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PubMedDate not supplied

A strategy for efficient characterization of macromolecular heteroassociations via measurement of sedimentation equilibrium.

A method is proposed for the selection of experimental conditions for sedimentation equilibrium experiments that will provide maximal information about the values of equilibrium association constants within a given scheme for heteroassociation of two solute components. A discriminator function is proposed that indicates the sensitivity of the experimentally observed gradient or gradients to alterations in the underlying association constants. The value of this function is plotted or tabulated as a function of the concentrations of the two components, over a broad range of solution compositions. It is suggested that experiments performed with loading compositions corresponding to large absolute values of the discriminator function will yield the most information with respect to determination of the underlying association constants. This method was tested by predicting optimal conditions for three different types of sedimentation equilibrium experiments: (i) measurement of total (natural) solute absorbance; (ii) measurement of individual component gradients via measurement of tracer absorbance; and (iii) global analysis of multiple experiments. Experimental data resulting from sedimentation equilibrium experiments carried out under the specified conditions were simulated by addition of realistic levels of random error to calculated equilibrium gradients. The simulated data were then analyzed exactly as real experimental data, i.e., without prior knowledge of the underlying association constants. It was found that the highest accuracy and precision in determination of heteroassociation constants are obtained by global analysis of multiple experiments performed using significantly different loading compositions, each of which is selected from 'sensitive' regions of the discriminator map.

Centrifugation, Density Gradient↗

PubMed1976

Hydrolysis-resynthesis equilibrium of the lysine-15--alanine-16 peptide bond in bovine trypsin inhibitor (Kunitz).

Catalytic amounts of bovine beta-trypsin, bovine alpha-chymotrypsin and porcine plasmin establish a true thermodynamic equilibrium between virgin (I) (reactive site Lys15-Ala16 peptide bond intact) and modified (I) (this bond hydrolyzed) bovine trypsin/kallikrein inhibitor (Kunitz). The very slow reaction rates for attaining equilibrium are pH-dependent and differ for different enzymes. Optimal rates are for beta-trypsin at pH 3.75, for alpha-chymotrypsin at pH 5.5, and for plasmin at pH 5.0. Under conditions of optimum pH the equilibrium is reached with the highest rate by plasmin. In 10(-5)M inhibitor solutions the equilibrium concentrations of virgin and modified inhibitor are established by plasmin after almost 300 days starting from either pure virgin or pure modified inhibitor. Thus, the hydrolysis constant KHyd = [I]/[I] is determined to be 0.33 at pH 5.0. In spite of many unsuccessful attempts, this demonstrates that the reactive site peptide bond Lys15-Ala16 in the bovine trypsin inhibitor (Kunitz) can be hydrolyzed by catalytic amounts of endopeptidase. It further confirms that the hydrolyzed Lys15-Ala16 peptide bond in modified inhibitor is subject to thermodynamic control resynthesis.

Alanine↗

PubMed1985

Synthesis of ATP catalyzed by the (Ca2+ + Mg2+)-ATPase from erythrocyte ghosts. Energy conservation in plasma membranes.

The (Ca2+ + Mg2+)-ATPase from erythrocyte ghosts catalyzed the hydrolysis of ATP together with the synthesis of ATP or ATP in equilibrium 'Pi exchange. The modulation of the ATPase reaction cycle was controlled by high- and low-affinity calcium-binding sites asymmetrically located on the enzyme. Calmodulin accelerated the reaction cycle in both directions, stimulating the overall turnover of the enzyme. Calcium transport was achieved utilizing optimal conditions for the expression of the ATP in equilibrium Pi exchange system.

Adenosine Triphosphate↗

PubMed1991

Optimal pension funding with demographic instability and endogenous returns on investment.

"This paper tries to explore some optimal funding policies for pension systems in a general equilibrium setting where funding affects returns on investment and wages through its impact on capital formation. This is done in the context of irregular demographic evolutions such as those expected in developed countries for the next century. Particular attention is given to the intergenerational welfare criterion which is used for designing optimal policies.... We will first present the model for the pension system and the economy and discuss a general one-parameter form for the intergenerational utility function. We will then present the simulated optimal paths for different numerical specifications of the model and the utility function. The last section will show by how much a simpler policy with fixed transfers and purely individual funding can depart from optimal paths...."

Developed Countries↗

PubMed1988

DESIGN: computerized optimization of experimental design for estimating Kd and Bmax in ligand binding experiments. I. Homologous and heterologous binding to one or two classes of sites.

We have developed a versatile computer program for optimization of ligand binding experiments (e.g., radioreceptor assay system for hormones, drugs, etc.). This optimization algorithm is based on an overall measure of precision of the parameter estimates (D-optimality). The program DESIGN uses an exact mathematical model of the equilibrium ligand binding system with up to two ligands binding to any number of classes of binding sites. The program produces a minimal list of the optimal ligand concentrations for use in the binding experiment. This potentially reduces the time and cost necessary to perform a binding experiment. The program allows comparison of any proposed experimental design with the D-optimal design or with assay protocols in current use. The level of nonspecific binding is regarded as an unknown parameter of the system, along with the affinity constant (Kd) and binding capacity (Bmax). Selected parameters can be fixed at constant values and thereby excluded from the optimization algorithm. Emphasis may be placed on improving the precision of a single parameter or on improving the precision of all the parameters simultaneously. We present optimal designs for several of the more commonly used assay protocols (saturation binding with a single labeled ligand, competition or displacement curve, one or two classes of binding sites), and evaluate the robustness of these designs to changes in parameter values of the underlying models. We also derive the theoretical D-optimal design for the saturation binding experiment with a homogeneous receptor class.

Binding Sites↗

PubMed2002

In vivo receptor assay with multiple ligand concentrations: an equilibrium approach.

The ligand-receptor binding potential determined by PET studies at high ligand-specific radioactivity reflects both the receptor density and ligand-receptor affinity. This ambiguity has been resolved by various methods based on the administration of multiple unlabeled ligand concentrations. The authors aimed to implement and refine an approach to multiple ligand concentration receptor assay that combined maximum simplicity and a minimum of assumptions and model dependence that would nonetheless reliably distinguish density from affinity effects. The approach uses administration by bolus followed by infusion to obtain a true equilibrium between bound ligand and the other components of the ligand concentration, and does not require measurements of ligand in blood plasma. Four approaches to the optimization of the desired density and affinity parameters from the measured equilibrium data were implemented and compared in the analysis of raclopride studies performed in both normal control and MPTP-lesioned nonhuman primates. The authors conclude that the method is simple enough for routine use and yet reliable enough to apply in ongoing studies of both chronic and acute drug effects in the dopamine system.

1-Methyl-4-phenyl-1,2,3,6-tetrahydropyridine↗

PubMed1995

Comparison of muscle forces and joint load from an optimization and EMG assisted lumbar spine model: towards development of a hybrid approach.

The purpose of this study was to determine whether the same estimates of individual muscle and L4/L5 lumbar joint compressive forces result from an optimization (OPT) compared to an electromyography (EMG) assisted approach for solving the inderminate moment equilibrium equations in the same anatomical model. Four male subjects performed near maximum, isometric, ramp efforts in trunk flexion, extension and lateral bending in a testing apparatus. The EMG approach was sensitive to subject and trial differences in the magnitudes of individual muscle forces needed to produce the same reaction moment. In contrast, the OPT method converged on a similar estimate of muscle forces for all subjects and trials producing the same moment. The OPT method predicted lower L4/L5 joint compression values, on average, by 32, 43 and 23% in trunk extension, flexion and lateral bending, respectively, because, unlike the EMG method, it could not predict co-contraction of anatomically antagonistic muscles. We incorporated the OPT method's advantage of forcing an equilibrium in the reaction moments into the EMG method in a new approach we have called 'EMG assisted optimization' (EMGAO). Muscle force estimates from the EMG and EMGAO methods differed from those from the OPT method, on average, by 123% (RMS) for flexion and extension and by 218% for lateral bends. Data from the two approaches result in different conclusions about spine mechanics. We have more confidence in the EMG assisted methods because they respond to variation in muscle synergy and co-contraction patterns commonly observed in different trials and subjects for the same reaction moments.

Adult↗

PubMed2002

Basal glycogenolysis in mouse skeletal muscle: in vitro model predicts in vivo fluxes.

A previously published mammalian kinetic model of skeletal muscle glycogenolysis, consisting of literature in vitro parameters, was modified by substituting mouse specific Vmax values. The model demonstrates that glycogen breakdown to lactate is under ATPase control. Our criteria to test whether in vitro parameters could reproduce in vivo dynamics was the ability of the model to fit phosphocreatine (PCr) and inorganic phosphate (Pi) dynamic NMR data from ischemic basal mouse hindlimbs and predict biochemically-assayed lactate concentrations. Fitting was accomplished by optimizing four parameters--the ATPase rate coefficient, fraction of activated glycogen phosphorylase, and the equilibrium constants of creatine kinase and adenylate kinase (due to the absence of pH in the model). The optimized parameter values were physiologically reasonable, the resultant model fit the [PCr] and [Pi] timecourses well, and the model predicted the final measured lactate concentration. This result demonstrates that additional features of in vivo enzyme binding are not necessary for quantitative description of glycogenolytic dynamics.

Animals↗

PubMed2000

Characterization and distribution of somatostatin binding sites in goldfish brain.

Somatostatin (SRIF) binding sites were characterized in goldfish brain. Binding of (125)I-[Tyr(11)]-SRIF-14 to a brain membrane preparation was found to be saturable, reversible, and time-, temperature-, and pH-dependent. Binding was also displaceable by different forms of SRIF. Under optimal conditions (22 degrees C, pH 7.2), the equilibrium binding of (125)I-[Tyr(11)]-SRIF-14 to goldfish brain membranes was achieved after 60 min incubation. Analysis of saturable equilibrium binding revealed a one-site model fit with K(a) of 1.3 nM. SRIF-14, mammalian SRIF-28, and salmon SRIF-25 displaced (125)I-[Tyr(11)]-SRIF-14 binding with similar affinity, whereas other neuropeptides, e.g., substance P, were unable to displace (125)I-[Tyr(11)]-SRIF-14. Autoradiography studies demonstrated that (125)I-[Tyr(11)]-SRIF-14 binding sites are found throughout the goldfish brain. A high density of (125)I-[Tyr(11)]-SRIF-14 binding sites was found in the forebrain, including the nucleus preopticus, nucleus preopticus periventricularis, nucleus anterioris periventricularis, nucleus lateralis tuberis, nucleus dorsomedialis thalami, nucleus dorsolateralis thalami, nucleus ventromedialis thalami, and nucleus diffusus lobi inferioris. In midbrain, (125)I-[Tyr(11)]-SRIF-14 binding sites were found in the optic tectum. The facial and vagal lobes and the mesencephalic-cerebellar tract were found to have a high density of binding sites. This study provides the first characterization and distribution of specific binding sites for SRIF in a fish brain.

Animals↗

PubMed1981

The steady-state kinetic mechanism of ATP hydrolysis catalyzed by membrane-bound (Na+ + K+)-ATPase from ox brain. III. A minimal model.

A steady-state kinetic investigation of the effect of K+ on the Na+-enzyme activity of the (Na+ + K+)-ATPase in broken membrane preparations is reported. Analysis of the kinetic patterns obtained, together with the results reported in the first two articles of this series permit the following conclusions. 1. K+ inhibits the Na+-enzyme (the enzyme activity measured at micromolar substrate concentrations in the presence of Na+). The inhibition of non-competitive at low and competitive at higher K+ concentrations and is enhanced by free Mg2+. 2. The results indicate that the Na+-enzyme at steady-state tends to be accumulated in an enzyme-potassium complex when K+ is added. 3. The enzyme-potassium complex, in turn, binds Mg2+ in a dead-end fashion. The dissociation constant for the enzyme-K-Mg complex, estimated from the data, is 7.2 mM. The same value was obtained earlier for the Mg2+ inhibition constant of the substrate-free form of the (Na+ + K+)-enzyme (the enzyme activity measured with Na+ and K+ and at millimolar substrate concentrations) suggesting that the two constants describe the same equilibrium. 4. On the basis of the known (optimal) activity of the (Na+ + K+)-ATPase, relative to that of the Na+-ATPase, a rate constant condition is found which must be met if the Post-Albers kinetic scheme is to satisfy the data. Kinetic data for the phosphoenzyme indicate that this condition is not satisfied. 5. On the basis of the kinetic results a model for the hydrolytic action of (Na+ + K+)-ATPase is proposed. This model encompasses the Post-Albers scheme but contains two distinctive hydrolysis cycles (an 'Na+-enzyme cycle' and a '(Na+ + K+)-enzyme cycle') with widely different affinities for the substrates. Only one of the cycles (the Na+-enzyme cycle) involves acid-stable phosphorylated enzyme intermediates at discernible steady-state concentrations. Which of the two main cycles is predominant in any particular system is determined by the concentration of ligands and substrates. 6. According to this scheme, an enzyme preparation may exhibit both a high (Na+-enzyme) and a low ((Na+ + K+)-enzyme) substrate affinity, without the necessity of assigning more than one substrate site to a particular enzyme unit at any one time.

Adenosine Triphosphate↗

PubMed1984

Identification and characterisation of L-[3H]aspartate binding sites on rat spinal cord synaptic membranes.

The binding of L-[3H] aspartate to extensively-washed rat spinal cord synaptic membranes was investigated. Specific binding was enriched in synaptic membranes and was optimal under physiological conditions of temperature and pH. Equilibrium binding was established relatively slowly over a period of 30 min, and was totally reversible within 40 min. Saturation analysis revealed complex binding patterns. Two sites were clearly demonstrable, only one of which was shown to be saturable over the ligand concentration range employed in the study (0.1-10 microM). There was also some indication of the presence of a higher affinity site, although this was not investigated in any detail. Saturable binding demonstrated a KD = 1.4 microM and Bmax = 105 pmole/mg protein. Structure-activity studies with a range of amino acid analogues indicated that binding was stereospecific and was inhibited by a very restricted range of compounds. The most potent inhibitors of binding were L-glutamate and L-aspartate. There was no evidence for the involvement of NMDA receptors. Effects of possible endogenous modulators, including ions and guanosine nucleotides were investigated, and the chemical nature of the binding site probed with a number of protein-modifying agents.

Animals↗

PubMed1995

Method for measuring the activities of cholesteryl ester transfer protein (lipid transfer protein).

A continuous recording fluorescence assay was developed for cholesteryl ester transfer protein (CETP). The assay measures the increase in fluorescence accompanying the relocation of fluorescent lipids, cholesteryl esters and triglycerides, from a donor emulsion to an acceptor emulsion. In the absence of CETP, the quantum yields of the fluorescent lipids is low because their high concentrations in the donor emulsions result in self-quenching. CETP catalyzes the redistribution of the fluorescent lipids from the donor to the acceptor emulsions and fluorescence increases substantially. Efficient sonication and incorporation of apolipoproteins from human HDL into the emulsions significantly increased the transfer rates. Under optimal conditions, the redistribution of fluorescent compounds reaches equilibrium within < 30 min and the kinetics of this process are consistent with a simple, first-order reaction pathway. The redistribution kinetics support a mechanism of adsorption --> exchange --> desorption --> diffusion.

Boron Compounds↗

PubMed1991

Physiological prediction of muscle forces--I. Theoretical formulation.

A physiological model for predicting muscle forces is described. Rigid-body mechanics and musculoskeletal physiology are used to describe the dynamics of the segment model and muscle model. Unknown muscle and joint contact forces outnumber the equilibrium equations resulting in an indeterminate problem. Mathematical optimization is utilized to resolve the indeterminacy. The modeling procedure relies entirely on established physiological principles. Data describing the muscle anatomy and body structures are included. A model defining the force-length-velocity-activation relationship of a muscle is adopted. The force a muscle produces is assumed to be proportional to its maximum stress, physiological cross-sectional area, activation, and its functional configurations including the muscle architecture, muscle length, contracting velocity, and passive tension. These factors are incorporated into inequality equations which limit the force for each muscle. Minimal muscular activation is forwarded as the optimization criterion for muscle force determination.

Biomechanical Phenomena↗

PubMed1991

Physiological prediction of muscle forces--II. Application to isokinetic exercise.

The successful application of a physiological model of the musculoskeletal system capable of accounting for nonequilibrium dynamic loading and predicting individual muscle forces in the knee is presented. The model incorporates rigid-body mechanics and musculoskeletal physiology. Unknown muscle and joint contact forces outnumber the equilibrium equations resulting in an indeterminant problem. Mathematical optimization is utilized to resolve the indeterminacy. The model is used to estimate individual muscle forces during isokinetic exercise. Five subjects were tested at speeds of 60 degrees/s and 180 degrees/s. A newly proposed optimal criterion, minimizing muscular activation, results in muscle force predictions which have significantly higher correlations with myoelectric activity than other linear and nonlinear optimal criteria. The results demonstrate that properly constrained linear programming methods do not limit the number of active muscles and allow for uniform recruitment of the active muscles.

Adult↗

PubMed1994

Localization of nicotinic cholinergic receptors in rat brain: autoradiographic studies with [3H]cytisine.

There is a great deal of interest in the role of nicotinic acetylcholine receptors in the central nervous system, although their function is not well understood at present. Currently, central nicotinic receptors can be classified broadly as either alpha-bungarotoxin binding sites with low affinity for acetylcholine agonists, or as high-affinity agonist binding sites with low affinity for alpha-bungarotoxin. Neuronal nicotinic receptors with a high affinity for agonists are distributed widely in the central nervous system. Evidence from molecular biology and electrophysiology suggests that multiple nicotinic receptor types exist in the brain. In this study we have used the agonist [3H]cytisine as a ligand for autoradiography to generate a detailed quantitative map of the high-affinity agonist binding nicotinic receptor in the rat brain. Optimized binding conditions, characterization of the kinetic and equilibrium binding properties, and demonstration of the nicotinic pharmacology of this binding site in tissue sections confirm the usefulness of [3H]Cytisine as a ligand for nicotinic receptor autoradiography. [3H]Cytisine autoradiography provides excellent anatomic resolution with very low non-specific binding. This property has allowed us to describe variations in receptor density within subnuclei and gradients of receptor density in larger brain regions. Data from several studies suggest that the predominant high-affinity agonist binding nicotine receptor in the central nervous system is composed of the alpha 4 and beta 2 subunits. The data in the current study are consistent with the suggestion that [3H]cytisine labels only the alpha 4 beta 2 nicotinic receptor with high affinity, offering the possibility of localizing a specific nicotinic receptor subtype in the central nervous system. In summary, we characterize the optimum experimental conditions for the use of [3H]cytisine in tissue section autoradiography. [3H]Cytisine proves to be an excellent marker for nicotinic cholinergic receptors with a very high affinity and very low background. We provide a detailed quantitative characterization of nicotinic receptor density in the rat central nervous system and we find there are significant variations and gradients in receptor density within specific brain regions, including subregions previously thought to be homogeneous.

Alkaloids↗

PubMed1989

Computer simulation of the hydrostatic skeleton. The physical equivalent, mathematics and application to worm-like forms.

The functional principles of a hydrostatic skeleton were combined to obtain a physical model which includes geometry, number and length-tension relationships of the elastic elements in the body wall, internal volume and internal pressure. The model skeleton with pre-set internal volume assumes a certain shape and develops a specific internal pressure in order to minimize the potential energy stored in the elastic elements. This shape is calculated as equilibrium state by using finite element methods and optimization techniques. This model is flexible enough to accommodate different geometries and length-tension-relationships of the elastic elements. Presently, the model is implemented with linear length-tension relationships and certain geometrical restrictions, such as uniform width over the entire animal, and rectangular cross sections; the general case is outlined. First simulations with the "unit-worm" yield stable solutions, i.e. stable shapes for all combinations of parameters tested so far. They define the conditions for bringing all muscles to an optimal operating point. We detected a pressure maximum with increasing volume, assessed the contribution of circular muscles to bending, and determined the shapes of animals with different muscle activations in each body half (Chapman-matrix). We summarize our results by the volume rule and stabilization rule, two simple concepts which predict changes in shape as the result of muscle activation.

Animals↗

PubMed1998

How organisms do the right thing: The attractor hypothesis.

Neo-Darwinian theory is highly successful at explaining the emergence of adaptive traits over successive generations. However, there are reasons to doubt its efficacy in explaining the observed, impressively detailed adaptive responses of organisms to day-to-day changes in their surroundings. Also, the theory lacks a clear mechanism to account for both plasticity and canalization. In effect, there is a growing sentiment that the neo-Darwinian paradigm is incomplete, that something more than genetic structure, mutation, genetic drift, and the action of natural selection is required to explain organismal behavior. In this paper we extend the view of organisms as complex self-organizing entities by arguing that basic physical laws, coupled with the acquisitive nature of organisms, makes adaptation all but tautological. That is, much adaptation is an unavoidable emergent property of organisms' complexity and, to some a significant degree, occurs quite independently of genomic changes wrought by natural selection. For reasons that will become obvious, we refer to this assertion as the attractor hypothesis. The arguments also clarify the concept of "adaptation." Adaptation across generations, by natural selection, equates to the (game theoretic) maximization of fitness (the success with which one individual produces more individuals), while self-organizing based adaptation, within generations, equates to energetic efficiency and the matching of intake and biosynthesis to need. Finally, we discuss implications of the attractor hypothesis for a wide variety of genetical and physiological phenomena, including genetic architecture, directed mutation, genetic imprinting, paramutation, hormesis, plasticity, optimality theory, genotype-phenotype linkage and puncuated equilibrium, and present suggestions for tests of the hypothesis. (c) 1998 American Institute of Physics.

Journal Article↗

PubMed1993

Do deleterious mutations act synergistically? Metabolic control theory provides a partial answer.

Metabolic control theory is used to derive conditions under which two deleterious mutations affecting the dynamics of a metabolic pathway act synergistically. It is found that two mutations tend to act mostly synergistically when they reduce the activity of the same enzyme. If the two mutations affect different enzymes, the conclusion depends on the way that fitness is determined by aspects of the pathway. The cases analyzed are: selection for (1) maximal flux, (2) maximal equilibrium concentration (pool size) of an intermediate, (3) optimal flux, (4) optimal pool size. The respective types of epistasis found are: (1) antagonistic, (2) partly synergistic, (3-4) synergism is likely to predominate over antagonism. This results in somewhat different predictions concerning the effect of metabolic mutations on fitness in prokaryotes and eukaryotes. The fact that bacteria are largely clonal but have often a mosaic gene structure is consistent with expectations from the model.

Enzymes↗