"Energy and Enzymes"
Energy and Enzymes
1. Living systems create order within by creating even more disorder in the outside world.
- The entropy of the universe (disorder) is always increasing.
- One can create order locally by putting energy into the system. However, one always creates more disorder outside the local region (a living cell, an organism) than the order created.
- Disorder created includes heat given off by the organism and waste products produced. Notice how waste products such as Carbon Dioxide and Urea are small fragments of larger molecules such as carbohydrates and proteins.
- Sunlight is the ultimate source of energy for life on Earth. (In some very local regions, such as volcanic vents under the sea, energy is provided by chemical processes and heat from the inner molten core of the Earth.) Sunlight drives photosynthesis which uses the Sun's energy to assemble large molecules from small ones (Carbon Dioxide)
- Cells obtain energy from large molecules (created by photosynthesis) by oxidation (removal of electrons). Note that oxidation can occur in the absence of Oxygen. Prokaryotes don't use oxygen for breakdown. But oxidation occurs nevertheless.
- Oxidations release energy, reductions require energy.
- The amount of energy obtained from the breakdown of a larger, more structured molecule, and available to build large, structured molecules from smaller, less complex ones (or power muscles or other contractile processes) is known as "Gibbs' Free Energy", G. Delta G is the change in Gibbs' Energy - energy released or energy required - to take a specified amount of reactant and convert it to product.
- At this point in our discussion, we examine the relationship between entropy, enthalpy, and Gibb's energy and the biochemical basis for changes in each of these factors.
2. Biochemical reactions are aided by enzymes.
3. So, enzymes catalyze biochemical reactions, not changing the direction of reaction, but speeding up the reactions tremendously! (Remember, free energy changes are functions of concentrations of reactants and products and don't have anything to do with the presence or absence of a catalyst.)
- Enzymes lower the activation energy for chemical reactions. (fig. 3-20, Lodish).
- Every chemical reaction has an equilibrium constant, Keq which represents the ratio of reactant and product concentrations at equilibrium - after a VERY long time. This ratio is independent of the activation energy and only depends upon the energies associated with the initial and final states (reactant and product). For a simple isomerization reaction, A <--> B, Keq = [B]eq/[A]eq, the ratio of the equilibrium concentrations of A and B. But, Keq also equals kf/kr, the ratio of the rate of the forward reaction to form B from A (kf) to the rate of the reverse reaction to form A from B (kr). If both the forward and reverse reactions are speeded up by the same amount, as the result of action by a catalyst, clearly the final concentrations of A and B will be reached sooner. But, the equilibrium constant and the equilibrium concentrations, don't change because the forward and reverse rate constants are being increased by the same factor - the numerator, kf, and the denominator, kf, are multiplied by the same number.
- Carbonic Anhydrase catalyzes the reaction of Carbon Dioxide and Water to form Bicarbonate. In the presence of the enzyme, Carbonic Anhydrase, the rate of the reaction is 105 per second. (It takes only 10-5 sec for a molecule to be converted!) In the absence of the enzyme, the reaction is 107 slower! However, if we wait a very, very long time, the equilibrium concentrations will be the same in the presence or absence of the enzyme. The enzyme increases both the forward and reverse rate constants by the same amount, leaving the ratio - the equilibrium constant - the same!
- The standard Gibbs' energy change can be computed from the log of the equilibrium constant. This energy change is the energy "step" from reactant to product which we saw previously - if concentrations are at one molar levels!
- Actual biological concentrations are not 1 Molar. (One mole of human DNA would fill a railroad car.) The "actual" delta G for a reaction under real conditions is the standard free energy change + a term which includes the ratio of concentrations under actual conditions. This "actual" free energy change predicts the direction of reactions - if the change is negative, the reaction will occur spontaneously; if the change is positive, the reaction will not occur spontaneously.
- Free energy changes for sequential reactions are additive - favorable reactions can overcome unfavorable ones!
- With all of this said about the approach to equlibrium, it is important to note that actual biological reactions are not at equlibrium. There is a quasi-equilibrium, so we often use equlibrium kinetics. But, really, all organisms and their biochemical reactions are in a steady state. A steady state means that the intake of reactants is balanced by the output of productss so that intermediate concentrations are unchanging. By contrast, equlibrium would mean that intermediate concentrations remained fixed because there was no input or output! Thermodynamics shows us an interesting result of the steady state - The rate of entropy production is minimum!!!!!!!
- Lysozyme is a good example of catalysis by a simple enzyme.
("Cartoon of lysozyme working") and
("Mechanism of lysozyme reaction")
- Michaelis-Menten kinetics describes many enzymes which follow a simple reaction scheme of E + S <-> ES -> E + P, where E is enzyme, S is substrate, ES is the bound enzyme-substrate complex, and P is the product.(fig. 3-23, Lodish) (fig. 3-22a, Lodish) (fig. 3-22b, Lodish).
("Reaction rate vs. substrate concentration")
With this reaction scheme and three additional assumptions:
- 1) The rate constant of the reaction, E + P -> EP, is zero,
- 2) S >> E, and
- 3) steady state conditions,
the chemical reaction equations can be
solved to give the fundamental equation of Michaelis-Menten kinetics:
where V is the velocity of the reaction - the rate of product formation
in mMoles/liter-second. The constants Vmax and Km characterize the
particular reaction - For example the value of Km depends upon the
values of the rate constants for the reaction. Note that Vmax is the
maximum velocity - which is approached as substrate concentration
I've simulated a laboratory experiment with an enzyme catalyzed reaction where conditions 1) and 2) (above) are met but without the assumption of steady state kinetics. Notice that the particular starting concentrations and rate constants used in my example (typical of real reactions) results in very close to steady-state conditions for the enzyme-substrate complex. (The left panel shows substrate concentration in orange and product concentration in blue. The right panel shows enzyme concentration.)
The following is the same enzyme kinetics scheme modified to permit product to combine with enzyme to go backwards to form enzyme-substrate complex. Notice that we now have typical equilibrium kinetics, with exponential rise and fall of concentrations to non-zero equilibrium levels. However, real enzymes usually don't permit product to combine with the enzyme.
- Competitive inhibitors increase the apparent KM while Vmax is unchanged. Non-competitive inhibitors decrease the apparent Vmax while KM is unchanged. Look at this
picture to see how the V vs. S plot changes when inhibitors are present.
Lineweaver-Burke plot can help determine if an enzyme obeys Michaelis-Menten kinetics. Lineweaver-Burke replotted Michaelis-Menten data by plotting 1/V vs. 1/S instead of V vs. S. When data points are replotted on the 1/V vs. 1/S plot, they lie on a straight line IF the data obey Michaelis-Menten kinetics. Your instructor will discuss how the following cases are related to the V vs. S plots. This first graph represents Michaelis-Menten kinetics with increasing concentrations of a competitive inhibitor:
and the second plot with increasing concentrations of a non-competitive inhibitor:
- (Obtain the algebraic expressions for the slope and intercept of an Eadie-Hofstee plot. There will be a question about this on the first exam. Hint - either rearrange the Michaelis-Menten equation to derive the answers yourself or search the web to find the answers.)
- Some enzymes are multisubunit. These "allosteric" enzymes have a sigmoid (S-shaped) relationship between reaction velocity and substrate concentration.
One of the relationships above is for an enzyme plus substrate alone, one is for an enzyme acting in presence of an inhibitor, and the remaining curve is for an enzyme acting in the presence of an activator. Do you know which is which? Do you see how a small change in enzyme structure and the resulting small change in the V vs. S relationship can cause a large change in reaction velocity?)
(Compare Michaelis-Menten and allosteric kinetics to oxygen binding by myoglobin and hemoglobin. Myoglobin has a binding curve identical in shape to that for Michaelis-Menten kinetics but hemoglobin has an sigmoid binding curve, like the V vs S relationship for allosteric enzymes.)
- Aspartate Transcarbamoylase (ATCase) is a multisubunit enzyme that catalyzes a reaction which leads to the synthesis of the pyrimidine ring of C, U, and T nucleotides. CTP, one of these products, is an inhibitor of this enzyme and ATP is an activator.
All text and images, not attributed to others, including course examinations and sample questions, are Copyright, 2008, Thomas J. Herbert and may not be used for any commercial purpose without the express written permission of Thomas J. Herbert.