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SYNTHESIS OF HYDROXYPROLINE IN VITRO BY THE HYDROXYLATION OF PROLINE IN A PRECURSOR OF COLLAGEN

1965; National Academy of Sciences; Volume: 53; Issue: 3 Linguagem: Inglês

10.1073/pnas.53.3.661

1091-6490

Darwin J. Prockop, Kale Juva,

Petroleum Processing and Analysis

PROCKOP AND JUVA 661 (Pr'v(Z2) ;Z2) -H*(H* (Z2,q;Z2),p;Z2), the latter furnished with the bigrading de- fined above; both sides are isomorphic to H*(Z2,p + q;Z2) with respect to the total di- mension.This theorem is an easy consequence of the following three propositions: PROPOSITION (4.2).E2*, *(PopPq(Z2);Z2) -H*(H*(Z2,q;Z2),p;Z2).PROPOSITION (4.3).H*(H* (Z2,q;Z2),p;Z2) --H*(Z2,p + q;Z2).PROPOSITION (4.4).E2* *(prP q(Z2);Z2) ==) H*(Z2;p + q; Z2).Notice that these propositions imply that E2*, * = E3** = ... = Et*, *.The first proposition follows from the Reduction Theorem (3.1).Proposition (4.3) depends heavily on Cartan's result.It follows from the fundamental theorem and Lemma 2 (ref.1, l'expos6 10-02 and 10-04) that there is an acyclic construction with initial algebra H* (Z2,q;Z2) and terminal algebra H* (Z2,q + 1 ;Z2), and that this con- struction is equivalent (through algebra homomorphisms) (ref. 1, Th. 5, to the acyclic bar construction.Iterate both constructions p times, then take cohomology, we have Proposition (4.3).To prove Proposition (4.4), we make use of the Eilenberg-Zilber-Cartier Theorem (ref.2, p. 213).It suffices to show that the diagonal simplicial abelian group of T0VP(K(Z2,q)), D(WHP(K(Z2,q))), is an K(Z2,p + q) space.Excluding the trivial case q = 0, K(Z2,q) is always connected, and the desired result follows from the following: LEMMA (4.5).If B = {Bi } is a bisimplicial abelian group with Boo = 0, then for all t, II t (3() ) __'II t+1(D(Tf(B)))-