We show that self-replication of a chemical system encapsulated within a membrane growing from within is possible without any explicit feature such as autocatalysis or metabolic closure, and without the need for their emergence through complexity. We use a protocell model relying upon random conservative chemical reaction networks with arbitrary stoichiometry, and we investigate the protocell's capability for self-replication, for various numbers of reactions in the network. We elucidate the underlying mechanisms in terms of simple minimal conditions pertaining only to the topology of the embedded chemical reaction network. A necessary condition is that each moiety must be fed, and a sufficient condition is that each siphon is fed. Although these minimal conditions are purely topological, by further endowing conservative chemical reaction networks with thermodynamically consistent kinetics, we show that the growth rate tends to increase on increasing the Gibbs energy per unit molecular weight of the nutrient and on decreasing that of the membrane precursor.

MOTIVATION: A k-point mutant of a given RNA sequence s = s(1), ..., s(n) is an RNA sequence s' = s'(1),..., s'(n) obtained by mutating exactly k-positions in s; i.e. Hamming distance between s and s' equals k. To understand the effect of pointwise mutation in RNA, we consider the distribution of energies of all secondary structures of k-point mutants of a given RNA sequence. RESULTS: Here we describe a novel algorithm to compute the mean and standard deviation of energies of all secondary structures of k-point mutants of a given RNA sequence. We then focus on the tail of the energy distribution and compute, using the algorithm AMSAG, the k-superoptimal structure; i.e. the secondary structure of a < or =k-point mutant having least free energy over all secondary structures of all k'-point mutants of a given RNA sequence, for k' < or = k. Evidence is presented that the k-superoptimal secondary structure is often closer, as measured by base pair distance and two additional distance measures, to the secondary structure derived by comparative sequence analysis than that derived by the Zuker minimum free energy structure of the original (wild type or unmutated) RNA.

We study a restricted programming language over tree structures. For this language, we give systematic translation rules which map programs into complexity descriptors. The descriptors are in the form of generating functions of average costs. Such a direct approach avoids the recourse to recurrences; it therefore simplifies the task of analyzing algorithms in the class considered and permits analysis of structurally complex programs. It also allows for a clear discussion of analytic properties of complexity descriptors whose singularities are related to the asymptotic behavior of average costs. Algorithms that are analyzed in this way include: formal differentiation, tree matching, tree embedding and simplification of expressions in a diversity of contexts. Some general results relating (average case) complexity properties to structural properties of programs in the class can also be derived in this framework.