A Well-Balanced Preexisting Equilibrium Governs Electron Flux Efficiency of a Multidomain Diflavin Reductase

Diflavin reductases are bidomain electron transfer proteins in which structural reorientation is necessary to account for the various intramolecular and intermolecular electron transfer steps. Using small-angle x-ray scattering and nuclear magnetic resonance data, we describe the conformational free-energy landscape of the NADPH-cytochrome P450 reductase (CPR), a typical bidomain redox enzyme composed of two covalently-bound flavin domains, under various experimental conditions. The CPR enzyme exists in a salt- and pH-dependent rapid equilibrium between a previously described rigid, locked state and a newly characterized, highly flexible, unlocked state. We further establish that maximal electron flux through CPR is conditioned by adjustable stability of the locked-state domain interface under resting conditions. This is rationalized by a kinetic scheme coupling rapid conformational sampling and slow chemical reaction rates. Regulated domain interface stability associated with fast stochastic domain contacts during the catalytic cycle thus provides, to our knowledge, a new paradigm for improving our understanding of multidomain enzyme function.     

Recurrent deformities following reduction mammaplasty and correction of breast asymmetry

In order to properly evaluate results after reduction mammaplasty and correction of breast asymmetry, it is necessary to follow patients for several years. Cases are presented in which unusual deformities occurred after an initial satisfactory result. Pregnancy, aging, and fluctuations in weight contributed to these deformities. A case of recurrent hypertrophy 4 years following a reduction mammaplasty is presented. Several cases of asymmetry corrected by a combination of reduction and augmentation had early satisfactory results but several years later again showed asymmetry due to recurrent ptosis or atrophy. In one case, a 10-year follow-up showed considerable deformity after an initial good result following asymmetrical augmentation. It is important to point out to patients that changes do occur and that occasionally additional surgery is necessary.     

Fluxes,first passage times,and the reduction of Hill diagrams

The steady-state flux resulting from the coupling of two multistate systems is considered. The dynamics of these systems are described (a) as diffusion along a continuous one-dimensional free-energy profile specified by a conformational coordinate or (b) in terms of transitions between a discrete but arbitrary number of substates. If these multistate systems are connected in a simple way, it is shown that the steady-state flux can be obtained analytically. For both the continuous and discrete cases, the exact flux is shown to be identical to that calculated from a simple kinetic scheme involving only four states, if the effective rate constants of this reduced scheme are appropriately defined in terms of the mean first passage times for moving between various points along the multistate cycles. These results clarify and quantify the manner in which the internal conformational dynamics of two multistate systems influences the steady-state flux.     

Functional Roles of Slow Enzyme Conformational Changes in Network Dynamics

Extensive studies from different fields reveal that many macromolecules, especially enzymes, show slow transitions among different conformations. This phenomenon is named such things as dynamic disorder, heterogeneity, hysteretic or mnemonic enzymes across these different fields, and has been directly demonstrated by single molecule enzymology and NMR studies recently. We analyzed enzyme slow conformational changes in the context of regulatory networks. A single enzymatic reaction with slow conformational changes can filter upstream network noises, and can either resonantly respond to the system stimulus at certain frequencies or respond adaptively for sustained input signals of the network fluctuations. It thus can serve as a basic functional motif with properties that are normally for larger intermolecular networks in the field of systems biology. We further analyzed examples including enzymes functioning against pH fluctuations, metabolic state change of Artemia embryos, and kinetic insulation of fluctuations in metabolic networks. The study also suggests that hysteretic enzymes may be building blocks of synthetic networks with various properties such as narrow-banded filtering. The work fills the missing gap between studies on enzyme biophysics and network level dynamics, and reveals that the coupling between the two is functionally important; it also suggests that the conformational dynamics of some enzymes may be evolutionally selected.     

Biological processes in organised media

Embedding a simple Michaelis-Menten enzyme in a gel slice may allow the catalysis of not only scalar processes but also vectorial ones, including uphill transport of a substrate between two compartments, and may make it seem as if two enzymes or transporters are present or as if an allosterically controlled enzyme/transporter is operating. The values of kinetic parameters of an enzyme in a partially hydrophobic environment are usually different from those actually measured in a homogeneous aqueous solution. This implies that fitting kinetic data (expressed in reciprocal co-ordinates) from in vivo studies of enzymes or transporters to two straight lines or a sigmoidal curve does not prove the existence of two different membrane mechanisms or allosteric control. In the artificial transport systems described here, a functional asymmetry was sufficient to induce uphill transport, therefore, although the active transport systems characterised so far correspond to proteins asymmetrically anchored in a membrane, the past or present existence of structurally symmetrical systems of transport in vivo cannot be excluded. The fact that oscillations can be induced in studies of the maintenance of the electrical potential of frog skin by addition of lithium allowed evaluation of several parameters fundamental to the functioning of the system in vivo (e.g., relative volumes of internal compartments, characteristic times of ionic exchanges between compartments). Hence, under conditions that approach real biological complexity, increasing the complexity of the behaviour of the system may provide information that cannot be obtained by a conventional, reductionist approach.     

Theoretical analysis of compartmented coupling in linear enzyme systems

Exact equations which describe the kinetic patterns of enzyme/enzyme complexes, when compartmented coupling occurs between them, are presented. Compartmented coupling refers to the creation of a local environment in which the concentration of an intermediate, shared by two enzymes, is higher than its solution concentration. This results in a higher coupling enzyme activity, a condition reflected in a shorter transition time for the system. In this paper, equations are presented which allow experimenters to quantitate the effect of compartmented coupling in terms of changes in the apparent Km and Vmax values. The equations presented in this paper are more exact than those previously derived since they do not incorporate first order assumptions before derivation.     

Response to temporal parameter fluctuations in biochemical networks

Metabolic response coefficients describe how variables in metabolic systems, like steady state concentrations, respond to small changes of kinetic parameters. To extend this concept to temporal parameter fluctuations, we define spectral response coefficients that relate Fourier components of concentrations and fluxes to Fourier components of the underlying parameters. It is also straightforward to generalize other concepts from metabolic control theory, such as control coefficients with their summation and connectivity theorems. The first-order response coefficients describe forced oscillations caused by small harmonic oscillations of single parameters: they depend on the driving frequency and comprise the phases and amplitudes of the concentrations and fluxes. Close to a Hopf bifurcation, resonance can occur: as an example, we study the spectral densities of concentration fluctuations arising from the stochastic nature of chemical reactions. Second-order response coefficients describe how perturbations of different frequencies interact by mode coupling, yielding higher harmonics in the metabolic response. The temporal response to small parameter fluctuations can be computed by Fourier synthesis. For a model of glycolysis, this approximation remains fairly accurate even for large relative fluctuations of the parameters.     

A kinetic study of the suicide inactivation of an enzyme measured through coupling reactions. Application to the suicide inactivation of tyrosinase.

A systematic procedure for the kinetic study of reaction mechanisms with enzyme inactivation induced by a suicide substrate in the presence or in the absence of an auxiliary substrate, when the enzyme activity is measured through coupling reactions, enzymically catalysed or not, was developed and analysed by using the transient-phase approach. The methodology is established to determine the parameters and kinetic constants corresponding to the enzyme suicide inactivation and the coupling reactions. This approach is illustrated by a study of the suicide inactivation of tyrosinase by catechol in the presence of L-proline. Treatment of the experimental data was carried out by non-linear regression.     

State selection in coupled identical biochemical systems with coexisting stable states

This work examines state selection for coupled biochemical systems with coexisting stable states. For biochemically identical biochemical systems, different coupled systems are examined for the coexistence of (a) one steady state and one oscillatory state or (b) two oscillatory states. For case (a), it is revealed that state selection is always governed by two key factors: the values of kinetic parameters and the coupling strength. When the coupling strength is small, the coupled systems remain in the basin of attraction of their original states. When it is sufficiently large, all coupled systems are always entrained, independently of their original states. Furthermore, for the entrainment, which of the two coexisting states is selected depends sensitively on the activity of recycling enzyme (one of kinetic parameters). It is shown that this is because changing the activity of recycling enzyme alters the size of basin of attraction of each state. When both systems in the same oscillatory state are coupled, an additional factor, namely phase shift between two oscillations, may also affect state selection, and coupling may cause the systems to select either the original oscillatory state or the coexisting steady state. In addition to the features of case (a), case (b) also supports quasiperiodic oscillations and synchronisation of two periodic oscillations. Implications of the results for understanding state selection during the evolution of coupled biochemical systems with coexisting stable states are discussed.     

Calcium binding to complexes of calmodulin and calmodulin binding proteins

The free energy of coupling for binding of Ca2+ and the calmodulin-sensitive phosphodiesterase to calmodulin was determined and compared to coupling energies for two other calmodulin binding proteins, troponin I and myosin light chain kinase. Free energies of coupling were determined by quantitating binding of Ca2+ to calmodulin complexed to calmodulin binding proteins with Quin 2 to monitor free Ca2+ concentrations. The geometric means of the dissociation constants (-Kd) for Ca2+ binding to calmodulin in the presence of equimolar rabbit skeletal muscle troponin I, rabbit skeletal muscle myosin light chain kinase, and bovine heart calmodulin sensitive phosphodiesterase were 2.1, 1.1, and 0.55 microM. The free-energy couplings for the binding of four Ca2+ and these proteins to calmodulin were -4.48, -6.00, and -7.64 kcal, respectively. The Ca2+-independent Kd for binding of the phosphodiesterase to calmodulin was estimated at 80 mM, indicating that complexes between calmodulin and this enzyme would not exist within the cell under low Ca2+ conditions. The large free-energy coupling values reflect the increase in Ca2+ affinity of calmodulin when it is complexed to calmodulin binding proteins and define the apparent positive cooperativity for Ca2+ binding expected for each system. These data suggest that in vitro differences in free-energy coupling for various calmodulin-regulated enzymes may lead to differing Ca2+ sensitivities of the enzymes.     

Transductions to generate plant form and pattern: an essay on cause and effect

Many complex processes can be broken into transduction steps where one state is converted to another by a well defined activity. One difficulty for analysis is that transductions occur in chains or networks. Another, of primary concern here, is that a single transduction can be complex. Some such transductions can efficiently explain phenomena often thought to be summations or orchestrations of many simple transductions. Pattern formation is in this category. For a wide range of transductions one can define cause and effect in a differential equation. In its integral one can define the before and after states. The main experimental tactic to characterize unknown transductions is co-variation. The before state (input) is altered, change in the after state (output) is assayed. Thus an unknown transduction, with cause and effect embodied in the differential, is investigated through long-term changes in its integral. This is fully practical when all of the integral is known or readily surmised, as in simple discrete biochemical transductions. As causal differential expressions become complex, their integrals become more versatile in generating output because this changes not only with variation in the expression itself but also with boundary conditions and limits. These very features, however, make such a function increasingly intractable to discovery by co-variation. Only a small part of the integral is embodied in the before and after states; the remainder is not readily surmised. Accordingly, in contrast to reliance on the role of controls to deduce unknown simple transductions, the complex ones are generally established through formalization of the differential nature of the process itself.     

Role of Small Oligomers on the Amyloidogenic Aggregation Free-Energy Landscape

We combine atomic-force-microscopy particle-size-distribution measurements with earlier measurements on 1-anilino-8-naphthalene sulfonate, thioflavin T, and dynamic light scattering to develop a quantitative kinetic model for the aggregation of β-lactoglobulin into amyloid. We directly compare our simulations to the population distributions provided by dynamic light scattering and atomic force microscopy. We combine species in the simulation according to structural type for comparison with fluorescence fingerprint results. The kinetic model of amyloidogenesis leads to an aggregation free-energy landscape. We define the roles of and propose a classification scheme for different oligomeric species based on their location in the aggregation free-energy landscape. We relate the different types of oligomers to the amyloid cascade hypothesis and the toxic oligomer hypothesis for amyloid-related diseases. We discuss existing kinetic mechanisms in terms of the different types of oligomers. We provide a possible resolution to the toxic oligomer-amyloid coincidence.     

Homochirality and the Need for Energy

The mechanisms for explaining how a stable asymmetric chemical system can be formed from a symmetric chemical system, in the absence of any asymmetric influence other than statistical fluctuations, have been developed during the last decades, focusing on the non-linear kinetic aspects. Besides the absolute necessity of self-amplification processes, the importance of energetic aspects is often underestimated. Going down to the most fundamental aspects, the distinction between a single object—that can be intrinsically asymmetric—and a collection of objects—whose racemic state is the more stable one—must be emphasized. A system of strongly interacting objects can be described as one single object retaining its individuality and a single asymmetry; weakly or non-interacting objects keep their own individuality, and are prone to racemize towards the equilibrium state. In the presence of energy fluxes, systems can be maintained in an asymmetric non-equilibrium steady-state. Such dynamical systems can retain their asymmetry for times longer than their racemization time.     

How Nature Modulates Inherent Fluctuations for Biological Self-Organization – The Case of Membrane Fusion

Biological systems in nano-scale, due to the weak electrostatic interactions and structural connectivity therein, are flexible so that they undergo conformational transition subject to thermal fluctuations and external noises. In the presence of barriers, nature utilizes the fluctuations to give rise to self-organization, typically accompanied by conformational transitions. In two opposing membranes with like-charges, the cooperative coupling between the undulation and charge fluctuations give rise to a dynamic instability to spontaneous growth of the in-phase membrane undulation, and thus a great reduction of the energy barrier to fusion. The multivalent counter-ions, the Ca²⁺ for example, enhance the necessary charge density fluctuation leading to surface charge inversion and overcondensation.     

Theory of transport noise in membrane channels with open-closed kinetics

A theoretical approach to transport noise in kinetic systems, which has recently been developed, is applied to electric fluctuations around steady-states in membrane channels with different conductance states. The channel kinetics may be simple two state (open-closed) kinetics or more complicated. The membrane channel is considered as a sequence of binding sites separated by energy barriers over which the ions have to jump according to the usual single-file diffusion model. For simplicity the channels are assumed to act independently. In the special case of ionic movement fast compared with the channel open-closed kinetics the results agree with those derived from the usual Master equation approach to electric fluctuations in nerve membrane channels.For the simple model of channels with one binding site and two energy barries the coupling between the fluctuations coming from the open-closed kinetics and from the jump diffusion is investigated.     

Conformational Transitions in Yeast Chorismate Mutase Important for Allosteric Regulation as Identified by Nuclear Magnetic Resonance Spectroscopy

Proteins fluctuate between different conformations in solution, and these conformational fluctuations can be important for protein function and allosteric regulation. The chorismate mutase from Saccharomyces cerevisiae (ScCM), a key enzyme in the biosynthesis of aromatic amino acids, is allosterically activated and inhibited by tryptophan and tyrosine, respectively. It was initially proposed that in the absence of effector, ScCM fluctuates between activated R and inhibited T conformations according to the Monod-Wyman-Changeux (MWC) model, although a more complex regulation pattern was later suggested by mutagenesis and kinetic data. Here we used NMR relaxation dispersion experiments to understand the conformational fluctuations on the microsecond-to-millisecond timescale that occur in ScCM. In the absence of allosteric effectors, ScCM did not exclusively exchange between T and R conformations, suggesting that the two-state MWC model is insufficient to explain conformational dynamics. Addition of tyrosine led to the quenching of much of the motion on this timescale, while new motions were identified in the presence of tryptophan. These new motions are consistent with conformational fluctuations into an alternative conformation that may be important for enzyme activity.     

Thermodynamics of the control of metabolism

A theory is presented, describing the control analysis of metabolic systems in terms of Gibbs free energies, extending earlier work of Kacser and Burns (25), and Heinrich and Rapoport (29). It is shown that relationships exist between flux control coefficients (the degree to which enzymes control steady-state fluxes) and free-energy elasticity coefficients, defined as the fractional change in the rate of a reaction induced by a standard change in one free-energy difference, while all the other free-energy differences are kept constant. Application of this extended control analysis to some biochemical reactions, including proton translocation, demonstrates that

1. Problems arising in the control analysis because of conservation (sum concentration of substrate and product constant) can be circumvented.
2. Although free-energy elasticity coefficients are maximal when the reaction is close to equilibrium, they can also be significant when the reaction is not close to equilibrium.
3. Problems in the control analysis caused by compartmentation can be resolved by defining control parameters that refer to the organelle as a whole.
4. These latter control parameters obey the above-mentioned relationships.