Clas Blomberg

Association kinetics with coupled diffusional flows: Special application to the lac repressor-operator system

The time development of the association of the lac repressor to the operator is considered in a model where the repressor is allowed to bind unspecifically to DNA and move along the DNA chain in a one-dimensional diffusion. The coupling to the three-dimensional diffusion outside the chain is introduced by letting the repressor associate and dissociate from the chain until it is finally bound to the operator. All distance correlations along the chain are included. The mean time of association is calculated and through a comparison with experimental data the molecular parameters are determined. The one-dimensional diffusion constant is found to be of the order of 10(-9) cm(2)s(-1). The model is sufficiently general to be applicable to other similar systems.

Association kinetics with coupled diffusion III. Ionic-strength dependence of the lac repressor-operator association.

The repressor-operator association is treated in a model where the repressor molecule can find its specific binding site, the operator, on a large DNA chain by performing a one-dimensional diffusion along the chain. The ionic-strength dependence is calculated by introducing a screened electrostatic potential around the DNA chain and coupling the free diffusion of the repressor in this potential to the proposed one-dimensional diffusion along the chain. The main influence on the association rate comes from the competitive binding of ions to the unspecific DNA sites. It is also demonstrated that during the time that the repressor is bound in a global sense, the diffusion along the chain will be made up of a strictly one-dimensional motion over fairly short distances, interspersed with many local dissociations during which the repressor in essence is free in solution.

Decay of angular correlation functions by multiple rotational potential diffusion in polymer chains, with applications to NMR relaxation in paraffin chains of lipid bilayers

Abstract Spectroscopic techniques as NMR give information about correlation functions of the motion. For polymer chains, this motion is the result of internal rotations about several bonds. These rotations are supposed to be independent of each other and are described by one-dimensional rotational diffusion in a suitable potential. The general case is described and calculations are made for a trigonometric potential with three minima. The free rotational diffusion and the trans-gauche model are limiting cases of this model. The correlation functions decay on two time scales, for short times due to motion within the wells of the potential, which however not causes a decay to zero. On a longer time scale the functions decay further to zero by passage over the potential barriers. The model is applied to NMR-relaxation in hydro-carbon chains of lipid bilayers, where it gives another dependence upon chain position than previous models.

Cluster compartmentalization may provide resistance to parasites for catalytic networks

Abstract We have performed calculations on reaction-diffusion equations with an aim to study two-dimensional spatial patterns. The systems explicitly studied are three different catalytic networks: a 4-component network displaying chaotic dynamics, a 5-component hypercycle network and a simple 1-component system. We have obtained cluster states for all these networks, and in all cases the clusters have the ability to divide. This contradicts recent conclusions that only systems with chaotic dynamics may give cluster states. On the contrary, we think that any network architecture may display cluster formation and cluster division. Our conclusion is in agreement with experimental results reported for an inorganic system corresponding to the simple 1-component system studied in this paper. In a partial differential equations model, the clusters do not provide resistance to parasites, which are assumed to arise by mutations. Parasites may spread from one cluster to another, and eventually kill all clusters. However, by combinding the partial differential equations with a suitable cut-off rule, we demonstrate a system of partly isolated clusters that is resistant against parasites. The parasites do not infect all clusters, and when the infected clusters have decayed, they are replaced by new ones, as neighbouring clusters divide.

Stretched exponentials and barrier distributions

Abstract Non exponential relaxation in complex macromolecular systems may be the consequence of dispersedness giving rise to different free energy barriers for different molecules. An approximate analytic formula that relates the time derivative of the decaying function to a probability distribution for the barrier is derived. From this, so called stretched exponentials, e − t β , are obtained from barrier distributions with width k B T / β in energy and some asymmetry towards low energies. They may be represented as double exponential functions. An exact general formula that relates the Fourier transforms of the barrier height distribution and the time decaying function is also derived. This is gives a much more stable method for the numerical determination of the barrier height distribution than direct inversion of the Laplace transform.

The β structure: Inter-strand correlations

Abstract β structures in 19 proteins have been analysed for pairwise residue-residue correlations. The results show that hydrophobic residues tend to go together mainly as inter-strand nearest-neighbours, a non-local sequence correlation. This suggests that hydrophobic residues in different parts of the protein molecule might “recognize” each other when a β sheet is formed.

Brownian motion description of activation energies from NMR-relaxation times for rotating molecular-groups

Abstract A general formula is derived (containing eigenvalues and eigenfunctions of some diffusion equation) for activation energies from NMR-relaxation times for rotating molecular groups. Numerical calculations for a trigonometric three well potential in the strong damping (Smoluchowski) limit show that there may be a considerable difference between activation energy and barrier height. In the low damping limit there is fairly good agreement.

A kinetic recognition process for tRNA at the ribosome.

Abstract In order to explain the great accuracy when amino acids are selected in protein synthesis, some authors have proposed a kinetic recognition process driven out of thermodynamic equilibrium. In this work, such a process for the recognition of the tRNA anticodon at the ribosome is considered. An important feature is that the discrimination possibility is determined not only by the differences of codon-anticodon binding energy (the only specific quantity) but also by the total binding energy including non specific bonds of other tRNA groups to the ribosome. In the context of this, the effects of streptomycin, and related features of mutant ribosome proteins or tRNAs which decrease or increase the selection accuracy can be interpreted by the kinetic model.

Mass action relations in vivo with application to the Lac operon

Abstract The traditional form of the law of mass action is valid for an unbounded system. In vivo there will be instead a collection of closed systems, cells, with no exchange of molecules between them. The appropriate binding relations for this situation are derived, and compared to the traditional ones and it is shown that for relatively small numbers of tight binding molecules the difference will be substantial. As a specific example the lac repressor-operator binding and the functioning of the lac operon is considered.

Translation and messenger RNA secondary structure

Abstract The possibility of translation being influenced by the messenger RNA secondary structure is investigated with the aid of a stochastic model. Simulations indicate that, at least for certain mRNAs, the mean ribosomal passage time decreases as the mean number of ribosomes on the messenger is increased. Furthermore, large variations in the passage times are found, in accordance with recent experimental results.