Enzymatic Catalysis

Recap What is Enzyme? Properties of water Basics of biochemical bonding Hierarchical structure of proteins Characteristics of enzymes Specificity Enzymes are highly specific in choice of reactions and substrates

Enzymes are Faster Enzymes accelerate reactions by factors of millions What’s the fastest enzyme? Carbonic anhydrase hydrates 10^6 molecules of CO 2 per second, 10^7 times faster than the uncatalyzed reaction

Thermodynamics! Description of the relationships among the various forms of energy and how energy affects matter on the macroscopic as opposed to the molecular level 3 laws You can’t win. First law of thermodynamics You can’t even break even. Second law of thermodynamics You can’t stay out of the game. Third law of thermodynamics

1 st Law of Thermodynamics System can be open, closed, or isolated Surroundings Mathematical statement of the law of conservation of energy: Energy can be neither created nor destroyed Here U is energy, q is the heat absorbed by the system from the surroundings, and w is the work done on the system by the surroundings Negative q, for exothermic processes and positive q for endothermic processes

2 nd Law of Thermodynamics Spontaneous processes occur in directions that increase the overall disorder of the universe The randomness or disorder of the components of a chemical system is known as Entropy, S Enthalpy, H reflects the number and kinds of chemical bonds

Free Energy Josiah Willard Gibbs, 1878 Free energy content, G, of any closed system can be defined in terms of three quantities: Enthalpy, H, Entropy, S, and the absolute temperature, T (In Kelvin) The definition of free energy is G= H-TS. When a chemical reaction occurs at constant temperature, the free energy change, ∆ G, is determined by the enthalpy change, ∆H, reflecting the kinds and numbers of chemical bonds and noncovalent interactions broken and formed, and the entropy change, ∆ S, describing the change in the system's randomness ∆G = ∆H- T∆ S

Free Energy ∆H is negative for a reaction that releases heat, and ∆S is positive for a reaction that increases the system's randomness A process tends to occur spontaneously only if ∆G is negative (If free energy is released in the process) To carry out thermodynamically unfavorable, energy-requiring (Endergonic) reactions, cells couple them to other reactions that liberate free energy (Exergonic reactions), so that the overall process is exergonic- The sum of the free-energy changes is negative

Equilibrium Constant The tendency of a chemical reaction to go to completion can be expressed as an equilibrium constant For the reaction in which a moles of A react with b moles of B to give c moles of C and d moles of D The equilibrium constant, Keq, is given by [A]eq is the concentration of A, [B]eq the concentration of B, and so on, where the system has reached equilibrium A large value of Keq means the reaction tends to proceed until the reactants are almost completely converted in to the products

Equilibrium Constant ∆ G for any chemical reaction is a function of the standard free-energy change, ∆ Gº, a constant that is characteristic of each specific reaction and a term that expresses the initial concentrations of reactants and products Where [A]i s the initial concentration of A, and so forth, R is the gas constant; and T is the absolute temperature When a reaction has reached equilibrium, no driving force remains and it can do no work, ∆ G = 0. For this special case, [A]i = [A]eq, and so on, for all reactants and products

Equilibrium Constant Substituting 0 for ∆ G and Keq’ (Equilibrium constant under standard conditions) for [C]i.[D]i/[A]i[B]i in above equation, we get ∆G˚ = -RTlnKeq’ ∆G˚ = RTlog10Keq’ The units of ∆G˚ and ∆G are joules per mole/ calories per mole When Keq > > 1, ∆G˚ is large and negative When Keq << 1, ∆G˚ is large and positive

Example

Enzymes Control only Reaction Rates Cannot alter laws of thermodynamics or the equilibrium of a reaction For a simple chemical reaction, where E, S, and P represent the enzyme, substrate, and product; E S and EP are transient complexes of the enzyme with the substrate and with the product

Transition State Theory Henry Eyring, 1930s A reaction, can be described by a reaction coordinate diagram, where the free energy of the system is plotted against the progress of the reaction (The reaction coordinate). The starting point for either the forward or the reverse reaction is called the ground state, the contribution to the free energy of the system by an average molecule (S or P) under a given set of conditions

Transition State Theory There is an energy barrier between S and P To undergo reaction, the molecules must overcome this barrier and therefore must be raised to a higher energy level At the top of the energy hill is a point at which decay to the S or P state is equally probable (It is downhill either way) This is called the transition state. The transition state is not a chemical species with any significant stability and should not be confused with a reaction intermediate (Such as ES or EP). It is simply a fleeting molecular moment in which events such as bond breakage, bond formation, and charge development have proceeded to the precise point at which decay to either substrate or product is equally likely

Transition State Theory The difference between the energy levels of the ground state and the transition state is the activation energy, ∆G‡ The rate of a reaction reflects this activation energy Higher activation energy corresponds to a slower reaction Reaction rates can be increased by raising the temperature and/pressure, thereby increasing th e number of molecules with sufficient energy to overcome the energy barrier. Alternatively, the activation energy can be lowered by adding a catalyst (Enzymes)

Enzymes Reduce Activation Energy Any enzyme that catalyzes the reaction S P also catalyzes the reaction P S. The role of enzymes is to accelerate the interconversion of S and P The enzyme is not used up in the process, and the equilibrium point is unaffected. The reaction reaches equilibrium much faster when the appropriate enzyme is present, because the rate of the reaction is increased

Multistep Reactions Have Rate- Determining Steps Any reaction may have several steps, involving the formation and decay of transient chemical species called reaction intermediates A reaction intermediate is any species on the reaction pathway that has a finite chemical Iifetime (Longer than a molecular vibration,~10^-13 seconds) When the S P reaction is catalyzed by an enzyme, the ES and EP complexes can be considered intermediates, even though S and P are stable chemical species The interconversion of two sequential reaction intermediates thus constitutes a reaction step When several steps occur in a reaction, the overall rate is determined by the step (Or steps) with the highest activation energy; called the rate-limiting step The rate-limiting step is the highest-energy point in the diagram for interconversion of S and P In practice, the rate-limiting step can vary with reaction conditions, and for many enzymes several steps may have similar activation energies, which means they are all partially rate-limiting

How Enzymes Actually Work? Rearrangement of covalent bonds during an enzyme-catalyzed reaction Covalent interactions between enzymes and substrates lower the activation energy (And thereby accelerate the reaction) by providing an alternative, lower-energy reaction path Much of the energy required to lower activation energies is derived from weak, noncovalent interactions between substrate and enzyme Weak interactions are optimized in the reaction transition state Enzyme active sites are complementary not to the substrates per se but to the transition states through which substrates pass as they are converted to products during an enzymatic reaction

ES Complex- 1 st Step in Enzymatic Catalysis Substrates bind to active sites, promoting formation of transition state Enzymatic reactions have maximal velocity, when all catalytic sites are bound Enzyme active sites are 1.3D cleft formed by groups coming from different parts of the enzyme 2.Relatively small 3.Unique micorenvironment 4.Binds substrates by multiple weak interactions 5.Specificity of binding depends on precise arrangement of atoms

Binding Energy The energy derived from enzyme-substrate interaction is called binding energy, ∆GB Only the correct substrate can participate in all/most of the interactions with the enzyme and maximize binding energy Full complement of such interactions is formed only when the substrate is in the transition state Contributes to specificity and catalytic power of enzymes Transition state is least stable, collapses to either substrate or product, depending on.....

Binding Energy Physical and thermodynamic factors contributing to ∆ G ‡, the barrier to reaction are: 1.The entropy (Freedom of motion) of molecules in solution, which reduces the possibility that they will react together 2.The solvation shell of hydrogen-bonded water that surrounds and helps to stabilize most biomolecules in aqueous solution 3.The distortion of substrates that must occur in many reactions 4.The need for proper alignment of catalytic functional groups on the enzyme Binding energy can be used to overcome all these barrier Entropy reduction, Desolvation, Formation of weak bonds, Induced fit

References Principles of Biochemistry, Lehninger, 5 th Edition, Chapters 1, 6 Biochemistry, Stryer, 6 th Edition, Chapters 1, 2, 8 Biochemistry, Voet and Voet, 4 th Edition, Chapters 8, 13