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1.  Exceptional error minimization in putative primordial genetic codes 
Biology Direct  2009;4:44.
Background
The standard genetic code is redundant and has a highly non-random structure. Codons for the same amino acids typically differ only by the nucleotide in the third position, whereas similar amino acids are encoded, mostly, by codon series that differ by a single base substitution in the third or the first position. As a result, the code is highly albeit not optimally robust to errors of translation, a property that has been interpreted either as a product of selection directed at the minimization of errors or as a non-adaptive by-product of evolution of the code driven by other forces.
Results
We investigated the error-minimization properties of putative primordial codes that consisted of 16 supercodons, with the third base being completely redundant, using a previously derived cost function and the error minimization percentage as the measure of a code's robustness to mistranslation. It is shown that, when the 16-supercodon table is populated with 10 putative primordial amino acids, inferred from the results of abiotic synthesis experiments and other evidence independent of the code's evolution, and with minimal assumptions used to assign the remaining supercodons, the resulting 2-letter codes are nearly optimal in terms of the error minimization level.
Conclusion
The results of the computational experiments with putative primordial genetic codes that contained only two meaningful letters in all codons and encoded 10 to 16 amino acids indicate that such codes are likely to have been nearly optimal with respect to the minimization of translation errors. This near-optimality could be the outcome of extensive early selection during the co-evolution of the code with the primordial, error-prone translation system, or a result of a unique, accidental event. Under this hypothesis, the subsequent expansion of the code resulted in a decrease of the error minimization level that became sustainable owing to the evolution of a high-fidelity translation system.
Reviewers
This article was reviewed by Paul Higgs (nominated by Arcady Mushegian), Rob Knight, and Sandor Pongor. For the complete reports, go to the Reviewers' Reports section.
doi:10.1186/1745-6150-4-44
PMCID: PMC2785773  PMID: 19925661
2.  Evolution of the genetic code: partial optimization of a random code for robustness to translation error in a rugged fitness landscape 
Biology Direct  2007;2:24.
Background
The standard genetic code table has a distinctly non-random structure, with similar amino acids often encoded by codons series that differ by a single nucleotide substitution, typically, in the third or the first position of the codon. It has been repeatedly argued that this structure of the code results from selective optimization for robustness to translation errors such that translational misreading has the minimal adverse effect. Indeed, it has been shown in several studies that the standard code is more robust than a substantial majority of random codes. However, it remains unclear how much evolution the standard code underwent, what is the level of optimization, and what is the likely starting point.
Results
We explored possible evolutionary trajectories of the genetic code within a limited domain of the vast space of possible codes. Only those codes were analyzed for robustness to translation error that possess the same block structure and the same degree of degeneracy as the standard code. This choice of a small part of the vast space of possible codes is based on the notion that the block structure of the standard code is a consequence of the structure of the complex between the cognate tRNA and the codon in mRNA where the third base of the codon plays a minimum role as a specificity determinant. Within this part of the fitness landscape, a simple evolutionary algorithm, with elementary evolutionary steps comprising swaps of four-codon or two-codon series, was employed to investigate the optimization of codes for the maximum attainable robustness. The properties of the standard code were compared to the properties of four sets of codes, namely, purely random codes, random codes that are more robust than the standard code, and two sets of codes that resulted from optimization of the first two sets. The comparison of these sets of codes with the standard code and its locally optimized version showed that, on average, optimization of random codes yielded evolutionary trajectories that converged at the same level of robustness to translation errors as the optimization path of the standard code; however, the standard code required considerably fewer steps to reach that level than an average random code. When evolution starts from random codes whose fitness is comparable to that of the standard code, they typically reach much higher level of optimization than the standard code, i.e., the standard code is much closer to its local minimum (fitness peak) than most of the random codes with similar levels of robustness. Thus, the standard genetic code appears to be a point on an evolutionary trajectory from a random point (code) about half the way to the summit of the local peak. The fitness landscape of code evolution appears to be extremely rugged, containing numerous peaks with a broad distribution of heights, and the standard code is relatively unremarkable, being located on the slope of a moderate-height peak.
Conclusion
The standard code appears to be the result of partial optimization of a random code for robustness to errors of translation. The reason the code is not fully optimized could be the trade-off between the beneficial effect of increasing robustness to translation errors and the deleterious effect of codon series reassignment that becomes increasingly severe with growing complexity of the evolving system. Thus, evolution of the code can be represented as a combination of adaptation and frozen accident.
Reviewers
This article was reviewed by David Ardell, Allan Drummond (nominated by Laura Landweber), and Rob Knight.
Open Peer Review
This article was reviewed by David Ardell, Allan Drummond (nominated by Laura Landweber), and Rob Knight.
doi:10.1186/1745-6150-2-24
PMCID: PMC2211284  PMID: 17956616
3.  Mathematical modeling of tumor therapy with oncolytic viruses: effects of parametric heterogeneity on cell dynamics 
Biology Direct  2006;1:30.
Background:
One of the mechanisms that ensure cancer robustness is tumor heterogeneity, and its effects on tumor cells dynamics have to be taken into account when studying cancer progression. There is no unifying theoretical framework in mathematical modeling of carcinogenesis that would account for parametric heterogeneity.
Results:
Here we formulate a modeling approach that naturally takes stock of inherent cancer cell heterogeneity and illustrate it with a model of interaction between a tumor and an oncolytic virus. We show that several phenomena that are absent in homogeneous models, such as cancer recurrence, tumor dormancy, and others, appear in heterogeneous setting. We also demonstrate that, within the applied modeling framework, to overcome the adverse effect of tumor cell heterogeneity on the outcome of cancer treatment, a heterogeneous population of an oncolytic virus must be used. Heterogeneity in parameters of the model, such as tumor cell susceptibility to virus infection and the ability of an oncolytic virus to infect tumor cells, can lead to complex, irregular evolution of the tumor. Thus, quasi-chaotic behavior of the tumor-virus system can be caused not only by random perturbations but also by the heterogeneity of the tumor and the virus.
Conclusion:
The modeling approach described here reveals the importance of tumor cell and virus heterogeneity for the outcome of cancer therapy. It should be straightforward to apply these techniques to mathematical modeling of other types of anticancer therapy.
Reviewers:
Leonid Hanin (nominated by Arcady Mushegian), Natalia Komarova (nominated by Orly Alter), and David Krakauer.
doi:10.1186/1745-6150-1-30
PMCID: PMC1622743  PMID: 17018145
4.  Mathematical modeling of tumor therapy with oncolytic viruses: Regimes with complete tumor elimination within the framework of deterministic models 
Biology Direct  2006;1:6.
Background
Oncolytic viruses that specifically target tumor cells are promising anti-cancer therapeutic agents. The interaction between an oncolytic virus and tumor cells is amenable to mathematical modeling using adaptations of techniques employed previously for modeling other types of virus-cell interaction.
Results
A complete parametric analysis of dynamic regimes of a conceptual model of anti-tumor virus therapy is presented. The role and limitations of mass-action kinetics are discussed. A functional response, which is a function of the ratio of uninfected to infected tumor cells, is proposed to describe the spread of the virus infection in the tumor. One of the main mathematical features of ratio-dependent models is that the origin is a complicated equilibrium point whose characteristics determine the main properties of the model. It is shown that, in a certain area of parameter values, the trajectories of the model form a family of homoclinics to the origin (so-called elliptic sector). Biologically, this means that both infected and uninfected tumor cells can be eliminated with time, and complete recovery is possible as a result of the virus therapy within the framework of deterministic models.
Conclusion
Our model, in contrast to the previously published models of oncolytic virus-tumor interaction, exhibits all possible outcomes of oncolytic virus infection, i.e., no effect on the tumor, stabilization or reduction of the tumor load, and complete elimination of the tumor. The parameter values that result in tumor elimination, which is, obviously, the desired outcome, are compatible with some of the available experimental data.
Reviewers
This article was reviewed by Mikhail Blagosklonny, David Krakauer, Erik Van Nimwegen, and Ned Wingreen.
doi:10.1186/1745-6150-1-6
PMCID: PMC1403749  PMID: 16542009

Results 1-4 (4)