isoforms, in particular PDE1C, contributes to decreased cAMP and increased proliferation of PASMC in patients with PHT. PDE1 isoforms may provide novel targets for the treatment of both primary and secondary forms of the disease.

11

Phillips, Peter G., Lu Long, Martin R. Wilkins, and Nicholas W. Morrell. "cAMP phosphodiesterase inhibitors potentiate effects of prostacyclin analogs in hypoxic pulmonary vascular remodeling." American Journal of Physiology-Lung Cellular and Molecular Physiology 288, no. 1 (January 2005): L103—L115. http://dx.doi.org/10.1152/ajplung.00095.2004.

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We investigated the effects of prostacyclin analogs and isoform-selective phosphodiesterase (PDE) inhibitors, alone and in combination, on pulmonary vascular remodeling in vitro and in vivo. Vascular smooth muscle cells (VSMC) isolated from pulmonary (proximal and distal) and systemic circulations demonstrated subtle variations in expression of PDE isoform mRNA. However, using biochemical assays, we found PDE3 and PDE4 isoforms to be responsible for the majority of cAMP hydrolysis in all VSMC. In growth assays, the prostacyclin analogs cicaprost and iloprost inhibited mitogen-induced proliferation of VSMC in a cAMP-dependent manner. In addition, isoform-selective antagonists of PDEs 1, 3, or 4 inhibited VSMC proliferation, an effect that synergized with the effect of prostacyclin analogs. The inhibitory effects were greater in cells isolated from pulmonary circulation. In an in situ perfused rat lung preparation, administration of prostacyclin analogs or the PDE inhibitors vinpocetine (PDE1), cilostamide (PDE3), or rolipram (PDE4), but not EHNA (PDE2), attenuated acute hypoxic vasoconstriction (HPV). Combinations of agents led to a greater reduction in HPV. Furthermore, during exposure to hypoxia for 13 days, Wistar rats were treated with iloprost, rolipram, cilostamide, or combinations of these agents. Compared with normoxic controls, hypoxic animals developed pulmonary hypertension and distal pulmonary artery muscularization. These parameters were attenuated by iloprost+cilostamide, iloprost+rolipram, and cilostamide+rolipram but were not significantly affected by single agents. Together, these findings provide a greater understanding of the role of cAMP PDEs in VSMC proliferation and provide rationale for combined use of prostacylcin analogs plus PDE3/4 inhibitors in treatment of pulmonary vascular remodeling.

12

Antil, Harbir, and Mahamadi Warma. "Optimal control of fractional semilinear PDEs." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 5. http://dx.doi.org/10.1051/cocv/2019003.

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In this paper, we consider the optimal control of semilinear fractional PDEs with both spectral and integral fractional diffusion operators of order 2s with s ∈ (0, 1). We first prove the boundedness of solutions to both semilinear fractional PDEs under minimal regularity assumptions on domain and data. We next introduce an optimal growth condition on the nonlinearity to show the Lipschitz continuity of the solution map for the semilinear elliptic equations with respect to the data. We further apply our ideas to show existence of solutions to optimal control problems with semilinear fractional equations as constraints. Under the standard assumptions on the nonlinearity (twice continuously differentiable) we derive the first and second order optimality conditions.

13

Lasiecka,, I., and GC Gaunaurd,. "Mathematical Control Theory of Coupled PDEs." Applied Mechanics Reviews 56, no. 1 (January 1, 2003): B3. http://dx.doi.org/10.1115/1.1523354.

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14

Antil, Harbir, Ratna Khatri, and Mahamadi Warma. "External optimal control of nonlocal PDEs." Inverse Problems 35, no. 8 (July 30, 2019): 084003. http://dx.doi.org/10.1088/1361-6420/ab1299.

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15

Smith, Carolyn J., Jing He, Jia-Zhen Ding, Sidonnie Ricketts, Elaine Huston, Miles Houslay, Richard A. Moggio, and Michael B. Stemerman. "Uupregulation of High Affinity Cyclic AMP Phosphodiesterase (PDE) Genes Following BALloon Catheter Deendothelialization (Bal) in Rat Aorta." Hypertension 36, suppl_1 (October 2000): 706. http://dx.doi.org/10.1161/hyp.36.suppl_1.706-d.

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P75 Inhibitors of PDE 3 and/or PDE4 block smooth muscle cell (SMC) proliferation/migration in vitro and reduce restenosis. To evaluate chronic regulation of SMC PDEs, rats were subjected to BAL. At several times after BAL (30 min to 10days/10D), medial SMC were isolated from the thoracic aortae. Tissues were fractionated for total RNA (analyzed by Northern blots/ RNAase protection) or cytosolic protein (Western blots or low Km [100 nM] cAMP PDE activity). BAL-dependent increases in PDE4B mRNA were biphasic: 2.7-fold at 1hr, which declined by 24hr below control values, followed by 2-3-fold increases by 4-7D (p<0.05 vs controls, n=3-6). PDE4B and c-myc mRNAs were selectively superinduced in cycloheximide-treated rats. Despite modest changes in PDE3 mRNAs, both 80 and 120 kDa PDE3A proteins were detected and only the 80kDa increased 7D post-BAL (10-fold increase, p<0.05, n=6). PDE4B2 (80kDa) persistently increased 2.5-3-fold (p<0.05, n=4-6) from 24 hr to 10D post-BAL, while 2-fold increases in PDE4D3 (90kDa) and PDE4B1 (104kDa) were evident at 24hr or 7D, respectively. PDE activity increased 50-60% (p<0.05; n=4) at 24 hr and 7D after BAL. Thus PDE4B resembles an immediate-early gene. Selective induction of the PDE4 family is associated with 2 waves of SMC proliferation in vivo, the latter of which is also accompanied by induction of PDE3A/80kDa. Upregulation of specific SMC PDEs following angioplasty represents an important response to injury that may be a useful therapeutic target in vascular disease.

16

Dubljevic, Stevan, and Panagiotis D. Christofides. "Predictive control of parabolic PDEs with boundary control actuation." Chemical Engineering Science 61, no. 18 (September 2006): 6239–48. http://dx.doi.org/10.1016/j.ces.2006.05.041.

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17

Matsumoto, Takayuki, Tsuneo Kobayashi, and Katsuo Kamata. "Alterations in EDHF-type relaxation and phosphodiesterase activity in mesenteric arteries from diabetic rats." American Journal of Physiology-Heart and Circulatory Physiology 285, no. 1 (July 2003): H283—H291. http://dx.doi.org/10.1152/ajpheart.00954.2002.

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In isolated superior mesenteric artery rings from age-matched control rats and streptozotocin (STZ)-induced diabetic rats, we investigated the role of cAMP in endothelium-derived hyperpolarizing factor (EDHF)-type relaxation. The ACh-induced EDHF-type relaxation was significantly weaker in STZ-induced diabetic rats than in control rats, and in both groups of rats it was attenuated by 18α-glycyrrhetinic acid (18α-GA), an inhibitor of gap junctions, and enhanced by IBMX, a cAMP-phosphodiesterase (PDE) inhibitor. These enhanced EDHF-type responses were very similar in magnitude between diabetic and age-matched control rats. The EDHF-type relaxation was enhanced by cilostamide, a PDE3-selective inhibitor, but not by Ro 20–1724, a PDE4-selective inhibitor. The expression levels of the mRNAs and proteins for two cAMP PDEs (PDE3A, PDE3B) were significantly increased in STZ-induced diabetic rats, but those for PDE4D were not. We conclude that the impairment of EDHF-type relaxations in STZ-induced diabetic rats may be attributed to a reduction in the action of cAMP via increased PDE activity.

18

Antil, Harbir, Deepanshu Verma, and Mahamadi Warma. "External optimal control of fractional parabolic PDEs." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 20. http://dx.doi.org/10.1051/cocv/2020005.

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In [Antil et al. Inverse Probl. 35 (2019) 084003.] we introduced a new notion of optimal control and source identification (inverse) problems where we allow the control/source to be outside the domain where the fractional elliptic PDE is fulfilled. The current work extends this previous work to the parabolic case. Several new mathematical tools have been developed to handle the parabolic problem. We tackle the Dirichlet, Neumann and Robin cases. The need for these novel optimal control concepts stems from the fact that the classical PDE models only allow placing the control/source either on the boundary or in the interior where the PDE is satisfied. However, the nonlocal behavior of the fractional operator now allows placing the control/source in the exterior. We introduce the notions of weak and very-weak solutions to the fractional parabolic Dirichlet problem. We present an approach on how to approximate the fractional parabolic Dirichlet solutions by the fractional parabolic Robin solutions (with convergence rates). A complete analysis for the Dirichlet and Robin optimal control problems has been discussed. The numerical examples confirm our theoretical findings and further illustrate the potential benefits of nonlocal models over the local ones.

19

Kazantzis, Nikolaos, and Michael A. Demetriou. "Singular Control-Invariance PDEs for Nonlinear Systems." Multiscale Modeling & Simulation 3, no. 4 (January 2005): 731–48. http://dx.doi.org/10.1137/040603218.

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20

Sassano, M., and A. Astolfi. "Approximate finite-horizon optimal control without PDEs." Systems & Control Letters 62, no. 2 (February 2013): 97–103. http://dx.doi.org/10.1016/j.sysconle.2012.08.015.

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21

Selivanov, Anton, and Emilia Fridman. "Sampled-data relay control of diffusion PDEs." Automatica 82 (August 2017): 59–68. http://dx.doi.org/10.1016/j.automatica.2017.04.022.

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22

Brett, Charles, Andreas Dedner, and Charles Elliott. "Optimal control of elliptic PDEs at points." IMA Journal of Numerical Analysis 36, no. 3 (August 25, 2015): 1015–50. http://dx.doi.org/10.1093/imanum/drv040.

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23

Buchheim, Christoph, Renke Kuhlmann, and Christian Meyer. "Combinatorial optimal control of semilinear elliptic PDEs." Computational Optimization and Applications 70, no. 3 (March 2, 2018): 641–75. http://dx.doi.org/10.1007/s10589-018-9993-2.

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24

Dubljevic, Stevan, Nael H. El-Farra, Prashant Mhaskar, and Panagiotis D. Christofides. "Predictive control of parabolic PDEs with state and control constraints." International Journal of Robust and Nonlinear Control 16, no. 16 (2006): 749–72. http://dx.doi.org/10.1002/rnc.1097.

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Tataru, D. "Boundary controllability for conservative PDEs." Applied Mathematics & Optimization 31, no. 3 (May 1995): 257–95. http://dx.doi.org/10.1007/bf01215993.

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26

Kouri, D. P., and T. M. Surowiec. "Risk-averse optimal control of semilinear elliptic PDEs." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 53. http://dx.doi.org/10.1051/cocv/2019061.

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In this paper, we consider the optimal control of semilinear elliptic PDEs with random inputs. These problems are often nonconvex, infinite-dimensional stochastic optimization problems for which we employ risk measures to quantify the implicit uncertainty in the objective function. In contrast to previous works in uncertainty quantification and stochastic optimization, we provide a rigorous mathematical analysis demonstrating higher solution regularity (in stochastic state space), continuity and differentiability of the control-to-state map, and existence, regularity and continuity properties of the control-to-adjoint map. Our proofs make use of existing techniques from PDE-constrained optimization as well as concepts from the theory of measurable multifunctions. We illustrate our theoretical results with two numerical examples motivated by the optimal doping of semiconductor devices.

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Selivanov, Anton, and Emilia Fridman. "Distributed event-triggered control of diffusion semilinear PDEs." Automatica 68 (June 2016): 344–51. http://dx.doi.org/10.1016/j.automatica.2016.02.006.

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28

Lou, Yiming, and Panagiotis D. Christofides. "Feedback control of surface roughness using stochastic PDEs." AIChE Journal 51, no. 1 (2004): 345–52. http://dx.doi.org/10.1002/aic.10299.

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Boonkumkrong, Nipon, Sinchai Chinvorarat, and Pichai Asadamongkon. "Passivity-based boundary control for vibration suppression of the shear beam." Advances in Mechanical Engineering 14, no. 11 (November 2022): 168781322211345. http://dx.doi.org/10.1177/16878132221134517.

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In this paper, the passivity-based boundary controller for the vibration suppression of the flexible beam is studied. The undamped shear beam model is used as a beam model. The beam is a parameter-distributed system represented by partial differential equations (PDEs). This technique uses the energy principle for control design by exploiting the passivity property of the beam. The storage or energy function of the beam is first introduced and then used to determine the passivity-based controller. The passivity of the system is proven using direct integration. The feedback system is proven in the sense of finite-gain [Formula: see text] stability. The proposed controller consists of the damping and elastic components applied at the beam end so that the domain (body) of the beam is not disturbed. The beam PDEs are treated directly without model reduction or truncation, so the control spillover problem is avoidable. The beam model PDEs are solved numerically by using the finite difference method. Numerical simulation results of the beam under control are presented to verify the performance of the control scheme.

30

Zhang, Xinxin, and Huaiqin Wu. "Bipartite consensus for multi-agent networks of fractional diffusion PDEs via aperiodically intermittent boundary control." Mathematical Biosciences and Engineering 20, no. 7 (2023): 12649–65. http://dx.doi.org/10.3934/mbe.2023563.

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<abstract><p>In this paper, the exponential bipartite consensus issue is investigated for multi-agent networks, whose dynamic is characterized by fractional diffusion partial differential equations (PDEs). The main contribution is that a novel exponential convergence principle is proposed for networks of fractional PDEs via aperiodically intermittent control scheme. First, under the aperiodically intermittent control strategy, an exponential convergence principle is developed for continuously differentiable function. Second, on the basis of the proposed convergence principle and the designed intermittent boundary control protocol, the exponential bipartite consensus condition is addressed in the form of linear matrix inequalities (LMIs). Compared with the existing works, the result of the exponential intermittent consensus presented in this paper is applied to the networks of PDEs. Finally, the high-speed aerospace vehicle model is applied to verify the effectiveness of the control protocol.</p></abstract>

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Tulsian, Nikhil K., Abhijeet Ghode, and Ganesh S. Anand. "Adenylate control in cAMP signaling: implications for adaptation in signalosomes." Biochemical Journal 477, no. 16 (August 21, 2020): 2981–98. http://dx.doi.org/10.1042/bcj20200435.

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In cAMP-Protein Kinase A (PKA) signaling, A-kinase anchoring protein scaffolds assemble PKA in close proximity to phosphodiesterases (PDE), kinase-substrates to form signaling islands or ‘signalosomes’. In its basal state, inactive PKA holoenzyme (R2:C2) is activated by binding of cAMP to regulatory (R)-subunits leading to dissociation of active catalytic (C)-subunits. PDEs hydrolyze cAMP-bound to the R-subunits to generate 5′-AMP for termination and resetting the cAMP signaling. Mechanistic basis for cAMP signaling has been derived primarily by focusing on the proteins in isolation. Here, we set out to simulate cAMP signaling activation-termination cycles in a signalosome-like environment with PDEs and PKA subunits in close proximity to each other. Using a combination of fluorescence polarization and amide hydrogen exchange mass spectrometry with regulatory (RIα), C-subunit (Cα) and PDE8 catalytic domain, we have tracked movement of cAMP through activation-termination cycles. cAMP signaling operates as a continuum of four phases: (1) Activation and dissociation of PKA into R- and C-subunits by cAMP and facilitated by substrate (2) PDE recruitment to R-subunits (3) Hydrolysis of cAMP to 5′-AMP (4) Reassociation of C-subunit to 5′-AMP-bound-RIα in the presence of excess ATP to reset cAMP signaling to form the inactive PKA holoenzyme. Our results demonstrate that 5′-AMP is not merely a passive hydrolysis end-product of PDE action. A ‘ligand-free’ state R subunit does not exist in signalosomes as previously assumed. Instead the R-subunit toggles between cAMP- or 5′-AMP bound forms. This highlights, for the first time, the importance of 5′-AMP in promoting adaptation and uncovers adenylate control in cAMP signaling.

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Calsavara, Bianca M. R., Enrique Fernández-Cara, Luz de Teresa, and José Antonio Villa. "New results concerning the hierarchical control of linear and semilinear parabolic equations." ESAIM: Control, Optimisation and Calculus of Variations 28 (2022): 14. http://dx.doi.org/10.1051/cocv/2022011.

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This paper deals with the application of multiple strategies to control some parabolic PDEs. We assume that we can act on the system through a hierarchy of distributed controls: with a first control (a follower), we drive the state exactly to zero; then, with an additional control (the leader), we minimize a prescribed cost functional. That means that we invert the roles played by leaders and followers in the recent literature. We study linear and semilinear problems. More precisely, we prove the existence (and uniqueness in the linear case) of a leader-follower couple. Then, we deduce an appropriate optimality system that must be satisfied by the controls and the corresponding state and adjoint states. We also indicate some generalizations to other controls, PDEs and systems. In particular, we establish similar existence and optimality results for hierarchical-biobjective (Pareto-Stackelberg) control problems, where there are two cost functionals and two independent leader controls whose main task is to find an associated Pareto equilibrium and one common follower in charge of null controllability.

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Puertas-Umbert, Lídia, Judith Alonso, Leif Hove-Madsen, José Martínez-González, and Cristina Rodríguez. "PDE4 Phosphodiesterases in Cardiovascular Diseases: Key Pathophysiological Players and Potential Therapeutic Targets." International Journal of Molecular Sciences 24, no. 23 (November 30, 2023): 17017. http://dx.doi.org/10.3390/ijms242317017.

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3′,5′-cyclic adenosine monophosphate (cAMP) is a second messenger critically involved in the control of a myriad of processes with significant implications for vascular and cardiac cell function. The temporal and spatial compartmentalization of cAMP is governed by the activity of phosphodiesterases (PDEs), a superfamily of enzymes responsible for the hydrolysis of cyclic nucleotides. Through the fine-tuning of cAMP signaling, PDE4 enzymes could play an important role in cardiac hypertrophy and arrhythmogenesis, while it decisively influences vascular homeostasis through the control of vascular smooth muscle cell proliferation, migration, differentiation and contraction, as well as regulating endothelial permeability, angiogenesis, monocyte/macrophage activation and cardiomyocyte function. This review summarizes the current knowledge and recent advances in understanding the contribution of the PDE4 subfamily to cardiovascular function and underscores the intricate challenges associated with targeting PDE4 enzymes as a therapeutic strategy for the management of cardiovascular diseases.

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Wu, Hongchun, Yulan Wang, and Wei Zhang. "Numerical Solution of a Class of Nonlinear Partial Differential Equations by Using Barycentric Interpolation Collocation Method." Mathematical Problems in Engineering 2018 (December 30, 2018): 1–10. http://dx.doi.org/10.1155/2018/7260346.

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Partial differential equations (PDEs) are widely used in mechanics, control processes, ecological and economic systems, chemical cycling systems, and epidemiology. Although there are some numerical methods for solving PDEs, simple and efficient methods have always been the direction that scholars strive to pursue. Based on this problem, we give the meshless barycentric interpolation collocation method (MBICM) for solving a class of PDEs. Four numerical experiments are carried out and compared with other methods; the accuracy of the numerical solution obtained by the present method is obviously improved.

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Krstic, Miroslav. "Control of systems on spatial domains with moving boundaries: 3D printing and traffic." Facta universitatis - series: Electronics and Energetics 32, no. 4 (2019): 503–12. http://dx.doi.org/10.2298/fuee1904503k.

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Until roughly the year 2000, control algorithms (of the kind that can be physically implemented and provided guarantees of stability and performance) were mostly available only for systems modeled by ordinary differential equations. In other words, while controllers were available for finite-dimensional systems, such as robotic manipulators of vehicles, they were not available for systems like fluid flows. With the emergence of the ?backstepping? approach, it became possible to design control laws for systems modeled by partial differential equations (PDEs), i.e., for infinite dimensional systems, and with inputs at the boundaries of spatial domains. But, until recently, such backstepping controllers for PDEs were available only for systems evolving on fixed spatial PDE domains, not for systems whose boundaries are also dynamical and move, such as in systems undergoing transition of phase of matter (like the solid-liquid transition, i.e., melting or crystallization). In this invited article we review new control designs for moving-boundary PDEs of both parabolic and hyperbolic types and illustrate them by applications, respectively, in additive manufacturing (3D printing) and freeway traffic.

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Gangl, Peter, and Kevin Sturm. "Topological Derivative for PDEs on Surfaces." SIAM Journal on Control and Optimization 60, no. 1 (January 4, 2022): 81–103. http://dx.doi.org/10.1137/20m1339040.

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Chao, Pin-Chun, and Kirk L. Hamilton. "Genistein stimulates electrogenic Cl− secretion via phosphodiesterase modulation in the mouse jejunum." American Journal of Physiology-Cell Physiology 297, no. 3 (September 2009): C688—C698. http://dx.doi.org/10.1152/ajpcell.00152.2009.

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Previously, we demonstrated that genistein stimulated Cl− secretion in the mouse jejunum (Baker MJ and Hamilton KL, Am J Physiol Cell Physiol 287: C1636–C1645, 2004); however, the mode of action of genistein still remains unclear. Here, we examined the activation of Cl− secretion by the modulation of phosphodiesterases (PDEs) by genistein (75 μM) in the mouse jejunum with the Ussing short-circuit current ( Isc) technique. Drugs tested included theophylline (10 mM), a nonspecific PDE inhibitor; 8-methoxymethyl-3-isobutyl-1-methylxanthine (8-MM-IBMX; 100 μM), erythro-9-(2-hydroxyl-3-nonyl)-adenine (EHNA; 40 μM), milrinone (100 μM), and rolipram (40 and 100 μM), which are specific inhibitors of PDE1–PDE4, respectively. Theophylline stimulated a bumetanide-sensitive Isc, indicative of Cl− secretion, and abolished genistein's stimulatory action on Isc. Neither 8-MM-IBMX nor EHNA altered the basal Isc nor did these PDE inhibitors affect the stimulatory action of genistein on the Isc of the mouse jejunum. Rolipram had no effect on basal Isc, but it reduced the genistein-stimulated Isc compared with time-matched control tissues. Milrinone stimulated a concentration-dependent increase in Isc. Bumetanide (10 μM) inhibited 60 ± 4% of milrinone-induced Isc. Pretreating tissues with milrinone prevented genistein from stimulating Isc, and pretreatment with genistein reduced the effect of milrinone on Isc. H89 (50 μM), a PKA inhibitor, reduced the milrinone-stimulated Isc. Likewise, H89 reduced the genistein-stimulated Isc. Here, we demonstrate, for the first time, that genistein activates Cl− secretion of the mouse jejunum via inhibition of a PDE3-dependent pathway.

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Shi, Xiaowen, Xiangyu Zhang, Renwu Tang, and Juan Yang. "Solve High-Dimensional Reflected Partial Differential Equations by Neural Network Method." Mathematical and Computational Applications 28, no. 4 (June 24, 2023): 79. http://dx.doi.org/10.3390/mca28040079.

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Reflected partial differential equations (PDEs) have important applications in financial mathematics, stochastic control, physics, and engineering. This paper aims to present a numerical method for solving high-dimensional reflected PDEs. In fact, overcoming the “dimensional curse” and approximating the reflection term are challenges. Some numerical algorithms based on neural networks developed recently fail in solving high-dimensional reflected PDEs. To solve these problems, firstly, the reflected PDEs are transformed into reflected backward stochastic differential equations (BSDEs) using the reflected Feyman–Kac formula. Secondly, the reflection term of the reflected BSDEs is approximated using the penalization method. Next, the BSDEs are discretized using a strategy that combines Euler and Crank–Nicolson schemes. Finally, a deep neural network model is employed to simulate the solution of the BSDEs. The effectiveness of the proposed method is tested by two numerical experiments, and the model shows high stability and accuracy in solving reflected PDEs of up to 100 dimensions.

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Geshkovski, Borjan, and Enrique Zuazua. "Turnpike in optimal control of PDEs, ResNets, and beyond." Acta Numerica 31 (May 2022): 135–263. http://dx.doi.org/10.1017/s0962492922000046.

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The turnpike property in contemporary macroeconomics asserts that if an economic planner seeks to move an economy from one level of capital to another, then the most efficient path, as long as the planner has enough time, is to rapidly move stock to a level close to the optimal stationary or constant path, then allow for capital to develop along that path until the desired term is nearly reached, at which point the stock ought to be moved to the final target. Motivated in part by its nature as a resource allocation strategy, over the past decade, the turnpike property has also been shown to hold for several classes of partial differential equations arising in mechanics. When formalized mathematically, the turnpike theory corroborates insights from economics: for an optimal control problem set in a finite-time horizon, optimal controls and corresponding states are close (often exponentially) most of the time, except near the initial and final times, to the optimal control and the corresponding state for the associated stationary optimal control problem. In particular, the former are mostly constant over time. This fact provides a rigorous meaning to the asymptotic simplification that some optimal control problems appear to enjoy over long time intervals, allowing the consideration of the corresponding stationary problem for computing and applications. We review a slice of the theory developed over the past decade – the controllability of the underlying system is an important ingredient, and can even be used to devise simple turnpike-like strategies which are nearly optimal – and present several novel applications, including, among many others, the characterization of Hamilton–Jacobi–Bellman asymptotics, and stability estimates in deep learning via residual neural networks.

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Wright, Lyndon C., Joachim Seybold, Annette Robichaud, Ian M. Adcock, and Peter J. Barnes. "Phosphodiesterase expression in human epithelial cells." American Journal of Physiology-Lung Cellular and Molecular Physiology 275, no. 4 (October 1, 1998): L694—L700. http://dx.doi.org/10.1152/ajplung.1998.275.4.l694.

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Epithelial cells play a critical role in airway inflammation and have the capacity to produce many inflammatory mediators, including bioactive lipids and proinflammatory cytokines. Intracellular levels of cAMP and cGMP are important in the control of inflammatory cell function. These cyclic nucleotides are inactivated via a family of phosphodiesterase (PDE) enzymes, providing a possible site for drug intervention in chronic inflammatory conditions. We studied the expression of PDE activity in an epithelial cell line (A549) and in primary human airway epithelial cells (HAECs). We measured PDE function using specific inhibitors to identify the PDE families present and used RT-PCR to elucidate the expression of PDE isogenes. Both A549 cells and HAECs predominantly expressed PDE4 activity, with lesser PDE1, PDE3, and PDE5 activity. RT-PCR identified HSPDE4A5 and HSPDE4D3 together with HSPDE7. Inhibition of PDE4 and PDE3 reduced secretion by these cells. Epithelial PDE may be an important target for PDE4 inhibitors in the development of the control of asthmatic inflammation, particularly when delivered via the inhaled route.

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Marquez, Alejandro, Jairo José Espinosa Oviedo, and Darci Odloak. "Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System." Journal of Control Science and Engineering 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/763165.

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This paper studies the application of proper orthogonal decomposition (POD) to reduce the order of distributed reactor models with axial and radial diffusion and the implementation of model predictive control (MPC) based on discrete-time linear time invariant (LTI) reduced-order models. In this paper, the control objective is to keep the operation of the reactor at a desired operating condition in spite of the disturbances in the feed flow. This operating condition is determined by means of an optimization algorithm that provides the optimal temperature and concentration profiles for the system. Around these optimal profiles, the nonlinear partial differential equations (PDEs), that model the reactor are linearized, and afterwards the linear PDEs are discretized in space giving as a result a high-order linear model. POD and Galerkin projection are used to derive the low-order linear model that captures the dominant dynamics of the PDEs, which are subsequently used for controller design. An MPC formulation is constructed on the basis of the low-order linear model. The proposed approach is tested through simulation, and it is shown that the results are good with regard to keep the operation of the reactor.

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Strnad, Irena, and Rok Marsetič. "Differential Evolution Based Numerical Variable Speed Limit Control Method with a Non-Equilibrium Traffic Model." Mathematics 11, no. 2 (January 4, 2023): 265. http://dx.doi.org/10.3390/math11020265.

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This paper introduces a numerical variable speed limit (VSL) control method on a motorway, modeled by the system of partial differential equations (PDEs) of a non- equilibrium continuum traffic model. The method consists of a macroscopic simulation (i.e., numerical solution of the system of PDEs of the continuum model), introduction of the solution-based cost function and numerical optimization with a differential evolution algorithm (DE). Due to the numerical solution scheme, the method enables application of a wide range of continuum traffic models without prior discretization of PDEs. In this way, the method overcomes the limitations of the basic continuum models and represents a step towards more accurate traffic modelling in control strategies. In this paper, we determine optimal variable speed limits with the DE algorithm on a motorway section modeled by the modified switching curve model, which is a non-equilibrium continuum model consistent with the three-phase traffic flow theory. The effectiveness of the determined variable speed limits is validated using microsimulations of the test section, which show promising reductions of queue lengths and number of stops.

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Hoppe, Fabian, and Ira Neitzel. "Optimal Control of Quasilinear Parabolic PDEs with State-Constraints." SIAM Journal on Control and Optimization 60, no. 1 (January 31, 2022): 330–54. http://dx.doi.org/10.1137/20m1383951.

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Clason, Christian, Kazufumi Ito, and Karl Kunisch. "A minimum effort optimal control problem for elliptic PDEs." ESAIM: Mathematical Modelling and Numerical Analysis 46, no. 4 (February 3, 2012): 911–27. http://dx.doi.org/10.1051/m2an/2011074.

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Anfinsen, Henrik, and Ole Morten Aamo. "Model reference adaptive control ofn+1coupled linear hyperbolic PDEs." Systems & Control Letters 109 (November 2017): 1–11. http://dx.doi.org/10.1016/j.sysconle.2017.08.006.

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Izadi, Mojtaba, and Stevan Dubljevic. "Backstepping output-feedback control of moving boundary parabolic PDEs." European Journal of Control 21 (January 2015): 27–35. http://dx.doi.org/10.1016/j.ejcon.2014.11.002.

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Yuan, Gonglin, and Xiangrong Li. "A Numerical Algorithm for the Coupled PDEs Control Problem." Computational Economics 53, no. 2 (October 10, 2017): 697–707. http://dx.doi.org/10.1007/s10614-017-9757-6.

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Auriol, Jean, and Florent Di Meglio. "Minimum time control of heterodirectional linear coupled hyperbolic PDEs." Automatica 71 (September 2016): 300–307. http://dx.doi.org/10.1016/j.automatica.2016.05.030.

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Weiser, Martin, and Sebastian Götschel. "State Trajectory Compression for Optimal Control with Parabolic PDEs." SIAM Journal on Scientific Computing 34, no. 1 (January 2012): A161—A184. http://dx.doi.org/10.1137/11082172x.

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Aksikas, I., A. Alizadeh Moghadam, and J. F. Forbes. "Optimal linear–quadratic control of coupled parabolic–hyperbolic PDEs." International Journal of Control 90, no. 10 (September 29, 2016): 2152–64. http://dx.doi.org/10.1080/00207179.2016.1237046.

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