The use of partial least squares (PLS) for handling collinearities among the independent variables X in multiple regression is discussed. Consecutive estimates $({\text{rank }}1,2,\cdots )$ are obtained using the residuals from previous rank as a new dependent variable y. The PLS method is equivalent to the conjugate gradient method used in Numerical Analysis for related problems.To estimate the “optimal” rank, cross validation is used. Jackknife estimates of the standard errors are thereby obtained with no extra computation.The PLS method is compared with ridge regression and principal components regression on a chemical example of modelling the relation between the measured biological activity and variables describing the chemical structure of a set of substituted phenethylamines.

The Collinearity Problem in Linear Regression. The Partial Least Squares (PLS) Approach to Generalized Inverses

To identify the role of the myocardial beta-adrenergic pathway in congestive heart failure, we examined beta-adrenergic-receptor density, adenylate cyclase and creatine kinase activities, muscle contraction in vitro, and myocardial contractile protein levels in the left ventricles of failing and normally functioning hearts from cardiac-transplant recipients or prospective donors. Eleven failing left ventricles had a 50 to 56 per cent reduction in beta-receptor density, a 45 per cent reduction in maximal isoproterenol-mediated adenylate cyclase stimulation, and a 54 to 73 per cent reduction in maximal isoproterenol-stimulated muscle contraction, as compared with six normally functioning ventricles (P less than 0.05 for each comparison). In contrast, cytoplasmic creatine kinase activity, adenylate cyclase activities stimulated by fluoride ion and by histamine, histamine-stimulated muscle contraction, and levels of contractile protein were not different in the two groups (P less than 0.05). We conclude that in failing human hearts a decrease in beta-receptor density leads to subsensitivity of the beta-adrenergic pathway and decreased beta-agonist-stimulated muscle contraction. Regulation of beta-adrenergic receptors may be an important variable in cardiac failure.

https://www.nejm.org/doi/pdf/10.1056/NEJM198207223070401?listPDF=true

Decreased catecholamine sensitivity and beta-adrenergic-receptor density in failing human hearts.

Cell membrane receptors for hormones and neurotransmitters form oligomeric complexes with GTP-regulatory proteins and inhibit the latter from reacting with GTP. Hormones and neurotransmitters act by releasing the inhibitory constraints imposed by the receptors, thus allowing the GTP-regulatory proteins to interact with and control the activity of enzymes such as adenylate cyclase. This theory may apply generally to membrane signal transduction involving surface receptors.

/pdf/the-role-of-hormone-receptors-and-gtp-regulatory-proteins-in-3mpm5095ux.pdf

The role of hormone receptors and GTP-regulatory proteins in membrane transduction

A ternary complex model explains the agonist-specific binding properties of the adenylate cyclase-coupled beta-adrenergic receptor.

Receptor-effector coupling by G proteins

Regulation of beta-adrenergic receptors by guanyl-5'-yl imidodiphosphate and other purine nucleotides.

https://www.jbc.org/content/251/22/6915.full.pdf

Identification of alpha-adrenergic receptors in uterine smooth muscle membranes by [3H]dihydroergocryptine binding.

Regulation of prostaglandin receptors by prostaglandins and guanine nucleotides in frog erythrocytes.

Magnesium dependence of agonist binding to adenylate cyclase-coupled hormone receptors.

Tolerance to catecholamines was studied using a frog erythrocyte model system in vitro. Incubation of cells with (-)-isoproterenol resulted in up to a 58% decline ( p epinephrine > norepinephrine. The beta antagonist propranolol, while having no effect of its own, blocked the desensitization caused by isoproterenol. In contrast, the alpha adrenergic antagonist phentolamine did not interfere with the phenomenon. The desensitized state was shown to be reversible. If isoproterenol was removed from desensitized cells by washing, and cells were further incubated with propranolol, receptor binding and enzyme activity returned to nearly normal levels. Incubation of cells with PGE1 produced desensitization to subsequent prostaglandin stimulation but had no effect on catecholamine sensitivity or beta receptor binding. Dibutyryl cAMP did not cause a decrease in binding or enzyme activity. It appears that catecholamines, through beta adrenergic receptor interactions, play a role in regulation of the number of functioning receptors at the cell surface. This may be a major mechanism for the induction of catecholamine tolerance.

D Mullikin

Papers

Regulation of beta-adrenergic receptors by guanyl-5'-yl imidodiphosphate and other purine nucleotides.

Identification of alpha-adrenergic receptors in uterine smooth muscle membranes by [3H]dihydroergocryptine binding.

Regulation of prostaglandin receptors by prostaglandins and guanine nucleotides in frog erythrocytes.

Magnesium dependence of agonist binding to adenylate cyclase-coupled hormone receptors.

Regulation of Adenylate Cyclase-Coupled Beta Adrenergic Receptor Binding Sites by Beta Adrenergic Catecholamines in Vitro