Gossips, Untruths And Then CB-5083
Consider a cell with a total number of ribosomes Rt and n genes each with Ai mRNA copies. Assuming no ribosomal interference during translation, the expected number of ribosomes bound to each mRNA can be approximated by solving the differential equation equation(2) dRibdt=��i?Rib?iwhere ��i and ?i are the rates of initiation and total elongation of the ith mRNA, respectively. At steady-state the total number of bound ribosomes is then given by equation(3) Rb=��i=1nAi��i?iThe rates of translation FXR initiation and total elongation in turn depend on the amounts of free ribosomes Rf and free tRNAs Tf, in addition to the characteristic times of these molecules. We assume that translation termination is instantaneous and does not contribute to the overall rate of translation. Thus the initiation rate on an mRNA can be given as equation(4) ��i=Rfpi��rNrwhere pi is the probability of initiation given that the ribosome has reached the mRNA. pi is sequence-specific and accounts for the A-1155463 in vitro variation in initiation rates of various mRNAs. Similarly, when a ribosome is bound to the mRNA, the time taken to elongate codon j ? depends on the number of the free cognate tRNAs T?(j)f, the wobble parameter wj, and the tRNA competition coefficient s: equation(5) cj=��tNtT?(j)fwjs.Thus at equilibrium, assuming no ribosomal collisions/interference, the expected total elongation rate of a ribosome on an mRNA?is equation(6) ?i=1��j=1kxjcjwhere xj is the number of CB-5083 order codons of type j, and k denotes the total types of codons (typically k?= 61). Consider a simple case of one gene of length L ? codons composed of a single amino acid with two types of codons, each translated by a single tRNA type (T ?1 or T ?2). Let the expression level of the gene be A ?, relative frequency of codon 1 be u ?, and the total number of ribosomes in the cell R ?t. Based on Equation (6), the total elongation rate of that gene is given by equation(7) ?=1L(uc1+(1?u)c2)where c ?1 and c ?2 are given by Equation (5) equation(8) c1=��tNtT1fw1s equation(9) c2=��tNtT2fw2sNote that whenever a ribosome is bound to an mRNA waiting for a tRNA corresponding to the codon at its A ?-site, a tRNA is bound at its P ?-site attached to the growing polypeptide chain. Assuming that the codons in the gene are randomly distributed, the frequency of tRNA types at ribosomal P ?-sites are independent of the waiting time for codons in the A ?-sites. In addition, the total number of bound ribosomes should equal the number of bound tRNAs of all types Rb=T1b+T2b. As a result, the number of bound tRNAs of each type is simply proportional to its codon usage. equation(10) T1b=Rbu equation(11) T2b=Rb(1?u)Note that the above relationship works if the number of bound ribosomes R ?b is less than the ratio of total tRNAs of either type to their codon usage: (Rb
