PtH

Here, (ATp) is the pth component of the electronic transition moment from state a to b,. and E j-are the energy... 

The Pth sub-Hilbert space is defined through the following two requirements ... 

All Np states belonging to the Pth sub-space interact strongly with each other in the sense that each pair of consecutive states have at least one point where they form a Landau-Zener type interaction. In other words, all j = I,... At/> — I form at least at one point in configuration space, a conical (parabolical) intersection. 

Figure 2. A schematic picture describing the three consecutive sub-Hilbert spaces, namely, the (P — l)th, the Pth, and the (P + l)th. The dotted lines are separation lines.

Step 3 Once formed the thiazolone derivative isomerizes to a more stable phenylthiohydantom (PTH) derivative which IS isolated and characterized thereby providing identification of the N terminal ammo acid The remainder of the peptide (formed m step 2) can be isolated and subjected to a second Edman degradation... 

Only the N terminal amide bond is broken m the Edman degradation the rest of the peptide chain remains intact It can be isolated and subjected to a second Edman procedure to determine its new N terminus We can proceed along a peptide chain by beginning with the N terminus and determining each ammo acid m order The sequence is given directly by the structure of the PTH derivative formed m each successive degradation... 

Edman degradation (Section 27 13) Method for determining the N terminal amino acid of a peptide or protein It in volves treating the material with phenyl isothiocyanate (CgH5N=C=S) cleaving with acid and then identifying the phenylthiohydantoin (PTH derivative) produced Elastomer (Section 10 11) A synthetic polymer that possesses elasticity... 

Fig. 2. Homeostatic control of blood Ca " level where PTH is parathyroid hormone [9002-64-6], CC, cholecalciferol, ie, vitamin D HCC, hydroxycholecalciferol DHCC, dihydroxycholecalciferol CaBP, calcium-binding protein NAD PH, protonated nicotinarnide-adenine dinucleotide...

Factors controlling calcium homeostasis are calcitonin, parathyroid hormone(PTH), and a vitamin D metabolite. Calcitonin, a polypeptide of 32 amino acid residues, mol wt - SGOO, is synthesized by the thyroid gland. Release is stimulated by small increases in blood Ca " concentration. The sites of action of calcitonin are the bones and kidneys. Calcitonin increases bone calcification, thereby inhibiting resorption. In the kidney, it inhibits Ca " reabsorption and increases Ca " excretion in urine. Calcitonin operates via a cyclic adenosine monophosphate (cAMP) mechanism. 

Parathyroid hormone, a polypeptide of 83 amino acid residues, mol wt 9500, is produced by the parathyroid glands. Release of PTH is activated by a decrease of blood Ca " to below normal levels. PTH increases blood Ca " concentration by increasing resorption of bone, renal reabsorption of calcium, and absorption of calcium from the intestine. A cAMP mechanism is also involved in the action of PTH. Parathyroid hormone induces formation of 1-hydroxylase in the kidney, requited in formation of the active metabolite of vitamin D (see Vitamins, vitamin d). 

Metabolites of vitamin D, eg, cholecalciferol (CC), are essential in maintaining the appropriate blood level of Ca ". The active metabolite, 1,25-dihydroxycholecalciferol (1,25-DHCC), is synthesized in two steps. In the fiver, CC is hydroxylated to 25-hydroxycholecalciferol (25-HCC) which, in combination with a globulin carrier, is transported to the kidney where it is converted to 1,25-DHCC. This step, which requites 1-hydroxylase formation, induced by PTH, may be the controlling step in regulating Ca " concentration. The sites of action of 1,25-DHCC are the bones and the intestine. Formation of 1,25-DHCC is limited by an inactivation process, ie, conversion of 25-HCC to 24,25-DHCC, catalyzed by 24-hydroxylase. 

Hydroxy vitamin D pools ia the blood and is transported on DBF to the kidney, where further hydroxylation takes place at C-1 or C-24 ia response to calcium levels. l-Hydroxylation occurs primarily ia the kidney mitochondria and is cataly2ed by a mixed-function monooxygenase with a specific cytochrome P-450 (52,179,180). 1 a- and 24-Hydroxylation of 25-hydroxycholecalciferol has also been shown to take place ia the placenta of pregnant mammals and ia bone cells, as well as ia the epidermis. Low phosphate levels also stimulate 1,25-dihydtoxycholecalciferol production, which ia turn stimulates intestinal calcium as well as phosphoms absorption. It also mobilizes these minerals from bone and decreases their kidney excretion. Together with PTH, calcitriol also stimulates renal reabsorption of the calcium and phosphoms by the proximal tubules (51,141,181—183). 

DHD = 24(R),25-dihydroxyvitamiQD2 250H = 25-hydroxyvitamia D PTH = parathyroid hormone CT = calcitonin F. = inorganic phosphoms. 

The overall effect in most animals is to stimulate intestinal absorption of calcium with a concomitant increase in semm calcium and a reduction in parathyroid hormone (PTH). Modest hypercalcemia allows the glomerular filtration rate to remain stable and hypercalciuria to occur because of increased filtered load of calcium and reduction of tubular resorption of calcium with reduced PTH. However, with further increases in semm calcium, the glomerular filtration rate decreases, resulting in an even more rapid increase in semm calcium and the subsequent fall in urinary calcium. 

Three hormones regulate turnover of calcium in the body (22). 1,25-Dihydroxycholecalciferol is a steroid derivative made by the combined action of the skin, Hver, and kidneys, or furnished by dietary factors with vitamin D activity. The apparent action of this compound is to promote the transcription of genes for proteins that faciUtate transport of calcium and phosphate ions through the plasma membrane. Parathormone (PTH) is a polypeptide hormone secreted by the parathyroid gland, in response to a fall in extracellular Ca(Il). It acts on bones and kidneys in concert with 1,25-dihydroxycholecalciferol to stimulate resorption of bone and reabsorption of calcium from the glomerular filtrate. Calcitonin, the third hormone, is a polypeptide secreted by the thyroid gland in response to a rise in blood Ca(Il) concentration. Its production leads to an increase in bone deposition, increased loss of calcium and phosphate in the urine, and inhibition of the synthesis of 1,25-dihydroxycholecalciferol. 

Richardson extrapolation can be used to improve the accuracy of a method. Suppose we step forward one step At with a pth-order method. Then redo the problem, this time stepping foi ward from the same initial point, but in two steps of length Af/2, thus ending at the same point. Call the solution of the one-step calculation y and the solution of the two-step calculation yo. Then an improved solution at the new time is given by... 

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