What Happens to an Enzyme When Exposed to Heat
Biochem J. 2007 Mar i; 402(Pt 2): 331–337.
Published online 2007 Feb 12. Prepublished online 2006 Nov iii. doi:x.1042/BJ20061143
The dependence of enzyme activity on temperature: determination and validation of parameters
Michelle E. Peterson
*Department of Biological Sciences, University of Waikato, Private Purse 3105, Hamilton, 3240, New Zealand
Roy M. Daniel
*Department of Biological Sciences, Academy of Waikato, Private Bag 3105, Hamilton, 3240, New Zealand
Michael J. Danson
†Centre for Extremophile Research, Department of Biology and Biochemistry, University of Bath, Bathroom BA2 7AY, U.K.
Robert Eisenthal
‡Department of Biology and Biochemistry, University of Bathroom, Bath BA2 7AY, U.G.
Received 2006 Jul 27; Revised 2006 Oct 30; Accepted 2006 Nov iii.
Abstract
Traditionally, the dependence of enzyme activity on temperature has been described by a model consisting of 2 processes: the catalytic reaction defined by ΔG Dagger cat, and irreversible inactivation divers past ΔThousand Dagger inact. However, such a model does non account for the observed temperature-dependent behaviour of enzymes, and a new model has been developed and validated. This model (the Equilibrium Model) describes a new mechanism by which enzymes lose action at high temperatures, by including an inactive form of the enzyme (Eastinact) that is in reversible equilibrium with the active form (Eact); it is the inactive class that undergoes irreversible thermal inactivation to the thermally denatured state. This equilibrium is described past an equilibrium constant whose temperature-dependence is characterized in terms of the enthalpy of the equilibrium, ΔH eq, and a new thermal parameter, T eq, which is the temperature at which the concentrations of Eastwardact and Eastinact are equal; T eq may therefore be regarded as the thermal equivalent of Thou grand. Characterization of an enzyme with respect to its temperature-dependent behaviour must therefore include a determination of these intrinsic properties. The Equilibrium Model has major implications for enzymology, biotechnology and understanding the evolution of enzymes. The present report presents a new direct data-plumbing fixtures method based on fitting progress curves direct to the Equilibrium Model, and assesses the robustness of this procedure and the effect of analysis data on the accurate conclusion of T eq and its associated parameters. It also describes simpler experimental methods for their determination than have been previously available, including those required for the awarding of the Equilibrium Model to non-ideal enzyme reactions.
Keywords: enzyme activeness, Equilibrium Model, kinetics, stability, thermal-dependence
Abbreviations: Eastdeed, active enzyme; Eastwardinact, inactive enzyme; pNAA, p-nitroacetanilide; pNPP, p-nitrophenylphosphate; T eq, temperature at which the concentrations of Eact and Eastwardinact are equal; T opt, temperature optimum
INTRODUCTION
The result of temperature on enzyme activity has been described by ii well-established thermal parameters: the Arrhenius activation free energy, which describes the effect of temperature on the catalytic rate abiding, one thousand true cat, and thermal stability, which describes the effect of temperature on the thermal inactivation rate abiding, k inact. Anomalies arising from this description have been resolved by the development [1] and validation [2] of a new model (the Equilibrium Model) that more than completely describes the effect of temperature on enzyme activeness by including an boosted machinery by which enzyme activity decreases equally the temperature is raised. In this model, the active form of the enzyme (Eastwardact) is in reversible equilibrium with an inactive (but non denatured) form (Due eastinact), and it is the inactive form that undergoes irreversible thermal inactivation to the thermally denatured state (Ten):
Figure 1 shows the most obvious graphical effect of the Model, which is a temperature optimum (T opt) at nada fourth dimension (Figures iA and 1B), matching experimental observations [2]. In dissimilarity, the 'Classical Model', which assumes a elementary two-state equilibrium between an agile and a thermally-denatured state (Ehuman action→X), and can exist described in terms of but ii parameters (the Arrhenius activation free energy and the thermal stability), shows that when the data are plotted in three dimensions there is no T opt at zero time (Figure 1C).
The temperature-dependence of enzyme activity
(A) Experimental data for alkaline phosphatase. The enzyme was assayed as described past Peterson et al. [2], and the data were smoothed as described hither in the Experimental department; the data are plotted as charge per unit (μM·s−1) confronting temperature (Grand) against time during assay (s). (B) The result of fitting the experimental data for alkaline phosphatase to the Equilibrium Model. Parameter values derived from this plumbing fixtures are: ΔChiliad‡cat, 57 kJ·mol−1; ΔG‡inact, 97 kJ·mol−1; ΔH eq, 86 kJ·mol−1; T eq, 333 G [ii]. (C) The effect of running a simulation of the Classical Model using the values of ΔG‡cat and ΔG‡inact derived from the fitting described above. The experimental data itself cannot be fitted to the Classical Model.
In improver to the obvious differences in the graphs representing the two models, it has been observed experimentally that at any temperature above the maximum enzyme activity, the loss of action attributable to the shift in the Eact/Einact equilibrium is very fast (<i s) relative to the loss of activity due to thermal denaturation (shown in Figure 1 by the lines of rate against time) [2]. This and other evidence to appointment [two] suggest that the phenomenon described by the model (i.e. the Due easthuman action/Einact equilibrium) arises from localized conformational changes rather than global changes in structure. Nonetheless, the extent of the conformational alter, and the extent to which it could be described equally a fractional unfolding, is not yet established.
The equilibrium betwixt the active and inactive forms of the enzyme tin be characterized in terms of the enthalpy of the equilibrium, ΔH eq, and a new thermal parameter, T eq, which is the temperature at which the concentrations of Eact and Einact are equal; T eq can therefore be regarded as the thermal equivalent of K chiliad. T eq has both central and technological significance. It has important implications for our understanding of the consequence of temperature on enzyme reactions within the cell and of enzyme evolution in response to temperature, and volition possibly be a improve expression of the consequence of environmental temperature on the evolution of the enzyme than thermal stability. T eq thus provides an important new parameter for matching an enzyme's backdrop to its cellular and environmental part. T eq must also be considered in engineering enzymes for biotechnological applications at high temperatures [three]. Enzyme engineering is frequently directed at stabilizing enzymes against denaturation; however, raising thermal stability may non enhance loftier temperature activity if T eq remains unchanged.
The detection of the reversible enzyme inactivation, which forms the basis of the Equilibrium Model, requires conscientious conquering and processing of analysis information due to the number of conflicting influences that arise when increasing the temperature of an enzyme assay. Determination of T eq to engagement has used continuous assays, because this method produces progress curves directly and obviates the demand to perform split activeness and stability experiments, and has utilized enzymes whose reactions are essentially irreversible (far from reaction equilibrium), do not evidence whatever substrate or production inhibition and remain saturated with substrate throughout the assay. However, there are a large number of enzymes that exercise not fit these criteria, narrowing the potential utility of determining T eq. The nowadays paper describes methods for the reliable conclusion of T eq under ideal or not-ideal enzyme reaction conditions, using either continuous or discontinuous assays, and outlines the assay data required for accurate determination of T eq and the thermodynamic constants (ΔG‡cat, Δ1000‡inact and ΔH eq) associated with the model [2]; information technology also introduces a method of fitting progress curves directly to the Equilibrium Model and determines the robustness of the data-fitting procedures. The results show directly how the Equilibrium Model parameters are affected by the data.
The methods described in the present paper let the determination of the new parameters ΔH eq and T eq, required for any description of the way in which temperature affects enzyme activity. In addition, they facilitate the straightforward and simultaneous decision of ΔK‡cat and ΔG‡inact under relatively physiological atmospheric condition. They therefore accept the potential to be of considerable value in the pure and applied study of enzymes.
EXPERIMENTAL
Materials
Aryl-acylamidase (aryl-acylamide amidohydrolyase; EC 3.5.1.13) from Pseudomonas fluorescens, β-lactamase (β-lactamhydrolase; EC 3.v.2.6) from Bacillus cereus and pNPP (p-nitrophenylphosphate) were purchased from Sigma–Aldrich. pNAA (p-nitroacetanilide) was obtained from Merck, wheat germ acid phosphatase [orthophosphoric-monoester phosphohydrolase (acid optimum); EC iii.1.3.2] from Serva Electrophoresis and nitrocefin from Oxoid. All other chemicals used were of analytical grade.
Instrumentation
All enzymic activities were measured using a Thermospectronic™ Helios γ-spectrophotometer equipped with a Thermospectronic™ single-cell Peltier-effect cuvette holder. This system was networked to a computer installed with Vision32™ (version 1.25, Unicam) software including the Vision Enhanced Rate plan capable of recording absorbance changes over time intervals downward to 0.125 s.
Temperature command
The temperature of each assay was recorded directly, using a Cole-Parmer Digi-Sense® thermocouple thermometer accurate to ±0.i% of the reading and calibrated using a Cole–Parmer NIST (National Institute of Standards and Technology)-traceable high-resolution drinking glass thermometer. The temperature probe was placed inside the cuvette adjacent to the light path during temperature equilibration before the initiation of the reaction and again immediately after completion of each enzyme reaction. Measurements of temperature were also taken at the top and bottom of the cuvette to check for temperature gradients. Where the temperature measured before and after the reaction differed by more than 0.ane °C, the reaction was repeated.
Analysis atmospheric condition
Assays at high temperature (and over any wide temperature range) can sometimes pose special problems and may need boosted intendance [4–half dozen]. Quartz cuvettes were used in all experiments for their relatively quick temperature equilibration and oestrus-retaining chapters. Where required, a plastic cap was fitted to the cuvette to foreclose loss of solvent due to evaporation (at college temperatures), or a constant stream of a dry inert gas (e.k. nitrogen) was blown across the cuvette to foreclose condensation at temperatures beneath ambient. Buffers were adapted to the advisable pH value at the assay temperature, using a combination electrode calibrated at this temperature. Where very low concentrations of enzyme were used, salts or low concentrations of not-ionic detergents were added to prevent loss of protein to the walls of the cuvette.
Substrate concentrations were maintained at not less than 10 times the Grand m to ensure that the enzyme remained saturated with substrate for the analysis duration. Where these concentrations could not be maintained (eastward.g. considering of substrate solubility), tests were conducted to ostend that at that place was no decrease in rate over the assay menses arising from substrate depletion. In addition, Chiliad m values over the full temperature range examined were determined. Since One thousand m values for enzymes tend to rising with temperature [seven,8], in some cases dramatically, this is particularly important. Any decrease in rate at college temperatures that is acquired by an increment in K thousand at higher temperatures is a potential source of large errors.
Assay reactions were initiated past the rapid add-on of a few microlitres of chilled enzyme, so that the addition had no pregnant consequence on the temperature of the solution inside the cuvette.
Enzyme assays
Aryl-acylamidase activity was measured past following the increment in absorbance at 382 nm (ϵ382=18.four mM−ane·cm−1) respective to the release of p-nitroaniline from the pNAA substrate [9]. Reaction mixtures contained 0.1 Chiliad Tris/HCl, pH 8.6, 0.75 mM pNAA and 0.003 units of enzyme. Ane unit is defined as the amount of enzyme required to catalyse the hydrolysis of 1 μmol of pNAA per min at 37 °C.
Acid phosphatase activity was measured discontinuously using pNPP as substrate [10]. Reaction mixtures (1 ml) contained 0.1 Yard sodium acetate, pH 5.0, 10 mM pNPP and 8 μ-units of enzyme. The analysis was stopped using 0.5 ml of ane Chiliad NaOH. The amount of p-nitrophenol released was measured at 410 nm (ϵ410=18.4 mM−one·cm−1). One unit is defined as the amount of enzyme that hydrolyses ane μmol of pNPP to p-nitrophenol per min at 37 °C.
β-Lactamase activeness was measured by following the increase in absorbance at 485 nm (ϵ485=twenty.five mM−1·cm−1) associated with the hydrolysis of the β-lactam ring of nitrocefin [11]. Reaction mixtures contained 0.05 Grand sodium phosphate, pH seven.0, i mM EDTA, 0.1 mM nitrocefin and 0.003 units of enzyme. 1 unit is defined as the amount of enzyme that will hydrolyse the β-lactam ring of one μmol of cephalosporin per min at 25 °C.
Poly peptide determination
Protein concentrations claimed past the manufacturers (adamant by Biuret) were checked using the far-UV method of Scopes [12].
Data capture and analysis
For each enzyme, reaction-progress curves at a variety of temperatures were collected; the time interval was set so that an absorbance reading was collected every 1 s. Three progress curves were collected at each temperature; where the slope for these triplicates deviated by more than 10%, the reactions were repeated.
When required, the initial (zero time) charge per unit of reaction for each assay triplicate was determined using the linear search role in the Vision32™ charge per unit plan.
Although earlier determinations of ΔYard‡cat, ΔG‡inact, ΔH eq and T eq used initial parameter estimates derived from the calculation of rates from progress curves (described in [2]), more than recent analysis of results indicates that the method described beneath is simpler and every bit accurate.
Using the values for ΔG‡true cat (80 kJ·mol−1), ΔChiliad‡inact (95 kJ·mol−1), ΔH eq (100 kJ·mol−1) and T eq (320 Grand) described in the original paper [1] as initial parameter estimates (deemed to be 'typical' or 'plausible' values for each of the parameters) and the concentration of protein in each assay (expressed in mol·50−i), the experimental data were fitted to the Equilibrium Model using MicroMath® Scientist® for Windows software (version 2.01, MicroMath Scientific Software).
The values for each parameter were first 'improved' by Simplex searching [13,14]. The experimental data were and so fitted to the Equilibrium Model using the parameters derived from the Simplex search, employing an iterative non-linear minimization of to the lowest degree squares. This minimization utilizes Powell's algorithm [xv] to observe a local minimum, possibly a global minimum, of the sum of squared deviations between the experimental data and the model calculations.
In each case, the fitting routine was set to take minimum and maximum iterative footstep-sizes of 1×10−12 and i respectively. The sum of squares goal (the termination criterion for the fitting routine) was set to 1×10−12.
The S.D. values in the Tables refer to the fit of the data to the model. On the footing of the variation between the individual triplicate rates from which the parameters are derived for all the enzymes we have assayed so far, we find that the experimental errors in the determination of ΔThousand‡cat, ΔG‡inact and T eq are less than 0.5%, and less than vi% in the decision of ΔH eq.
A stand-alone Matlab® [version vii.1.0.246 (R14) Service Pack 3; Mathworks] application, enabling the facile derivation of the Equilibrium Model parameters from a Microsoft® Office Excel file of experimental progress curves (production concentration against fourth dimension) can be obtained on CD from R.M.D. This application is suitable for computers running Microsoft® Windows XP, and is for non-commercial research purposes just.
RESULTS AND DISCUSSION
The Equilibrium Model has four data inputs: enzyme concentration, temperature, concentration of product and time. From the terminal ii, an guess of the rate of reaction (in M·s−1) tin can be obtained. In describing the effect of temperature on catalytic action, the charge per unit of the catalytic reaction is the measurement of interest. The quantitative expression of the dependence of rate on temperature, T, and time, t, is given by eqn (i):
(ane)
where thousand B is Boltzmann's constant and h is Planck's constant. This is the expression that we accept used in our proposal [1] and validation [ii] of the Equilibrium Model to date. Experimentally, however, rates are rarely measured directly; rather, product concentration is determined at increasing times, either by continuous or discontinuous assay, giving a serial of progress curves. The quantitative expression relating the product concentration, fourth dimension and temperature for the Equilibrium Model can be obtained by integrating eqn (1), giving eqn (2):
(2)
We find that data candy as enzyme rates using eqn (one), or equally product concentration changes using eqn (two), give essentially the aforementioned results. However, since eqn (2) involves a more direct measurement, the experimental protocol used in the present study involves measuring progress curves of product concentration against time at dissimilar temperatures and fitting these data to eqn (2).
Robustness of the fitted constants
If the enzyme preparation used in the determination of T eq is not pure, then overestimation of the enzyme concentration is probable. Few methods of determining protein concentration give answers that are right in accented terms; autonomously from any limitations in terms of sensitivity and interferences, most are based on a comparison with a standard of uncertain equivalence to the enzyme under investigation. The determination of enzyme concentration is thus a potential source of fault.
To determine how dependent the fitted constants are on the accuracy of the enzyme concentration, data for β-lactamase [2] were fitted against the experimentally determined progress curves with the enzyme concentration reduced two-, five- and 10-fold compared with that determined experimentally (Tabular array 1). It is axiomatic that errors in determining enzyme concentration have piddling effect upon parameter determination, except, of course, in respect of ΔG‡cat, which is reduced as the model attempts to relate the reduced enzyme concentration to the observed rates of reaction. Even with changing the enzyme concentration 5-fold, errors in the values for ΔG‡inact, ΔH eq and T eq are small.
Tabular array ane
The effect of input data accuracy on parameter values
The experimental data for β-lactamase were used to generate the Equilibrium Model parameters equally described in the Experimental section. Changes were then made to the experimentally determined enzyme concentration to decide the dependence of the fitted constants on the accuracy of the protein concentration. Parameter values are ±S.D.
| Parameter | Determined [Eastward0] | [East0] reduced 2-fold | [E0] reduced 5-fold | [Eastward0] reduced 10-fold |
|---|---|---|---|---|
| ΔGrand‡cat (kJ·mol−ane) | 68.nine±0.01 | 67.1±0.01 | 64.8±0.01 | 63.0±0.01 |
| ΔG‡inact (kJ·mol−1) | 93.7±0.08 | 93.6±0.07 | 93.iv±0.07 | 93.4±0.07 |
| ΔH eq (kJ·mol−one) | 138.two±ane.1 | 139.four±ane.1 | 140.2±one.1 | 144.2±1.1 |
| T eq (Thou) | 325.6±0.1 | 326.ii±0.1 | 327.0±0.i | 327.6±0.ane |
| [E0] (Thou) | five.5×10−ix | ii.75×10−9 | 1.one×x−ix | 0.55×10−9 |
Data sampling requirements: sampling rate
The increasing need for automation in enzyme assays has led to the development of instruments that use sampling techniques to assay enzymes at unlike times. Additionally, some assays are difficult to carry out continuously. It is therefore important to know whether the fitting procedures described herein are sufficiently robust to deal with discontinuous information collection. To determine the sampling requirement, progress curves for the reaction catalysed by aryl-acylamidase were collected in triplicate at 1 s intervals over a 25 min period at a diverseness of temperatures. Progress curves were and so manipulated past the successive removal of a proportion of the data points to determine the effect of sampling charge per unit on the fitting of the information to the Equilibrium Model and on the resulting parameters (Tabular array two). Using the 1 s sampling interval as a reference, the accented values of ΔChiliad‡true cat, Δ1000‡inact, ΔH eq and T eq are essentially the aforementioned at all sampling rates (upwardly to a 150 s interval), despite the increase in the S.D. values as the sampling interval increases. The results betoken that discontinuous enzyme assays can be used for the conclusion of T eq. The minimum number of points per progress curve required to give accurate values for the parameters volition depend upon the length of the assay and the curvature of the progress curve, only, as expected, the larger number of data points arising from continuous assays give more accurate results. The results also show that accuracy is not dominated past a requirement for 'early' data, taken very soon after zero fourth dimension, and that the S.D. provides a good guide to the accuracy of the parameters.
Table ii
Data sampling requirements: the issue of sampling rate on parameter values
Progress curves for aryl-acylamidase, collected over 25 min and at ten different temperatures, were used to generate the Equilibrium Model parameters as described in the Experimental section. Experimental data points were then successively removed to give the upshot of reduced frequency of data points to determine the consequence of various sampling rates on the last parameter values. Parameter values are ways±Southward.D.
| Sampling interval (s)… | 1 | v | 20 | 60 | 150 | |
|---|---|---|---|---|---|---|
| Parameter | Data points per progress bend… | 1500 | 300 | 75 | 25 | ten |
| ΔChiliad‡cat (kJ·mol−one) | 74.iv±0.01 | 74.4±0.02 | 74.iv±0.03 | 74.four±0.06 | 74.4±0.09 | |
| ΔG‡inact (kJ·mol−one) | 94.5±0.04 | 94.5±0.09 | 94.5±0.18 | 94.5±0.31 | 94.5±0.48 | |
| ΔH eq (kJ·mol−1) | 138.5±0.half-dozen | 138.v±ane.4 | 138.5±two.8 | 138.7±4.eight | 138.eight±7.4 | |
| T eq (Chiliad) | 310.0±0.1 | 310.0±0.1 | 310.0±0.two | 310.0±0.iii | 310.0±0.5 |
The results presented higher up imply that the parameters can be obtained accurately from as few equally ten information points (sampling just every 150 s in the example of the 1500 s aryl-acylamidase assays). We would await the 'data sampling' shown in Table 2 to be a satisfactory proxy for a discontinuous assay. Withal, this was confirmed using another enzyme. Acid phosphatase was incubated with the substrate pNPP for a full assay duration of 30 min, and the reaction was sampled in triplicate every 60 s, stopped with NaOH, and the absorbance was read at 410 nm. Three progress curves (absorbance confronting time) at each temperature were generated from the triplicate absorbance values obtained when the reaction was stopped. Product concentrations (expressed in mol·l−1) were and so calculated for each absorbance reading, and the data set was fitted to the Equilibrium Model as described previously and compared with data obtained in a continuous analysis [2]. Taking experimental fault into account, the parameter values generated from fitting these information (Table three) indicate no significant difference between the two methods, except in the case of ΔG‡inact. The increased value of the errors on each parameter determined using the discontinuous data point that, as expected, continuous assays give more accurate results.
Tabular array 3
Concluding parameter values for an enzyme employing a discontinuous assay
Acid phosphatase was assayed discontinuously over a period of 30 min with a sampling rate of 60 s and at 5 °C intervals from 20 to 80 °C (13 temperature points). The results of plumbing fixtures data for the same enzyme over the same temperature range and using the aforementioned intervals, but using a continuous assay (effective sampling rate of i south) have been included for comparison [2]. The progress curves generated for both methods were fitted to the Equilibrium Model and the parameters generated as described in the Experimental section. Parameter values are means±S.D.
| Parameter | Discontinuous analysis | Continuous analysis |
|---|---|---|
| ΔG‡true cat (kJ·mol−one) | 79.0±0.02 | 79.i±0.01 |
| ΔG‡inact (kJ·mol−1) | 96.1±0.23 | 94.5±0.04 |
| ΔH eq (kJ·mol−1) | 146.0±2.2 | 142.5±0.five |
| T eq (K) | 333.6±0.five | 336.9±0.1 |
Data sampling requirements: temperature range
Progress curves at 12 temperatures were nerveless for acid phosphatase [2]. Analysis of the initial rate of reaction (i.e. at zero time) shows three points higher up the temperature at which maximum product is formed (Figure 2). By sequentially truncating the data gear up from the highest or the lowest temperature point and re-plumbing fixtures the resulting data sets, nosotros proceeds some insight into the dependence of the plumbing equipment routine and accurate estimation of the parameters on the data points above and below the T opt (Table 4).
The effect of temperature on the initial (zero-time) rate of reaction of acrid phosphatase
Acid phosphatase was assayed continuously as described by Peterson et al. [two]. For each triplicate progress curve, the initial charge per unit of reaction was determined using the linear search function in the programme, Vision32™. The data are plotted equally rate (μM·s−i) against temperature (K).
Table 4
Data sampling requirements: the effect of temperature range on parameter values
A full set of experimental information for acrid phosphatase was used to generate the Equilibrium Model parameters equally described in the Experimental section. Temperature points to a higher place the T opt (Figure two) were sequentially truncated from the consummate information set to make up one's mind the influence of data points in a higher place the T opt on the final parameter values. Temperature points were also sequentially truncated from the lowest temperature bespeak to the highest from the complete data set (12 temperature points) to determine how many points, in total, below the T opt are required for the accurate determination of T eq and the other thermodynamic parameters. In this case, each data set included all temperature points above the T opt. Parameter values are means±S.D.
| Truncated from highest temperature signal | Truncated from lowest temperature indicate | ||||||
|---|---|---|---|---|---|---|---|
| Parameter | Minus 3 temperature points (9 points) | Minus two temperature points (10 points) | Minus one temperature point (eleven points) | Full data set (12 points) | Minus two temperature points (x points) | Minus 4 temperature points (eight points) | Minus half dozen temperature points (six points) |
| ΔG‡cat (kJ·mol−ane) | 78.8±0.01 | 79.1±0.01 | 79.i±0.01 | 79.1±0.01 | 79.i±0.01 | 79.0±0.01 | 79.3±0.02 |
| ΔG‡inact (kJ·mol−1) | 94.3±0.03 | 94.6±0.05 | 94.6±0.05 | 94.v±0.04 | 94.five±0.05 | 94.5±0.05 | 94.ii±0.06 |
| ΔH eq (kJ·mol−1) | 108.5±0.5 | 148.eight±0.7 | 146.5±0.5 | 142.5±0.five | 142.8±0.6 | 142.1±0.7 | 149.8±0.eight |
| T eq (K) | 337.3±0.1 | 336.8±0.1 | 336.8±0.1 | 336.9±0.1 | 337.0±0.1 | 336.9±0.1 | 338.3±0.ii |
For data truncated from the highest temperature point, the values of ΔG‡true cat, ΔG‡inact and T eq exercise not vary greatly with the various data treatments. However, for the fit excluding the last three temperature points, in that location is a substantial loss in accuracy for the Equilibrium Model parameter, ΔH eq. This difference is not reflected in the Southward.D. values. Figure three, which illustrates the differences in each plumbing fixtures of the truncated data sets to the Equilibrium Model presented as a three-dimensional plot of rate (μM·s−1) against temperature (M) against fourth dimension (due south), shows the reason for this. The plots betoken that when only one or two data points are removed, there is fiddling difference in the shape of the plot when the data are simulated in three dimensions, but without a information point to a higher place the T opt, the equilibrium model finer relapses towards the Classical Model (Figure 1), with a sharp refuse in ΔH eq, even though a reasonable value for T eq has been obtained. These results suggest that it is possible to obtain adequate estimates of the parameters with just i temperature signal above the T opt.
Data sampling requirements: the effect of data points beyond T opt
Acid phosphatase was assayed every bit described by Peterson et al. [2]. Temperature points above the T opt (see Figure 2) were sequentially truncated from the complete data fix to decide the influence of information points above the T opt on the final parameter values. Illustrated here are the results plotted as rate (μM·s−1) against temperature (G) against fourth dimension (s) for the fit of acrid phosphatase data to the Equilibrium Model using (A) the full data ready, (B) the data set excluding the last data betoken, (C) the data set excluding the last two data points, and (D) the data fix excluding the last three data points.
All the foregoing discussion is based on an ab initio presumption that the temperature-dependence of enzyme action is described by the Equilibrium Model. Of the 50 or so enzymes studied in detail by usa, all follow the model. Still, information that do non evidence clear evidence of a T opt when initial (zilch time) rates are plotted against temperature may in fact be fitted equally well by the simpler Classical Model. In this situation, it would exist foolhardy to carry out the procedure described in the nowadays paper. Information technology must therefore be stressed that if only ane or two points in a higher place the T opt are adamant, the measured initial rates at those temperatures must exist sufficiently lower than that at T opt for the assumption of the Equilibrium Model to be justified. Ideally, ii or more rate measurements above T opt showing a articulate tendency of falling rates should be obtained to apply the Equilibrium Model with confidence.
For data sequentially truncated from the everyman temperature point to the highest, a trend in the parameter values was seen (Table 4). Parameter values were maintained close to the 'consummate' data set level downwards to 8 points; below 8 points, values moved outside the Due south.D. limits, but were however relatively close in all cases.
The results of this data manipulation advise that data at eight temperatures with two points above T opt (showing a articulate downwards tendency) are sufficient to yield parameter values for ΔG‡true cat, ΔYard‡inact, ΔH eq and T eq with reasonable precision.
Enzymes operating under 'non-ideal' weather condition: the employ of initial rates
To utilise data from progress curves collected over extended periods of time for valid fitting to the Equilibrium Model requires that whatever decrease in activity observed is due solely to thermal factors and not to some other process. This means that the enzyme and its reaction exist 'platonic'; that is, the enzyme is non production inhibited, the reaction is essentially irreversible and the enzyme operates at V max for the entire assay. To engagement, the enzymes that we have fitted to the Equilibrium Model take been called to meet, or come very shut to meeting, these criteria over the three–5 min elapsing of the analysis.
All the same, many enzyme reactions are necessarily assayed nether not-ideal weather condition. For example, the reaction may be sufficiently reversible that the back reaction contributes to the observed charge per unit during the assay and/or the products of the reaction may exist inhibitors of the enzyme. Application of the Equilibrium Model to these non-ideal enzyme reactions can usually exist accomplished by restricting assays to the initial rate of reaction. Setting t=0 in eqn (1) gives eqn (three) below. Using this, it is possible to fit the experimental data for zero time (i.e. initial rates) to the Equilibrium Model to determine ΔThou‡cat, ΔH eq and T eq, although the time-dependent thermal denaturation parameter, ΔYard‡inact, cannot be determined. At t=0,
(3)
Another circumstance where 'non-ideality' may occur is when the decrease of rate during the assay is partially due to substrate depletion. If the enzyme is saturated at the get-go of the assay, lowering the enzyme concentration or increasing the sensitivity of the analysis may remove this problem. In either case, using initial rates will allow the equilibrium model to be practical. Still, if insufficient substrate is present at nix time to saturate the enzyme, either considering of, e.g., solubility limitations, or as a effect of increases in K chiliad [7,8] equally the temperature is altered, so considerable errors may arise. Even here, it may be possible, if the Grand m is known at each temperature, to obtain reasonable approximations of the initial rates at saturation by calculating the degree of saturation using the relationship five/V max=S/(K m+Southward), and applying the appropriate corrections.
To simulate the determination of the Equilibrium Model parameters for an enzyme that operates nether non-ideal atmospheric condition, initial rates of reaction were calculated from each progress curve in the β-lactamase data ready [2] and fitted to the modified nada-fourth dimension version of the Equilibrium Model using the Scientist® software (Table five). No significant differences in any of the parameters determined this way were found, suggesting that this manner of determination is potentially as authentic as plumbing fixtures the entire time grade to the Equilibrium Model for the determination of ΔK‡true cat, ΔH eq and T eq.
Table five
The use of initial rate data to make up one's mind parameters associated with the Equilibrium Model
To simulate the decision of the Equilibrium Model parameters for an enzyme that operates under non-ideal weather condition, initial rates of reaction were calculated from each progress curve in the β-lactamase data set [2] using the linear search role in the programme, Vision32™, and fitted to the Equilibrium Model via eqn (3). Parameters calculated for the complete data set (entire time course) take been included for comparing [2]. Parameter values are means±S.D.
| Parameter | Progress curves | Initial rates |
|---|---|---|
| ΔG‡true cat (kJ·mol−1) | 68.nine±0.01 | 68.ix±0.22 |
| ΔThou‡inact (kJ·mol−1) | 93.7±0.08 | − |
| ΔH eq (kJ·mol−one) | 138.two±1.ane | 132.2±12.4 |
| T eq (K) | 325.vi±0.1 | 325.half-dozen±ane.3 |
Conclusions
To date, determination of the parameters associated with the Equilibrium Model for individual enzymes has involved continuous assays with collection of data at 1 southward intervals over five min periods at ii–3 °C temperature intervals over at to the lowest degree a 40 °C range, with each temperature run beingness carried out in triplicate; i.due east. processing approx. 15000 information points gathered in approx. l experimental runs [ii]. Using a unproblematic technique of fitting the raw data (product concentration against fourth dimension) to the Equilibrium Model, we have shown that data collection (and thus labour) can be reduced considerably without compromising the accurateness of the derived parameters. Accurate results crave preferably more than than ane data betoken taken above T opt and more than than viii temperature points in total. Major errors in enzyme decision touch on but the determination of ΔG‡cat. Although continuous assays will give the well-nigh accurate results, ΔThousand‡true cat, ΔThousand‡inact, ΔH eq and T eq can be determined accurately using discontinuous assays. Amid other things, this will allow the decision of the parameters of enzymes from extreme thermophiles; since T opt for these enzymes may be above 100 °C, and since few continuous assay methods are practical at such temperatures, most such assays will take to be discontinuous [four]. Finally, we have demonstrated that the use of initial, zero-time rates enables the prepare determination of the Equilibrium Model parameters (except ΔG‡inact) of most not-ideal enzyme reactions.
The method described here enables the determination of the new key enzyme thermal parameters arising from the Equilibrium Model. It should be noted that the Equilibrium Model itself enables an accurate clarification of the issue of temperature on enzyme action, simply does non purport to describe the molecular basis of this behaviour. Evidence so far ([two], and Thousand. E. Peterson, C. Chiliad. Lee, C. Monk and R. M. Daniel, unpublished work) suggests that the conformational changes between the active and inactive forms of the enzyme described by the model are local rather than global, and possibly quite slight. The model, and the piece of work described here, provides the foundation, and one of the tools needed to decide the molecular basis of these newly described backdrop of enzymes. The focus of future work must now be to apply the appropriate physicochemical techniques to determine the precise nature of this proposed structural change.
Acknowledgments
This work was supported past the Royal Society of New Zealand's International Science and Engineering science Linkages Fund, and the Marsden Fund.
References
1. Daniel R. M., Danson M. J., Eisenthal R. The temperature optima of enzymes: a new perspective on an erstwhile phenomenon. Trends Biochem. Sci. 2001;26:223–225. [PubMed] [Google Scholar]
2. Peterson M. E., Eisenthal R., Danson M. J., Spence A., Daniel R. M. A new, intrinsic, thermal parameter for enzymes reveals true temperature optima. J. Biol. Chem. 2004;279:20717–20722. [PubMed] [Google Scholar]
3. Eisenthal R., Peterson M. E., Daniel R. Chiliad., Danson 1000. J. The thermal behaviour of enzymes: implications for biotechnology. Trends Biotechnol. 2006;24:289–292. [PubMed] [Google Scholar]
4. Daniel R. M., Danson 1000. J. Assaying activity and assessing thermostability of hyperthermophilic enzymes. Methods Enzymol. 2001;334:283–293. [PubMed] [Google Scholar]
5. Tipton K. F. Principles of enzymes assays and kinetic studies. In: Eisenthal R., Danson K. J., editors. Enzyme Assays, a Applied Approach. Oxford: Oxford University Press; 1992. pp. i–58. [Google Scholar]
6. John R. A. Photometric Assays. In: Eisenthal R., Danson G. J., editors. Enzyme Assays, a Practical Arroyo. Oxford: Oxford University Press; 1992. pp. 59–92. [Google Scholar]
7. Thomas T. Grand., Scopes R. K. The furnishings of temperature on the kinetics and stability of mesophilic and thermophilic 3-phosphoglycerate kinases. Biochem. J. 1998;330:1087–1095. [PMC gratis commodity] [PubMed] [Google Scholar]
viii. Liang Z., Tsigos I., Bouriotis V., Klinman J. P. Impact of poly peptide flexibility on hydride-transfer parameters in thermophilic and psychrophilic alcohol dehydrogenases. J. Am. Chem. Soc. 2004;126:9500–9501. [PubMed] [Google Scholar]
9. Hammond P. M., Price C. P., Scawen M. D. Purification and backdrop of aryl acylamidase from Pseudomonas fluorescens ATCC 39004. Eur. J. Biochem. 1983;132:651–655. [PubMed] [Google Scholar]
10. Hollander V. P. Acid phosphatases. In: Boyer P. D., editor. The Enzymes, vol. 4. New York: Academic Press; 1971. pp. 449–498. [Google Scholar]
11. O'Callaghan C. H., Morris A., Kirby S. Chiliad., Shingler A. H. Novel method for detection of β-lactamases by using a chromogenic cephalosporin substrate. Antimicrob. Agents Chemother. 1972;1:283–288. [PMC free article] [PubMed] [Google Scholar]
12. Scopes R. One thousand. Analysis – Measurement of protein and enzyme activity. In: Cantor C. R., editor. Protein Purification: Principles and Exercise. 3rd edn. San Diego: Springer Verlag; 1994. pp. 44–50. [Google Scholar]
thirteen. Deming Southward. N., Morgan S. L. Simplex optimization of variables in analytical chemistry. Anal. Chem. 1973;45:278A–283A. [Google Scholar]
14. Caceci Thou. S., Cacheris West. P. Fitting curves to data: the simplest algorithm is the answer. Byte. 1984;9:340–362. [Google Scholar]
fifteen. Powell Chiliad. J. D. A hybrid method for non-linear equations. In: Rabinowitz P., editor. Numerical Methods for Nonlinear Algebraic Equations. New York: Gordon and Breach Scientific discipline Publishers; 1970. pp. 87–144. [Google Scholar]
Articles from Biochemical Journal are provided hither courtesy of The Biochemical Guild
lawrencewilitsehey.blogspot.com
Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1798444/
0 Response to "What Happens to an Enzyme When Exposed to Heat"
Post a Comment