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Does pH affect Michaelis constant?

Does pH affect Michaelis constant?



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I have been trying to confirm the Km of a substrate (which is 34 +/- 4 mM). This value was obtained in 50 mM MOPS, pH 6.3. I conducted my kinetics assay in a buffer of pH 7 and obtained a Km value in the 21.5. According to this paper, Fig. 2C, the normalized specific activity of the enzyme is about 70% at pH 6.3 and about 47% at pH 7. If I divide 34 mM at pH 6.3 by 0.7 (which should get me the optimum Km at the optimum pH of 5.5) and then multiply by 0.48, then I get 23 mM. However, the paper says Km is between 30 - 38 mM, so if I divide 30 and 38 separately by 0.7 and multiply by 0.47, I get 20 and 25.6 mM respectively. Because my value falls within this range, this then must mean that I have the right enzyme and the same result as the paper.

So my questions are:

  1. When the paper says Km is "34 +/- 4 mM", can I assume that means the Km can be anywhere between 30 - 38 mM? I'm surprised to see how wide the range is. I assumed Km is usually just one value with a deviation of at most 0.1.

  2. Do pH change Km values? I understand that pH changes the shape(s) of the enzyme and/or substrate. Therefore that must affect how much it wants to bind to the substrate. If the enzyme's desire to bind to a substrate decreases due to increase in pH, for example, that would mean more substrates are needed to surround the enzyme, thus increasing Km.

  3. If pH does change Km, is this how I determine the Km value of a different pH value if the Km value at another pH is already known? I know that specific activity and Michaelis constant are different, but how much product can be converted per minute depends on how much the enzyme likes to bind to a substrate, which is represented by the Michaelis constant. Did my reasoning and calculation arrive at the right conclusion? If not, how is the calculation done?


From the derivation of Michaelis-Menten kinetics you can see that:

$$K_m=frac{k_f + k_{cat}}{k_r}$$

Where $k_f$ and $k_r$ are binding and unbinding rate constants (for Enzyme-Substrate binding), respectively, and $k_{cat}$ is the turnover number. This is for the Quasi-Steady-State approximation (QSSA). For the equilibrium approximation:

$$K_m=frac{k_f}{k_r}$$ which is same as the association constant.

In both the cases pH can affect the rate of binding and unbinding by affecting the affinity between the enzyme and the substrate. For example lets assume that the substrate binding site is negatively charged. Low pH would increase the electrostatic potential of the substrate binding site towards zero by affecting the ionization of the functional groups.

pH can also have indirect effects on the substrate binding site because it can modify the overall structure of the protein.

Many enzyme catalysed reactions involve acid-base catalysis i.e. there is a transfer of proton. In reactions like these, pH can affect $k_{cat}$.

If pH does change Km, is this how I determine the Km value of a different pH value if the Km value at another pH is already known?

You can do that by making a Lineweaver-Burk plot for the changed pH.


3.7: The Effect of pH on Enzyme Kinetics

In the same way that every enzyme has an optimum temperature, so each enzyme also has an optimum pH at which it works best. For example, trypsin and pepsin are both enzymes in the digestive system which break protein chains in the food into smaller bits - either into smaller peptide chains or into individual amino acids. Pepsin works in the highly acidic conditions of the stomach. It has an optimum pH of about 1.5. On the other hand, trypsin works in the small intestine, parts of which have a pH of around 7.5. Trypsin's optimum pH is about 8.

Table (PageIndex<1>): pH for Optimum Activity
Enzyme Optimal pH Enzyme Optimal pH
Lipase (pancreas) 8.0 Invertase 4.5
Lipase (stomach) 4.0 - 5.0 Maltase 6.1 - 6.8
Lipase (castor oil) 4.7 Amylase (pancreas) 6.7 - 7.0
Pepsin 1.5 - 1.6 Amylase (malt) 4.6 - 5.2
Trypsin 7.8 - 8.7 Catalase 7.0
Urease 7.0

If you think about the structure of an enzyme molecule, and the sorts of bonds that it may form with its substrate, it isn't surprising that pH should matter. Suppose an enzyme has an optimum pH around 7. Imagine that at a pH of around 7, a substrate attaches itself to the enzyme via two ionic bonds. In the diagram below, the groups allowing ionic bonding are caused by the transfer of a hydrogen ion from a -COOH group in the side chain of one amino acid residue to an -NH2 group in the side chain of another.

In this simplified example, that is equally true in both the substrate and the enzyme.

Now think about what happens at a lower pH - in other words under acidic conditions. It won't affect the -NH3 + group, but the -COO - will pick up a hydrogen ion. What you will have will be this:

You no longer have the ability to form ionic bonds between the substrate and the enzyme. If those bonds were necessary to attach the substrate and activate it in some way, then at this lower pH, the enzyme won't work. What if you have a pH higher than 7 - in other words under alkaline conditions. This time, the -COO - group won't be affected, but the -NH3 + group will lose a hydrogen ion. That leaves . . .

Again, there is no possibility of forming ionic bonds, and so the enzyme probably won't work this time either. At extreme pH's, something more drastic can happen. Remember that the tertiary structure of the protein is in part held together by ionic bonds just like those we've looked at between the enzyme and its substrate. At very high or very low pH's, these bonds within the enzyme can be disrupted, and it can lose its shape. If it loses its shape, the active site will probably be lost completely. This is essentially the same as denaturing the protein by heating it too much.


Michaelis constant

Since the substrate concentration at Vmax cannot be measured exactly, enzymes must be characterized by the substrate concentration at which the rate of reaction is half its maximum. This substrate concentration is called the Michaelis-Menten constant (KM ) a.k.a. Michaelis constant. This represents (for enzyme reactions exhibiting simple Michaelis-Menten kinetics) the dissociation constant (affinity for substrate) of the enzyme-substrate (ES) complex. Low values indicate that the ES complex is held together very tightly and rarely dissociates without the substrate first reacting to form product.


Methods

Experimental setup in continuous culture

In contrast to many other groups handling batch cultures of C. acetobutylicum, we used continuous cultures in order to study the effect of pH on solvent production, in particular on the production of butanol. A fermentation process that can be operated continuously has several advantages over a batch process in industrial and biotechnological manufacturing: only one series of precultures is needed for a long production period, the "dead season" necessary for the filling, sterilization, cooling and clearing of the equipment is largely diminished and the volume of the fermenter vessel can be reduced without a loss of production capacity [17]. Stable solvent production can be maintained for much longer in a synthetic medium under phosphate limitation in a chemostat culture than in the traditional batch process [21].

Our model is based around continuous culture dynamic shift experiments. Experiments were performed according to a standardized experimental setup [16, 18] and using standard operating procedures for extracting and handling different types of samples. The strain C. acetobutylicum ATCC824 was grown under anaerobic conditions at 37°C and the precultures were prepared as previously described [18]. The phosphate-limited chemostat experiments were performed in a BiostatB 1.5-l fermenter system (BBI, Melsungen, Germany) with 0.5 mM KH2PO4 and 4% (wt/vol) glucose in the supplying medium [22] and a dilution rate of D = 0.075 h -1 . The external pH in the culture medium was adjusted to and kept constant at pH 5.7 and pH 4.5 by automatic addition of 2 M KOH. The analysis of the fermentation products was accomplished as described previously [18]. Three individual experiments were performed shifting the culture from pH 5.7 to pH 4.5 (which we call the 'forward shift' experiments) and one from pH 4.5 to pH 5.7 (the 'reverse shift' experiment). Data were taken over the full length of the observation time. The biological data is given in Additional file 1: Tables S1 - S4.

PH-dependent modeling of the AB fermentation

As mentioned before, the metabolism of AB fermentation in C. acetobutylicum displays two characteristic metabolic phases, acidogenesis and solventogenesis. A detailed representation of the corresponding metabolic pathways has been published by Jones and Woods [10]. Up to the present, only a few metabolic models describing this fermentative process have been published. Papoutsakis [23] developed a stoichiometric model that could be used to estimate the rates of reactions occurring within the AB fermentation pathways of several (AB-producing) clostridial bacteria in batch culture. Importantly, however, these results are not transferable to continuous cultivations like the chemostat cultures used in this study where the cells are growing exponentially throughout. Votruba et al. [24] formulated a model of the fermentation process for batch cultures without including the intermediate metabolites, restricting the variables to biomass, glucose and the end products and this model captures well the two phases. Metabolic flux analysis has been applied since to the pathway [25–27]. Existing kinetic models describing the dynamics of ABE fermentation do not seek to capture the effect of pH upon the metabolic network: in Shinto et al. [28] (which actually considers Clostridium saccharoperbutylacetonicum) the switch is assumed to be glucose-dependent and enzyme levels are taken to be constant, while in Li et al. [29] enzyme activity is incorporated, but regulation is fed in directly to the model from experimental data (rather than being allowed to vary freely within the model or be influenced by other model components). To our knowledge, therefore, the model presented here is the first to consider the effect of pH upon the metabolic network.

The reduced metabolic network

Here we present a model of the AB fermentation in C. acetobutylicum in continuous culture. Because there is a lack of published information on the kinetic parameters governing these reactions under the conditions used in our experimental work in the literature, we aggregate a number of reactions of the metabolic network published by Jones and Woods [10]. This enables us to minimize the number of parameters that need to be estimated from the experimental work by focusing the model upon those reactions which are most likely to be regulated by the pH of the environment. Thus, as shown in Figure 1, five glycolytic steps were combined into one reaction (R1), adopting the assumption that there is a constant flux from glucose to acetyl-CoA. Additionally, we reduce the number of steps in five other reactions: the conversions of acetyl-CoA into two molecules of acetate (R2), of butyryl-CoA into two of butanol (R10), of butyryl-CoA into two of butyrate (R8), and of acetyl-CoA into two of ethanol (R5), we reduce two steps into one. Finally, we represent the three steps in the conversion of acetoacetyl-CoA to butyryl-CoA by one (R9). All intermediate reactions are listed in Table 1.

When gene regulation is not included explicitly in the representation of a reaction, we employ Michaelis-Menten expressions. In the following section we explain our approach when gene regulation is included explicitly.

Incorporating gene regulation

The reactions required for solventogenesis are tightly regulated at the genetic level: production of the enzymes required to catalyze these reactions can be switched on or off (or, more generally, increased or decreased) at the transcriptional level by regulatory proteins binding at the appropriate DNA sites. The levels of the specific regulatory proteins are adjusted in response to both internal and external signals (for example pH) that are transmitted through the cell. It is therefore expected that the switch from acidogenesis to solventogenesis (or, indeed, vice versa), can be explained, at least partially, via pH-regulation of the enzyme-associated genes.

The principal enzymes involved in solventogenesis are encoded by the genes adc, adhE, bdhA/B, ctfA/B and thlA - see Table 1. We note that there are two adhE genes in C. acetobutylicum the one we incorporate into our model is sometimes referred to as adhE1. For reasons outlined below, we include the influence of only three of these genes in our dynamic model, namely adc, adhE and ctfA/B.

Expression of the ctfA/B gene results in the acetoacetyl-CoA: acetate/butyrate:CoA-transferase [8] (or simply CoA-transferase), which is the enzyme responsible for converting acetoacetyl-CoA and the previously secreted acetate or butyrate into acetoacetate and acetyl-CoA or butyryl-CoA, respectively. The adhE gene is part of the same operon as ctfA/B, namely the sol operon [30]. The dehydrogenase AdhE catalyzes the conversion of butyryl-CoA and acetyl-CoA into butanol and ethanol, respectively [31, 32].

The adc gene encodes acetoacetate decarboxylase (Adc), which is the enzyme responsible for the decarboxylation of acetoacetate into acetone and CO2[14, 15]. There are two known bdh genes: bdhA and bdhB the products of both genes are butanol dehydrogenases [33] which (in addition to AdhE) convert butyryl-CoA into butanol. Since their roles are similar to that of AdhE their effects can be absorbed into the parameter choice for AdhE. Thus, we neglected them from our dynamic model. The gene product of thlA is a thiolase which catalyzes the conversion of acetyl-CoA into acetoacetyl-CoA and is therefore needed for both acidogenesis and solventogenesis [34]. It is speculated that expression of the thlA gene is constitutive [35] and recent experiments indicate that the difference in transcription levels of thlA between acidogenesis and solventogenesis is much less marked than that of ctfA/B, adc, and adhE[36]. Therefore, ThlA was also neglected from our dynamic model as we assume ThlA levels remain relatively constant throughout the experiments as found in [16]. The adc, adhE and ctfA/B genes are regulated in accordance with the metabolic phase, with their transcription increasing in the solventogenic phase [36]. Thus, they are likely to be induced via a pH-related signal and we therefore incorporate each of these genes into the model. We assume that they are each transcribed at two distinct rates: basal (r E for enzyme E, see the dashed downward arrow in (1) below) when the pH is sufficiently high (indeed, low levels of these transcripts exist before the onset of solventogenesis, see for example [37, 38]) and at a higher rate (, see dashed upward arrow in (1)) when the pH of the environment is low.

We assume that all enzymatic reactions are governed by

where S is the substrate, E the enzyme, C the complex formed by S and E, and P the resulting product. As in the derivation of Michaelis-Menten dynamics, we assume that the concentration of C is in a quasi-steady state [13, 39] but, in contrast, we do not take E to be constant because its production is regulated by pH [13]. Thus where we wish to include enzyme concentration explicitly, we use conventional kinetic theory to obtain the following equations [40]:

where α = k1·k2/(k-1 + k2), though the equations involving CtfA/B require the product of three variables in equations (2a) and (2b) since the reactions it catalyzes involve two substrates. The production of the enzyme is determined by the expression rate of the corresponding gene as the mechanisms by which solventogenesis is induced have not been fully elucidated, we include a generic pH-dependent switch F(p) which turns on increased enzyme production below some threshold pH. The switch takes the form of the smoothed step function,

where p* represents the threshold pH level around which the switch occurs and n dictates the steepness of the smooth switch function.

Since pH was set and controlled externally in the dynamic shift experiments, we do not introduce a differential equation for this variable. For each experiment pH is measured at regular time points. We fit a function (using ' nlinfit ' in Matlab [41]) of the form

to the pH data, where c1,c2 and c3 are constants, to gain a distinct function representing pH for each simulation this function is then fed into the model via the switch function F(p).

Combining the pH-dependent metabolic network with gene regulation

Where enzyme concentrations are to be included explicitly the reactions take the form outlined in the above section otherwise Michaelis-Menten kinetics are adopted. The reactions displayed in Figure 1 and Table 1 are therefore represented by:

where the limiting rate of reaction i is given by and the corresponding dissociation constant is . We include the stoichiometric constant of two in R1 since two molecules of acetyl-CoA are formed from one of glucose. Similarly, the constant 0.5 in R4 represents the formation of one acetoacetyl-CoA from two acetyl-CoA. The resulting metabolic model is given by:

where we have added to each equation an out-flow term which is the product of the dilution rate with the concentration of the corresponding metabolite because we have a constant out-flow of both extracellular and intracellular (as a result of cell out-flow) products through the chemostat.

In addition we require the following equations to represent enzyme concentrations:

We fit the model to experimental data as described in the following section.

Data normalization, parameter estimation and model simulation

All parameters are estimated from three 'forward' experiments using the SBToolbox in Matlab [42]. As mentioned before, GC data from the dynamic shift experiments are used, measuring the time until the medium reaches a certain pH level. The time span of the whole switch differed between experiments, varying from 22 ('forward' experiment 1, see Figure 2(a)) to 33.5 hours ('forward' experiment 2, see Figure 2(b)) see Supplementary File 1 for the raw data. Thus, in order to take an average of the data to be used for parameter estimation, the data had to be normalized across the dynamic shift interval to make comparisons between time points meaningful (i.e. time points for each data set should correspond to equivalent phases, namely acidogenesis, the dynamic shift, or solventogenesis). To achieve this, data sets 1 and 3 were normalized onto data set 2, i.e. the time points occurring during the dynamic shift were scaled so that the dynamic shift phase lasts 33.5 hours in all normalized data sets solventogenesis phase time points were translated so that the start of solventogenesis occurs 33.5 hours after the start of the dynamic shift phase for all normalized data sets. Each data set was interpolated at identical time points, enabling the average of the three scaled sets to be calculated for parameter estimation, the results of which are displayed in Table 2. In all comparisons between the data and numerical solutions, the original and unscaled data sets are used.

Comparison of our model (solid lines) with the data of the dynamic shift chemostat experiments (dots). Figure 2(a) shows results for the 'forward' dynamic shift experiment. The two repetitions of this 'forward' dynamic shift experiment are shown in Figure 2(b) and Figure 2(c). The cells produce mainly acetate and butyrate when grown at a pH value of 5.7. During the transition phase C. acetobutylicum switches its metabolism (as a function of the external pH) towards the generation of the solvents acetone and butanol at a pH of 4.5. Ethanol is produced during acidogenesis and solventogenesis at approximately the same levels. In Figure 2(d) we demonstrate the comparison of the model and the data for the 'reverse' dynamic shift experiment.

Steady-state analysis of the metabolic network

For the purposes of developing genetic engineering strategies for enhancing butanol yield, we wish to examine changes to the steady states of the metabolic network in response to variations in transcription rates of the solvent-associated genes. Having neglected thlA, bdhA and bdhB from the model for studying the time-dependent dynamics in order to minimize the number of parameters to be estimated for the wild-type model, we introduce them to the steady-state studies because it is possible that overexpression or underexpression of these genes will have an effect upon the fermentation product yield. Thus, in order to explicitly vary expression of these genes, we need to derive alternative representations for the reactions in which their gene products are involved, i.e. we require parameters to represent production from each of these genes. At steady state, the concentrations of ThlA and BhdA/B are given by r T /λ and r B/ λ, where r T and r B are the aforementioned production rates, the latter representing the combined levels of BdhA and BdhB (both play equivalent roles and so it is sufficient to look at them in combination). Then the rates R4 and R9 become

We note, however, that equation (7a) is required only when the production rate of ThlA is varied (i.e. in Figure 3(f)) in all other simulations R4 is given by the Michaelis-Menten expression in equation (4).

Steady-state curves of butanol (Bn) for varying production of (a) Adc (acetoacetate decarboxylase), (b) and (c) the CtfA/B (CoA-transferase), (d) AdhE (alcohol aldehyde dehydrogenase), (e) BdhA and/or BdhB (butanol dehydrogenases) and (f) ThlA (thiolase). In (c) we have altered the axes of (b) in order to be able to see clearly the effect of downregulation of ctfA/B.

For simplicity, we assume that the rates of binding of butyryl-CoA with BdhA and BdhB are the same (meaning that we can consider the combined level of Bdh proteins) and that this rate is the same as that between butyryl-CoA and AdhE. We also do not include a rate of binding between acetyl-CoA and ThlA. These assumptions do not reduce the generality of the steady-state results as only the ratios of binding and production to dilution appear and no such constraints are imposed on the values of these ratios. Since we are not concerned in this section with the time-dependent behavior of the system (butanol fermentation on a large scale would presumably be carried out in a continuous culture with the system therefore at steady state), we associate a single production rate, , with each solvent-associated enzyme this rate is different for each enzyme and is the sum of the basal production rate (r E for enzyme E), occurring regardless of pH, and the faster low-pH-induced production rate () occurring during solventogenesis, i.e. . In Table 3, we display the values of these combined enzyme production rates which correspond to those used for the wild-type-associated dynamic model.


The effect of pH on the activity, thermokinetics and inhibition of polyphenol oxidase from peach

This study focused on the effect of pH on the activity, thermokinetics and inhibition of polyphenol oxidase (PPO) from honeydew peach pulp with (+)-catechin as the substrate. The optimum pH for the PPO activity was around 6.5–7.0, and the optimum temperature was pH dependent and it was 40 °C at pH 6.8 while 30 °C at pH 4.0. The enzyme was stable in the pH range of 6.0–8.0 during the storage at 4 °C. However, the thermokinetics parameters (D, z, k, Ea) of PPO suggested that the enzyme was much more stable at pH 6.8 than at pH 6.0 and pH8.0 during the thermal treatments. Moreover, the results also indicated that the enzyme was more sensitive to the change of temperature at pH 6.8 than at the others pH. The inhibition study indicated that L-cysteine and glutathione were highly effective for the inhibition of the enzyme while NaF inhibited moderately at pH 6.8. However, the inhibition abilities of those inhibitors were pH dependent, and acidic medium could greatly increase the inhibition ability of NaF for peach pulp PPO.

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FACTORS AFFECTING ENZYME ACTIVITY

Here is just a quick recap about factors affecting enzymes activity.

WHAT ARE FACTORS THAT AFFECT ENZYMES ACTIVITY?

HOW DOES SUBSTRATE CONCENTRATION AFFECTS ENZYMES ACTIVITY?

As substrate concentration increases the rate at which enzyme substrate complex formed increases because there are more substrate available for free enzymes active site to bind with. Also with an increase in substrate concentration the greater the collision frequency of substrate to enzyme active site. However at Vmax all the enzyme active site is occupied by substrate therefore the rate of reaction is constant so increasing [S] doesn’t affect the rate of reaction. When observing the effects of substrate concentration on enzyme activity the following variables must be kept constant pH, temperature and enzyme concentration. The effect of substrate concentration can be illustrated by using either line weaver Burk plot (equation) or Michaelis–Menten graph (equation).

FIGURE 1: ILLUSTRATES THE EFFECT OF SUBSTRATE CONCENTRATION ON ENZYME ACTIVITY.

HOW DOES pH AFFECT ENZYME ACTIVITY?

When the pH is too acidic or too basic for an enzyme, its hydrogen bonds begin to break resulting in the enzyme active site losing its shape. Each enzyme operates within an pH range (optimal pH). For example: lipase in the stomach operates within the optimum pH 4-5.

FIGURE 2: ILLUSTRATES THE EFFECT OF pH ON ENZYME ACTIVITY.

HOW DOES TEMPERATURE AFFECT ENZYME ACTIVITY?

As temperature increase the rate of reaction increases however beyond the point of optimum temperature the rate of enzyme catalyzed reaction decreases because the hydrogen bond and the hydrophobic interaction in the enzyme structure is being broken. When this occur enzyme losses it shape and the substrate is unable to bind properly to the active site thus reducing enzyme activity. Furthermore, as temperature increases the amount of kinetic energy increases in the system thus increasing the rate of reaction since the collision frequency between the substrate and the enzyme active site increases. Also as temperature increases the substrate molecules gain more energy to overcome the activation barrier hence forming more ES complex which alternately increases rate of enzyme reaction.

FIGURE 2: ILLUSTRATES THE EFFECT OF TEMPERATURE ON ENZYME ACTIVITY.

HOW DOES INHIBITORS AFFECT ENZYME ACTIVITY?

There are irreversible inhibitors and reversible inhibitors which affect rate of enzyme reaction. Reversible inhibitors binds to the enzyme by non- covalent bond therefore dilution of the enzyme-inhibitor complex releases the inhibitor and the enzyme can carry on its activity. There are four types of reversible inhibitors are competitive, uncompetitive, mixed and non-competitive.

1. Competitive inhibitor s compete with the substrate for the active site, therefore the shape of the inhibitor resemble the shape of the substrate. When the inhibitor binds to the active site it reduces the rate of enzyme reaction since the substrates unable to bind to the active site because the inhibitor is currently occupying the active site . Competitive inhibitor increases Km therefore more substrate is needed to achieve ½ Vmax. Vmax however is unaffected by competitive inhibitor.

FIGURE 3: ILLUSTRATES THE EFFECT OF COMPETITIVE INHIBITOR ON Vmax AND Km IN LINEWEAVER- BURK PLOT.

2. Non-competitive inhibitor binds to free enzyme or ES complex it doesn’t bind to the active site. Therefore the shape of the inhibitor is different from the substrate. This type of inhibitor reduces the ability of the enzyme to convert substrate into product. Vmax is reduced and Km remains the same since the substrate can still bind to the active site as well as before the inhibitor is present.

FIGURE 4: ILLUSTRATES THE EFFECT OF NON-COMPETITIVE INHIBITOR ON Vmax AND Km IN MICHAELLIS MENTEN CURVE AND LINEWEAVER- BURK PLOT RESPECTIVELY.

3. Uncompetitive inhibitor occurs when the inhibitor binds only to the ES complex. They do not bind to free enzymes. It reduces both Vmax and Km in the same amount. The slope of the graph will remain constant because both the Km and Vmax will be changing proportionally to each other and so the line will simply be observed to shift up and to the left.

FIGURE 5: ILLUSTRATES THE EFFECT OF UNCOMPETITIVE INHIBITOR ON Km AND Vmax IN A LINEWEAVER BURK PLOT.

4. Mixed inhibitor binds to free enzyme or enzyme substrate complex. They do not bind to the active site. When the inhibitor binds to the enzymes it changes the shape of the enzyme thereby reducing the affinity of the substrate to the enzyme active site. Vmax is always reduced whereas Km is either increase or decrease.

Mixed inhibitor may seem similar to non- competitive inhibitor however they are different. When non-competitive inhibitors binds to the enzymes it form the EIS complex that caused the product not to be formed whereas in mixed inhibitor when the inbitor bind to the enzyme forming the EIS complex some product are still formed although the inhibitor is present.

FIGURE 6: ILLUSTRATES THE EFFECT OF MIXED INHIBITOR ON Km AND Vmax USING A LINEWEAVER BURK PLOT.


Kinetics - Why doesn't a change in concentration affect the rate constant?

A rise in temperature and the use of catalysts both increase the rate of reaction and therefore the rate constant, but even though an increase in concentration also increases the rate of reaction, why doesn't it affect the rate constant?

never mind, i've found the answer:

"The rate equation shows the relationship between the concentration of reactants and the rate of reaction.

If the concentration of one of the reactants increases, the rate of reaction will also increase, the rate constant, k will not change.

If the pressure increases, the concentration of all the reactants will increase and so the rate of reaction will also increases. Again the rate constant will not change.

The rate constant k is thus independent of concentration and pressure.

If the temperature increases, however, or a catalyst is added, the rate of reaction increases without a change in concentration, and so it must be the rate constant, k, that is changing.

The rate constant k thus varies with temperature, and is also affected by the addition of a catalyst."

For anybody else who was having the same problem.

Not what you're looking for? Try&hellip

Check out Arrhenius equation. Rate constant is dependent on presence/absence of catalyst and temperature.

lnk = -Ea/RT + lnA
y = mx + c
(The Arrhenius equation).
As you can see, concentration doesn't appear in this equation.
lnk = natural log of rate constant (k)
Ea= activation energy
R= relative gas constant (8.314)
T= Temperature, kelvin.
lnA= natural log of preexponential factor A (don't worry about what this is).

You use this equation in A2 to find the activation energy (and sometimes A) from graphs.

Another way you can tell that concentration doesn't affect the rate constant is the "simpler" rate equation:

Rate =k [M] m [N] n where m and n are the orders of the reactants (basically the effect that increasing concentration of these reactants has on the overall reaction). The square brackets represent concentrations of the reactants.

As you can see, rate is affected by concentration- if [M] were to increase, so would the rate because k and [N] are being multiplied by a larger number.
But, k in itself isn't affected by concentration. It is the rate constant for a reaction at a given temperature.
Think about the kinetics of a reaction. Increasing concentration means there are more molecules/atoms in a certain volume, increasing the likelihood of molecules colliding, but not affecting the number of molecules above activation energy.
However, increasing temperature means that more molecules are above activation energy (look at Boltzmann distributions).
This links back to the Arrhenius equation, which talks about activation energy but not concentration- hence catalysts and temperature does change the rate constant.

Sorry this is badly explained, it's been a while since I did this rate constant nonsense XD


How pH Affects Enzymes

A pH environment has a significant effect on an enzymes. It can affect the intramolecular forces and change the enzyme's shape -- potentially to the point where it is rendered ineffective. With these effects in mind, typical enzymes have a pH range in which they perform optimally. For example, alpha amylase, which found in the mouth, operates most effectively near a neutral pH. However, lipases operate better at more basic pH levels. Buffer systems built into most organisms prevent pH levels from reaching the point where essential enzymes are rendered ineffective. If an enzyme is rendered ineffective by pH level, adjusting the pH can cause the enzyme to become effective again.


Does pH affect Michaelis constant? - Biology

THE EFFECT OF CHANGING CONDITIONS IN ENZYME CATALYSIS

This page looks at the effect of changing substrate concentration, temperature and pH on reactions involving enzymes. It follows on from a page describing in simple terms how enzymes function as catalysts. Please remember that this series of pages is written for 16 - 18 year old chemistry students. If you want something more advanced, you are looking in the wrong place.

Note: This page assumes that you have already read the page about how proteins function as enzymes. If you have come straight to this page via a search engine, you really ought to go back and read that page first. In fact, unless you already have a good knowledge of protein structure, you may have to go back further still to a page about the structure of proteins.

The effect of substrate concentration on the rate of enzyme-controlled reactions

Remember that in biology or biochemistry, the reactant in an enzyme reaction is known as the "substrate".

What follows is a very brief and simple look at a very complicated topic. Anything beyond this is the stuff of biochemistry degree courses!

A reminder about the effect of concentration on rate in ordinary chemical reactions

If you have done any work on rates of reaction (especially if you have done orders of reaction), you will have come across cases where the rate of reaction is proportional to the concentration of a reactant, or perhaps to the square of its concentration.

You would discover this by changing the concentration of one of the reactants, keeping everything else constant, and measuring the initial rate of the reaction. If you measure the rate after the reaction has been going for a while, the concentration of the reactant(s) will have changed and that just complicates things. That's why initial rates are so useful - you know exactly how much you have of everything.

If you plotted a graph of initial reaction rate against the concentration of a reactant, then there are various possibilities depending on the relationship between the concentration and the rate.

If the rate is independent of the concentration

This is called a zero order reaction.

If the rate is proportional to the concentration

This is called a first order reaction.

If the rate is proportional to some power of the concentration greater than one

In this case, you get a curve. If the rate was proportional to the square of the concentration, that's a second order reaction.

With reactions controlled by enzymes, you get a completely different type of graph.

Plotting initial rates of enzyme-controlled reactions against substrate concentration

The graph for enzyme controlled reactions looks like this:

Two minor things to notice before we discuss it . . .

Biochemists talk about a reaction velocity instead of a reaction rate. If you have done any physics, you will know that this is a complete misuse of the word "velocity"! But that's what you will find in biochemistry sources, so that's what we will have to use.

So why is the graph the shape it is?

For very, very low substrate concentrations, the graph is almost a straight line - like the second chemistry rate graph above. In other words, at very, very low concentrations, the rate is proportional to the substrate concentration.

But as concentration increases, increasing the concentration more has less and less effect - and eventually the rate reaches a maximum. Increasing the concentration any more makes no difference to the rate of the reaction.

If you know about orders of reaction, the reaction has now become zero order with respect to the substrate.

The reason for this is actually fairly obvious if you think about it. After a certain concentration of substrate is reached, every enzyme molecule present in the mixture is working as fast as it can. If you increase the substrate concentration any more, there aren't any enzyme molecules free to help the extra substrate molecules to react.

Is this unique to enzyme-controlled reactions? No! It can happen in some ordinary chemistry cases as well, usually involving a solid catalyst working with gases. At very high gas pressures (in other words, very high concentrations of gas molecules), the surface of the catalyst can be completely full of gas molecules. If you increase the amount of gas any more, there isn't any available surface for it to stick to and react.

The maximum rate for a particular enzyme reaction is known as Vmax. (That's V for velocity - a bit confusing for chemists where V is almost always used for volume!)

This is easily measured by drawing a line on the graph:

This is sometimes reported as a "turnover number", measured as the number of molecules of substrate processed by a single enzyme molecule per second, or per minute.

KM is known as the Michaelis constant or the Michaelis-Menten constant (for reasons which needn't concern us), and is a useful measure of the efficiency of an enzyme.

KM is the concentration of the substrate in mol dm -3 which produces a reaction rate of half Vmax. So it is found like this . . .

A low value of KM means that the reaction is going quickly even at low substrate concentrations. A higher value means the enzyme isn't as effective.

Note: You might possibly wonder why you have to go to the trouble of halving the maximum rate to get this information. Couldn't you just find the concentration of the substrate which produced the maximum rate?

If you look at the shape of the graph, it would be impossible to get any accurate measure of the concentration which first produced a maximum rate. The curve just gradually gets closer and closer to the horizontal, and there is no clear cut-off point at which it suddenly becomes horizontal.

The effect of temperature on the rate of enzyme-controlled reactions

A reminder about the effect of temperature on rate in ordinary chemical reactions

Remember that for molecules to react, they have to collide with an energy equal to or greater than the activation energy for the reaction.

Heating a reaction makes the molecules move faster and so collide more often. More collisions in a given time means a faster reaction.

But far more importantly, increasing the temperature has a very big effect on the number of collisions with enough energy to react. Quite a small temperature rise can produce a large increase in rate.

As a reasonable approximation for many (although not all) reactions close to room temperature, a 10°C increase in temperature will double the rate of a chemical reaction. This is only an approximation - it may take 9°C or 11°C or whatever, but it gives you an idea of what to expect.

Note: If you aren't sure about any of this, have a quick look at the page about the effect of temperature on rates of reaction.

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Plotting rates of enzyme-controlled reactions against temperature

For low temperatures up to about 40°C, enzyme-controlled reactions behave much as you would expect any other chemical reaction to behave. But above about 40°C (the exact temperature varies from enzyme to enzyme), there is a dramatic fall in reaction rate.

A typical graph of rate against temperature might look like this:

The temperature at which the rate is fastest is called the optimum temperature for that enzyme.

Different enzymes have different optimum temperatures. Some enzymes, for example, in organisms known as thermophiles or extremophiles are capable of working at temperatures like 80°C or even higher.

The optimum temperature for a particular enzyme varies depending on how long it is exposed to the higher temperatures. Enzymes can withstand temperatures higher than their normal optimum if they are only exposed to the higher temperatures for a very short time.

Explaining the rate against temperature graph

At lower temperatures, the shape of the graph is exactly what you would expect for any reaction. All that needs explaining is why the rate falls above the optimum temperature.

Remember that the enzyme works because its substrate fits into the active site on the protein molecule. That active site is produced because of the way the protein is folded into its tertiary structure.

Heating an enzyme gives the protein chains extra energy and makes them move more. If they move enough, then the bonds holding the tertiary structure in place will come under increasing strain.

The weaker bonds will break first - van der Waals attractions between side groups, and then hydrogen bonds. As soon as these bonds holding the tertiary structure together are broken, then the shape of the active site is likely to be lost.

Obviously, the longer the enzyme is held at the higher temperature, the more time there is for the enzyme structure to be broken up. Given enough time and high enough temperatures, the enzyme structure is broken permanently. The enzyme is said to be denatured. For example, boiling an egg for 5 minutes denatures the proteins in the egg. Once that has happened, you can't un-boil it by cooling it!

The effect of pH on the rate of enzyme-controlled reactions

In the same way that every enzyme has an optimum temperature, so each enzyme also has an optimum pH at which it works best.

For example, trypsin and pepsin are both enzymes in the digestive system which break protein chains in the food into smaller bits - either into smaller peptide chains or into individual amino acids.

Pepsin works in the highly acidic conditions of the stomach. It has an optimum pH of about 1.5.

On the other hand, trypsin works in the small intestine, parts of which have a pH of around 7.5. Trypsin's optimum pH is about 8.

If you think about the structure of an enzyme molecule, and the sorts of bonds that it may form with its substrate, it isn't surprising that pH should matter.

Suppose an enzyme has an optimum pH around 7. Imagine that at a pH of around 7, a substrate attaches itself to the enzyme via two ionic bonds. In the diagram below, the groups allowing ionic bonding are caused by the transfer of a hydrogen ion from a -COOH group in the side chain of one amino acid residue to an -NH2 group in the side chain of another.

In this simplified example, that is equally true in both the substrate and the enzyme.

Now think about what happens at a lower pH - in other words under acidic conditions.

It won't affect the -NH3 + group, but the -COO - will pick up a hydrogen ion.

What you will have will be this:

You no longer have the ability to form ionic bonds between the substrate and the enzyme. If those bonds were necessary to attach the substrate and activate it in some way, then at this lower pH, the enzyme won't work.

What if you have a pH higher than 7 - in other words under alkaline conditions.

This time, the -COO - group won't be affected, but the -NH3 + group will lose a hydrogen ion.

Again, there is no possibility of forming ionic bonds, and so the enzyme probably won't work this time either.

Note: If you think about it, this argument only works using ionic bonding if the enzyme has an optimum pH around 7. Under fairly acidic or alkaline conditions, all the charges present in the enzyme and substrate would be the same - as in the examples above.

Under those circumstances, you would be looking at other sorts of bonding - hydrogen bonding, for example, perhaps involving hydrogen bonds between an ion on one of either the enzyme and substrate, and a suitable hydrogen atom or lone pair on the other.

The example given is easy to follow. Don't worry about complications at this level. As long as you can see why changing the pH might affect a simple case, that's all you need.

At extreme pH's, something more drastic can happen. Remember that the tertiary structure of the protein is in part held together by ionic bonds just like those we've looked at between the enzyme and its substrate.

At very high or very low pH's, these bonds within the enzyme can be disrupted, and it can lose its shape. If it loses its shape, the active site will probably be lost completely. This is essentially the same as denaturing the protein by heating it too much.

This enzyme topic continues onto a final page about enzyme inhibitors.

Questions to test your understanding

If this is the first set of questions you have done, please read the introductory page before you start. You will need to use the BACK BUTTON on your browser to come back here afterwards.


Human pancreatic alpha-amylase. II. Effects of pH, substrate and ions on the activity of the enzyme

Purified human pancreatic alpha-amylase (alpha-1,4-glucan 4-glucano-hydrolase, EC 3.2.1.1) was found to be stable over a wide range of pH values (5.0 to 10.5) with an optimal pH for the enzymatic activity of 7.0. The Michaelis constant of the enzyme at optimal pH and assay conditions was found to be 2.51 mg per ml for soluble starch. Halide ions were required for the activity of the enzyme whereas sulfate and nitrate were not. The order of effectiveness of activation was found to be: Cl- greater than Br- greater than I- greater than F-. Calcium and magnesium were activators at concentrations of 0.001M and 0.005M, respectively, but exhibited inhibitory effects at concentrations higher than 0.005M. At 0.01M ethylenediamine tetraacetic acid (EDTA) concentration the enzymatic activity upon seven min incubation, was inhibited up to 96%. The inhibition of EDTA and calcium could be reversed upon addition of calcium and EDTA, respectively.


Does pH affect Michaelis constant? - Biology

Many biologically important molecules have multiple binding sites. For example hemoglobin, the oxygen carrying molecule in red blood cells, binds four molecules of molecular oxygen, each binding at its own distinct binding site. Hemoglobin is an example of a cooperative molecule, that is one where the binding of a ligand at one site alter that the affinity of other binding sites for their ligands. In the case of hemoglobin, the binding of a molecule of O2 at one site increases the affinity of the other sites for O2.

This property is critical for the function of hemoglobin, which picks up four molecules of O2 in the oxygen-rich environment of the lungs, then delivers it to the tissues that have a much lower concentration of oxygen. As each molecule of O2bind to hemoglobin, the affinity of the remaining binding site increases, making it easier for more O2 to bind . Conversely, as each molecule of O2 is released to a tissue, the affinity of the remaining sites for O2 decreases, making it easier for subsequent molecules of O2 to dissociate.

Scanning electron micrograph of blood. The doughnut-shaped cells are red blood cells. Photo credit: Bruce Wetzel. Courtesy of the National Cancer Institute.

The problem of how hemoglobin delivers oxygen throughout the body has been studied for the past 100 years. In 1910, biochemist Archibald Hill modeled this property of hemoglobin using the rational function,

where &theta is the percentage of binding sites occupied, [L] is the concentration of ligand, n is the Hill coefficient, which represents the degree of cooperativity, and Kd is the dissociation constant. Recall that Kd is equal to the ligand concentration when half of the binding sites are filled.

A common application of the Hill equation is modeling cooperative enzymes. These enzymes are under allosteric control, that is the binding of a molecule at one site alters the affinity of the enzyme for its substrate and hence regulates the enzyme activity. In this case, the Hill equation is rewritten as the rational function,

where V is the reaction velocity, Vmax is the maximum reaction velocity, and [S] is the substrate concentration. The constant K is analogous to the Michaelis constant (Km) and n is the Hill coefficient indicating the degree of cooperativity.

Hill coefficient Cooperativity
n = 1 none
n > 1 positive
n < 1 negative

Positive cooperativity occurs when an enzyme has several sites to which a substrate can bind, and the binding of one substrates molecules increases the rate of binding of other substrates. Cooperativity can be recognized by plotting velocity against substrate concentration. An enzyme that displays positive cooperativity sill be sigmoidal (or S-shaped), while noncooperative enzymes display Michaelis-Menten kinetics and the plots are hyperbolic.

Use the Hill equation to answer the following questions: