arXiv subjects
Publications and source records attributed to Jean-Louis Sikorav.
The concept of nearest integer is used to derive theorems and algorithms for the best approximations of an irrational by rational numbers, which are improved with the pigeonhole principle and used to offer an informed presentation of the theory of continued fractions.
It is often stated that there are no laws in biology, where everything is contingent and could have been otherwise, being solely the result of historical accidents. Furthermore, the customary introduction of fundamental biological entities such as individual organisms, cells, genes, catalysts and motors remains largely descriptive; constructive approaches involving deductive reasoning appear, in comparison, almost absent. As a consequence, both the logical content and principles of biology need to be reconsidered. The present article describes an inquiry into the foundations of biology. The foundations of biology are built in terms of elements, logic and principles, using both the language and the general methods employed in other disciplines. This approach assumes the existence of a certain unity of human knowledge that transcends discipline boundaries. Leibniz's principle of sufficient reason is revised through the introduction of the complementary concepts of symmetry and asymmetry and of necessity and contingency. This is used to explain how these four concepts are involved in the elaboration of theories or laws of nature. Four fundamental theories of biology are then identified: cell theory, Darwin's theory of natural selection, an informational theory of life (which includes Mendel's theory of inheritance) and a physico-chemical theory of life. Atomism and deductive reasoning are shown to enter into the elaboration of the concepts of natural selection, individual living organisms, cells and their reproduction, genes as well as catalysts and motors. This work contributes to clarify the philosophical and logical structure of biology and its major theories. This should ultimately lead to a better understanding of the origin of life, of system and synthetic biology, and of artificial life.
Renaturation and hybridization reactions lead to the pairing of complementary single-stranded nucleic acids. We present here a theoretical investigation of the mechanism of these reactions in vitro under thermal conditions (dilute solutions of single-stranded chains, in the presence of molar concentrations of monovalent salts and at elevated temperatures). The mechanism follows a Kramers' process, whereby the complementary chains overcome a potential barrier through Brownian motion. The barrier originates from a single rate-limiting nucleation event in which the first complementary base pairs are formed. The reaction then proceeds through a fast growth of the double helix. For the DNA of bacteriophages T7, T4 and $ϕ$X174 as well as for Escherichia coli DNA, the bimolecular rate $k_2$ of the reaction increases as a power law of the average degree of polymerization $ $ of the reacting single- strands: $k_2 \prop ^α$. This relationship holds for $100 \leq \leq 50 000$ with an experimentally determined exponent $α= 0.51 \pm 0.01$. The length dependence results from a thermodynamic excluded-volume effect. The reacting single-stranded chains are predicted to be in universal good solvent conditions, and the scaling law is determined by the relevant equilibrium monomer contact probability. The value theoretically predicted for the exponent is $α= 1-νθ_2$, where $ν$ is Flory's swelling exponent ($nu approx 0.588$) and $θ_2$ is a critical exponent introduced by des Cloizeaux ($θ_2 \approx 0.82$), yielding $α= 0.52 \pm 0.01$, in agreement with the experimental results.
DNA adsorption on solid or liquid surfaces is a topic of broad fundamental and applied interest. Here we study by x-ray reflectivity the adsorption of monodisperse double-stranded DNA molecules a positively-charged surface, obtained through chemical grafting of a homogeneous organicmonomolecular layer of N-(2-aminoethyl) dodecanamide on an oxide-free monocrystalline Si(111) wafer. The adsorbed dsDNA is found to embed into the soft monolayer which is deformed in the process. The surface coverage is very high and this adsorbed layer is expected to display 2D nematic ordering.
We study DNA adsorption and renaturation in a water-phenol two-phase system, with or without shaking. In very dilute solutions, single-stranded DNA is adsorbed at the interface in a salt-dependent manner. At high salt concentrations the adsorption is irreversible. The adsorption of the single-stranded DNA is specific to phenol and relies on stacking and hydrogen bonding. We establish the interfacial nature of a DNA renaturation at a high salt concentration. In the absence of shaking, this reaction involves an efficient surface diffusion of the single-stranded DNA chains. In the presence of a vigorous shaking, the bimolecular rate of the reaction exceeds the Smoluchowski limit for a three-dimensional diffusion-controlled reaction. DNA renaturation in these conditions is known as the Phenol Emulsion Reassociation Technique or PERT. Our results establish the interfacial nature of PERT. A comparison of this interfacial reaction with other approaches shows that PERT is the most efficient technique and reveals similarities between PERT and the renaturation performed by single-stranded nucleic acid binding proteins. Our results lead to a better understanding of the partitioning of nucleic acids in two-phase systems, and should help design improved extraction procedures for damaged nucleic acids. We present arguments in favor of a role of phenol and water-phenol interface in prebiotic chemistry. The most efficient renaturation reactions (in the presence of condensing agents or with PERT) occur in heterogeneous systems. This reveals the limitations of homogeneous approaches to the biochemistry of nucleic acids. We propose a heterogeneous approach to overcome the limitations of the homogeneous viewpoint.