The SH2 domain regulates c-Abl kinase activation by a cyclin-like mechanism and remodulation of the hinge motion.

Regulation of the c-Abl (ABL1) tyrosine kinase is important because of its role in cellular signaling, and its relevance in the leukemiogenic counterpart (BCR-ABL). Both auto-inhibition and full activation of c-Abl are regulated by the interaction of the catalytic domain with the Src Homology 2 (SH2) domain. The mechanism by which this interaction enhances catalysis is not known. We combined computational simulations with mutagenesis and functional analysis to find that the SH2 domain conveys both local and global effects on the dynamics of the catalytic domain. Locally, it regulates the flexibility of the αC helix in a fashion reminiscent of cyclins in cyclin-dependent kinases, reorienting catalytically important motifs. At a more global level, SH2 binding redirects the hinge motion of the N and C lobes and changes the conformational equilibrium of the activation loop. The complex network of subtle structural shifts that link the SH2 domain with the activation loop and the active site may be partially conserved with other SH2-domain containing kinases and therefore offer additional parameters for the design of conformation-specific inhibitors.

Non-self-consistent Density-Functional Theory Exchange-Correlation Forces for GGA Functionals.

When using density functional theory (DFT), generalized gradient approximation (GGA) functionals are often necessary for accurate modeling of important properties of biomolecules, including hydrogen-bond strengths and relative energies of conformers. We consider the calculations of forces using non-self-consistent (NSC) methods based on the Harris-Foulkes expression for energy. We derive an expression for the GGA NSC force on atoms, valid for a hierarchy of methods based on local orbitals, and discuss its implementation in the linear scaling DFT code Conquest, using a standard (White-Bird) approach. We investigate the use of NSC structural relaxations before full self-consistent relaxations as a method for improving convergence. Example calculations for glycine and small alanine peptides suggest that NSC pre-relaxations of the structure are indeed useful to save computer effort and time.

Susceptibilities of an irreversible Michaelis-Menten enzyme.

The nonlinear response of the simplest irreversible Michaelis-Menten enzyme is considered. In the context of metabolic networks, i.e. in vivo, the enzyme is subject to sustained, frequently time-dependent, input fluxes that keep the system out of equilibrium. The connection between the fluxes and the response is investigated by means of a new sensitivity analysis. The kinetics of the enzyme is simple enough to allow for the computations to be carried out analytically. In particular, a set of sensitivities of the response with respect to the substrate influx, the susceptibilities, is derived. The susceptibilities are multivariate functions and thus are suitable for predicting complete progress curves of several variables of biochemical interest, namely, rates and concentrations. This is shown by means of an example. The relationship between the susceptibilities and the stoichiometry of the reaction is also taken into account. Moreover, all the required information comes from decay experiments of initial concentrations, which are common in enzymological setups.

Susceptibility of non-linear systems as an approach to metabolic responses.

MOTIVATION: Recent developments of several analytical techniques and fast sampling procedures are making it possible to study non-linear dynamics on an automated basis. Approaches that suggest experimental setups and fully exploit the data are needed. To prevent unreliable fits of parameters to experimental data, model-independent methods would be advantageous. One such method consists in representing the response of a system by means of a transformation or functional, of an excitation, i.e. a flux of a metabolite. RESULTS: A functional of unknown form can be expanded in series if its functional derivatives are known. An algorithm for calculating such generalized derivatives from impulse-perturbation experiments was developed. The only assumption was that the implicit kinetics is time-independent, i.e. the system is time-invariant. The method is illustrated on a part of fructose catabolism. A reaction network that involves 14 metabolites and 11 enzymes and includes several branches and feedback loops is considered. It is shown that the method provides good approximations to the responses of this complex system. AVAILABILITY: FUNDER is available from http://bbm1.ucm.es/torralba/funder/down/ SUPPLEMENTARY INFORMATION: http://bbm1.ucm.es/torralba/funder/

Phenomenological definition of response times with application to metabolic reactions.

The metabolic response time, i.e. the delay the system introduces in the response to an input flux, is considered. A novel phenomenological definition is presented, which is valid for any kind of behavior, including transitory or permanent oscillatory responses. In order to calculate the response time of single-input systems, output fluxes have to be deconvoluted with the input flux. The bases for this are established. The resulting function (unit impulse response in time-invariant linear systems) is transformed by subtracting its final state, taking the absolute value and normalizing by the resulting area, so that a norm can be applied that weights the response at every time. This response time can also be interpreted as an average. It coincides with the transition (characteristic) time of an output flux, provided that the input is performed instantaneously (step function). A strictly non-negative response function is needed for the response time to be interpreted as a mass balance. A simple example is used to study the deviation otherwise. The method is advantageous in that it provides clues on the phenomenological behavior of biochemical systems. For example, deconvolution reveals the intrinsic oscillation-generating mechanism of an allosteric enzyme, which becomes hidden when the input flux increases in a slow way. This is illustrated by means of a model.

Equivalence of branched and unbranched Michaelian pathways concerning periodic signal transmission.

Sinusoidal oscillation transmission through branched metabolic pathways is studied. Two systems are analyzed, which are composed of two convergent reaction branches and differ in the length of one of them. Linear kinetics is assumed first. Michaelis-Menten enzymes are then considered by using previous results that suggest their behavior with respect to propagation of oscillations is close to linearity around the mean input flux. As a result, there exist ways to modulate the activity of the enzymes so that propagation is equivalent for branched and specific unbranched pathways. Cells may have taken advantage of such a possibility in cases where oscillations have a biological role.

Experimental test of a method for determining causal connectivities of species in reactions.

Theoretical analysis has shown the possibility of determining causal connectivities of reacting species and the reaction mechanism in complex chemical and biochemical reaction systems by applying pulse changes of concentrations of one or more species, of arbitrary magnitude, and measuring the temporal response of as many species as possible. This method, limited to measured and pulsed species, is given here an experimental test on a part of glycolysis including the sequence of reactions from glucose to fructose 1,6-biphosphate, followed by the bifurcation of that sequence into two branches, one ending in glycerol 3-phosphate, the other in glyceraldehyde 3-phosphate. Pulses of concentrations of one species at a time are applied to the open system in a non-equilibrium stationary state, and the temporal responses in concentrations of six metabolites are measured by capillary zone electrophoresis. From the results of these measurements and the use of the theory for their interpretation, we establish the causal connectivities of the metabolites and thus the reaction mechanism, including the bifurcation of one chain of reactions into two. In this test case of the pulse method, no prior knowledge was assumed of the biochemistry of this system. We conclude that the pulse method is relatively simple and effective in determining reaction mechanisms in complex systems, including reactants, products, intermediates, and catalysts and their effectors. The method is likely to be useful for substantially more complex systems.