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This paper examines a number of aspects of evaluating the reaction path Hamiltonian (RPH) of Miller, Handy, and Adams. The reaction path is represented as a Taylor series expansion of mass weighted Cartesian coordinates as a function of arc length. The second (path tangent) and third (path curvature) coefficients in the Taylor series are important in the RPH. General analytical formulas for all the coefficients as explicit functions of energy derivatives are derived. If the Taylor series is expanded about the saddle point, special limiting formulas for the coefficients are required. These are obtained using L′Hospital’s rule. In a local quadratic approximation (LQA) third and higher energy derivatives are ignored. Within this approximation all but the first two coefficients in the Taylor series expansion of the path are zero when the expansion point is the saddle point. At nonstationary points on the path the first three Taylor series coefficients are evaluated exactly within the LQA while the others have nonzero approximate values. The resulting LQA Taylor series can be summed exactly. This leads to a new method of stepping along the reaction path which is superior to the traditional Euler method and should be used whenever second energy derivatives are available. Extensions of this method which include third energy derivative information are also presented. Exact analytical formulas for the RPH coupling parameters are derived. These include simplified formulas for the projection matrix and its derivative. At nonstationary points, the couplings of the transverse vibrations to the path depend only on first and second energy derivatives and hence are exactly calculated in the LQA. The remaining RPH parameters depend on third energy derivatives as well but have nonzero approximate values in the LQA. At the saddle point, all of the RPH parameters depend on third energy derivatives and they are zero when third derivatives are ignored. In general, when the complete set of RPH parameters are calculated, the same energy derivative information is required at the saddle point as at nonstationary points, namely the gradient, the force constants, and the components of the third derivatives along the path tangent. It is demonstrated that severe errors can occur when the RPH parameters are calculated at a point near the saddle point lying on the eigenvector corresponding to the negative eigenvalue of the force constant matrix at the saddle point. These errors occur even when the exact formulas are used and are due to slight deviations of this eigenvector from the exact reaction path. A remedy is described.

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Serine peptidases play key roles in human health and disease and their biochemical properties shaped the molecular evolution of these processes. Of known proteolytic enzymes, the serine peptidase family is the major cornerstone of the vertebrate degradome. We describe the known diversity of serine peptidases with respect to structure and function. Particular emphasis is placed on the S1 peptidase family, the trypsins, which underwent the most predominant genetic expansion yielding the enzymes responsible for vital processes in man such as digestion, blood coagulation, fibrinolysis, development, fertilization, apoptosis and immunity.

Metal complexation is a key mediator or modifier of enzyme structure and function. In addition to divalent and polyvalent metals, group IA metals Na+ and K+ play important and specific roles that assist function of biological macromolecules. We examine the diversity of monovalent cation (M+)-activated enzymes by first comparing coordination in small molecules followed by a discussion of theoretical and practical aspects. Select examples of enzymes that utilize M+ as a cofactor (type I) or allosteric effector (type II) illustrate the structural basis of activation by Na+ and K+, along with unexpected connections with ion transporters. Kinetic expressions are derived for the analysis of type I and type II activation. In conclusion, we address evolutionary implications of Na+ binding in the trypsin-like proteases of vertebrate blood coagulation. From this analysis, M+ complexation has the potential to be an efficient regulator of enzyme catalysis and stability and offers novel strategies for protein engineering to improve enzyme function.

The publication of the Turnbull guidance represented a radical redefinition of the nature of internal control as a feature of corporate governance in the UK, explicitly aligning internal control with risk management. This paper explores this change, using sociological perspectives on risk and its conceptualisation to frame the debate about internal control and risk management within the UK corporate governance arena – the most recent manifestation of an ongoing competition for the control of economic and social resources. The paper demonstrates that developments in corporate governance reporting requirements offer opportunities for the appropriation of risk and its management by groups wishing to advance their own interests. This is illustrated by a review of recent changes in internal audit.

The two-coordinate cationic Ni(I) bis-N-heterocyclic carbene complex [Ni(6-Mes)2]Br (1) [6-Mes =1,3-bis(2,4,6-trimethylphenyl)-3,4,5,6-tetrahydropyrimidin-2-ylidene] has been structurally characterized and displays a highly linear geometry with a C-Ni-C angle of 179.27(13)°. Density functional theory calculations revealed that the five occupied metal-based orbitals are split in an approximate 2:1:2 pattern. Significant magnetic anisotropy results from this orbital degeneracy, leading to single-ion magnet (SIM) behavior.