Michaelis Menton Equation

ENZYME KINETICS

The Michaelis Menton Equation: a generalized theory of enzyme action was formulated by Leonor Michaelis and Maud Menton in 1913. The derivation starts with a basic step involving formation and breakdown of the ES complex.

The overall reaction is:

                    k₁                                        k₂

E + S           ES             E + P    

                        k_-1

the initial velocity V₀ can be determined by the breakdown of ES complex into product which is give by:

                                                V₀  =  k₂ [ES]           Eq No. 1

Since it is not easy to measure [ES] experimentally we should figure out an alternative expression of [ES]. So , we will consider [E_t ], that denotes for total enzyme concentration.

Free or unbound enzyme can be represented by:

                                                [E_t] – [ES]

The rate of formation and breakdown of ES can be determined by:

Rate of ES formation =  k₁ ([E_t] – [ES])[S]

Rate of ES breakdown = k_-1 [ES] + k₂ [ES]

At the steady state rate of [ES] formation will be equal to ES breakdown so above equation can be written as:

k₁ ([E_t] – [ES])[S]  = k_-1 [ES] + k₂ [ES]

To solve the above equation multiply the left side and simplify the right side:

k₁[E_t][S]  - k₁[ES][S] = (k-_{1 ­+} k₂)[ES]

add the term k₁[ES][S] to both sides of the equation:

k₁[E_t][S] = (k₁[S] + k_-1 + k₂)[ES]

and then solve the equation for [ES]:

[ES]  =                   [E_t][S]

               

                     [S] + (k₂ + k_-1)/k₁

The term (k₂ + k_-1)/k₁  is defined as Michaelis constant K_m

Substitute k_m  into above equation:

            

[ES]  =                   [E_t][S]

                           

                             [S] + K_m

Now V₀ can be expressed in terms of [ES] by substituting above equation into equation no.1:

V_{0   =}                                   k₂[E_t][S]

                          

                                            [S] + K_m

Since maximum velocity occurs when enzyme is saturated with [ES] = [E_t] so V_max can be defined as k₂ [E_t] so substitute the value of V₀ into above equation:

V_{0   =}                                     V_max [S]

                           

                                            [S] + K_m

The above equation is called as Michaelis Menton equation.

A numerical relationship exists in the Michaelis menton equation when V₀  is exactly one half of V_{max .} then:

      V_max   / 2  =                              V_max [S]

                                                

                                                       [S] + K_m

Divide above equation by V_max we get:

½  =    [S] / K_m + [S]

Solving for K_m we get K_{m  +} [S] = 2 [S],

Or  k_m  = [S] , when V₀  = ½ V_max

Transformation of Michaelis Menton equation: Double Reciprocal plot

V_{0   =}                                  V_max [S]

                          

                                         [S] + K_m

Take the reciprocal of above equation:

1/V₀   =                   K_m  + [S] / V_max [S]

Separate the components of numerator on the R.H.S of the equation and after simplification we get:

1/V₀  =     K_m           +      [S]

V_max[S]            V_max

This equation is known as double reciprocal plot or Lineweaver Burk equation.

ENZYME INHIBITION

Enzyme Inhibition

Enzyme inhibitors are the agents that interfere with the catalysis and slow down or even halt the reactions. There are 2 broad classes of enzyme inhibitors:

1.      Reversible

2.      Irreversible

Reversible inhibition: is characterized by a rapid dissociation of the enzyme inhibitor complex. Reversible inhibition can be:

Ø  Competitive

Ø  Uncompetitive

Ø  Mixed / non competitive

Competitive Inhibition: In this type of inhibition a competitive inhibitor competes with the substrate for an active site of enzyme; as a result inhibitor occupies the active site and prevents the interaction of substrate with the enzyme. The competitive inhibitors are the compounds having similarity with substrate and thus they combine with enzyme to form EI (enzyme inhibitor) complex.

This theory can be better justified by the example in case of medical science; in which the therapy is based upon the competition at the active site and is used to treat patients who ingest a solvent, methanol which is usually found in the gas line antifreeze. The enzyme alcohol dehydrogenase found in our liver converts methanol to formaldehyde and results in damage to the tissues and in severe cases it causes blindness. The reason behind this blindness is that eyes are quite sensitive to formaldehyde.

The medical therapy here is to give intravenous infusion of ethanol to the patients because ethanol competes effectively with the methanol as an alternative substrate for the enzyme alcohol dehydrogenase. In other words ethanol acts as a competitive inhibitor to ethanol and the effect of ethanol can be nullified as its concentration decrease over time as the dehydrogenase enzyme converts ethanol into acetaldehyde. So intravenous infusion should be given at a rate that maintains a controlled concentration in the blood stream for several hours. This will slow down the production of formaldehyde and ultimately kidneys will excrete out the methanol harmlessly in the urine.

Uncompetitive inhibition: can be distinguished by the fact that inhibitor binds only to the enzyme substrate complex. This type of inhibition cannot be overcome by addition of more substrates.

E + S              ES                   E + P

                        +

                        I

                   

                       

                  ESI complex

UNCOMPETITIVE INHIBITION

Mixed inhibition: the inhibitor will bind at a site distinct from the substrate active site but it will bind to either ES or E

Non competitive inhibition: the inhibitor and substrate can bind simultaneously to an enzyme molecule at different binding sites. This inhibition cannot be overcome by increasing the substrate concentration.

Both mixed and uncompetitive can be observed only for the enzymes with 2 or more substrates.

Irreversible inhibition: here the inhibitors will covalently bind to the enzyme and provides an alternative approach: they will modify the functional groups which can then be identified. Basically irreversible inhibition is important to determine what functional groups are required for enzymic activity and X-ray crystallography is the best approach. Irreversible inhibitors can be divided into 2 categories:

Suicide inhibitors: which are modified substrates that provide the most specific means to modify an enzyme active site. The inhibitors bind to the enzyme as substrates. The catalytic mechanism then generates intermediate that inactivates the enzyme through covalent modification. The fact that enzyme participates in its own irreversible inhibition; that’s why it is called as suicide inhibitor.

Affinity labels: are molecules that are structurally similar to the substrates for the enzyme and that covalently bind to the active site residues. Thus they are specific for the enzyme active site.

PHOTOSYNTHESIS

Photosynthesis is a mechanism in which complex organic substances are synthesised from the inorganic substances or in other words it is a oxidation – reduction process in which water molecules are oxidised to form oxygen and carbon dioxide molecules are reduced to form sugars (carbohydrates). This reduction of CO₂ into sugars requires an energy source like ATP and NADPH (assimilatory powers). This reduction process takes place in dark conditions while production of assimilatory powers takes place in light. So there are 2 phases that occurs during photosynthesis.

Light Dependent Phase: This phase requires light so it light dependent and it is also best known as HILL Reaction after the name of its discoverer.

Light Independent Phase: This phase does not require light so it is called as DARK Reaction or BLACKMAN’s Reaction (after the name of its discoverer).

MECHANISM OF ABSORPTION OF LIGHT:

When a visible photon of light with a wavelength between 380nm and 780nm strikes the chlorophyll molecule it releases an electron from chlorophyll to an outer molecular orbital. This state of chlorophyll molecule is called as excited or an activated state. Usually the normal state of an atom or molecule is called as Ground state or Singlet state (S₀) in which the electrons are present in the even number and paired state. The excited chlorophyll molecule shows four states:

Singlet state first (S₁)

Singlet state second (S₂)

Triplet state first (T₁₎

Triplet state second (T₂)

So S₁ state would be the one when a red light photon strikes a chlorophyll molecule which becomes photo excited and an electron will be released from its ground molecular orbital to the outer molecular orbital. This state is unstable state as it has half life period of only 10^-9 s and it produces two molecular orbitals each having one electron.

S₂ state  will be produced in the same way as the S₀; the only difference is that this time blue light photon will photo excite the chlorophyll molecule and release electron into outer MO. The electron is raised more higher than the S₁ state because blue light photon possesses more energy than red light photons. This state also produces 2 MO’s and is unstable with a half life period of 10_-9 s.

Since S ₁ and S ₂states both are unstable they are converted into S₀ state by releasing energy through some processes like heat, phosphorescence and fluorescence. The S₁ state is converted in to S₀ state by releasing energy in the form of heat. This is called as fluorescence.

But all of the energy is not lost as fluorescence; still some of energy is left which is being utilised to drive photosynthetic reactions. The S₂ state is first converted into S₁ state by releasing small amount of energy and when S₁ state loses energy it is converted into 2 interconvertible states called as T₁ and T₂ states. T₁ state is then converted in to S₀ state by loosing small amount of energy. This phenomenon is known as phosphorescence.

ABSORPTION SPECTRUM

It can be defined as the amount of the light of different wavelengths absorbed by the pigment. if the light of different wavelengths is passed through the extracted chlorophyll the absorption of each wavelength can be measured by spectrophotometer. And when this absorption is plotted the resulting plot we get is called as absorption spectra. Different pigments absorb different wavelength of light. For instance, the absorption spectra of chl a is in blue and red region. Other lights like yellow green and orange are absorbed only slightly. That’s why chlorophyll is not green because it absorbs green but actually it reflects and transmits green. The exact position of the peaks in the spectra depends upon the solvent used for the extraction of pigments. Chl a shows max absorption at 662nm in red region and 430nm in blue region. While Chl b shows max absorption peak at 644 nm in red region and 455nm in blue region.

Figure shows absorption spectra of chl a and chl b : vertical axis has absorption and horizontal axis is wavelength in nm. 

In next post we will be doing action spectra and mechanism of photosynthesis!!!!!!

ENZYMES

ENZYMES

Enzymes are the substances present in the cell in the minute amounts and capable of speeding up chemical reactions which are associated with life processes; so any impairment of enzymic activity is evident by any change in the cell which could be death as well!!! So it is not wrong to say that any substance that have unique capacity of speeding up a chemical reaction along with accelerating the velocity of reaction without necessarily initiating it is called as CATALYST and enzyme duly qualify to fit into this property.

All enzymes are produced in the cell but some of them would function in the cellular environment and some will be secreted through cell wall. On this basis we have got two types of enzymes: the former ones are Intracellular enzymes and the latter ones are extracellular enzymes. Intracellular enzymes perform catabolic reactions and provide energy required by the cell. Extracellular enzymes make necessary changes on the nutrients in the medium to allow them to enter the cell.

Properties of Enzymes

Enzymes are proteinaceous in nature and therefore possess properties specific to the proteins i.e. they are non dialyzable and easily denatured by heat.

A complete enzyme is a Holoenzyme which is composed of a protein part and non protein part (organic molecule). The protein portion is referred to as Apoenzyme. The organic molecule is referred to as Coenzyme. In some cases non protein portion of an enzyme can be metal. In fact many enzymes require the addition of metal ions in order to be activated. these metal ions function in combination with the enzyme protein and they are regarded as cofactors.

In my next post i will be adding up some more notes for the inhibition  & kinetics.

BEER (Schematic Representation)

BEER PRODUCTION

THE VERSATILE MICROORGANISMS

Latter part of the nineteenth century can be considered the beginning of industrial food microbiology. Once it was established that certain yeast grown under certain conditions produced beer and that certain bacteria could spoil the beer; then brewers were able to understand the microbiological role and were in a position to control the quality of their products. Microorganisms have proved their versatility by exhibiting their special qualities and their role in not only in the food industry but in brewing industry as well.

We will begin with some non dairy fermentation like alcoholic beverages and vinegar.

Beer production:

Beer is an undistilled beverage produced from fermentation of barley malt by yeast especially Sacccharomyces crevisiae and S. carsibergenesis. Generally materials rich in starch like rice, wheat and maize are also added to increase the amount of fermentable sugars. They are called as ADJUNCTS.

Beer production involves four main steps:

1.      MALTING

2.      MASHING

3.      SACCHARIFICATION

4.      FERMENTATION

It’s always better to explain any industrial fermentation schematically as it gives a better view of the whole process and from examination point of view; it leaves better impact. I would suggest the schematic view but if you are comfortable with the paragraph explanations then even its perfect!!!

i have posted  schematic self explanatory sketch for beer production in next post !!!

Have a great learning and let me know how you find it!!

Industrial Microbiological Processes

Introduction

Microorganisms have been exploited for useful purposes from a long time back before anything else was known about their existence or their characteristics. Looking back to history we will find that there are  many applications of microbial processes that have resulted in the production of the desirable materials; especially food products and beverages.Because of the industrial point of view we can call microorganisms as chemical factories; as they have the capacity to convert a raw material into the products and if those products are important for human beings; then it is obviously attractive to exploit the microbiological processes i.e the end products on a commercial scale.

The revolutionary step in setting up industrial microbiology is the Recombinant DNA technology. It is very likely that engineering of microorganisms is  a desired step  to produce new products on a commercial scale.

I will be following up this topic in my next post.

REFERENCES:  Microbiology: Pelczar. J.M, Chan .E.C.S, Krieg.R.N