Potential use of additivity of mutational effects in simplifying protein engineering.

The problem of rationally engineering protein molecules can be simplified where effects of mutations on protein function are additive. Crystal structures of single and double mutants in the hydrophobic core of gene V protein indicate that structural and functional effects of core mutations are additive when the regions structurally influenced by the mutations do not substantially overlap. These regions of influence can provide a simple basis for identifying sets of mutations that will show additive effects.

A model-based approach for assessing in vivo combination therapy interactions

We present an approach for evaluating the efficacy of combination antitumor agent schedules that accounts for order and timing of drug administration. Our model-based approach compares in vivo tumor volume data over a time course and offers a quantitative definition for additivity of drug effects, relative to which synergism and antagonism are interpreted. We begin by fitting data from individual mice receiving at most one drug to a differential equation tumor growth/drug effect model and combine individual parameter estimates to obtain population statistics. Using two null hypotheses: (i) combination therapy is consistent with additivity or (ii) combination therapy is equivalent to treating with the more effective single agent alone, we compute predicted tumor growth trajectories and their distribution for combination treated animals. We illustrate this approach by comparing entire observed and expected tumor volume trajectories for a data set in which HER-2/neu-overexpressing MCF-7 human breast cancer xenografts are treated with a humanized, anti-HER-2 monoclonal antibody (rhuMAb HER-2), doxorubicin, or one of five proposed combination therapy schedules.

Predicting the reactivity of proteins from their sequence alone: Kazal family of protein inhibitors of serine proteinases

An additivity-based sequence to reactivity algorithm for the interaction of members of the Kazal family of protein inhibitors with six selected serine proteinases is described. Ten consensus variable contact positions in the inhibitor were identified, and the 19 possible variants at each of these positions were expressed. The free energies of interaction of these variants and the wild type were measured. For an additive system, this data set allows for the calculation of all possible sequences, subject to some restrictions. The algorithm was extensively tested. It is exceptionally fast so that all possible sequences can be predicted. The strongest, the most specific possible, and the least specific inhibitors were designed, and an evolutionary problem was solved.

Trials of the beta model for complex inheritance.

Theoretical advantages of nonparametric logarithm of odds to map polygenic diseases are supported by tests of the beta model that depends on a single logistic parameter and is the only model under which paternal and maternal transmissions to sibs of specified phenotypes are independent. Although it does not precisely describe recurrence risks in monozygous twins, the beta model has greater power to detect family resemblance or linkage than the more general delta model which describes the probability of 0, 1, or 2 alleles identical by descent (ibd) with two parameters. Available data on ibd in sibs are consistent with the beta model, but not with the equally parsimonious but less powerful gamma model that assumes a fixed probability of 1/2 for 1 allele ibd. Additivity of loci on the liability scale is not disproven. A simple equivalence extends the beta model to multipoint analysis.

A general additive distance with time-reversibility and rate variation among nucleotide sites.

As additivity is a very useful property for a distance measure, a general additive distance is proposed under the stationary time-reversible (SR) model of nucleotide substitution or, more generally, under the stationary, time-reversible, and rate variable (SRV) model, which allows rate variation among nucleotide sites. A method for estimating the mean distance and the sampling variance is developed. In addition, a method is developed for estimating the variance-covariance matrix of distances, which is useful for the statistical test of phylogenies and molecular clocks. Computer simulation shows (i) if the sequences are longer than, say, 1000 bp, the SR method is preferable to simpler methods; (ii) the SR method is robust against deviations from time-reversibility; (iii) when the rate varies among sites, the SRV method is much better than the SR method because the distance is seriously underestimated by the SR method; and (iv) our method for estimating the sampling variance is accurate for sequences longer than 500 bp. Finally, a test is constructed for testing whether DNA evolution follows a general Markovian model.

Documentation of reticulate evolution in peonies (Paeonia) using internal transcribed spacer sequences of nuclear ribosomal DNA: implications for biogeography and concerted evolution.

The internal transcribed spacers (ITS) of nuclear ribosomal DNA of 33 species of genus Paeonia (Paeoniaceae) were sequenced. In section Paeonia, different patterns of nucleotide additivity were detected in 14 diploid and tetraploid species at sites that are variable in the other 12 species of the section, suggesting that reticulate evolution has occurred. Phylogenetic relationships of species that do not show additivity, and thus ostensibly were not derived through hybridization, were reconstructed by parsimony analysis. The taxa presumably derived through reticulate evolution were then added to the phylogenetic tree according to additivity from putative parents. The study provides an example of successfully using ITS sequences to reconstruct reticulate evolution in plants and further demonstrates that the sequence data could be highly informative and accurate for detecting hybridization. Maintenance of parental sequences in the species of hybrid origin is likely due to slowing of concerted evolution caused by the long generation time of peonies. The partial and uneven homogenization of parental sequences displayed in nine species of putative hybrid origin may have resulted from gradients of gene conversion. The documented hybridizations may have occurred since the Pleistocene glaciations. The species of hybrid origin and their putative parents are now distantly allopatric. Reconstruction of reticulate evolution with sequence data, therefore, provides gene records for distributional histories of some of the parental species.