PETER PAZMANY SEMMELWEIS UNIVERSITYCATHOLIC UNIVERSITY Development of Complex Curricula for Molecular Bionics and Infobionics Programs within a consortial* framework** Consortium leader PETER PAZMANY CATHOLIC UNIVERSITY Consortium members SEMMELWEIS UNIVERSITY, DIALOG CAMPUS PUBLISHER The Project has been realised with the support of the European Union and has been co-financed by the European Social Fund *** **Molekuláris bionika és Infobionika Szakok tananyagának komplex fejlesztése konzorciumi keretben * * * A p ro j e kt a z Eu ró p a i U n i ó t á m o g a t á sá v a l , a z E u r ó p a i S z o c i á l i s A l a p t á rsf i n a n sz í ro z á sá v a l v a l ó su l m e g . INTRODUCTION TO BIOPHYSICS (Bevezetés a biofizikába) ENZYMES (Enzimek) GYÖRFFY DÁNIEL, ZÁVODSZKY PÉTER . Catalysts are substances that can acceleratereactions taking place spontaneously even inthe absence of the catalyst . Catalysts are reclaimed in unchanged form after the reaction occurs . Enzymes are catalysts of biological processes . Enzymes are proteins often containing cofactors such as metal ions . The substance converted in the reaction catalyzed by the enzyme is called thesubstrate . The substance produced in this reaction iscalled product Classification of enzymes . Enzymes are classified into six groups basedon the type of reaction catalyzed by them . The coenzyme is responsible for the type ofreaction to be catalyzed while the apoenzymedetermines the type of the substrateconverted in the reaction Classes of enzymes GAPDH MAP kinase ERK2 Trypsin Fumarase Triose phosphate isomerase DNA ligase Enzymes in action . Enzymes can catalyze only reactions takingplace spontaneously, i.e. in the absence ofcatalyst . Reactions can take place spontaneously if thefree energy of products is less than that of the reactants . Thus, catalysts such as enzymes do not affectthe thermodynamics of reactions but influencetheir kinetics . Usually, for a reaction to take place, an energybarrier must be passed . The height of this barrier will determine the rate of the reaction . The higher the barrier the slower the reaction . Catalysts can make this barrier lower, and thusaccelerate the reaction even by several ordersof magnitude . Now let us examine where this barrier comes from Recall: Arrhenius theory . The Swedish chemist Arrhenius found a relation between the rate of reaction and the temperature . The Arrhenius equation says: a / RT k=Ae-E where k is the rate constant, Ea is the activation energy, R is the gas constant, T is the temperature and A is a constant called Arrhenius constant or pre-exponential factor 09/10/11. TÁMOP – 4.1.2-08/2/A/KMR-2009-0006 k as a function of T Recall: Boltzmann distribution . Ludwig Boltzmann found the energy distribution of particles in a system at equilibrium . The Boltzmann distribution is: 1 - Ei/ k BT p. Ei .= Ze where p(Ei) is the probability that a particle is in a state having Ei energy, kB is the Boltzmann constant and Z is the partition function . The partition function - Ei / kBT Z =. e i is the sum of the Boltzmann factors for all of the i states and serves as a scaling factor to ensurethat the sum of probabilities equals 1 Boltzmann distribution . Thus, the rate of a reaction is proportional to the fraction of particles having an energyhigher than the activation energy . Hence, if a catalyst lowers the activationenergy, a higher fraction of particles will havean energy higher than the activation energythus, the rate of the reaction will be higher Fraction of particles of energy E in an uncatalyzed and a catalyzed reaction Recall: reaction profile . The progress of a reaction can be characterized by one or more reaction coordinates . Now, let us consider a reaction with one reaction coordinate . The free energy of the system can be plottedas a function of a reaction coordinate . This plot is called reaction profile Reaction profile . The effect of a catalyst on the reaction profileis that it lowers the activation energy and thus lowers the barrier that must be passed for thesystem the reaction to occur . It can be seen that a catalyst accelerates areaction not only in one direction but in theopposite direction as well . However, enzymes do not alter the reaction free energy .G r, and therefore do not influence whether the reaction occurs spontaneously Effect of a catalyst on the reaction profile Hypotheses for enzyme action . Several hypotheses have been proposed to explain how enzymes can accelerate reactionseven by several orders of magnitude . Enzymes often open up a by-pass pathwaywith lower activation energy for the reaction, which can thus proceed faster . Let us consider the reaction to be catalyzed by an enzyme as K‡ k‡ S . S‡ .P where S is the substrate, S‡ is the transition state, P is the product, K‡ is the equilibriumconstant for the formation of the transition state from the substrate, and k‡ is the rate constant of the conversion of the transition state to the product 09/10/11. TÁMOP – 4.1.2-08/2/A/KMR-2009-0006 . It is assumed that the equilibrium step of thereaction is far faster than the second step . Thus, the overall rate of the reaction can be approximated by v=k [S ]. k‡[S ‡ ] . It can be seen that the rate of the overall reaction is proportional to the concentration ofthe transition state . Since [S ‡ ] -. G‡ / RT K ‡ ==e [S ] where .G‡ is the activation free energy, describing the stability of transition state relativeto the substrate . The more stable the transition state the higher its concentration . Thus, enzymes accelerate reactions by stabilizing the transition state Enzyme-substrate complex . In the course of catalysis, a complex of the enzyme and the substrate(s) is formed . The transition state is also formed in an enzyme substrate complex . The specificity of enzymes is brought about bythe specific binding of substrate . The region of the enzyme where the bindingoccurs is called the active site Lock and key hypothesis . To explain substrate specificity, several theories have been proposed . The lock and key hypothesis assumes that theshape of the active site is a negative of theshape of the substrate . Later, several enzymes were found to be ableto catalyze the reaction of substrates havingsignificantly different shapes but not ofsubstances having almost the same shape as aknown substrate The lock and key hypothesis Induced fit hypothesis . Due to the above mentioned difficulties, a new model has been proposed to better explainsubstrate specificity . This new model, called induced fit model assumes that, when the substrate approaches the active site of the enzyme, a conformationalchange occurs in the enzyme, allowing thebinding based on shape complementarity The induced fit mechanism Transition state fit . According to a more modern view, it is thetransition state whose shape fits the shape ofthe active site . Thus, a lock and key binding occurs notbetween the enzyme and the ground state but between the enzyme and the transition stateof the substrate Transition state fit . The transition state is a high-energy state ofthe substrate . According to the Boltzmann distribution, stateswith high energy have a low but non-zeroprobability to occur . Thus, a small amount of substrate molecules in the transition state is present in the medium . Transition state fit occurs when the enzymeselects a substrate molecule being in thetransition state for binding rather thanmolecules in the ground state . Not only the enzyme can select from thereservoir of substrate states but substrates can also select from the preexisting enzymeconformations . This mechanism is called conformational selection or fluctuation fit Conformational selection by the enzyme Conformational selection by the substrate Transition-state analogues . Based on the model assuming the selectivebinding of the transition state by the enzyme, it has been proposed that analogues of thetransition state compounds, that is acompound having similar conformation to itshould be good inhibitors of the enzyme . Indeed, several observations have been accumulated that support the concept thattransition state analogues are good inhibitors Abzymes . The existence of abzymes lends further support for the transition state fit model . Abzymes are catalytic antibodies . They have catalytic activity for reactions for which they can selectively bind the transition state . Immunizing animals by a transition state analogue, an effective enzyme can be obtained . The Michaelis-Menten model of enzymekinetics accounts for dependence of the rate ofthe enzyme reactions on the substrateconcentration . A steady-state approximation has been used toconstruct a model fitting well the experimentalresults for many enzymes Kinetic curves of an enzyme reaction . The following scheme can be proposed for ageneric enzyme reaction k1 k 2 E .S . ES . P k-1 k-2 where E is the enzyme and S is the substrate intheir free forms, ES is the enzyme-substratecomplex and P is the product . The corresponding rate constants are also shown . Assuming that the rate of formation of productfrom the enzyme-substrate complex is far higher than the rate of the reverse reaction, that is k2 »k-2 the general scheme of enzyme reactions can besimplified to be k1 k 2 E .S . ES . P k-1 v0 =k2 [ ES ] . Since we do not know the concentration of the enzyme-substrate complex, we need toexpress it in terms of the known quantitiessuch as the initial substrate or enzyme concentration d [ ES ] =k1 [ E ][S ]-.k-1.k2 .[ ES ] d t . Making use of the steady state approximation, i.e. that the concentration of the enzyme-substrate complex does not change for a widetime range d [ ES ] =0 d t and thus k1 [ E ][S ]=.k-1.k2 .[ ES ] [ E ][ S ]/[ ES ]=.k-1 .k2 ./ k1 . If we define a new constant called Michaelis constant, KM KM =.k-1 .k2 ./ k1 we get a simpler equation [ E ][S ] [ ES ]= KM . The concentration of the free enzyme can beobtained from the equation [ E ]=[ E ]T -[ ES ] where [E]T is the total enzyme concentration . Since the total amount of the enzyme does notchange through the reaction, it will be equal tothe amount of enzyme initially put into thereaction mixture . Substituting the expression for the enzymeconcentration into the equation above, we get .[E ]T -[ ES ].[S ] [ ES ]= KM . Solving the equation for [ES], we obtain [ S ][ ES ]=[ E ]T [S ]. KM . Substituting this expression into the equation for the reaction rate, we obtain [S ] v0 =k2 [ E ]T [S ].KM . The reaction can proceed with the maximalspeed when all of the enzyme molecules are incomplex with a substrate molecule, that iswhen [ ES ]=[ E ]T . Thus the maximal velocity is vmax =k2 [ E ]T . Based on this, the relationship between themaximal and the actual velocity is [ S ] v0 =vmax [ S ]. KM . It can be seen in the equation above that KM corresponds to the substrate concentration where the rate of reaction is half of the maximal rate . It also shows that the Michaelis constant is an important kinetic property of enzymes the substrate concentration . If the substrate concentration is far lower than the Michaelis constant, that is [S ]« KM then the rate of reaction is approximately vmax v0.[ S ] KM . It can be seen that at low substrate concentration, the reaction is first-order with respect to the substrate . On the other hand, if the substrate concentration is far higher than the Michaelisconstant, that is [S ]» KM then the rate of reaction is approximately v0.vmax . It can be seen that at high substrateconcentration, the reaction is zeroth-order with respect to the substrate . The turnover number of an enzyme is thenumber of molecules converted into a productin unit time when the enzyme is fully saturatedby the substrate . The turnover number is equal to the rate constant k2 which is also called kcat . The maximal velocity, v in terms of kis maxcat v= max kcat[ E ]T . When the substrate concentration is far lower than the Michaelis constant, the enzymatic rate is much less than kcat . From equation v0 =kcat [ ES ] and [ E ][S ][ ES ]= KM we can obtain a new equation k cat v0 =[ E ][ S ] K M . kcat/KM behaves as a second-order rate constant for the reaction between the substrate and the free enzyme, and thus can serve as a measureof catalytic efficiency . The physical limit on the value of kcat/KM is the rate constant of formation of the enzyme- substrate complex which cannot be faster thanallowed by the velocity of diffusion Inhibitors . Enzymes can be inhibited by specific inhibitors . Two main classes of inhibitors can be distinguished – Competitive inhibitors – Non-competitive inhibitors . Competitive inhibitors use the same bindingsite on the enzyme as the substrate and acompetition occurs between the substrate andthe inhibitor for the binding site . Non-competitive inhibitors bind to a differentsite on the enzyme than the substrate . They cause a conformational change in theenzyme, leading to a reduction of the action ofthe enzyme . Competitive and non-competitive inhibitors have a different effect on the kinetics of the enzyme reaction and thus they can bekinetically distinguished . In the case of a competitive inhibitor, if theconcentration of substrate is high enough, themaximal velocity, vmax, can be attained but the substrate concentration where the velocity is the half of vmax, KM, will be higher . In the case of non-competitive inhibitors, the maximum velocity vmax cannot be attained even at very high substrate concentration, but thesubstrate concentration where the velocity is the half of the modified maximal velocity is unchanged Introduction to biophysics: Enzymes N ii i hibi Catalytic strategies . The function of enzymes is based on one or more of a few strategies – Through covalent catalysis, a reactive group of theactive site becomes covalently modified • In the active site of trypsin, the catalytic serineresidue forms an acyl-enzyme intermediate withthe N-terminal part of the cleaved polypeptidechain Acyl-enzyme intermediate in the active site of trypsin – In acid-base catalysis, a proton transfer occurs where the donor or acceptor group is not water – Metal ions can take part in the catalytic reactions inseveral ways, for example they can supply positivecharge if the intermediate is negatively charged, orthey can take part in the substrate binding – The enzyme can help substrates to approach eachother in a proper orientation, entropically decreasingthe activation free energy Ribozymes . Catalytic capability is a property not exclusively of proteins but also of RNAs . Several catalytic RNAs called ribozymes areknown . Ribozymes take part mainly in the catalysis ofreactions related to RNA conversion . Ribozymes are important constituents of ribosomes, the molecular machines responsible for protein synthesis Large subunit of a bacterial ribosome Small subunit of a bacterial ribosome . Another important process catalyzed partly byribozymes is splicing through which exons arecleaved out from the premature mRNAmolecule . Inspired by the discovery of catalytic RNAs, anevolutionary concept called the RNA world was proposed . According to these hypothesis, at an earlier stage of evolution, it was RNA that wasresponsible for catalysis and informationstorage instead of proteins and DNA, respectively RNA splicing . The RNA world hypothesis is supported by theexistence of catalytic RNAs and the fact thatmany enzymes have a coenzyme, i.e. aribonucleotide derivative such as NAD, the most important electron carrier molecule of the cell and ATP, the most important energy currency Adenosine triphosphate (ATP) Nicotinamid adenine dinucleotide (NAD)