Carbohydrates
A carbohydrate is an organic compound that is composed of atoms of carbon, hydrogen and oxygen in a ratio of 1 carbon atom, 2 hydrogen atoms, and 1 oxygen atom. Some carbohydrates are relatively small molecules, the most important to us is glucose which has 6 carbon atoms. These simple sugars are called monosaccharides.

The primary function of carbohydrates is for short-term energy storage (sugars are for Energy). A secondary function is intermediate-term energy storage (as in starch for plants and glycogen for animals). Other carbohydrates are involved as structural components in cells, such as cellulose which is found in the cell walls of plants.

Two common Monosaccharides, (single sugars) Glucose and Fructose

Hooking two monosaccharides together forms a more complex sugar, such as the union of glucose and fructose to give sucrose, or common table sugar. Compounds such as sucrose are called Disaccharides (two sugars). Both monosaccharides and disaccharides are soluble in water.

Larger, more complex carbohydrates are formed by linking shorter units together to form long or very long sugar chains called Polysaccharides. Because of their size, these are often times not soluble in water. Many biologically important compounds such as starches and cellulose are Polysaccharides. Starches are used by plants, and glycogen by animals, to store energy in their numerous carbon-hydrogen bonds, while cellulose is an important compound that adds strength and stiffness to a plant's cell wall.

Sugars are most often found in the form of a "RING". The glucose molecule in the image above and the one in the image below (Glc) are really the same molecule, just arranged differently. The corners of the "stop sign" represent Carbon atoms even thought they are not labeled with a "C" (its chemistry shorthand). To form these rings, the Carbonyl (C=0) Carbon of the straight-chain form (above) forms a bond with the next to last Carbon in the chain, making the ring.

The image on the left shows two monosaccharides, Glucose and Galactose (Gal). Examine their structure and you will notice there is very little difference. Their molecular formulas, C6H1206, are even the same. Molecules with the same chemical formula, but different molecular structures are called Isomers.

The sugar subunits can be linked by the reaction, dehydration synthesis, to form larger molecules. The disaccharide, Sucrose, is formed from two monosaccharides, Glucose and Fructose.

The disaccharide Lactose is a dimer (two subunits) of Glucose and Galactose, the disaccharide Maltose is a dimer of Glucose.

Large polymers of sugars are called Carbohydrates. Carbohydrates can be 100's of sugars long and either straight or branched. The term Complex Carbohydrate, or sometimes even just Carbohydrate refers to long chains of sugars. Three common types of complex carbo's we will examine are: Starch, Cellulose, and Glycogen. All three are composed only of Glucose. They differ only in the bonding arrangements between the Glucose subunits. Not all complex carbs are composed of glucose alone, many have highly unusual sugars in their chains.

Starch is a long (100's) polymer of Glucose molecules, where all the sugars are oriented in the same direction. Starch is one of the primary sources of calories for humans.

Cellulose is a long (100's) polymer of Glucose molecules. However the orientation of the sugars is a little different. In Cellulose, every other sugar molecule is "upside-down". This small difference in structure makes a big difference in the way we use this molecule.

Glycogen is another Glucose polymer. Glycogen is a stored energy source, found in the Liver and muscles of Humans. Glycogen is different from both Starch and Cellulose in that the Glucose chain is branched or "forked".

 

Enzymes are protein catalysts that, like all catalysts, speed up the rate of a chemical reaction without being used up in the process.

They achieve their effect by temporarily binding to the substrate and, in doing so, lowering the activation energy needed to convert it to a product. The rate at which an enzyme works is influenced by several factors, e.g.,

• the concentration of substrate molecules (the more of them available, the quicker the enzyme molecules collide and bind with them). The concentration of substrate is designated [S] and is expressed in unit of molarity.
• the temperature. As the temperature rises, molecular motion - and hence collisions between enzyme and substrate - speed up. But as enzymes are proteins, there is an upper limit beyond which the enzyme becomes denatured and ineffective.
• the presence of inhibitors.
  • competitive inhibitors are molecules that bind to the same site as the substrate - preventing the substrate from binding as they do so - but are not changed by the enzyme.
  • noncompetitive inhibitors are molecules that bind to some other site on the enzyme reducing its catalytic power.
• pH. The conformation of a protein is influenced by pH and as enzyme activity is crucially dependent on its conformation, its activity is likewise affected.

The study of the rate at which an enzyme works is called enzyme kinetics. Let us examine enzyme kinetics as a function of the concentration of substrate available to the enzyme.

• We set up a series of tubes containing graded concentrations of substrate, [S].
• At time zero, we add a fixed amount of the enzyme preparation.
• Over the next few minutes, we measure the concentration of product formed. If the product absorbs light, we can easily do this in a spectrophotometer.
• Early in the run, when the amount of substrate is in substantial excess to the amount of enzyme, the rate we observe is the initial velocity of V_i.

Plotting V_i as a function of [S], we find that

• At low values of [S], the initial velocity,V_i, rises almost linearly with increasing [S].
• But as [S] increases, the gains in V_i level off (forming a rectangular hyperbola).
• The asymptote represents the maximum velocity of the reaction, designated V_max
• The substrate concentration that produces a V_i that is one-half of V_max is designated the Michaelis-Menten constant, K_m(named after the scientists who developed the study of enzyme kinetics).

K_m is (roughly) an inverse measure of the affinity or strength of binding between the enzyme and its substrate. The lower the K_m, the greater the affinity (so the lower the concentration of substrate needed to achieve a given rate).

---

Plotting the reciprocals of the same data points yields a "double-reciprocal" or Lineweaver-Burk plot. This provides a more precise way to determine V_max and K_m.

• V_max is determined by the point where the line crosses the 1/V_i = 0 axis (so the [S] is infinite).
• Note that the magnitude represented by the data points in this plot decrease from lower left to upper right.
• K_m equals V_max times the slope of line. This is easily determined from the intercept on the X axis.

---

The Effects of Enzyme Inhibitors

Enzymes can be inhibited

• competitively, when the substrate and inhibitor compete for binding to the same active site or
• noncompetitively, when the inhibitor binds somewhere else on the enzyme molecule reducing its efficiency.

The distinction can be determined by plotting enzyme activity with and without the inhibitor present.

Competitive Inhibition

In the presence of a competitive inhibitor, it takes a higher substrate concentration to achieve the same velocities that were reached in its absence. So while V_max can still be reached if sufficient substrate is available, one-half V_max requires a higher [S] than before and thus K_m is larger.

Noncompetitive Inhibition

With noncompetitive inhibition, enzyme molecules that have been bound by the inhibitor are taken out of the game so

• enzyme rate (velocity) is reduced for all values of [S], including
• V_max and one-half V_max but
• K_m remains unchanged because the active site of those enzyme molecules that have not been inhibited is unchanged.

This Lineweaver-Burk plot displays these results.

An Example

When a slice of apple is exposed to air, it quickly turns brown. This is because the enzyme o-diphenol oxidase catalyzes the oxidation of phenols in the apple to dark-colored products. (A similar enzyme, tyrosinase, converts tyrosine to melanin.) Let us determine: 

• the maximum rate at which the enzyme can perform (V_max) and
• the Michaelis-Menten constant (K_m) for this enzyme
  1. when it acts alone. We shall use catechol as the substrate. The enzyme converts it into o-quinone (A), which is then further oxidized to dark products.
  2. when it acts in the presence of a competitive inhibitor. We shall use para-hydroxybenzoic acid (PHBA) (B), which binds the same site as catechol but is not acted upon.
  3. when it acts in the presence of a noncompetitive inhibitor. We shall use phenylthiourea which binds to a copper atom in the enzyme which is essential for its activity.

Preparing for the Assay:

• Grind up pieces of apple and centrifuge the resulting soup.
• The supernatant is your enzyme preparation.
• Because of the speed with which colored products are formed, we can use the intensity of the color as a measure of product formation.
• We measure this in a spectrophotometer, an instrument that measures the absorbance of monochromatic light passed through the sample. Because the products are yellow-brown, they absorb green light (540 nm) best.

First Experiment: No Inhibitor

• Set up four tubes with different concentrations of catechol (the substrate). (Catechol is a relative of the active ingredients in the poison ivy plant and, like them, can cause serious contact sensitivity if it gets on one's skin.)
  • A = 4.8 mM; B = 1.2 mM; C = 0.6 mM; D = 0.3 mM
• Add a fixed amount of enzyme preparation to Tube A and measure the change in absorbance (Optical Density) at 540 nm) at 1 minute intervals for several minutes.
• Record the average change in OD₅₄₀ per minute (Δ OD₅₄₀).
• Because the OD is directly proportional to the concentration of the products, we can use it as a measure of the rate or velocity of the reaction (V_i).
• Repeat with the other three tubes.

	Tube A	Tube B	Tube C	Tube D
[S]	4.8 mM	1.2 mM	0.6 mM	0.3 mM
1/[S]	0.21	0.83	1.67	3.33
Δ OD540 (Vi)	0.081	0.048	0.035	0.020
1/Vi	12.3	20.8	31.7	50.0

The table above summarizes the results. 

Making a Lineweaver-Burk plot of these results shows (red) that

• 1/V_max = 10, so V_max = 0.10
• −1/K_m = − 0.8, so K_m = 1.25 mM
• (In other words, when [S] is 1.25 mM, 1/V_i = 20, and V_i = 0.05 or one-half of V_max.)

Second Experiment: Effect of para-hydroxybenzoic acid (PHBA)

As before, but this time add a fixed amount of a solution of PHBA to each of the four tubes.

The table below summarizes the results.

	Tube A	Tube B	Tube C	Tube D
[S]	4.8 mM	1.2 mM	0.6 mM	0.3 mM
1/[S]	0.21	0.83	1.67	3.33
ΔOD540 (Vi)	0.060	0.032	0.019	0.011
1/Vi	16.7	31.3	52.6	90.9

The Lineweaver-Burk plot of these results is shown above in green.

• 1/V_max = 10, so V_max remains 0.10.
• Now, however, −1/K_m = − 0.4, so K_m = 2.50 mM
• (In other words, it now takes a substrate concentration [S] of 2.50 mM, to achieve one-half of V_max.)

Third Experiment: Effect of phenylthiourea

As before, but this time add a fixed amount of a solution of phenylthiourea in each of the four tubes.

The table below summarizes the results.

	Tube A	Tube B	Tube C	Tube D
[S]	4.8 mM	1.2 mM	0.6 mM	0.3 mM
1/[S]	0.21	0.83	1.67	3.33
ΔOD540 (Vi)	0.040	0.024	0.016	0.010
1/Vi	25	41	62	102

The Lineweaver-Burk plot of these results is shown above in blue.

• Now 1/V_max = 20, so V_max = 0.05.
• But −1/K_m = − 0.8, so K_m = 1.25 mM as it was in the first experiment.
• So once again it only takes a substrate concentration,[S], of 1.25 mM to achieve one-half of V_max.

Summary

Here, then, is a method by which catalytic power of different enzymes can be compared.

The table gives K_m values (mM) for several enzymes - some of which you can encounter with links to other pages on this site.

Enzyme	Substrate	Km (mM)
Catalase	H2O2	1,100
Chymotrypsin	Gly-Tyr-Gly	108
Carbonic anhydrase	CO2	12
beta-galactosidase	D-lactose	4
Acetylcholinesterase	acetylcholine (ACh)	0.09
beta-lactamase	benzylpenicillin	0.02

 

The favoured model for the enzyme–substrate interaction is the induced fit model.This model proposes that the initial interaction between enzyme and substrate is relatively weak, but that these weak interactions rapidly induce conformational changes in the enzyme that strengthen binding. These conformational changes also bring catalytic residues in the active site close to the chemical bonds in the substrate that will be altered in the reaction. After binding takes place, one or more mechanisms of catalysis lower the energy of the reaction's transition state, by providing an alternative chemical pathway for the reaction. Mechanisms of catalysis include catalysis by bond strain: by proximity and orientation: by active-site proton donors or acceptors: covalent catalysis and quantum tunnelling.

Enzyme kinetics cannot prove which modes of catalysis are used by an enzyme. However, some kinetic data can suggest possibilities to be examined by other techniques. For example, a ping–pong mechanism with burst-phase pre-steady-state kinetics would suggest covalent catalysis might be important in this enzyme's mechanism. Alternatively, the observation of a strong pH effect on V_max but not K_m might indicate that a residue in the active site needs to be in a particular ionisation state for catalysis to occur.

An important goal of measuring enzyme kinetics is to determine the chemical mechanism of an enzyme reaction, i.e., the sequence of chemical steps that transform substrate into product. The kinetic approaches discussed above will show at what rates intermediates are formed and inter-converted, but they cannot identify exactly what these intermediates are.

Kinetic measurements taken under various solution conditions or on slightly modified enzymes or substrates often shed light on this chemical mechanism, as they reveal the rate-determining step or intermediates in the reaction. For example, the breaking of a covalent bond to a hydrogen atom is a common rate-determining step. Which of the possible hydrogen transfers is rate determining can be shown by measuring the kinetic effects of substituting each hydrogen by deuterium, its stable isotope. The rate will change when the critical hydrogen is replaced, due to a primary kinetic isotope effect, which occurs because bonds to deuterium are harder to break then bonds to hydrogen.^[25] It is also possible to measure similar effects with other isotope substitutions, such as ¹³C/¹²C and ¹⁸O/¹⁶O, but these effects are more subtle.

Isotopes can also be used to reveal the fate of various parts of the substrate molecules in the final products. For example, it is sometimes difficult to discern the origin of an oxygen atom in the final product; since it may have come from water or from part of the substrate. This may be determined by systematically substituting oxygen's stable isotope ¹⁸O into the various molecules that participate in the reaction and checking for the isotope in the product. The chemical mechanism can also be elucidated by examining the kinetics and isotope effects under different pH conditions,^[26] by altering the metal ions or other bound cofactors, by site-directed mutagenesis of conserved amino acid residues, or by studying the behaviour of the enzyme in the presence of analogues of the substrate(s).

In the first moment after an enzyme is mixed with substrate, no product has been formed and no intermediates exist. The study of the next few milliseconds of the reaction is called pre-steady-state kinetics. Pre-steady-state kinetics is therefore concerned with the formation and consumption of enzyme–substrate intermediates (such as ES or E*) until their steady-state concentrations are reached.

This approach was first applied to the hydrolysis reaction catalysed by chymotrypsin. Often, the detection of an intermediate is a vital piece of evidence in investigations of what mechanism an enzyme follows. For example, in the ping–pong mechanisms that are shown above, rapid kinetic measurements can follow the release of product P and measure the formation of the modified enzyme intermediate E*.In the case of chymotrypsin, this intermediate is formed by the attack of the substrate by the nucleophilic serine in the active site and the formation of the acyl-enzyme intermediate.

In the figure to the right, the enzyme produces E* rapidly in the first few seconds of the reaction. The rate then slows as steady state is reached. This rapid burst phase of the reaction measures a single turnover of the enzyme. Consequently, the amount of product released in this burst, shown as the intercept on the y-axis of the graph, also gives the amount of functional enzyme which is present in the assay.

Non-Michaelis–Menten kinetics

Some enzymes produce a sigmoid v by [S] plot, which often indicates cooperative binding of substrate to the active site. This means that the binding of one substrate molecule affects the binding of subsequent substrate molecules. This behaviour is most common in multimeric enzymes with several interacting active sites.^[17] Here, the mechanism of cooperation is similar to that of haemoglobin, with binding of substrate to one active site altering the affinity of the other active sites for substrate molecules. Positive cooperativity occurs when binding of the first substrate molecule increases the affinity of the other active sites for substrate. Negative cooperativity occurs when binding of the first substrate decreases the affinity of the enzyme for other substrate molecules.

Allosteric enzymes include mammalian tyrosyl tRNA-synthetase, which shows negative cooperativity,^[18] and bacterial aspartate transcarbamoylase^[19] and phosphofructokinase^[20], which show positive cooperativity.

Cooperativity is surprisingly common and can help regulate the responses of enzymes to changes in the concentrations of their substrates. Positive cooperativity makes enzymes much more sensitive to [S] and their activities can show large changes over a narrow range of substrate concentration. Conversely, negative cooperativity makes enzymes insensitive to small changes in [S].

The Hill equation^[21] is often used to describe the degree of cooperativity quantitatively in non-Michaelis–Menten kinetics. The derived Hill coefficient n measures how much the binding of substrate to one active site affects the binding of substrate to the other active sites. A Hill coefficient of <1 indicates negative cooperativity and a coefficient of >1 indicates positive cooperativity.

 Ternary-complex mechanisms

In these enzymes, both substrates bind to the enzyme at the same time to produce an EAB ternary complex. The order of binding can either be random (in a random mechanism) or substrates have to bind in a particular sequence (in an ordered mechanism). When a set of v by [S] curves (fixed A, varying B) from an enzyme with a ternary-complex mechanism are plotted in a Lineweaver–Burk plot, the set of lines produced will intersect.

Enzymes with ternary-complex mechanisms include glutathione S-transferase,^[12] dihydrofolate reductase^[13] and DNA polymerase.^[14] The following links show short animations of the ternary-complex mechanisms of the enzymes dihydrofolate reductase^[β] and DNA polymerase^[γ].

Ping–pong mechanisms

As shown on the right, enzymes with a ping-pong mechanism can exist in two states, E and a chemically modified form of the enzyme E*; this modified enzyme is known as an intermediate. In such mechanisms, substrate A binds, changes the enzyme to E* by, for example, transferring a chemical group to the active site, and is then released. Only after the first substrate is released can substrate B bind and react with the modified enzyme, regenerating the unmodified E form. When a set of v by [S] curves (fixed A, varying B) from an enzyme with a ping–pong mechanism are plotted in a Lineweaver–Burk plot, a set of parallel lines will be produced.

Enzymes with ping–pong mechanisms include some oxidoreductases such as thioredoxin peroxidase^[15] and serine proteases such as trypsin and chymotrypsin.^[16] Serine proteases are a very common and diverse family of enzymes, including digestive enzymes (trypsin, chymotrypsin, and elastase), several enzymes of the blood clotting cascade and many others. In these serine proteases, the E* intermediate is an acyl-enzyme species formed by the attack of an active site serine residue on a peptide bond in a protein substrate. A short animation showing the mechanism of chymotrypsin is linked here.^[δ]

Multi-substrate reactions

Multi-substrate reactions follow complex rate equations that describe how the substrates bind and in what sequence. The analysis of these reactions is much simpler if the concentration of substrate A is kept constant and substrate B varied. Under these conditions, the enzyme behaves just like a single-substrate enzyme and a plot of v by [S] gives apparent K_m and V_max constants for substrate B. If a set of these measurements is performed at different fixed concentrations of A, these data can be used to work out what the mechanism of the reaction is. For an enzyme that takes two substrates A and B and turns them into two products P and Q, there are two types of mechanism: ternary complex and ping–pong.

Michaelis–Menten kinetics

As enzyme-catalysed reactions are saturable, their rate of catalysis does not show a linear response to increasing substrate. If the initial rate of the reaction is measured over a range of substrate concentrations (denoted as [S]), the reaction rate (v) increases as [S] increases, as shown on the left. However, as [S] gets higher, the enzyme becomes saturated with substrate and the rate reaches V_max, the enzyme's maximum rate.

The Michaelis-Menten kinetic model of a single-substrate reaction is shown on the right. There is an initial bimolecular reaction between the enzyme E and substrate S to form the enzyme–substrate complex ES. Although the enzymatic mechanism for the unimolecular reaction reaction can be quite complex, there is typically one rate-determining enzymatic step that allows the mechanism to be modeled as a single kinetic step of rate constant k₂.

    (Equation 1).

k₂ is also called k_cat or the turnover number, the maximum number of enzymatic reactions catalyzed per second.

At low concentrations of substrate [S], the enzyme exists in an equilibrium between both the free form E and the enzyme–substrate complex ES; increasing [S] likewises increases [ES] at the expense of [E], shifting the binding equilibrium to the right. Since the rate of the reaction depends on the concentration [ES], the rate is sensitive to small changes in [S]. However, at very high [S], the enzyme is entirely saturated with substrate, and exists only in the ES form. Under these conditions, the rate (v≈k₂[E]_tot=V_max) is insensitive to small changes in [S]; here, [E]_tot is the total enzyme concentration

which is approximately equal to the concentration [ES] under saturating conditions.

The Michaelis–Menten equation^[7] describes how the reaction rate v depends on the position of the substrate-binding equilibrium and the rate constant k₂. Michaelis and Menten showed when k₂ is much less than k_-1 (the equilibrium approximation) they could derive the following equation:

    (Equation 2)

This Michaelis-Menten equation is the basis for most single-substrate enzyme kinetics.

The Michaelis constant K_m is defined as the concentration at which the rate of the enzyme reaction is half V_max. This may be verified by substituting [S] = K_m into the Michaelis-Menten equation. If the rate-determining enzymatic step is slow compared to substrate dissociation (k₂ << k_-1), the Michaelis constant K_m is roughly the dissociation constant of the ES complex, although this situation is relatively rare.

The more normal situation where k₂ > k_-1 is sometimes called Briggs-Haldane kinetics.^[8] The Michaelis–Menten equation still holds under these more general conditions, as may be derived from the steady-state approximation. During the initial-rate period, the reaction rate v is roughly constant, indicating that [ES] is similarly constant (cf. equation 1):

Therefore, the concentration [ES] is given by the formula

where the Michaelis constant K_m is defined

([E] is the concentration of free enzyme). Taken together, the general formula for the reaction rate v is again the Michaelis-Menten equation:

The specificity constant k_cat / K_m is a measure of how efficiently an enzyme converts a substrate into product. Using the definition of the Michaelis constant K_m, the Michaelis-Menten equation may be written in the form

where [E] is the concentration of free enzyme. Thus, the specificity constant is an effective bimolecular rate constant for free enzyme to react with free substrate to form product. The specificity constant is limited by the frequency with which the substrate and enzyme encounter each other in solution, roughly 10¹⁰ M^-1 s^-1 at 25°C. Remarkably, this maximum does not depend on the size of either the substrate or the enzyme. The ratio of the specificity constants for two substrates is a quantitative comparison of how efficient the enzyme is in converting those substrates. The slope of the Michaelis-Menten equation at low substrate concentration [S] (when [S] << K_m) also yields the specificity constant.

 Linear plots of the Michaelis-Menten equation

 

Using an interactive Michaelis–Menten kinetics tutorial at the University of Virginia,^[α] the effects on the behaviour of an enzyme of varying kinetic constants can be explored.

The plot of v versus [S] above is not linear; although initially linear at low [S], it bends over to saturate at high [S]. Before the modern era of nonlinear curve-fitting on computers, this nonlinearity could make it difficult to estimate K_m and V_max accurately. Therefore, several researchers developed linearizations of the Michaelis-Menten equation, such as the Lineweaver-Burk plot and the Eadie-Hofstee diagram.

The Lineweaver-Burk plot or double reciprocal plot is common way of illustrating kinetic data. This is produced by taking the reciprocal of both sides of the Michaelis–Menten equation. As shown on the right, this is a linear form of the Michaelis–Menten equation and produces a straight line with the equation y = mx + c with a y-intercept equivalent to 1/V_max and an x-intercept of the graph representing -1/K_m.

Naturally, no experimental values can be taken at negative 1/[S]; the lower limiting value 1/[S] = 0 (the y-intercept) corresponds to an infinite substrate concentration, where 1/v=1/V_max as shown at the right; thus, the x-intercept is an extrapolation of the experimental data taken at positive concentrations. More generally, the Lineweaver-Burk plot skews the importance of measurements taken at low substrate concentrations and, thus, can yield inaccurate estimates of V_max and K_m.^[9] A more accurate linear plotting method is the Eadie-Hofstee plot although, in modern research, all such linearizations have been superseded by more reliable nonlinear regression methods.

 Practical significance of kinetic constants

The study of enzyme kinetics is important for two basic reasons. Firstly, it helps explain how enzymes work, and secondly, it helps predict how enzymes behave in living organisms. The kinetic constants defined above, K_m and V_max, are critical to attempts to understand how enzymes work together to control metabolism.

Making these predictions is not trivial, even for simple systems. For example, oxaloacetate is formed by malate dehydrogenase within the mitochondrion. Oxaloacetate can then be consumed by citrate synthase, phosphoenolpyruvate carboxykinase or aspartate aminotransferase, feeding into the citric acid cycle, gluconeogenesis or aspartic acid biosynthesis, respectively. Being able to predict how much oxaloacetate goes into which pathway requires knowledge of the concentration of oxaloacetate as well as the concentration and kinetics of each of these enzymes. This aim of predicting the behaviour of metabolic pathways reaches its most complex expression in the synthesis of huge amounts of kinetic and gene expression data into mathematical models of entire organisms. Although this goal is far in the future for any eukaryote, attempts are now being made to achieve this in bacteria, with models of Escherichia coli metabolism now being produced and tested.

Enzyme assays

 

Enzyme assays are laboratory procedures that measure the rate of enzyme reactions. Because enzymes are not consumed by the reactions they catalyse, enzyme assays usually follow changes in the concentration of either substrates or products to measure the rate of reaction. There are many methods of measurement. Spectrophotometric assays observe change in the absorbance of light between products and reactants; radiometric assays involve the incorporation or release of radioactivity to measure the amount of product made over time. Spectrophotometric assays are most convenient since they allow the rate of the reaction to be measured continuously. Although radiometric assays require the removal and counting of samples (i.e., they are discontinuous assays) they are usually extremely sensitive and can measure very low levels of enzyme activity.^[2] An analogous approach is to use mass spectrometry to monitor the incorporation or release of stable isotopes as substrate is converted into product.

The most sensitive enzyme assays use lasers focused through a microscope to observe changes in single enzyme molecules as they catalyse their reactions. These measurements either use changes in the fluorescence of cofactors during an enzyme's reaction mechanism, or fluorescent dyes added onto specific sites of the protein that report movements that occur during catalysis.^[3] These studies are providing a new view of the kinetics and dynamics of single molecules, as opposed to traditional enzyme kinetics, which observes the average behaviour of populations of millions of enzyme molecules.

On the left is shown a typical progress curve for an enzyme assay. The enzyme produces product at a linear initial rate at the start of the reaction. Later in this progress curve, the rate slows down as substrate is used up or products accumulate. The length of the initial rate period depends on the assay conditions and can range from milliseconds to hours. Enzyme assays are usually set up to produce an initial rate lasting over a minute, to make measurements easier. However, equipment for rapidly mixing liquids allows fast kinetic measurements on initial rates of less than one second.^[4] These very rapid assays are essential for measuring pre-steady-state kinetics, which are discussed below.

Most enzyme kinetics studies concentrate on this initial, linear part of enzyme reactions. However, it is also possible to measure the complete reaction curve and fit this data to a non-linear rate equation. This way of measuring enzyme reactions is called progress-curve analysis.^[5] This approach is useful as an alternative to rapid kinetics when the initial rate is too fast to measure accurately.

Enzyme kinetics is the study of the rates of chemical reactions that are catalysed by enzymes. The study of an enzyme's kinetics provides insights into the catalytic mechanism of this enzyme, its role in metabolism, how its activity is controlled in the cell and how drugs and poisons can inhibit its activity.

Enzymes are molecules that manipulate other molecules — the enzymes' substrates. These target molecules bind to an enzyme's active site and are transformed into products through a series of steps known as the enzymatic mechanism. Some enzymes bind multiple substrates and/or release multiple products, such as a protease cleaving one protein substrate into two polypeptide products. Others join substrates together, such as DNA polymerase linking a nucleotide to DNA. Although these mechanisms are often a complex series of steps, there is typically one rate-determining step that determines the overall kinetics. This rate-determining step may be a chemical reaction or a conformational change of the enzyme or substrates, such as those involved in the release of product(s) from the enzyme.

Knowledge of the enzyme's structure is helpful in visualizing the kinetic data. For example, the structure can suggest how substrates and products bind during catalysis; what changes occur during the reaction; and even the role of particular amino acid residues in the mechanism. Some enzymes change shape significantly during the mechanism; in such cases, it is helpful to determine the enzyme structure with and without bound substrate analogs that do not undergo the enzymatic reaction.

Enzyme mechanisms can be divided into single-substrate and multiple-substrate mechanisms. Kinetic studies on enzymes that only bind one substrate, such as triosephosphate isomerase, aim to measure the affinity with which the enzyme binds this substrate and the turnover rate. When enzymes bind multiple substrates, such as dihydrofolate reductase (shown right), enzyme kinetics can also show the sequence in which these substrates bind and the sequence in which products are released.

Not all biological catalysts are protein enzymes; RNA-based catalysts such as ribozymes and ribosomes are essential to many cellular functions, such as RNA splicing and translation. The main difference between ribozymes and enzymes is that the RNA catalysts perform a more limited set of reactions, although their reaction mechanisms and kinetics can be analysed and classified by the same methods.

General principles

The reaction catalysed by an enzyme uses exactly the same reactants and produces exactly the same products as the uncatalysed reaction. Like other catalysts, enzymes do not alter the position of equilibrium between substrates and products.^[1] However, unlike normal chemical reactions, enzymes are saturable. This means as more substrate is added, the reaction rate will increase, because more active sites become occupied. This can continue until all the enzyme becomes saturated with substrate and the rate reaches a maximum.

The two most important kinetic properties of an enzyme are how quickly the enzyme becomes saturated with a particular substrate, and the maximum rate it can achieve. Knowing these properties suggests what an enzyme might do in the environment of the cell and can show how the enzyme will respond to changes in these conditions.

The activation energy in chemistry and biology is the threshold energy, or the energy that must be overcome in order for a chemical reaction to occur. Activation energy may otherwise be denoted as the minimum energy necessary for a specific chemical reaction to occur. The activation energy of a reaction is usually denoted by E_a.

Basically, activation energy is the height of the potential barrier separating two minima of potential energy (of the reactants and of the products of reaction). For chemical reaction to have noticeable rate, there should be noticeable number of molecules with the energy equal or greater than the activation energy.

 

Known as the "collisional model", there are three necessary requirements in order for a reaction to take place:

1. the molecules must collide to react.

If two molecules simply collide, however, they will not always react; therefore, the occurrence of a collision is not enough. The second requirement is that:

2. there must be enough energy (energy of activation) for the two molecules to react.

This is the idea of a transition state; if two slow molecules collide, they might bounce off one another because they do not contain enough energy to reach the energy of activation and overcome the transition state (the highest energy point). Lastly, the third requirement is:

3. the molecules must be oriented with respect to each other correctly.

For the reaction to occur between two colliding molecules, they must collide in the correct orientation, and possess a certain, minimum, amount of energy. As the molecules approach each other, their electron clouds repel each other. Overcoming this repulsion requires energy (activation energy), which is typically provided by the heat of the system; i.e., the translational, vibrational, and rotational energy of each molecule, although sometimes by light (photochemistry) or electrical fields (electrochemistry). If there is enough energy available, the repulsion is overcome and the molecules get close enough for attractions between the molecules to cause a rearrangement of bonds.

At low temperatures for a particular reaction, most (but not all) molecules will not have enough energy to react. However there will nearly always be a certain number with enough energy at any temperature because temperature is a measure of the average energy of the system — individual molecules can have more or less energy than the average. Increasing the temperature increases the proportion of molecules with more energy than the activation energy, and consequently the rate of reaction increases. Typically the activation energy is given as the energy in kilojoules needed for one mole of reactants to react.

 

 

 

 

There are two types of cells, eukaryotic and prokaryotic. Prokaryotic cells are usually singletons, while eukaryotic cells are usually found in multi-cellular organisms.

Prokaryotic cells

 

Prokaryotes are distinguished from eukaryotes on the basis of nuclear organization, specifically their lack of a nuclear membrane. Prokaryotes also lack most of the intracellular organelles and structures that are characteristic of eukaryotic cells (an important exception is the ribosomes, which are present in both prokaryotic and eukaryotic cells). Most of the functions of organelles, such as mitochondria, chloroplasts, and the Golgi apparatus, are taken over by the prokaryotic plasma membrane. Prokaryotic cells have three architectural regions: appendages called flagella and pili — proteins attached to the cell surface; a cell envelope consisting of a capsule, a cell wall, and a plasma membrane; and a cytoplasmic region that contains the cell genome (DNA) and ribosomes and various sorts of inclusions. Other differences include:

• The plasma membrane (a phospholipid bilayer) separates the interior of the cell from its environment and serves as a filter and communications beacon.

• Most prokaryotes have a cell wall (some exceptions are Mycoplasma (a bacterium) and Thermoplasma (an archaeon)). It consists of peptidoglycan in bacteria, and acts as an additional barrier against exterior forces. It also prevents the cell from "exploding" (cytolysis) from osmotic pressure against a hypotonic environment. A cell wall is also present in some eukaryotes like fungi, but has a different chemical composition.

• A prokaryotic chromosome is usually a circular molecule (an exception is that of the bacterium Borrelia burgdorferi, which causes Lyme disease). Even without a real nucleus, the DNA is condensed in a nucleoid. Prokaryotes can carry extrachromosomal DNA elements called plasmids, which are usually circular. Plasmids can carry additional functions, such as antibiotic resistance.

Eukaryotic cells

Eukaryotic cells are about 10 times the size of a typical prokaryote and can be as much as 1000 times greater in volume. The major difference between prokaryotes and eukaryotes is that eukaryotic cells contain membrane-bound compartments in which specific metabolic activities take place. Most important among these is the presence of a cell nucleus, a membrane-delineated compartment that houses the eukaryotic cell's DNA. It is this nucleus that gives the eukaryote its name, which means "true nucleus". Other differences include:

• The plasma membrane resembles that of prokaryotes in function, with minor differences in the setup. Cell walls may or may not be present.
• The eukaryotic DNA is organized in one or more linear molecules, called chromosomes, which are associated with histone proteins. All chromosomal DNA is stored in the cell nucleus, separated from the cytoplasm by a membrane. Some eukaryotic organelles also contain some DNA.
• Eukaryotes can move using cilia or flagella. The flagella are more complex than those of prokaryotes.

Table 1: Comparison of features of prokaroytic and eukaryotic cells

	Prokaryotes	Eukaryotes
Typical organisms	bacteria, archaea	protists, fungi, plants, animals
Typical size	~ 1-10 µm	~ 10-100 µm (sperm cells, apart from the tail, are smaller)
Type of nucleus	nucleoid region; no real nucleus	real nucleus with double membrane
DNA	circular (usually)	linear molecules (chromosomes) with histone proteins
RNA-/protein-synthesis	coupled in cytoplasm	RNA-synthesis inside the nucleus protein synthesis in cytoplasm
Ribosomes	50S+30S	60S+40S
Cytoplasmatic structure	very few structures	highly structured by endomembranes and a cytoskeleton
Cell movement	flagella made of flagellin	flagella and cilia made of tubulin
Mitochondria	none	one to several dozen (though some lack mitochondria)
Chloroplasts	none	in algae and plants
Organization	usually single cells	single cells, colonies, higher multicellular organisms with specialized cells
Cell division	Binary fission (simple division)	Mitosis (fission or budding) Meiosis

Table 2: Comparison of structures between animal and plant cells

	Typical animal cell	Typical plant cell
Organelles	Nucleus Nucleolus (within nucleus) Rough endoplasmic reticulum (ER) Smooth ER Ribosomes Cytoskeleton Golgi apparatus Cytoplasm Mitochondria Vesicles Vacuoles Lysosomes Centrosome Centrioles	Nucleus Nucleolus (within nucleus) Rough ER Smooth ER Ribosomes Cytoskeleton Golgi apparatus (dictiosomes) Cytoplasm Mitochondria Vesicles Chloroplast and other plastids Central vacuole Tonoplast (central vacuole membrane) Peroxisome Glyoxysome
Additional structures	Cilium Flagellum Plasma membrane	Plasma membrane Cell wall Plasmodesmata Flagellum (only in gametes)

Subcellular components

All cells, whether prokaryotic or eukaryotic, have a membrane, which envelopes the cell, separates its interior from its environment, regulates what moves in and out (selectively permeable), and maintains the electric potential of the cell. Inside the membrane, a salty cytoplasm takes up most of the cell volume. All cells possess DNA, the hereditary material of genes, and RNA, containing the information necessary to build various proteins such as enzymes, the cell's primary machinery. There are also other kinds of biomolecules in cells.