米氏常数的测定实验报告

Determination of Michaelis Constant

1. Objectives

1.1 To study influence of substrate concentration on enzymatic reaction;

1.2 Master the methods and principles of determination of Michalis constant Km.

2. Experiment Principles

The relation of the velocity of enzymatic reaction and substrate concentration can be expressed by Michaelis equation:

v=

In which,

v – initial velocity of reaction (change of micromole concentration/mm);

V - maximum reaction velocity (change of micromole concentration/mm);

[S] - substrate concentration (mol/L);

Km - Michaelis constant.

This equation indicates the quantitative relation of the velocity of enzymatic reaction and substrate concentration if Km and V are given. Km value equals to the corresponding substrate concentration when the velocity of enzymatic reaction reaches half of maximum reaction velocity, which is one of the characteristic constants of enzyme. Different enzyme has different Km value, when the same kind of enzyme reacts with different substrate, the Km value will be different, Km value can indicate approximately the extent of affinity between enzyme and substrate: big Km value indicates low extent of affinity, and small Km value indicates high extent of affinity. Determination of Km value is an important method of enzymology research. The Km values of most pure enzymes range from 0.01mmol/L to 100mmol/L.

Linewaever—Burk graphing method is the most frequently-used short-cut method to determine Km value:

1K%11= ×+ %&'%&'

Different [S] can be selected to determine corresponding v; draw a graph for 1/

[S] with UV to obtain a straight line whose rake ratio is, Km/V and the intercept 1/

[S] is — 1/ Km, by which Km value (negative reciprocal of the intercept) is determined. V%&'[S]%

Example m' this experiment is that casein is digested by trypsin, Km value is determined by using Linewaever—Burk double reciprocal graphing method. Peptide bond generated m' the way that carboxyl of alkaline amino acid ( L-Arginine and L- Lysine) is catalyzed by trypsin is hydrolyzed. Free ammo is generated in hydrolysis process, and formaldehyde titration can be used to

determine the increased number of free amino to track the reaction and obtain the initial velocity.

3. Reagents, Materials & Equipment

I Reagents

40g/L casein' solution: get 40g of casein to be dissolved in about 900ml of hot water, add 20ml of 1M NaOH, and shake the solution continuously, heat it slightly until dissolved, adjust pH to 8.5 with 1M HCl or IM NaOH, fix the volume to 1L.

I0g/L, 20g/L, 30g/L casein solution are obtained by diluting 40g/L casein solution (pH8.5) respectively to get four types of standard casein solutions with different [S]

Neutral formaldehyde solution: add 15ml of 0.25% phenolphthalein ethanol solution to 75mL analytically pure formaldehyde, titrate the solution with 0.1M NaOH to reddish color, and keep it in a sealed glass bottle.

0.25% phenolphthalein added with 50% ethanol solution: dissolve 2.5g of phenolphthalein in 50% ethanol solution, fix the volume to 1L.

Standard 0.1M NaOH solution.

II Materials

Trypsin solution: get 1g of trypsin to be dissolved in 25ml of distilled water, and put the solution in refrigerator for conservation.

III equipment

50ml conical flask (x8), 150ml conical flask(x4); suction tube 5ml (x1),

10ml (x5); measuring cylinder 50ml(x4); 25ml alkali burette and titration platform, burette clamp; thermostatic water bath.

4. Experiment Operation

1. Get four 50ml conical flasks to be added with 5ml of neutral formaldehyde and one drop of phenolphthalein, titrate the solution with 0.1M NaOH to reddish color, the color of the four triangular flasks should be accordant, give them numbers.

2. Get 50ml of 40g/L casein to be added in a 150ml conical flask, keep it under 37 Celsius for 10 minutes, meanwhile, keep trypsin liquid under 37C, and then suck up 5ml of enzyme liquid in the casein liquid. (Keep the meanwhile!) Take out 10ml of reaction liquid (determined as the sample at time 0) immediately after mixed up adequately to be added in a small triangular flask (No.1) contains formaldehyde, and then add 10 drops of phenolphthalein in the flask; titrate the solution to faint and continuous reddish color. In the near the finish, per the mL number of the consumed NaOH, add one drop of phenolphthalein for every milliliter, continue to add until the finish, take notes of the mL number of the consumed 0.1M standard NaOH.

3. Take out 10ml reaction liquid respectively after 2 minutes, 4 minutes, 6 minutes to be added in small triangular flask 1, flask 2, flask 3, operate as above, take notes of the Ml number of the consumed NaOH.

Draw a graph based on titer value (i.e. the mL number of the consumed NaOH) and time to obtain" a straight line whose slope is 1m"tial velocity

V40(relative to the concentration of 40g/L casein).

Get 30g/L, 20g/L, 10g/L casein solution respectively, repeat abovementioned operation to measure out V30, V20, V10 respectively.

Draw a graph based on 1/[s] and 1/v making use of abovementioned result to obtain the values of V and Km.

5. Result and Analysis

I Data Processing

The reaction was done in 37 Celsius water bath with 10mL casein of corresponding concentration (40g/L, 30g/L, 20g/L, 10g/L) added. At time point 0, 2min, 4min, 6min, the reaction was terminated by formaldehyde added. 0.1M NaOH was used for titration. The original data was the volume of NaOH consumed for each group of titration.

The original and processed data was shown below: [S] /M

0s

120s

240s

360s 40 2.05 3.22 3.70 4.37 30 2.20 3.31 3.82 4.23 20 1.64 2.22 2.65 2.94 10 0.55 0.82 1.04 1.14

Chart. 1 Volume of NaOH consumed in titration

To determine the actual reaction rate on different casein concentration, NaOH consumption (mL) – time (s) graph was generated:

The reaction rate (demonstrated as mL NaOH consumed per second) is shown as the slope of each fitting line. On the bases that NaOH is 0.1M, The volume of the reaction system is 10mL, and NaOH reacts with H3N- residue as 1 : 1, product (P) concentration changing rate VP can be converted from NaOH consuming rate (v).

The molecule mass of casein was 25107 Da (Beta-casein, UniProtKB - P02666

(CASB_BOVIN), http://www.uniprot.org/uniprot/P02666), converting the substrate (casein) mass concentration into molecule concentration (M). The data is processed based on the above data and is shown below: [S] /M

1/[S] /M

v /mL NaOH·s

v /M·s

1/v /s·M -1-1-1-1+0.00159 0.00119 0.00080

0.00040 627.67500 836.90000 1255.35000 2510.70000 0.00620 0.00550 0.00361 0.00166 0.0000620 0.0000550 0.0000361 0.0000166 16129 18182 27701 60241

Chart. 2 Processed [S] and v data

As the Michaelis Equation’s derivation, the Linewaever-Burk graph shows the critical parameters in the Michaelis Equation. Draw Linewaever-Burk graph based on Chart. 2. As is shown both in Fig. 1 and below. The data of 40g/L casein deviates severely from the overall trend. Thus, this data point (10g/L) was omitted in the linear regression. The

Linewaever-Burk graph is shown below:

The derivate Michaelis equation (parameters attached) was:

11=19.05×+3397 v[S}

Them the Michaelis constant can be calculated as:

−7

89=−::;@7=−178.3M@7, K%=−7@7

The maximum speed Vm can then be export:

5.609×10@:

VMs@7=2.944×10@GMs@7 %=The mass of trypsin is 26558Da (Trypsin -1, UniProtKB - P07477 (TRY1_HUMAN),

http://www.uniprot.org/uniprot/P07477), The total enzyme concentration:

[E]I =51×M=1.369×10@GM Then it is possible to give the kcat value:

kK&IV2.944×10@G@7%== s=2.15 s@7 [E]I 1.369×10To sum up the experimental value of Km , kcat and Vm are:

K m = 5.609×10@:M

k cat = 2.15 s@7

V m = 2.944×10

@GMs@7

II Analysis

1. Error analysis. The Km value represents the binding affinity of substrate (casein) and enzyme (trypsin) while kcat reveals the release rate of product from [ES] complex. Each set of K m and k cat is unique depending on the specific set of enzyme and substrate (more on enzyme). Thus, there are many different values of Km and kcat of enzyme. Unfortunately, no data of trypsin with casein as substrate was found. However, from “The New Method for the Determination of the Amidase Activity of Trypsin: Kinetics of Hydrolysis of Benzoyl-Arginineamide”, S. A. Bernhard, 1954, Km and kcat values are found as Km =3.1×10@:M and kcat =0.043s@7(substrate is Benzoyl Arginineamide). After comparison of two sets of data, it is clear the experimental data is in correct level as Bernhard’s. As the result is dependent on so many variables let along error, it is reasonable to say that the experimental result is sensible. We will analyze the potential errors below:

2. Inaccurate timing. Timing is the most important factor in this experiment, as speed is all about time. If more accurate data is to be acquired, the current plan cannot be used. The current method assumes that formaldehyde can freeze (deactivate) all enzymes when samples are extracted from the reaction system. However, the extraction procedure takes more time that cannot be ignored compared with the entire experiment length. Moreover, extracting time is variable because of manual operation. In some situations, to transfer 10mL reaction liquid into the flask takes more than 20s, which can be an enormous error. To acquire more accurate data, physical detection method such as UV absorbance, if the product has significant UV absorbance.

3. Reaction rate changes with time. As can be seen from Fig. 1, The reaction rate decreases slightly as the reaction proceeds. The reasons can be: decreased substrate rate, increased concentration of product inhibits enzyme activity, impropriate environmental pH and/or temperature leads to enzyme partial denaturation. If possible, the shorter the experiment lasts, the better regression line obtained.

4. Changed concentration of substrate. The initial volume of substrate solution is 50mL. However, 5mL of enzyme solution is added to the system. For accuracy, this additional volume should to considered while in data processing, it is not, which can lead to certain error.

5. Limited data points. Limited experiment data and incomplete [S] gradient lead to uncertainty and random errors that may affect the result severely. As in data processing, we take out the 10g/L data point which is far from accuracy. The remaining points have greater

linear quality but also pose uncertainty as the total amount of points is very limited. Thus, the result of Km and kcat may not be trustworthy.

6. Additional analysis of the result. In this result, Km = 5.609×10@:M, kcat = 2.15 s@7. The catalytic efficiency of trypsin on casein can be quantified as kcat / Km = 383sM . Compared with the equivalent value of chymotrypsin, this result is sensible as a mean value for all cleavable peptide bonds existing in casein. The result also shows that the Turnover Number of trypsin is 2.15, indicating that on average trypsin can cleave 2.15 peptide bonds per second, which is of moderate speed. -1-1

6. Questions

1. Try to state the influence of substrate concentration on the velocity of enzymatic reaction. For an enzyme that is subjective to Michaelis Equation, the situation can be described as follows: as [S] increases, the reaction rate also increases but the slope of increase decreases. when [S] reaches very high level, the reaction rate nearly reaches the maximum value and become a terrace. If the enzyme is not subjective to Michaelis Equation (like isomerases), then the v-[s] situation is different.

2. In which cases, Km value of enzyme can be a method to identify enzyme, and why? What are the practical applications of Km value in Michaelis Equation? First , the enzyme kinetics must satisfy the Michaelis-Menten model. Second , all candidate enzymes must react with the same substrate, as the constant differs with different substrates. Third , the pH and temperature must be the same in the reaction system, because Km is different in different environment. Michaelis constant can be used in enzymatic research, where Km can serve as the index for substrate affinity, when comparing different mutants and choosing the right one for industrial application. Furthermore, Km can be used in physical training and pharmaceutical kinetics to achieve optimum outcome and drug performance.

3. The function of formaldehyde in experiment? First , formaldehyde is an efficient denaturant, which can deactivate trypsin when the test sample are transferred to the designated flask which is important because it can ‘freeze’ the sample and retain the concentration of the product, which can be determined by titration. Second , the titration itself requires formaldehyde. Amino acids exist in the form of zwitterions in water solution. It is impossible to titrate them with NaOH. Formaldehyde can react with –NH 3 and become –NH-CH2OH and a H is released. Then can NaOH be used to titrate the free proton. The amount of proton is equivalent to the amount of –NH 3, so we can calculate the amount of the product. +++