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A new set of energy values to predict the secondary structures in RNA molecules has been derived through a multiple-step refinement procedure. It achieves more than 80% success in predicting the cloverleaf pattern in tRNA (200 sequences tested) and more than 60% success in predicting the consensus folding of 5S RNA (100 sequences). Improvements in our initial program for predicting secondary structures, based on the principle of the "incompatibility islets" made possible the work on 5S RNA. The program was speeded up by introducing a dynamic grouping of the islets into three disjoint blocks. The novel features in the energy model include i) an evaluation of the contribution of odd pairs according to their position within a segment ii) a penalty for internal loops related to their dissymmetry iii) a bonus for bulge loops when the two terminal paired bases at the junction point are both pyrimidines.

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A population of bacteria growing in a nonlimiting medium includes mutator bacteria and transient mutators defined as wild-type bacteria which, due to occasional transcription or translation errors, display a mutator phenotype. A semiquantitative theoretical analysis of the steady-state composition of an Escherichia coli population suggests that true strong genotypic mutators produce about 3 x 10(-3) of the single mutations arising in the population, while transient mutators produce at least 10% of the single mutations and more than 95% of the simultaneous double mutations. Numbers of mismatch repair proteins inherited by the offspring, proportions of lethal mutations and mortality rates are among the main parameters that influence the steady-state composition of the population. These results have implications for the experimental manipulation of mutation rates and the evolutionary fixation of frequent but nearly neutral mutations (e.g., synonymous codon substitutions).

An alternative method for deriving rate equations in enzyme kinetics is presented. An enzyme is followed as it moves along the various pathways allowed by the reaction scheme. The times spent in various sections of the scheme and the pathway probabilities are computed, using simple rules. (5,6): If one starts with a population of A molecules and watches their evolution, one finds (i) that for any t(Ao --Ai) = 1/(k1+ k2 + . . . + kn). [2] It is independent of the state of arrival. Note also that p = kit. The general idea in the method I shall develop is to take one enzyme and follow its fate as it progresses along the reaction scheme. The time spent on a pathway is obtained by adding (with an adequate weighting) the relaxation times. The rate is obtained by computing, for various sections of the reaction scheme, (i) the probability that a molecule of product is formed, and (ii) the time spent by the enzyme in the considered section. Times and probabilities are then concatenated over larger and larger sections.

Fast algorithms for analysing sequence data are presented. An algorithm for strict homologies finds all common subsequences of length greater than or equal to 6 in two given sequences. With it, nucleic acid pieces five thousand nucleotides long can be compared in five seconds on CDC 6600. Secondary structure algorithms generate the N most stable secondary structures of an RNA molecule, taking into account all loop contributions, and the formation of all possible base-pairs in stems, including odd pairs (G.G., C.U., etc.). They allow a typical 100-nucleotide sequence to be analysed in 10 seconds. The homology and secondary structure programs are respectively illustrated with a comparison of two phage genomes, and a discussion of Drosophila melanogaster 55 RNA folding.

Geometrical illusions are known through a small core of classical illusions that were discovered in the second half of the nineteenth century. Most experimental studies and most theoretical discussions revolve around this core of illusions, as though all other illusions were obvious variants of these. Yet, many illusions, mostly described by German authors at the same time or at the beginning of the twentieth century have been forgotten and are awaiting their rehabilitation. Recently, several new illusions were discovered, mainly by Italian authors, and they do not seem to take place into any current classification. Among the principles that are invoked to explain the illusions, there are principles relating to the metric aspects (contrast, assimilation, shrinkage, expansion, attraction of parallels) principles relating to orientations (regression to right angles, orthogonal expansion) or, more recently, to gestalt effects. Here, metric effects are discussed within a measurement framework, in which the geometric illusions are the outcome of a measurement process. There would be a main “convexity” bias in the measures: the measured value m(x) of an extant x would grow more than proportionally with x. This convexity principle, completed by a principle of compromise for conflicting measures can replace, for a large number of patterns, both the assimilation and the contrast effects. We know from evolutionary theory that the most pertinent classification criteria may not be the most salient ones (e.g., a dolphin is not a fish). In order to obtain an objective classification of illusions, I initiated with Kevin O'Regan systematic work on “orientation profiles” (describing how the strength of an illusion varies with its orientation in the plane). We showed first that the Zöllner illusion already exists at the level of single stacks, and that it does not amount to a rotation of the stacks. Later work suggested that it is best described by an “orthogonal expansion”—an expansion of the stacks applied orthogonally to the oblique segments of the stacks, generating an apparent rotation effect. We showed that the Poggendorff illusion was mainly a misangulation effect. We explained the hierarchy of the illusion magnitudes found among variants of the Poggendorff illusion by the existence of control devices that counteract the loss of parallelism or the loss of collinearity produced by the biased measurements. I then studied the trapezium illusion. The oblique sides, but not the bases, were essential to the trapezium illusion, suggesting the existence of a common component between the trapezium and the Zöllner illusion. Unexpectedly, the trapeziums sometimes appeared as twisted surfaces in 3d. It also appeared impossible, using a nulling procedure, to make all corresponding sides of two trapeziums simultaneously equal. The square-diamond illusion is usually presented with one apex of the diamond pointing toward the square. I found that when the figures were displayed more symmetrically, the illusion was significantly reduced. Fur...

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