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At least 19 recordsLinked to original sources
PubMed1975

Kinetic behavior of associating enzyme systems ofthe type M in equilibrium M2 in equilibrium M3 in equilibrium ... and of the type 2M in equilibrium D in equilibrium D2 in equilibrium D3 in equilibrium ...

A theoretical analysis has been made of dependencies of specific enzymatic activity (a) on the concentration of the enzyme for associating enzyme systems, in which the association of protein molecules leads to the formation of linear associates of an unlimited length (M in equilibrium M2 in equilibrium M3 in equilibrium ...) and is accompanied by steric shielding of active centers, and also for systems of the type 2 M in equilibrium D in equilibrium D2 in equilibrium D3 in equilibrium ... (M is an inactive monomer and D is an active dimer), in which the specific enzymatic activity of the dimer does not depend on the degree of association. For both models an analysis has been made of the S-shape of the curves of the dependence of a on the concentration of the substrate. Experimental data for glutamate dehydrogenase from ox liver and phosphofructokinase from rabbit skeletal muscles have been used as illustrations.

Animals↗
PubMed1992

Role of sn-1-saturated,sn-2-polyunsaturated phospholipids in control of membrane receptor conformational equilibrium: effects of cholesterol and acyl chain unsaturation on the metarhodopsin I in equilibrium with metarhodopsin II equilibrium.

The effect of phospholipid bilayer acyl chain packing free volume on the equilibrium concentration of the form of photolyzed rhodopsin which initiates visual signal transduction, metarhodopsin II (meta II), is examined in reconstituted systems formed from the saturated phospholipid dimyristoylphosphatidylcholine (DMPC) and in the polyunsaturated phospholipid sn-1-palmitoyl-sn-2-arachidonoylphosphatidylcholine (PAPC) with and without 30 mol% cholesterol. The extent of meta II formation is determined from both flash photolysis measurements and rapidly acquired absorbance spectra. Equilibrium and dynamic properties of the lipid bilayer are characterized by the dynamic fluorescence properties of 1,6-diphenyl-1,3,5-hexatriene (DPH). DPH orientational properties are characterized by fv, a parameter which reflects the volume available for probe reorientation in the bilayer, relative to that available in an unhindered, isotropic environment [Straume, M., & Litman, B. J. (1987) Biochemistry 26, 5121-5126]. The metarhodopsin I in equilibrium with meta II equilibrium constant, Keq has a linear relationship with fv for rhodopsin in PAPC vesicles with and without cholesterol as well as for rhodopsin in DMPC vesicles, and these two correlation lines have different slopes. The correlations between Keq and fv in PAPC and DMPC systems are compared with a similar correlation in the native rod outer segment disk membrane and one reported previously in an egg phosphatidylcholine (egg PC) system [Mitchell, D. C., Straume, M., Miller, J. L., & Litman, B. J. (1990) Biochemistry 29, 9143-9149].(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed1977

Chimeric drift in allophenic mice: analysis of changes in red blood cell and white blood cell populations in C57Bl/6 in equilibrium (A X SJL)F1, C57Bl/6 in equilibrium (CBA X CBA/H-T6)F1, and C57Bl/6 in equilibrium DBA/1 mice.

Forty-seven allophenic mice of three different types (C57BL/6 in equilibrium (A X SJL), C57BL/6 in equilibrium (CBA X CBA/H-T6), and C57BL/6 in equilibrium DBA/1) were analyzed for changes in their peripheral white blood cell composition and hemoglobin composition with age. It was found that 10 of the 47 mice showed significant changes termed "chimeric drift" in one or the other or both of these parameters. These 10 mice were classified as unstable chimeras, as opposed to the 37 stable chimeras, which showed no apparent chimeric drift. There was an excellent correlation of peripheral white blood cell and hemoglobin compositions of the stable chimeras. However, the unstable chimeras showed little or no correlation of these two markers. Possible mechanisms of chimeric drift are discussed.

Aging↗
PubMed1983

Influence of thyroid function on the in vivo cortisol in equilibrium cortisone equilibrium in man.

To evaluate the effect of thyroid function on the in vivo cortisol in equilibrium cortisone (F in equilibrium E) equilibrium, double-labeled cortisol tracer techniques were used to measure separately the rates of the F leads to E and E leads to F reactions in 4 euthyroid, 2 hypothyroid, and 2 hyperthyroid subjects. The rate of the F leads to E reaction was calculated from the appearance rate of 3H in body water after the i.v. injection of [11 alpha-3H]-cortisol; the rate of the E leads to F reaction was calculated from the difference in the plasma turn-over rates of [11 alpha-3H]-cortisol, and [4-14C]-cortisol after simultaneous i.v. injection of both tracers; the F in equilibrium E set-point was calculated by dividing the F leads to E rate by the E leads to F rate. In euthyroid subjects the F leads to E reaction rate averaged 1.6%/min, the E leads to F reaction rate averaged 1.0%/min, and the F in equilibrium E set-point averaged 1.6. In hyperthyroid subjects the two reaction rates were supranormal: the F leads to E rate averaged greater than or equal to 3.9%/min and the E leads to F rate averaged 1.54%/min; since the increase in the F leads to E rate was proportionally greater, the F in equilibrium E set-point (average greater than or equal to 2.6) was displaced towards cortisone. In hypothyroid subjects both reaction rates were equally slowed, to an average of 1.0%/min (F leads to E) and 0.68%/min (E leads to F); the F in equilibrium E set-point averaged 1.65, the same as in euthyroid subjects. Displacement of the F in equilibrium E equilibrium towards cortisone in hyperthyroid subjects appears to account for their elevated urinary THE/THF ratios, but the normal F in equilibrium E set-point in hypothyroid subjects makes it necessary to invoke a different mechanism for their depressed THE/THF ratio; it is suggested that increased conversion of THE to cortoic acids may be the responsible factor.

Adult↗
PubMed2003

Non-equilibrium capillary electrophoresis of equilibrium mixtures--appreciation of kinetics in capillary electrophoresis.

We describe a new electrophoretic method (patent pending), Non-Equilibrium Capillary Electrophoresis of Equilibrium Mixtures (NECEEM), and demonstrate its application to the study of protein-DNA interactions. A single NECEEM experiment allows for the determination of equilibrium and kinetic parameters of protein-DNA complex formation. The equilibrium mixture is prepared by mixing protein and DNA; it contains three components: free protein, free DNA, and the protein-DNA complex. A small plug of such a mixture is injected onto a capillary and the three components are separated under non-equilibrium conditions using a run buffer that does not contain the components of the equilibrium mixture. The protein-DNA complex decays during the NECEEM separation; the resulting electropherograms contain characteristic peaks and exponential curves. A simple analysis of a single electropherogram reveals two parameters: the equilibrium dissociation constant of the protein-DNA complex and the monomolecular rate constant of complex decay. The bimolecular rate constant of complex formation can then be calculated as the ratio of the two experimentally-determined constants. NECEEM was applied to find the equilibrium and kinetic parameters of interaction between an E. coli single-stranded DNA binding protein and a fluorescently-labeled oligonucleotide. The constants determined by NECEEM are in good agreement with those obtained by other methods. The new method is simple, fast, and accurate. It can be equally applied to other non-covalent molecular complexes.

Animals↗
PubMedDate not supplied

[Comparison of the heme electron state of reduced cytochrome P450 and P420 in equilibrium and non-equilibrium protein conformations. The nature of the protein heme ligand].

Magnetic circular dichroism (MCD) spectra of reduced cytochromes P450 and P420 in equilibrium and non-equilibrium protein conformations are compared at 4.2 K for the 350-800 spectral region. Non-equilibrium forms have been produced by photolysis of CO-complexes at 4.2 K. The differences between MCD spectra of proteins in equilibrium and non-equilibrium conformations, in particular for the visible region, show clearly the structural changes in the heme iron coordination sphere to occur on ligand binding. The comparison of the Soret MCD spectra of reduced proteins in their equilibrium and non-equilibrium forms with those of other high-spin ferrous hemoproteins suggest that mercaptide (RS-) is the protein ligand of the heme iron in reduced P450, as well as in its CO-complex, and that imidazole of histidine is the fifth ligand of the iron both in reduced P420 and its CO-complex. The thermal recombination of the photoproducts with CO have been studied. When temperature rises from 4.2 to 77 K for two hours both proteins have similar temperature characteristics during the recombination processes. The recombination begins at T approximately equal to 10 K and is completed at approximately equal to 50 K. The temperature at which half of the total photolyzed molecules are restored to the CO-form is equal to 25 K. For products of photolysis of CO-complexes of myoglobin and hemoglobin under the same heating conditions these temperatures are equal to 35 and 23 K respectively. Thus, the photoproducts of P450, P420 and hemoglobin have similar parameters of low-temperature recombination and the kinetics of this process is faster than for photodissociated myoglobin.

Animals↗
PubMedDate not supplied

Codon equilibrium I: Testing for homogeneous equilibrium.

We present theoretical considerations that suggest that synonymous-codon usage might be expected to be close to an equilibrium distribution given a very homogeneous process of silent substitution. By homogeneous we mean that substitution depends only on the two bases involved, so that 12 base-substitution rates completely describe the silent substitution process. We have developed a method of statistically testing for such homogeneous equilibrium and applied it to reported data on the codon usages of different classes of organisms. Weakly expressed bacterial sequences and both mammalian and nonmammalian eukaryotic sequences deviate significantly from a random pattern of codon usage, in the direction of homogeneous equilibrium. On the other hand, highly expressed bacterial sequences do not exhibit homogeneous equilibrium, which may be correlated with recent experimental results showing that they are optimized to accept the most abundant tRNAs. To examine the effect of amino acid replacements on the homogeneous model of silent substitution, we divided the amino acids with degenerate codes into two classes, those with high mutabilities and those with low, and performed the same analysis on bacterial and eukaryotic data sets. The codon sets of the highly mutable class of amino acids are not further from homogeneous equilibrium than are the codon sets of the class with low mutabilities. We also found for the eukaryotic data that these independent classes of codon sets show very similar equilibrium patterns. The various results suggest a high level of uniformity in the process of silent fixation in the different synonymous-codon sets, especially in eukaryotes.

Amino Acid Sequence↗
PubMed1977

Equilibrium and kinetics of the unfolding of alpha-lactalbumin by guanidine hydrochloride (IV): dependence of the N equilibrium A transconformation on the temperature.

The reversible unfolding from the native (N) state to the acid (A) state of alpha-lactalbumin by guanidine-HCl (0.8-2.0 M) was studied at 10-35 degrees C by means of difference spectra and pH-jump measurements. At each temperature, all points plotted as the logarithmic equilibrium constant log KNA of the N equilibrium A process against pH could fall on a curve independent of the denaturant concentration by shifting each point along the log KNA axis, where the shift factor f did not depend on temperature. Moreover, by shifting the points at each temperature along the log (KNA/f) axis, a master curve, independent of both temperature and the denaturant concentration, could be obtained for the pH-dependence of log KNA. From the dependence of the logarithmic rate constants on pH, master curves independent of both temperature and the denaturant concentration could also be made for the N leads to A and the A leads to A processes, where A mean the activated state. The results show the two-state character of the N equilibrium A process. The enthalpy changes and the differences in heat capacity for the N equilibrium A, N equilibrium A and A equilibrium A processes were determined from the accurate measurements of temperature dependence of the unfolding at pH 4.3 and 1.0 M guanidine-HCl. The results show that the disruption of hydrophobic interaction is caused mainly in the A leads to A process, while most of the changes in the pK values of the ionizing groups are caused in the N leads to A process.

Guanidines↗
PubMed1975

Time hierarchy, equilibrium and non-equilibrium in metabolic systems.

A metabolic system consists of cooperating biochemical reactions. The motion is described by differential equations in the metabolites. The right-hand sides of these equations are linear combinations of the velocities of the individual reactions. These velocities depend in a non-linear manner on the metabolite concentrations (according to the law of mass action). A characteristic "metabolic" time may be defined for the motion of the whole system. It scales the essential metabolic events whose evolution time is comparable to this metabolite time unit. The constituent reactions of the metabolic system have an individual characteristic time which need not coincide with the general metabolic time. The individual time characterises the approach to the individual equilibrium of the isolated undisturbed reaction. According to the ratio of these two time scales, a single reaction may be fast, or slow, or essential, as compared with the metabolic events. Characteristic time of a single reaction and its steady-state deviation from equilibrium are closely related. It can be shown that the relative deviation from equilibrium of a reaction within the metabolic network is of the same numerical order as the ratio between individual time to metabolic time. The interaction of many reactions with different characteristic times introduces a time hierarchy into the system. This can be made transparent by appropriate scaling and by linear transformation of the system. The subsystem of fast cooperating reactions (dehydrogenases, phosphotransferases) attains a state which is near to the individual equilibrium and reestablishes this state after perturbation. The equilibration is fast; an ultrarapid phase of cofactor equilibrium can be distinguished from the fast phase of substrate equilibrium (exchange of metabolic material between different pathways). During the slower metabolic phase these near-equilibria manifest themselves as stoichiometric linkage between unrelated metabolites. The latter cease to be independent variables and combine to metabolic pools. It can be strictly shown that the essential variables at the metabolic time scale are carrier pools and the degree of occupancy of these carriers by metabolic groups. Chemically different types of carrier pools may be functionally linked together by fast reactions. A consequence of such an arrangement of reactions are distance effects: Changes at one end of a metabolic map may be directly conveyed to other pathways via stoichiometric linkage brought about by fast equilibration of cofactor reactions.

Enzymes↗
PubMed2005

Selection of smart aptamers by equilibrium capillary electrophoresis of equilibrium mixtures (ECEEM).

We coin a term of "smart aptamers", which describes aptamers with predefined binding parameters of their interaction with the target. Here, we introduce a method for selection of smart aptamers with predefined values of Kd: equilibrium capillary electrophoresis of equilibrium mixtures (ECEEM). Conceptually, a mixture of a target with a DNA (RNA) library is prepared and equilibrated. A plug of the equilibrium mixture is injected into a capillary prefilled with a run buffer containing the target at the concentration identical to the target concentration in the equilibrium mixture. The components of the equilibrium mixture are separated by capillary electrophoresis while equilibrium is maintained between the target and aptamers. The unique feature of ECEEM is that aptamers with different Kd values migrate with different and predictable mobilities. Thus, collecting fractions with different mobilities results in smart aptamers with different and predefined Kd values. In this proof-of-principle work, we used ECEEM to select smart aptamers for MutS protein, for which aptamers have never been previously selected. Three rounds of ECEEM-based selection were sufficient to obtain smart aptamers with Kd values approaching theoretically predicted ones. ECEEM is the first method for aptamer selection whose ability to generate smart aptamers has been experimentally proven.

Base Sequence↗
PubMed2006

Relation between absorbed dose, charged particle equilibrium and nuclear transformations: a non-equilibrium thermodynamics point of view.

We present a discussion to show that the absorbed dose D is a time-dependent function. This time dependence is demonstrated based on the concepts of charged particle equilibrium and on radiation equilibrium within the context of thermodynamic non-equilibrium. In the latter, the time dependence is due to changes of the rest mass energy of the nuclei and elementary particles involved in the terms summation operator Q and Q that appear in the definitions of energy imparted epsilon and energy deposit epsilon(i), respectively. In fact, nothing is said about the averaging operation of the non-stochastic quantity mean energy imparted epsilon, which is used in the definition of D according to ICRU 60. It is shown in this research that the averaging operation necessary to define the epsilon employed to get D cannot be performed with an equilibrium statistical operator rho(r) as could be expected. Rather, the operation has to be defined with a time-dependent non-equilibrium statistical operator rho(r, t); therefore, D is a time-dependent function D(r,t).

Computer Simulation↗
PubMed2006

Trunk biomechanical models based on equilibrium at a single-level violate equilibrium at other levels.

Accurate estimation of muscle forces in various occupational tasks is critical for a reliable evaluation of spinal loads and subsequent assessment of risk of injury and management of back disorders. The majority of biomechanical models of multi-segmental spine estimate muscle forces and spinal loads based on the balance of net moments at a single level with no consideration for the equilibrium at remaining levels. This work aimed to quantify the extent of equilibrium violation and alterations in estimations when such models are performed at different levels. Results are compared with those of kinematics-driven model that satisfies equilibrium at all levels and EMG data. Regardless of the method used (optimization or EMG-assisted), single-level free body diagram models yielded estimations that substantially altered depending on the level considered (i.e., level dependency). Equilibrium of net moment was also grossly violated at remaining levels with the error increasing in more demanding tasks. These models may, however, be used to estimate spinal compression forces.

Back↗
PubMed2006

Unfolding single RNA molecules: bridging the gap between equilibrium and non-equilibrium statistical thermodynamics.

During the last 15 years, scientists have developed methods that permit the direct mechanical manipulation of individual molecules. Using this approach, they have begun to investigate the effect of force and torque in chemical and biochemical reactions. These studies span from the study of the mechanical properties of macromolecules, to the characterization of molecular motors, to the mechanical unfolding of individual proteins and RNA. Here I present a review of some of our most recent results using mechanical force to unfold individual molecules of RNA. These studies make it possible to follow in real time the trajectory of each molecule as it unfolds and characterize the various intermediates of the reaction. Moreover, if the process takes place reversibly it is possible to extract both kinetic and thermodynamic information from these experiments at the same time that we characterize the forces that maintain the three-dimensional structure of the molecule in solution. These studies bring us closer to the biological unfolding processes in the cell as they simulate in vitro, the mechanical unfolding of RNAs carried out in the cell by helicases. If the unfolding process occurs irreversibly, I show here that single-molecule experiments can still provide equilibrium, thermodynamic information from non-equilibrium data by using recently discovered fluctuation theorems. Such theorems represent a bridge between equilibrium and non-equilibrium statistical mechanics. In fact, first derived in 1997, the first experimental demonstration of the validity of fluctuation theorems was obtained by unfolding mechanically a single molecule of RNA. It is perhaps a sign of the times that important physical results are these days used to extract information about biological systems and that biological systems are being used to test and confirm fundamental new laws in physics.

Animals↗
PubMed2002

Nonequilibrium capillary electrophoresis of equilibrium mixtures--a single experiment reveals equilibrium and kinetic parameters of protein-DNA interactions.

We introduce a novel electrophoretic method, nonequilibrium capillary electrophoresis of equilibrium mixtures (NECEEM), and demonstrate its use for studying protein-DNA interactions. The equilibrium mixture of protein and DNA contains three components: free protein, free DNA, and the protein-DNA complex. A short plug of such a mixture is injected into the capillary, and the three components are separated under nonequilibrium conditions. The resulting electropherograms are composed of characteristic peaks and exponential curves. An easy nonnumerical analysis of a single electropherogram reveals two parameters: the equilibrium binding constant and the monomolecular rate constant of complex decay. The bimolecular rate constant of complex formation can then be calculated as the product of the two experimentally determined constants. NECEEM was applied to study the interaction between single-stranded DNA binding protein and a fluorescently labeled 15-mer oligonucleotide. It allowed us to measure for the first time the rate constant of complex decay for this important protein-DNA pair, k-1 = 0.03 s-1. The value of the equilibrium binding constant, Kb = 3.6 x 10-6 M-1, was in good agreement with those measured by other methods. As low as 10-18 mol of the protein was sufficient for the measurements. Thus, the new method is simple, informative, and highly sensitive. Moreover, it can be equally applied to other noncovalent protein-ligand complexes. These features of NECEEM make this method an indispensable tool in studies of macromolecular interactions. They also emphasize the potential role of NECEEM in the development of extremely sensitive protein assays using nucleotide aptamers.

DNA↗
PubMed2000

Simulations of NMR pulse sequences during equilibrium and non-equilibrium chemical exchange.

The McConnell equations combine the differential equations for a simple two-state chemical exchange process with the Bloch differential equations for a classical description of the behavior of nuclear spins in a magnetic field. This equation system provides a useful starting point for the analysis of slow, intermediate and fast chemical exchange studied using a variety of NMR experiments. The McConnell equations are in the mathematical form of an inhomogeneous system of first-order differential equations. Here we rewrite the McConnell equations in a homogeneous form in order to facilitate fast and simple numerical calculation of the solution to the equation system. The McConnell equations can only treat equilibrium chemical exchange. We therefore also present a homogeneous equation system that can handle both equilibrium and non-equilibrium chemical processes correctly, as long as the kinetics is of first-order. Finally, the same method of rewriting the inhomogeneous form of the McConnell equations into a homogeneous form is applied to a quantum mechanical treatment of a spin system in chemical exchange. In order to illustrate the homogeneous McConnell equations, we have simulated pulse sequences useful for measuring exchange rates in slow, intermediate and fast chemical exchange processes. A stopped-flow NMR experiment was simulated using the equations for non-equilibrium chemical exchange. The quantum mechanical treatment was tested by the simulation of a sensitivity enhanced 15N-HSQC with pulsed field gradients during slow chemical exchange and by the simulation of the transfer efficiency of a two-dimensional heteronuclear cross-polarization based experiment as a function of both chemical shift difference and exchange rate constants.

Flow Injection Analysis↗
PubMed2004

Phases, periphases, and interphases equilibrium by molecular modeling. I. Mass equilibrium by the semianalytical stochastic perturbations method and application to a solution between (120) gypsum faces.

The SASP (semianalytical stochastic perturbations) method is an original mixed macro-nano-approach dedicated to the mass equilibrium of multispecies phases, periphases, and interphases. This general method, applied here to the reflexive relation C(k)<=>mu(k) between the concentrations C(k) and the chemical potentials mu(k) of k species within a fluid in equilibrium, leads to the distribution of the particles at the atomic scale. The macroaspects of the method, based on analytical Taylor's developments of chemical potentials, are intimately mixed with the nanoaspects of molecular mechanics computations on stochastically perturbed states. This numerical approach, directly linked to definitions, is universal by comparison with current approaches, DLVO Derjaguin-Landau-Verwey-Overbeek, grand canonical Monte Carlo, etc., without any restriction on the number of species, concentrations, or boundary conditions. The determination of the relation C(k)<=>mu(k) implies in fact two problems: a direct problem C(k)=>mu(k) and an inverse problem mu(k)=>C(k). Validation of the method is demonstrated in case studies A and B which treat, respectively, a direct problem and an inverse problem within a free saturated gypsum solution. The flexibility of the method is illustrated in case study C dealing with an inverse problem within a solution interphase, confined between two (120) gypsum faces, remaining in connection with a reference solution. This last inverse problem leads to the mass equilibrium of ions and water molecules within a 3 A thick gypsum interface. The major unexpected observation is the repulsion of SO(4) (2-) ions towards the reference solution and the attraction of Ca(2+) ions from the reference solution, the concentration being 50 times higher within the interphase as compared to the free solution. The SASP method is today the unique approach able to tackle the simulation of the number and distribution of ions plus water molecules in such extreme confined conditions. This result is of prime importance for all coupled chemical-mechanical problems dealing with interfaces, and more generally for a wide variety of applications such as phase changes, osmotic equilibrium, surface energy, etc., in complex chemical-physics situations.

Journal Article↗