Quasi species

The situation is somewhat more complex for virus sample amphfied or isolated directly from patient plasma, as these samples comprise a heterologous mix of related yet genetically distinct quasi-species. Often these samples contain mixtures of CCR5-tropic (R5), CXCR4-tropic (X4), and/or dual-tropic viruses these samples are classified in phenotypic ttopism assays as dual/mixed tropic (D/M) (Whitcomb etal. 2007). 

Like most viral RNA polymerases, NS5B does not possess 3 -5 exonuclease editing capability and is relatively error prone. This results in a mutation rate of approximately 1.4 x 10 nucleotide changes per site per year [18, 19]. Combined with the estimated production of up to 10 virions per day in an infected individual [20], HCV sequences clearly have the potential to evolve rapidly. This results in the appearance of multiple sequence variants or quasi-species in each infected individual [21]. 

A hypercycle is a more complex organisation form. Its precondition is the presence of several RNA quasi-species which are able to amalgamate chemically with certain proteins (enzymes or their precursors). If such a protein is linked to a quasi-species, the resulting duo favours the replication of a second quasispecies. According to Dyson, the linked populations get stuck in a stable equilibrium. Problems occur at this level Any theory on the origin of replication has the central problem that the replication process must occur perfectly in order to ensure survival . If there are replication errors, these will increase from generation to generation, until the system collapses the error catastrophe has then occurred ... 

The absence of mutational changes in these assays is not an indicator that the selected drug is successful, because success is a function of the entire regimen rather than of individual drugs, and because viral quasi-species often change rapidly and dramatically. 

A vaccine The search for a vaccine against the virus is intense. Unfortunately, progress is difficult since the virus frequently mutates. It is estimated that 10 to 10 variants may be present in a single infected patient and different variants may be present in patients in different parts of the world. Such a mixed population of a virus has been called a quasi species . 

These results express the fact that any linear combination of conserved densities (a generalized moment density) is itself a conserved density in thermodynamics. We have shown, therefore, that if the free energy of the system depends only on K moment densities p,... pK, we can view these as the densities of K quasi-species of particles and can construct the phase diagram via the usual construction of tangencies and the lever rule. Formally this has reduced the problem to finite dimensionality, although this is trivial... 

Here V(m ) is the probability distribution for the generalized mean size in the first phase, taken over partitions with fixed and N with equal a priori probabilities. Note that given m, irP is fixed in the second phase by the moment equivalent of particle conservation iV W1) + N mPl = Nm(° The integral in (17) can be replaced by the maximum of the integrand in the thermodynamic limit, because In V(m ) is an extensive quantity. Introducing a Lagrange multiplier pm for the above moment constraint then shows that the quantity pm has the same status as the density p = p0 itself Both are thermodynamic density variables. This reinforces the discussion in the introduction, where we showed that moment densities can be regarded as densities of quasi-species of particles. 

Eigen, M., McCaskill, J., Schuster, P. (1989). The molecular quasi-species. Adv. Chem. Phys. 75, 149-163. 

CTP), which are the building blocks for polynucleotide synthesis. The rate of RNA synthesis (lower part) is measured through incorporation of radioactive GTP into the newly produced RNA molecules. The rate of replication shows stepwise increase. An early decrease is observed, because first a quasi-species is formed by the master sequence through production of mutants of lower fitness. The figure is redrawn from the data in [12]. 

Often it is very difficult to find out whether or not an experimentally observed distribution of genotypes is stationary. The notion of virus quasi-species has been coined to characterize a distribution of variants around a fittest genotype irrespectively of its closeness to a steady state. 

Fig. 2.5. A quasi-species-type mutant distribution around a master sequence. The quasi-species is an ordered distribution of polynucleotide sequences (RNA or DNA) in sequence space. A fittest genotype or master sequence /m, which is commonly present at highest frequency, is surrounded in sequence space by a cloud of closely related sequences. Relatedness of sequences is expressed (in terms of error classes) by the number of mutations which are required to produce them as mutants of the master sequence. In case of point mutations the distance between sequences is the Hamming distance. In precise terms, the quasi-species is defined as the stable stationary solution of Eq. (2) [16,19, 20], In reality, such a stationary solution exists only if the error rate of replication lies below a maximal value called the error threshold. In this region, i.e. below...

An interesting detail of the quasi-species concept was predicted more than twelve years ago [24] and has been observed recently with virus populations [25] and computer simulations [26] We assume two genotypes of high fitness, each one surrounded by a specific mutant doud (Fig. 2.5). Genotype Iml has higher fitness compared to Im2 but less efficient mutants in the sense of a mutant cloud with lower mean fitness. The quasi-species considered as a function of the mutation rate p may show a rearrangement reminiscent of a phase transition at some critical replication accuracy qa = 1 - pCT. At low mutation rates, p>pCI, the difference in fitness values determines selection and hence, the master sequence with higher fitness, fml, dominates. Above the critical mutation rate, p>pCI, however, mutational backflow to the master is decisive and then fm2 is selected. 

HCV shows pronounced genetic variability. The cause lies in the fact that HCV mutates swiftly and continuously under immune pressure, so that several variants result (known as quasi species). The mutation rate is about 10 times higher than that of HBV. Worldwide, different virus isolates have been found and characterized in great detail. The genes for the envelope proteins El and E2 seem to be particularly variable. Up to now, 6 genotypes and 13 subtypes have been distin-... 

Appendix 6. Brillouin-Wigner Perturbation Theory of the Quasi-species. Appendix 7. Renormalization of the Perturbation Theory Appendix 8. Statistical Convergence of Perturbation Theory Appendix 9. Variables, Mean Rate Constants, and Mean Selective Values for the Relaxed Error Threshold... 

While in general these expressions are of only limited realistic value — since many mutants indeed are (nearly) degenerate—they show very clearly one fact. The surviving quasi-species for which A( = Aq is dominated by the sequence with the largest diagonal rate coefficient W . We call it the master species. It is dominant as long as the sum term of Eqn. (II.IO) is negligible, that is, > Wi i, for any k m. Since the products are usually... 

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