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Bioenergética Mirko Zimic [email protected] Qué es la Bioenergética? • Es la disciplina que estudia los aspectos energéticos en los sistemas vivos, tanto a nivel molecular como a nivel celular. – Interacciones moleculares – ATP como biomolécula almacenadora de energía – Biocatálisis – Reacciones acopladas Conversión entre la Energía cinética y la Energía potencial Interacciones Fundamentales • • • • Interacción Gravitacional (masa-masa) Interacción Electromagnética (carga-dipolo) Interacción Nuclear Débil (electrones-núcleo) Interacción Nuclear Fuerte (protones-neutrones) Los Sistemas Biológicos son guiados fundamentalmente por Interacciones Electromagnéticas – Enlaces Covalentes – Enlaces No-covalentes (Interacciones Débiles): • • • • • • Puentes de Hidrógeno Efecto Hidrofóbico Interacciones Iónicas Interacciones Ión-Dipolo Interacciones Dipolo-Dipolo Fuerzas de Van der Waals Enlace Covalente La Energía de Activación es el resultado de la repulsión de las nubes electrónicas Las interacciones Iónicas se dan entre partículas cargadas Participación de los Puentes de Hidrógeno: Replicación, Transcripción y Traducción Las interacciones débiles dirigen el proceso de ‘docking’ molecular El efecto hidrofóbico colabora en el plegamiento de las proteínas Temperatura Es la medida de la energía cinética interna de un sistema molecular Ek = N K T /2 Calor Es la energía cinética que se propaga debido a un gradiente de temperatura, cuya dirección es de mayor temperatura a menor temperatura Entropía S = K Ln(W) La entropía es la medida del grado de desorden de un sistema molecular S1 > S2 Entalpía H=E+PV La entalpía es la fracción de la energía que se puede utilizar para realizar trabajo en condiciones de presión y volumen constante dH<0 proceso exotérmico dH>0 proceso endotérmico Energía Libre G=H-TS La energía libre es la fracción de la energía que se puede utilizar para realizar trabajo en condiciones de presion, volumen y temperatura constante dG<0 proceso exergónico (espontáneo) dG>0 proceso endergónico Las Enzimas o biocatalizadores, reducen la Energía de Activación La molécula de ATP Los seres vivos utilizan la molécula de ATP como medio principal para almacenar energía potencial proveniente de la degradación de los alimentos La manera de utilizarse la energía en la molécula de ATP es mediante la separación de un grupo fosfato el cual está unido mediante un enlace covalente de alta energía La síntesis de ATP ocurre durante la glicólisis y la respiración celular en la mitocondria usualmente En las plantas, la síntesis de ATP ocurre asistida por luz durante la fotosíntesis, la cual es luego empleada en las denominadas reacciones oscuras. Este es un ejemplo de transformación de energía radiante en energía química. El ATP participa en una serie de reacciones acopladas Diversas moléculas biológicas requieren la capacidad de ‘moverse’ para cumplir sus funciones… Por lo tanto hace falta energía para realizar esta función. La fuente de energía para el movimiento molecular es fundamentalmente el ATP El ATP contribuye a diversos tipos de reacciones El ATP suele participar en el correcto plegamiento de las proteínas Thermodynamics First Law: Energy conservation Internal energy (E).- Total energy content of a system. It can be changed by exchanging heat or work with the system: Heat-up the system Cool-off the system E E Do work on the system Extract work from the system E = q + w w -PV w´ Thermodynamics A more useful concept is: ENTHALPY (H) H = E + PV 0 0 H q p - PV w PV VP At constant pressure… E Only P-V work involved… w´ = 0 (as in most biological systems) So… H q p At constant pressure, the enthalpy change in a process is equal to amount of heat exchanged in the process by the system. Thermodynamics We have… H = E + PV 0 H = E + PV + VP 0 in biological systems P = 0 V 0 H E at P = 0 and since V 0 Q: How is this energy stored in the system? A: 1) As kinetic energy of the molecules. In isothermal (T = 0) processes this kinetic energy does not change. 2) As energy stored in chemical bonds and interactions. This “potential” energy could be released or increased in chemical reactions Thermodynamics Second Law: Entropy and Disorder Energy conservation is not a criterion to decide if a process will occur or not: Examples… THot TCold T q E = H = 0 This rxn occurs in one direction and not in the opposite T these processes occur because the final state ( with T = T & P = P) are the most probable states of these systems Let us study a simpler case… tossing 4 coins Thermodynamics All permutations of tossing 4 coins… Macroscopic states… 1 way to obtain 4 heads 4 ways to obtain 3 heads, 1 tail 6 ways to obtain 2 heads, 2 tails 4 ways to obtain 1 head, 3 tails 1 way to obtain 4 tails 6 4 The most probable state is also the most disordered 4 2 H, 2 T 1 4 H, 0 T 3 H, 1 T 1 H, 3 T Microscopic states… HTTH HHTT 4! HTHT 6 THHT 2! 2! TTHH THTH 1 0 H, 4 T Thermodynamics In this case we see that H = 0, i.e.: there is not exchange of heat between the system and its surroundings, (the system is isolated ) yet, there is an unequivocal answer as to which is the most probable result of the experiment The most probable state of the system is also the most disordered, i.e. ability to predict the microscopic outcome is the poorest. Thermodynamics A measure of how disordered is the final state is also a measure of how probable it is: 6 P2H, 2T 16 Entropy provides that measure (Boltzmann)… S k B ln W Molecular Entropy Boltzmann Constant Number of microscopic ways in which a particular outcome (macroscopic state) can be attained Criterion for Spontaneity: For Avogadro number’s of molecules… S (N Avogadrok B ) ln W R (gas constant) Therefore: the most probable outcome maximizes entropy of isolated systems S > 0 (spontaneous) S < 0 (non-spontaneous) Thermodynamics The macroscopic (thermodynamic) definition of entropy: dS = dqrev/T i.e., for a system undergoing a change from an initial state A to a final state B, the change in entropy is calculated using the heat exchanged by the system between these two states when the process is carried out reversibly. Thermodynamics S final initial S final (Carried through a reversible path) CP dT (If process occurs at contant pres sure) T final CV dT (If process occurs at cons tant volume) T initial S dqrev T initial Spontaneity Criteria In thes e equations, the equal s ign applies for revers ible process es . The inequalities apply for irrevers ible, spontaneous, process es : S(system) S(surroundings) 0 S(isolated system) 0 Thermodynamics Free-energy… •Provides a way to determine spontaneity whether system is isolated or not •Combining enthalpic and entropic changes G H - TS (Gibbs free energy) What are the criteria for spontaneity? Take the case of H = 0: G - TS <0 >0 G > 0 G < 0 G = 0 non-spontaneous process spontaneous process process at equilibrium Thermodynamics Free energy and chemical equilibrium… Consider this rxn: A+B C+D Suppose we mix arbitrary concentrations of products and reactants… •These are not equilibrium concentrations •Reaction will proceed in search of equilibrium •What is the G is associated with this search and finding?: [C][D] o G G RT ln i.e. G when A, B, [A][B] C, D are mixed in o G is the Standard Free Energy of reaction their standard state: G Rxn 1 1 G RT ln 1 1 Biochemistry: 1M, 25oC, pH = 7.0 o G Rxn G o Thermodynamics Now… Suppose we start with equilibrium concentrations: Reaction will not proceed forward or backward… G Rxn 0 Then… G - RT ln o [C]eq [D] eq [A]eq [B] eq [C]eq [D] eq [A]eq [B] eq Go - RT ln Keq K eq e Rearranging 0 G RT ln o K eq e o G RT Ho - TSo RT H RT RS K eq e e o o Thermodynamics Graph: o Ho RT RS ln K eq e e H o So ln K eq RT R So R Van’t Hoff Plot H o Slope = R ln K eq 1 T K o -1 Thermodynamics Summary: in chemical processes Ho So 1) Change in potential energy stored in bonds and interactions 2) Accounts for T-dependence of Keq 1) Measure of disorder 3) Reflects: #, type, and quality of bonds 3) Reflects order-disorder in bonding, conformational flexibility, solvation 4) So Keq Rxn is favored 4) If Ho < 0: T Keq If Ho > 0: T Keq S = R ln (# of microscopic ways of macroscopic states can be attained) 2) T-independent contribution to Keq Thermodynamics Examples: Consider the Reaction… A Free energy change when products and reactants are present at standard conditions B [A]initial = 1M [B]initial = 10-5M Keq = 1000 Go - RT ln Keq G o - 1.98 molcalK 298 K ln 1000 G o - 4.076 Kcal mol How about GRxn… Spontaneous rxn [B] G Rxn G RT ln [A] o -3 G Rxn - 4.076 Kcal 1.98 10 mol G Rxn -10.9 Kcal mol Kcal mol K 10-5 298K ln 1 Even more spontaneous Thermodynamics Another question… What are [A]eq and [B]eq? [A] [B] 1 10-5 1M [A] 1 - [B] K eq [B] eq [A]eq 1000 [B]eq 1000 1 - [B]eq 1001[B]eq 1000 1000 [B]eq 0.999M 1M 1001 [A]eq 0.001M Thermodynamics Another Example… Acetic Acid Dissociation Ho ~ 0 CH3 – COOH + H2O CH3 – COO- + H3O+ Creation of charges Requires ion solvation Organizes H2O around ions At 1M concentration, this is entropically unfavorable. Keq ~ 10-5 [CH 3 COO- ][H 3O ] K eq ~ 10-5 [CH 3 COOH] If [CH3 – COOH]total ~ 10-5 50% ionized Percent ionization is concentration dependent. We can favor the forward rxn (ionization) by diluting the mixture If [CH3 – COOH]total ~ 10-8 90% ionized Thermodynamics CH3 – COOH + H2O CH3 – COO- + H3O+ [CH COO- ][H O ] 3 3 2 [CH 3 COO ][H 3 O ] [CH 3 COOH]T K eq = [CH 3 COOH] [CH 3 COOH]T [CH 3 COO ] 2 [CH COOH] 3 T 2 [CH 3 COOH]T [CH 3 COO ] K eq with 1 [CH 3 COOH]T and = 2 -K eq K eq + 4[CH 3 COOH]T K eq 2[CH COOH] 3 T Thermodynamics CH3 -COOH total Thermodynamics Third Example… Amine Reactions H + R – N – H + H2O R – NH2 + H3O+ H So 0 not favorable H o 14 Kcal mol K eq 10-10 Backbone Conformational Flexibility R H C N N C H H O For the process… folded unfolded (native) (denatured) S o backbone conf. Wunfolded R ln Wfolded How many ways to form the unfolded state?… Backbone Conformational Flexibility degrees of freedom = 2 Assume 2 possible values for each degree of freedom. Then… Total of 4 conformati onal isomers residue For 100 amino acids… 4100 ~ 1060 conformations These results do not take into account excluded volume effects. When these effects are considered the number of accessible configurations for the chain is quite a bit smaller… Wunfolded ~ 1016 conformations Backbone Conformational Flexibility Thermodynamic considerations… Sobackbone conf. R ln 1016 1.987 16 2.303 73 molcalK o G obackbone conf. - TSo - 22 Kcal at 25 C mol In addition other degrees of freedom may be quite important, for example… R H C N N C H H O We will see this later in more detail Ionization of Water •Water is the silent, most important component in the cell •Its properties influence the behavior and properties of all other components in the cell. Here we concern ourselves with its ionization properties: H2O + H2O H3O+ + OH- [H 3O ][OH - ] K eq [H 2 O] Since in the cell, [H2O] ~ 55M, and ionization is very weak, then [H2O] ~ constant, so se can define… “the ionic product of K w [H 3O ][OH - ] water” Ionization of Water From the previous equation… K w [H 3O ][OH - ] K w 10-14 For pure water… [H ] [H 3O ] [OH - ] 10-7 M i.e. in a neutral soln: [H 3O ] 10-7 M [OH- ] 10-7 M The overall acidity of the medium greatly affects many biochemical reactions, because most biological components can function either as bases or acids. A measure of acidity is given by the pH scale, defined as… 1 pH log 10 log [H O ] 3 [H 3O ] 1 So, in fact for pH log 10 -7 7 10 pure water: Weak Acids and Bases All biological acids and bases belong to this category Consider acetic acid… AH A- + H+ The Dissociation Constant… Ka rearrange… [H ][A- ] [AH] [A - ] HendersonpH pK a log Hasselbalch [AH] equation where, pKa = - logKa Weak Acids and Bases Fraction of deprotonated acid is… f A [A ] [A ] [AH] So, we can re-write the Henderson-Hasselbalch equation Also… f AH 1 f A pH pK a log f A 1 - f A 1.0 fA 0.5 pKa 0 pH i.e. pKa is the pH at which the acid is 50% ionized Weak Acids and Bases Based on the previous page… pH pK a 1 ; f A If… pH pK a 1 ; f A 10 90% 11 9% pH pK a 2 ; f A 0.9%, etc. Morever… the lower the pKa, the stronger the acid 1.0 fA stronger acid 0.5 weaker acid 0 pH pH pK a log f A 1 - f A Weak Acids and Bases Some useful relationships… f AH H AH A AH Ka H fAH Ka f A A Ka A AH K a H fA- Ka Multiple Acid-Base Equilibria Consider Alanine… CH3 NH3+ CH COOH = 9.7 Please correct in your notes = 2.3 (fraction deprotonated) mL of base added Titrate a solution of ala, using a gas electrode (pH meter), and a buret to add a strong base of known concentration: pK1 pK2 pH Macroscopic experiment shows 2 inflection points (2 pKs) Multiple Acid-Base Equilibria As we vary the pH of the solution from low to high: H CH3 N+ H CH H H COOH CH3 N+ H CH H COO – H Cation Zwitterion CH3 N COO – CH H Anion So, in fact the two inflection points seen correspond to the deprotonation of the carboxylic group (at low pH) and then to the deprotonation of the amine group (at high pH). So, How can we estimate the fraction of these different species in solution? If we assume that the ionization of a given group is independent of the state of ionization of the others, then… Multiple Acid-Base Equilibria f HAH fCOOH fNH 3 H H Ka1 H Ka 2 H K a H 1 f HA fCOO fNH 3 Ka 1 H K a 2 H K a H 2 f AH fCOOH fNH 2 Ka 1 H K a 2 H K K a a 1 2 f A f COO fNH 2 Ka 1 H Ka 2 H f HAH f HA f AH f A 1