The reliability of Michaelis constants and maximum velocities estimated by using the integrated Michaelis–Menten equation

1. Experimental progress curves were simulated for a reaction obeying Michaelis-Menten kinetics. 2. K(m) and V were estimated (a) by fitting the integrated Michaelis-Menten equation to the progress curves, and (b) from the initial slopes of the curves (i.e. from initial velocities). 3. The integrated equation could not be fitted successfully by a non-linear method, so it was transformed and fitted by a linear method. 4. Provided that the initial substrate concentration was greater than K(m) and the data were precise enough, the integrated equation gave parameter estimates which were unbiased and as reliable as those derived from initial velocities although based on fewer experiments. 5. The integrated equation could be used for progress curves of unknown origin.     

The affinity of rabbit muscle fructose-bisphosphatase for fructose bisphosphate

This paper reports that microM concentrations of fructose bisphosphate are titrated by rabbit muscle fructose-bisphosphatase (D-fructose-1,6-bisphosphate 1-phosphohydrolase, EC 3.1.3.11) when the enzyme concentration is varied in the range which secures measurable initial velocities of reaction: a result that can only be explained by supposing that the enzyme has a greater affinity for fructose bisphosphate than suggested by Fernando, J., Enser, M., Pontremoli, S. and Horecker, B.L. (1968) Arch. Biochem. Biophys. 126, 599-606. The results also suggest that the keto form of the substrate may be the preferred configuration and that the enzyme is inhibited by magnesium-bound fructose bisphosphate.     

The kinematic consequences of invariant dynamics in children 6-18 years of age

The effect of limb dynamics on trajectory formation is unclear. The natural frequency of a limb is the major factor in its dynamics. It has previously been shown with an indirect measurement method that the natural frequency of body segments is invariant during human growth from the age of 6 to 18. The aim of our study was to determine, using a direct measurement method, whether human growth affects: (1) lower limb dynamics (i.e. the natural frequency of the lower leg) and (2) the maximum velocities of the knee during selected motor tasks. In 20 non-disabled children, 6-18 years of age, measurements were taken of the natural frequency of the lower leg (including the foot), and the maximum velocities of knee flexion and extension during voluntary movement (MVV) and at initial and terminal swing phases of self-paced walking (WAL). The velocities were also estimated using a dynamic model and the results were compared to the measured velocities with a paired t-test. Correlations among the frequencies, velocities, and body height (an indicator of growth) were calculated. The natural frequency of the lower leg (mean+/-standard deviation, omega(0)=6.58+/-0.54s(-1)), maximum velocities of knee extension and flexion during voluntary movement (MVV(e)=10.1+/-1.8rads(-1) and MVV(f)=7.8+/-1.3rads(-1), respectively), and maximum velocities of knee flexion and extension during the swing phase of walking (WAL(f)=5.4+/-0.6rads(-1) and WAL(e)=6.3+/-0.87rads(-1), respectively) were each found to be independent of body height. The MVV measured velocities were 22% larger and WAL(f) measured velocities were 25% smaller than the velocities predicted from the dynamic model (p<0.05). The study found that a segment's dynamic properties, as well as selected kinematics, may be considered invariant with human growth.     

Further studies on the purine phosphoribosyltransferase 'burst' velocity reaction.

In the assays used to determinate the adenine and hypoxanthine-guanine phosphoribosyltransferases activities from Artemia cysts two phases of velocity are observed in the synthesis of AMP, IMP and GMP: one initial burst and a second, slower, steady-state velocity. Both reaction velocities are divalent cation-dependent and temperature-resistant, as they are detectable at temperatures from 0 to 100 degrees C. Butanol, frequently employed to interrupt the purine phosphoribosyltransferase reactions, does not inhibit the enzyme activities. The 'burst' phase is not detected when the reaction is ended by the addition of EDTA. These data support that the initial velocities of these enzymatic reactions may be due to the accumulation of products formed by the overall reaction, developed subsequent to the controlled reaction period, being the 'burst' a result from the relative resistance of these enzymes to the agents that are often used to stop the reaction, such as heat or butanol.     

SUCCESSION AND CURRENT DEMAND RELATIONSHIPS OF DIATOMS ON ARTIFICIAL SUBSTRATES IN PRATER'S CREEK,SOUTH CAROLINA1,2

A study concerning the colonization of glass slides by diatoms was conducted in Prater's Creek, Pickens County. S. C., to observe qualitatively and quantitatively the responses of the periphytic community to current velocities for varied lengths of time. Over short time periods (1, 2 and 4 weeks) diatoms seemed to adhere best at slow current velocities. Over longer periods (6 weeks) growth, of the initial colonizers seemed to be the density governing factor; consequently, the highest diatom densities developed at the higher current, velocities. The interaction of time and current resulted in a reversal of the diatom deposition phenomenon.     

Kinetics of enzymes subject to very strong product inhibition: Analysis using simplified integrated rate equations and average velocities

Enzymes which catalyze energetically unfavorable reactions in the physiological direction are likely to be strongly inhibited by the reaction products. (Some energetically favorable reactions may also display strong "product inhibition" when assayed in the reverse direction.) In some cases, the inhibition caused by an accumulating product is so potent that true initial velocities cannot be directly determined using conventional assay methods. Continuous removal of the inhibitory product may be mitigated against by the nature of the assay or the unavailability of the appropriate coupling enzyme. It can be shown that if (a) only one inhibitory product is allowed to accumulate and (b) the substrate concentrations remain essentially constant over the assay period (i.e. Kproduct less than or equal to 10(-2)Ksubstrate, so that the decreasing reaction rate stems only from progressive product inhibition), then plots of reciprocal average (apparent) velocity (i.e. 1/v = t/[P]) versus [P] are linear and extrapolate to 1/v0, the reciprocal of the initial uninhibited velocity at the fixed substrate concentrations. Intercept replots give the usual initial velocity reciprocal plot patterns and permit Vmax and the substrate Km's to be determined. Slope replots are diagnostic of the type of inhibition exerted by the accumulating product and permit the inhibition constants to be determined. If all the appropriate coupling enzymes are available, some kinetic mechanisms can be diagnosed using data derived from the reaction progress curves in the presence of one accumulating product at a time.     

Transient relative motion of two cells in a channel flow

The hydrodynamic interaction of a red blood cell and a white blood cell in microvessels is studied, by use of a two-dimensional numerical model. The red blood cell, modeled as a small rigid circular cylinder, and the white blood cell, modeled as a larger rigid circular cylinder, are immersed in an incompressible Newtonian fluid in a two-dimensional channel. It is assumed that no external force or moment acts on the model cells, and the effect of inertia forces on the motion of the fluid and the cells is neglected. The velocity field of the suspending fluid and the instantaneous velocities of the two model cells are computed by the finite element method. Using the translational velocities of the model cells obtained, the trajectories of their relative motion are determined, for various initial positions. It is shown that the cells may or may not pass each other or separate, depending on the initial positions. The present results compare well to the experimental results.     

On the validity of using semilogarithmic plots to determine initial velocities of enzyme-catalyzed reactions

It has been proposed (Johnston & Diven, 1969a) that it is valid to use semilogarithmic (first-order) plots of the extent of reaction versus time for graphic determination of initial velocities of enzyme-catalyzed reactions. This proposition suggests the assumption that the initial velocity error expected to be introduced by the proposed procedure is smaller than or comparable to the error introduced by the customary graphic procedure. The latter is based on the assumption that the progress curves of enzyme-catalyzed reactions have an initial linear segment of sufficient duration to permit accurate determination of slope. The validity of the procedure proposed by Johnston and Diven is examined in this report. It is concluded that the procedure is applicable to a very small class of enzyme-catalyzed reactions and only under certain experimental conditions.     

An assay for inhibitors of nucleoside transport based upon the use of 5-[125I]iodo-2'-deoxyuridine as permeant

5-[125I]Iodo-2'-deoxyuridine (IdUrd) has been shown to serve as a permeant for the nucleoside transport system of human erythrocytes and to be matabolically inert in these cells. Linear initial velocities were obtained at 20 degrees C for 125IdUrd transport, yielding a Km of 73 +/- 18 microM (n = 6). Low-affinity inhibitors of 125IdUrd transport, such as adenosine (Ki = 32 +/- 2 microM, n = 2), could be characterized by Michaelis-Menten kinetics. However, high-affinity inhibitors, such as 6-[(4-nitrobenzyl)thio]-9-beta-D-ribofuranosylpurine, caused nonlinear initial velocities when added to the cells simultaneously with 125IdUrd. Conditions were defined (viz., 20-min pretreatment of cells with test compound followed by 5.0-min incubation with 1.0 microM 125IdUrd, all at 20 degrees C) whereby high-affinity inhibitors of IdUrd transport can be identified and evaluated according to their 50% inhibitory concentrations. The use of 125IdUrd as permeant greatly expedites the testing of compounds as inhibitors of nucleoside transport by allowing the cell pellets generated in these assays to be monitored directly in a gamma spectrometer, thereby circumventing the solubilization and decolorization of cell pellets required by assays that use 3H- or 14C-labeled nucleoside permeants.     

Random coil scission rates determined by time-dependent total intensity light scattering: hyaluronate depolymerization by hyaluronidase

A recently developed theory of the light scattering by random coils undergoing random scission is applied to the digestion of hyaluronate by hyaluronidase. The time dependence of the scattered light from solutions undergoing digestion was monitored. Working at a high angle with high molecular weight hyaluronate allowed the use of a powerful approximation for determining initial velocities and the Henri-Michaelis-menten coefficients, without explicit knowledge of the hyaluronate molecular weight, radius of gyration, second virial coefficient, or polydispersity. Effects due to a molecular weight dependent second virial coefficient and to non-Gaussian behavior are briefly considered. Assays were performed over nearly two orders of magnitude in substrate concentration. The initial velocities are compared with those obtained by a standard reducing sugar assay, which was performed on identical samples. The main advantages of the light scattering assay procedure over the more traditional assays are that many relatively high-precision data points can be quickly and automatically collected with simple apparatus, and that the technique is most sensitive for the initial period of digestion, where the other assays are least sensitive. The shapes of the scattering curves also provide evidence that hyaluronate in these solutions is not a stable double strand and that the hyaluronidase cleaves bond randomly. The curves also indicate that enzyme deactivation occurs, which accounts for the lower velocities yielded by the slower reductimetric assay, which is measured over longer initial periods.     

The regulatory properties of rabbit muscle pyruvate kinase. The influence of effector concentrations

The initial velocity of the reaction catalysed by rabbit muscle pyruvate kinase was studied as a function of the concentrations of the modifiers phenylalanine and fructose 1,6-bisphosphate under conditions where the relationships between the initial velocities and the concentrations of substrates are non-hyperbolic. It is shown that these data can be represented by the exponential model for a regulatory enzyme.     

Prior storage conditions and loading rate affect the in vitro fracture response of spinal segments under impact loading

Traumatic injuries of the spine are mostly the consequence of rapid overload e.g. impact loading. In vitro investigations on this topic usually encompass biomechanical testing using frozen/thawed specimens and employ quasi-static loading conditions. It is generally accepted that a freezing/thawing cycle does not alter mechanical properties for slow loading rates. However, this has never been investigated for high impact velocities. In order to assess the effects of freezing/thawing and the influence of different impact velocities, we loaded 27 fresh and 15 frozen/thawed cadaveric rabbit spinal segments (intervertebral disc with one third of the adjacent vertebrae) with different impact energies and velocities using a custom-made, dropped-weight loading device. Endplate fractures were assessed by micro-CT scans. Specimen dimensions (disk, bone, and total height) and vertebrae bone density (BV/TV) were compared pre- and post-trauma. Energy absorption by spinal segments was quantified by measuring the initial ball rebound. We found that freezing/thawing increased endplate fracture frequency and decreased the energy absorption of the segments. Higher impact velocities increased the energy absorption, while higher impact energy increased both energy absorption and fracture frequency. Two conclusions are drawn: first, under impact loading, freezing alters permanently the biomechanical response, and second, for different impact velocities, different fracture initiation mechanisms apply. Therefore, quasi-static loading of frozen/thawed spinal segments is not a valid model for traumatic endplate injuries. However, caution should be exercised in extrapolating these findings to human vertebrae until tests on larger vertebrae are performed.     

Mechanics of gliding in birds with special reference to the influence of the ground effect

A model of the mechanics of gliding without loss of altitude (horizontal gliding) is developed. The model can be employed to assess the influence of the principal drag components (induced, profile and parasite drag), choice of initial and final glide velocities and height above the ground on glide distance. For birds gliding near to the ground the ground effect acts to decrease the induced drag and increase the lift to drag ratio of the wings. Minimum drag speed is reduced for birds gliding near to the ground. The model is applied to the gliding flight of the black skimmer (Rhyncops nigra). Glide distances for given initial and final velocities are significantly increased in the influence of the ground effect over out of ground effect values.     

Internal carotid and vertebral arterial flow velocity in men at high altitude

Cerebral blood flow increases at high altitude, but the mechanism of the increase and its role in adaptation to high altitude are unclear. We hypothesized that the hypoxemia at high altitude would increase cerebral blood flow, which would in turn defend O2 delivery to the brain. Noninvasive Doppler ultrasound was used to measure the flow velocities in the internal carotid and the vertebral arteries in six healthy male subjects. Within 2-4 h of arrival on Pikes Peak (4,300 m), velocities in both arteries were slightly and not significantly increased above sea-level values. By 18-44 h a peak increase of 20% was observed (combined P less than 0.025). Subsequently (days 4-12) velocities declined to values similar to those at sea level. At altitude the lowest arterial O2 saturation (SaO2) and the highest end-tidal PCO2 was observed on arrival. By day 4 and thereafter, when the flow velocities had returned toward sea-level values, hemoglobin concentration and SaO2 were increased over initial high-altitude values such that calculated O2 transport values were even higher than those at sea level. Although the cause of the failure for cerebral flow velocity to increase on arrival is not understood, the subsequent increase may act to defend brain O2 transport. With further increase in hemoglobin and SaO2 over time at high altitude, flow velocity returned to sea-level values.     

Primitive nervous systems: electrophysiology of the pharynx of the polyclad flatworm, Enchiridium punctatum.

1. Electrical activity accompanying motor activity can be recorded from the excised pharynx of Enchiridium punctatum. Multiple stimuli elicit behaviour which consists of an initial aperture closure followed by extension and then peristalsis. If the stimulus parameters are increased the preparation bends from side to side instead of proceeding through the behavioural sequence. Bending appears to inhibit other movements differentially. 2. The conduction involved with peristalsis is polarized and proceeds in a proximal direction. 3. With stimulus intensities greater than those needed to produce the behavioural response an initial muscle potential (IMP) is evoked. The IMP is frequency sensitive. Maximum facilitation occurs within 100 ms and drops to 50% of maximum within 250 ms. 4. Conduction velocities of the IMP range from 0-05 m s-1 to 1-9 m s-1. Conduction velocities appear to increase with facilitation.     

The nature of experimental error in enzyme kinetic measurments.

The nature of experimental error in the determination of initial velocities of enzyme-catalysed reactions was investigated. No support was found for the generalization that such velocities should be homogeneous in variance. Instead the variance increased with the velocity in all of the cases studied. The weighting of sets of replicate observations according to their sample variances was tested in simulated experiments and found to give unacceptable results. It was practicable to decide on the best weighting scheme by examining the variability of the deviations from fitted curves, provided that the number of observations was large enough.     

Studies on the biosynthesis of cytochrome P-450 in rat liver--a probe with phenobarbital.

The reaction of NAD(P)H:flavin oxidoreductase (flavin reductase) from Photobacterium fischeri is proposed to follow a ping-pong bisubstrate-biproduct mechanism. This is based on a steady-state kinetic analysis of initial velocities and patterns of inhibition by NAD⁺ and AMP. The double reciprocal plots of initial velocities versus concentrations of FMN or NADH show, in both cases, a series of parallel lines. The Michaelis constants for NADH (FMN saturating) and FMN (NADH saturating) are 2.2 and 1.2 × 10^?4m, respectively. The product NAD⁺ has been found to be an inhibitor competitive with FMN but non-competitive with NADH. Using AMP as an inhibitor, noncompetitive inhibition patterns were observed with respect to both NADH and FMN as the varied substrate. In addition, the reductase was not inactivated by treatment with N-ethylmaleimide either alone or in the presence of FMN, but the enzyme was inactivated by N-ethylmaleimide in the presence of NADH. These findings suggest that flavin reductase shuttles between disulfide- and sulfhydryl-containing forms during catalysis.     

Purine base transport in normal and mutant erythrocytes.

The uptake of adenine and hypoxanthine in HGPRT-deficient and normal human erythrocytes was measured using a rapid filtering centrifugation technique. The transport of hypoxanthine as well as of adenine is impaired in the mutant cells. The transport of hypoxanthine into HGPRT-deficient erythrocytes differs from that into normal cells with respect to a higher accumulation capacity, to lower initial velocities and to the kinetic properties of the translocator. In addition, a higher accumulation capacity and lower initial velocities of adenine uptake could be demonstrated in mutant cells. A linkage of the purine translocator with purine phosphoribosyltransferases associated with the erythrocyte membrane is discussed.     

Do the hamstrings operate at increased muscle–tendon lengths and velocities after surgical lengthening?

Children with crouch gait frequently walk with improved knee extension during the terminal swing and stance phases following hamstrings lengthening surgery; however, the mechanisms responsible for these improvements are unclear. This study tested the hypothesis that surgical lengthening enables the hamstrings of persons with cerebral palsy to operate at longer muscle-tendon lengths or lengthen at faster muscle-tendon velocities during walking. Sixty-nine subjects who had improved knee extension after surgery were retrospectively examined. The muscle-tendon lengths and velocities of the subjects' semimembranosus muscles were estimated by combining kinematic data from gait analysis with a three-dimensional computer model of the lower extremity. Log-linear analyses confirmed that the subjects who walked with abnormally short muscle-tendon lengths and/or slow muscle-tendon velocities preoperatively tended to walk with longer lengths (21 of 29 subjects, p<0.01) or faster velocities (30 of 40 subjects, p<0.01) postoperatively. In these cases, surgical lengthening may have slackened the subjects' tight hamstrings and/or diminished the hamstrings' spastic response to stretch. Other subjects walked with muscle-tendon lengths and velocities that were neither shorter nor slower than normal preoperatively (22 of 69 subjects), and the semimembranosus muscles of most of these subjects did not operate at increased lengths or velocities after surgery; in these cases, the subjects' postsurgical improvements in knee extension may have been unrelated to the hamstrings surgery. Analyses of muscle-tendon lengths and velocities may help to distinguish individuals who have "short" or "spastic" hamstrings from those who do not, and thus may augment conventional methods used to describe patients' neuromusculoskeletal impairments and gait abnormalities.     

Acquisition of the lateral inconsistency in involuntary behaviour of upper limbs in 12-year-old children during walking at moderate speed.

The aim of this work was to investigate possible lateralisation in the behaviour of periodic motion of the human upper limb, during normal walking at a comfortable speed of locomotion. Ten healthy pre-adolescent, strongly right-handed, 12-year-old males participated in the experiment. Participants were walking on a treadmill with a standardised velocity of 1.1m/s (comfortable speed for all of them). A video analysis system with Silicon software was used to synchronically measure various angles of arms and forearms. The initial, final and interim angular positions of both arms and forearms in 10 cycles of each participant were compared in terms of variations (cycle to cycle) between both upper extremities at corresponding phases of each cycle for distal and proximal segments, respectively. We compared the coefficients of variation in relation to the spatial and temporal data of both limbs and their angular velocities. In addition we investigated the level of cycle-to-cycle regularity (constancy) of behaviour in relation to various positions, periods and velocities of movement of upper extremities (specifically arms and forearms) using the Eta non-linear method of correlation. All participants exhibited a lower level of regularity for the distal segments. The spatial and temporal variations in the dominant limb were also greater than the non-dominant limb for all participants. This may be due to a larger contribution from the right-sided muscles that are considered to be the main contributing factor to the motion of the dominant upper limb during walking, rather than simply gravity force acting alone. A possible practical application of this information may be useful in the objective clinical identification of the level of dominance of the upper extremity (arm plus forearm), in addition to 'traditional' handedness.