Epidermal growth factor receptor binding is not a simple one-step process

The binding kinetics of 125I-labeled mouse epidermal growth factor (EGF) to receptors on human fibroblast cells in monolayer culture were measured at 4 degrees C. Initial binding rates as a function of hormone concentration allowed estimation of simple two-state on-off rate constants of 1.2 x 10(6) M-1 s-1 and 4.9 x 10(-3) s-1, respectively. These two-state parameters gave inadequate computer fits to long term kinetic and equilibrium-binding data, suggesting that an additional process(es) was occurring. Nonlinear equilibrium Scatchard plots and transient "pseudo-Scatchard" plots taken at pre-equilibrium times support the idea that at least one other process is occurring during receptor binding. 125I-EGF-receptor dissociation kinetic plots were biphasic, yielding rate constants of 1.5 x 10(-2) s-1 and 5.6 x 10(-5) s-1 with the ratio of the two components changing with the time of initial incubation with 125I-EGF. Application of a ternary complex model which assumed complexation of the bound receptor with a cell surface interaction molecule gave satisfactory fits to all data.     

Effect of substrates and coenzymes on the molecular symmetry-related properties of horse liver and yeast alcohol dehydrogenases

Thermal inactivation of horse liver alcohol dehydrogenase (LADH) exhibits the following biphasic kinetics A = Afast.e-Kfast.t + Aslow.e-Kslow.t Where A is the per cent residual activity at time t,Afast and Aslow are amplitudes (expressed as % of initial activity) and kfast and kslow first-order rate constants of the fast and slow phases, respectively. For apoenzyme, Afast = Aslow = 50% of the initial activity under all conditions of temperature and pH. On the addition of a substrate or coenzyme ligand, there is a ligand concentration-dependent increase in per cent Aslow and a decrease in kslow. At sufficiently high ligand concentration, the entire time-course of inactivation can be described as a single exponential decay. The variations of per cent Aslow and of kslow with ligand concentration are consistent with the existence of two binding sites of different ligand affinities. Inactivation of LADH by excess EDTA also exhibits a similar biphasic kinetics with Afast = Aslow = 50% of the initial activity. Addition of ethanol or NAD+ brings about a concentration-dependent decrease in kfast and kslow without affecting amplitudes of the two phases. The NAD+ concentration-dependence of this decrease is consistent with a single dissociation constant for the coenzyme. Inactivation of yeast alcohol dehydrogenase by heat or excess EDTA can be represented as a single exponential decay of activity under all conditions of temperature and pH in the absence as well as presence of ethanol or NAD+. Implications of these results for the molecular symmetry of the two oligomeric enzymes in solution are discussed.     

Kinetics of Chemical Modification of Arginine Residues in Mitochondrial Creatine Kinase from Bovine Heart: Evidence for Negative Cooperativity

The kinetics of chemical modification of arginine residues in mitochondrial creatine kinase (mit-CK) from beef heart by 4-hydroxy-3-nitrophenylglyoxal (HNPG) have been studied with simultaneous registration of enzyme inactivation. Experiments showed that complete inactivation of mit-CK corresponded to modification of two arginine residues per mit-CK monomer. The data on the modification kinetics can be described by the sum of two exponential terms and suggest strong negative cooperativity in the binding of HNPG to arginine residues. The rate constants for the fast and slow phases of modification differ by a factor of about 50. The corresponding rate constants for inactivation differ by a factor of about 30. The rate constant for the slow stage of inactivation is twice as large as that for the rate constant for the slow stage of modification, i.e., the inactivation process is ahead of the modification process.     

A Kinetic Model for Human Platelet Survival with Long-Lasting Time-Activity Curves

A model is presented that allows for the interpretation of the time course of the level of radiolabeled platelets in terms of platelet survival times, rate constant for removal from circulation, pooling time in an extra pool, the rate at which platelets re-enter circulation from the extra-pool, and the size of the plasma pool and extra-pools. The tenets of the model are that: (1) platelets leave the circulation at a rate proportional to their number per unit volume; (2) of the leaving platelets, a fraction b goes into a pool from which they return into circulation after a pooling time and another fraction (1 - b) is irreversibly destroyed; (3) the platelets in the extra-pool do not “queue up”, and thus the distribution function describing the probability of return is exponential; and (4) the time activity curve of the radiolabeled platelets can be described by the sum of two exponentials. Under steady state conditions, curve fitting allows determination of the constants determining the time activity curve (the respective amplitudes and rate constants of the two exponentials); mean pooling time; relative pool size; and survival time of platelets. The model is applied to data collected from patients over a period from 10 days following reinjection of autologous radiolabeled platelets.     

Investigation of the Effect of Data Error in the Analysis of Biological Tracer Data

Data obtained from tracer studies often consist of serial measurements after administration of radioisotope. Very little work has been published on how the error in the data affects the mathematical analysis. Computer simulation was here employed to produce data with error of different magnitude and form for each of several values of rate constant and amplitude. The data were terminated when the value of the last point was 5% of the value of the first point, and also in other ways arranged to simulate experimental situations. The sets of simulated data for a two compartment system were analyzed by the gaussian iterative technique. With a rate constant ratio of at least four the technique converged for data errors of 5% or less. The calculated error in the rate constants ranged from 2 to 85%, and in the amplitudes from 1 to 50%, for data error of 0.5 to 10%. The lesser rate constant and amplitude had the greater errors. If a wrong assumption was made in the analysis about the variation of data error over the time interval of measurement, then the calculated values of parameter standard deviations were greatly in error. The results can be used to decide what experimental accuracy is needed for a given accuracy of model parameters for a variety of biological problems.     

Autonomic correlates of the formation of a functional self-stimulation system

Capability of intracerebral electrostimulation to serve as an unconditioned reinforcing stimulus in classical conditioning was studied in rabbits. Changes of such vegetative characteristics as respiration frequency and ECG were taken as criterion of conditioned response (CR) elaboration. In preliminary experiments, optimal parameters of stimulation maintaining the highest level of instrumental self-stimulation behaviour were found for each of the animals. Isolated presentation of the unconditioned reinforcing stimulus led to the increase of respiratory rate. Such kind of stimulation induced tachicardia in 5 animals, bradicardia in 3 ones, and in the remaining 6 rabbits a biphasic reaction was observed with initial tachicardia changing for bradicardia. Reactions were taken as CRs if they were similar to those to the unconditioned stimulus and appeared at the moment of omitted reinforcement. After 10 pairings of conditioned sound stimulus with positive reinforcement, CR changes of the two vegetative parameters were observed in 21,4 per cent of cases. After 40 pairings CRs were observed in 87,5 per cent of trials for cardiac and in 78,5 per cent cases for respiratory components. The results obtained confirm the idea of validity and efficiency of intracerebral stimulation of self-stimulation zones as a factor of positive reinforcement.     

Studies on the Analysis of Fluorescence Decay Data by the Method of Moments

The method of moments, as presented by Isenberg and Dyson (1969; Biophys. J. 9:1337) has been shown to be a reliable way of obtaining the amplitudes and time constants of several simultaneously emitting species, even in the presence of an overlapping excitation. Recent improvements in the method include (a) a component incrementation test for determining the number of relaxations, (b) a procedure, which we call exponential depression, for dramatically improving convergence, and (c) a new algorithm for implementing the method of moments on a digital computer with a high degree of flexibility and efficiency. These improvements, as well as new general theory, are described and tested using both synthetic and real experimental data. Component incrementation consists of examining models with increasing numbers of exponential terms. Given adequate precision, we find that an analysis for N + 1 components, of data that are actually represented by N components, provides the correct amplitudes and time constants plus an N + 1 term with an insignificant amplitude. Exponential depression is a transformation in which the original excitation and fluorescence, E(t) and F(t), are multiplied by exp (-λt), where λ is an arbitrary parameter. While the convolution is invariant to this transformation, the proper choice of λ greatly reduces the number of iterations necessary to obtain the amplitudes and time constants and may even improve their accuracy. In addition, an appendix by John P. Mullooly presents a statistical analysis of the effect of counting error on the method of moments estimates of fluorescence decay parameters, applicable when data are obtained by the monophoton technique. Formulas are derived that give the approximate precision of the decay parameters for the general case of N exponential components, with calculational details for one and two component systems.     

A Fourier method for the analysis of exponential decay curves.

A method based on the Fourier convolution theorem is developed for the analysis of data composed of random noise, plus an unknown constant "base line," plus a sum of (or an integral over a continuous spectrum of) exponential decay functions. The Fourier method's usual serious practical limitation of needing high accuracy data over a very wide range is eliminated by the introduction of convergence parameters and a Gaussian taper window. A computer program is described for the analysis of discrete spectra, where the data involves only a sum of exponentials. The program is completely automatic in that the only necessary inputs are the raw data (not necessarily in equal intervals of time); no potentially biased initial guesses concerning either the number or the values of the components are needed. The outputs include the number of components, the amplitudes and time constants together with their estimated errors, and a spectral plot of the solution. The limiting resolving power of the method is studied by analyzing a wide range of simulated two-, three-, and four-component data. The results seem to indicate that the method is applicable over a considerably wider range of conditions than nonlinear least squares or the method of moments.     

Dissociation of the lactose repressor-operator DNA complex: effects of size and sequence context of operator-containing DNA

The dissociation kinetics for repressor-32P-labeled operator DNA have been examined by adding unlabeled operator DNA to trap released repressor or by adding a small volume of concentrated salt solution to shift the Kd of repressor-operator interaction. The dissociation rate constant for pLA 322-8, an operator-containing derivative of pBR 322, was 2.4 X 10(-3) s-1 in 0.15 M KCl. The dissociation rate constant at 0.15 M KCl for both lambda plac and pIQ, each of which contain two pseudooperator sequences, was approximately 6 X 10(-4) s-1. Elimination of flanking nonspecific DNA sequences by use of a 40 base pair operator-containing DNA fragment yielded a dissociation rate constant of 9.3 X 10(-3) s-1. The size and salt dependences of the rate constants suggest that dissociation occurs as a multistep process. The data for all the DNAs examined are consistent with a sliding mechanism of facilitated diffusion to/from the operator site. The ability to form a ternary complex of two operators per repressor, determined by stoichiometry measurements, and the diminished dissociation rates in the presence of intramolecular nonspecific and pseudooperator DNA sites suggest the formation of an intramolecular ternary complex. The salt dependence of the dissociation rate constant for pLA 322-8 at high salt concentrations converges with that for a 40 base pair operator. The similarity in dissociation rate constants for pLA 322-8 and a 40 base pair operator fragment under these conditions indicates a common dissociation mechanism from a primary operator site on the repressor.     

A New Secondary Model Developed for the Growth Rate of <Emphasis Type="Italic">Escherichia coli</Emphasis> O157:H7 in Broth

This study was attempted to develop a new exponential sum model to describe the effect of temperature on growth rate (GR) of Escherichia coli O157:H7 in broth. The growth rates of E. coli O157:H7 at different storage temperatures (4, 10, 15, 20, 25, 30, and 35°C) estimated by fitting with the modified Gompertz model were used to develop secondary models such as square root model, Ratkowsky model and exponential sum model. Measures of coefficient of determination (R ²), root mean square error (RMSE) and the sum of squares due to error (SSE) were employed to compare the performances of these three secondary models. Based on these criteria, the developed exponential sum model showed the better goodness-of-fit and performance.     

Measurement of rate constants for the contractile cycle of intact mammalian muscle fibers.

Small, random length changes were applied to bundles of intact fibers from rat and mouse extensor digitorum longus (EDL) and soleus muscles, while they were being tetanically stimulated. With increasing frequency of length changes, EDL muscle stiffness (tension change per unit change in length) increased, then decreased and increased again. The decrease was not seen in the soleus muscles. The EDL frequency-response could be well fitted by three exponential components with apparent rate constants of approximately 25, 150, and 500 s-1 at 20 degrees C. All rate constants increased steadily with temperature and for each 10 degrees C increase in temperature, the rates in the mouse EDL increased by a factor (Q10) between 1.8 and 2.4. With tetanic stimulation, force increased nearly exponentially to a steady level with a rate constant of 24 s-1 at 20 degrees C in mouse EDL muscles, and a Q10 of 2.4. These values correspond closely to the lowest frequency rate constant measured with length perturbations, which suggests that this process may limit the rate of rise of force in intact muscle fibers. During fatigue the high frequency and intermediate frequency rate constants declined, but the low frequency rate constant remained unchanged. These results are discussed in relation to current biochemical models for cross-bridge cycling.     

Growth of Sclerotiumrolfsiiat Different Concentration of Oxygen and Carbon Dioxide

Sclerotium rolfsii was grown in various atmospheres, the compositionsof which were controlled by the diffusion column technique.Growth-rate of mycelium was constant within a range of oxygenconcentrations from 3 to 21 per cent, but dirminished steadilyas carbon dioxide concentration increased from about 0.03 percent. The rate of sclerotial germination was reduced by oxygenconcentrations less than 6 per cent and by carbon dioxide concentrationsgreater than about 10 per cent. No sclerotia were formed ifthe concentration of oxygen fell below 15 per cent or if thatof carbon dioxide exceeded 4 per cent. The effects of inverserationof gases, from 0 per cent oxygen: 20 per cent carbon dioxideto 21 per cent oxygen: 0 per cent carbon dioxide, were in eachcase similar to the effect of the corresponding carbon dioxideconcentration when combined with 21 per cent oxygen.     

Kinetic comparison of normal and thyrotoxic bovine cardiac myosin subfragment-1

A comparison of the transient kinetics of cardiac ventricular normal and hyperthyroid modified myosin subfragment-1 reveals substantial similarities between the two proteins. The nucleotide-binding kinetics are nonexponential for both proteins, but the large tryptophan fluorescence changes, 34% for ATP binding and 12% for ADP binding which are comparable to those of rabbit skeletal myosin subfragment-1, permit the kinetic data to be resolved into a sum of two exponentials. Both the fast and slow forms of the proteins reach limiting rate constants at high nucleotide concentration. The fast forms of normal and thyrotoxic cardiac subfragment-1 are kinetically identical for nucleotide binding at 20 degrees C and pH 7 and the slow forms differ by less than a factor of 2. The kinetic data for ADP release and the single turnover of ATP could neither be fit by a single exponential nor resolved into two components, which indicates a difference in the rate constants by a factor of 2 or less. The largest difference found was in the steady state turnover of ATP for which thyrotoxic subfragment-1 had a 2.5 times faster turnover as compared to normal subfragment-1. The fractions of fast and slow forms of the two proteins are dependent on the nucleotide concentration and the fractions as well as the rate constants are a function of the protein concentration. This is consistent with the kinetic heterogeneity of cardiac myosin subfragment-1 resulting from aggregation. The differences in the rate constant for the steady state turnover of ATP and in aggregation properties between normal and hyperthyroid cardiac subfragment-1 are consistent with the induction of a myosin isozyme by thyroxine treatment. Moreover, the increase in the steady state turnover of ATP is consistent with the increase in contractility of the muscle in the hyperthyroid state.     

Modelling of agrobacteran production in a batch culture ofAgrobacterium radiobacter

A deterministic model of production of the exopolysaccharide agrobacteran, including the effect of the product on oxygen transfer into the medium, was used for evaluation of a batch cultivation ofAgrobacterium radiobacter. Application of mass-energy balance made it possible to reduce the number of identified parameters. The resulting yield coefficients and rate constants were largely independent of the method of aeration of the culture, with the exception of the maximum specific rate of agrobacteran production which was lower if the culture in an exponential growth phase was subjected to oxygen limitation.     

Rate-amplitude correlation from single-channel records. A hidden structure in ion channel gating kinetics?

Lifetime probability density functions from single-channel recording are usually assumed to follow a multiexponential form. The amplitudes and rate constants for each exponential component are presumed to be independent. We have explored this assumption and have found a correlation between the amplitudes and the rate constants in certain cases. We examine this correlation and the possibility that other functional forms may also properly describe these distribution functions.     

Kinetic properties of cholinergic desensitization in Aplysia neurons

The kinetic properties of desensitization onset of excitatory cholinergic responses were studied in isolated, voltage-clamped Aplysia neurons. Desensitization of the acetylcholine (ACh)-induced current in response to microperfused acetylcholine occurred in two phases, and was best modelled as the sum of two exponential components plus a constant. Both exponential components were accelerated by increasing ACh dose. At the higher ACh doses the current decline was dominated by the fast exponential component, and the ratio of the plateau-peak current was reduced. Over the range of membrane potentials -50 to -110 mV, no change in the kinetics of desensitization onset was observed. The mean time constants of both exponential components were doubled by cooling from 20 degrees C to 5 degrees C. These results demonstrate that, as at the vertebrate neuromuscular junction, the onset of desensitization of this ACh response involves at least two processes which are dose- and temperature-sensitive. The lack of voltage dependence contrasts with results from vertebrate preparations, and indicates a fundamental difference between the properties of the excitatory ACh response in Aplysia neurons and the vertebrate neuromuscular junction.     

Effect of ajmaline on transient outward current in rat ventricular myocytes

The mechanism of ajmaline-induced inhibition of the transient outward current (I(to)) has been investigated in right ventricular myocytes of rat using the whole cell patch clamp technique. Ajmaline decreased the amplitude and the time integral of I(to) in a concentration-dependent, but frequency- and use-independent manner. In contrast to the single exponential time course of I(to)-inactivation in control conditions (tau(i) = 37.1 +/- 2.7 ms), the apparent inactivation was fitted by a sum of two exponentials under the effect of ajmaline with concentration-dependent fast and slow components (tau(f) = 11.7 +/- 0.8 ms, tau(s) = 57.6 +/- 2.7 ms at 10 micromol/l) suggesting block development primarily in the open channel state. An improved expression enabling to calculate the association and dissociation rate constants from the concentration dependence of tau(f) and tau(s) was derived and resulted in k(on) = 4.57 x 10(6) +/- 0.32 x 10(6) mol(-1).l.s(-1) and k(off) = 20.12 +/- 5.99 s(-1). The value of K(d) = 4.4 micromol/l calculated as k(off) / k(on) was considerably lower than IC(50) = 25.9 +/- 2.9 micromol/l evaluated from the concentration dependence of the integrals of I(to). Simulations on a simple model combining Hodgkin-Huxley type gating kinetics and drug-channel interaction entirely in open channel state agreed well with the experimental data including the difference between the K(d) and IC(50). According to the model, the fraction of blocked channels increases upon depolarization and declines if depolarization is prolonged. The repolarizing step induces recovery from block with time constant of 52 ms. We conclude that in the rat right ventricular myocytes, ajmaline is an open channel blocker with fast recovery from the block at resting voltage.     

Kinetics of thermal inactivation and quaternary structure symmetry of rabbit muscle glyceraldehyde 3-phosphate dehydrogenase

Kinetics of thermal inactivation of apo-glyceraldehyde 3-phosphate dehydrogenase have been investigated under various conditions. At most pH values, the loss of enzyme activity takes place in two phases, a fast and a slow phase. The data correspond to the rate equation A = Afast.e-kfast.t + Aslow.e-kslow, where A is the observed residual activity (expressed as % of initial activity) at time t, Afast and Aslow are amplitudes (expressed as % of initial activity, so that Afast + Aslow = 100) and kfast and kslow the rate constants of the fast and slow phases, respectively. At pH 9 or below, Afast = Aslow = 50%. As pH is increased above 9, Afast increases gradually till at pH 10 or above when it accounts for the entire initial activity (single exponential decay). The rate constants of the two phases are strongly affected by the nature of the buffer, temperature and pH, but the amplitudes depend on pH alone. It has been suggested that the tetrameric enzyme exists in two conformations of different molecular symmetry, namely C2 (two pairs of sites of unequal stability, predominating at pH 9 or below) and D2 symmetry (four equivalent sites, predominating at pH 10 or above). The C2 in equilibrium D2 transformation is found to be highly cooperative with midpoint at pH 9.6.     

Two components of voltage-dependent inactivation in Ca(v)1.2 channels revealed by its gating currents

Voltage-dependent inactivation (VDI) was studied through its effects on the voltage sensor in Ca(v)1.2 channels expressed in tsA 201 cells. Two kinetically distinct phases of VDI in onset and recovery suggest the presence of dual VDI processes. Upon increasing duration of conditioning depolarizations, the half-distribution potential (V(1/2)) of intramembranous mobile charge was negatively shifted as a sum of two exponential terms, with time constants 0.5 s and 4 s, and relative amplitudes near 50% each. This kinetics behavior was consistent with that of increment of maximal charge related to inactivation (Qn). Recovery from inactivation was also accompanied by a reduction of Qn that varied with recovery time as a sum of two exponentials. The amplitudes of corresponding exponential terms were strongly correlated in onset and recovery, indicating that channels recover rapidly from fast VDI and slowly from slow VDI. Similar to charge "immobilization," the charge moved in the repolarization (OFF) transient became slower during onset of fast VDI. Slow VDI had, instead, hallmarks of interconversion of charge. Confirming the mechanistic duality, fast VDI virtually disappeared when Li(+) carried the current. A nine-state model with parallel fast and slow inactivation pathways from the open state reproduces most of the observations.