The influence of the flow of the reacting gas on the conditions for a thermal explosion

The classical problem of thermal explosion is modified so that the chemically active gas is not at rest but is flowing in a long cylindrical pipe. Up to a certain section the heat-conducting walls of the pipe are held at low temperature so that the reaction rate is small and there is no heat release; at that section the ambient temperature is increased and an exothermic reaction begins. The question is whether a slow reaction regime will be established or a thermal explosion will occur. The mathematical formulation of the problem is presented. It is shown that when the pipe radius is larger than a critical value, the solution of the new problem exists only up to a certain distance along the axis. The critical radius is determined by conditions in a problem with a uniform axial temperature. The loss of existence is interpreted as a thermal explosion; the critical distance is the safe reactor’s length. Both laminar and developed turbulent flow regimes are considered. In a computational experiment the loss of the existence appears as a divergence of a numerical procedure; numerical calculations reveal asymptotic scaling laws with simple powers for the critical distance.

Unbinding forces of single antibody-antigen complexes correlate with their thermal dissociation rates

Point mutants of three unrelated antifluorescein antibodies were constructed to obtain nine different single-chain Fv fragments, whose on-rates, off-rates, and equilibrium binding affinities were determined in solution. Additionally, activation energies for unbinding were estimated from the temperature dependence of the off-rate in solution. Loading rate-dependent unbinding forces were determined for single molecules by atomic force microscopy, which extrapolated at zero force to a value close to the off-rate measured in solution, without any indication for multiple transition states. The measured unbinding forces of all nine mutants correlated well with the off-rate in solution, but not with the temperature dependence of the reaction, indicating that the same transition state must be crossed in spontaneous and forced unbinding and that the unbinding path under load cannot be too different from the one at zero force. The distance of the transition state from the ground state along the unbinding pathway is directly proportional to the barrier height, regardless of the details of the binding site, which most likely reflects the elasticity of the protein in the unbinding process. Atomic force microscopy thus can be a valuable tool for the characterization of solution properties of protein-ligand systems at the single molecule level, predicting relative off-rates, potentially of great value for combinatorial chemistry and biology.

Involvement of a cytosine side chain in proton transfer in the rate-determining step of ribozyme self-cleavage

Ribozymes of hepatitis delta virus have been proposed to use an active-site cytosine as an acid-base catalyst in the self-cleavage reaction. In this study, we have examined the role of cytosine in more detail with the antigenomic ribozyme. Evidence that proton transfer in the rate-determining step involved cytosine 76 (C76) was obtained from examining cleavage activity of the wild-type and imidazole buffer-rescued C76-deleted (C76Δ) ribozymes in D2O and H2O. In both reactions, a similar kinetic isotope effect and shift in the apparent pKa indicate that the buffer is functionally substituting for the side chain in proton transfer. Proton inventory of the wild-type reaction supported a mechanism of a single proton transfer at the transition state. This proton transfer step was further characterized by exogenous base rescue of a C76Δ mutant with cytosine and imidazole analogues. For the imidazole analogues that rescued activity, the apparent pKa of the rescue reaction, measured under kcat/KM conditions, correlated with the pKa of the base. From these data a Brønsted coefficient (β) of 0.51 was determined for the base-rescued reaction of C76Δ. This value is consistent with that expected for proton transfer in the transition state. Together, these data provide strong support for a mechanism where an RNA side chain participates directly in general acid or general base catalysis of the wild-type ribozyme to facilitate RNA cleavage.