Conformation, allostery Petr Louša 16. 11. 2017 Petr Louša Conformation, allostery 16. 11. 2017 1 / 28 Outline 1 Introduction 2 Allostery 3 Kinetics of conformational changes 4 Folding Petr Louša Conformation, allostery 16. 11. 2017 2 / 28 Introduction Outline 1 Introduction 2 Allostery 3 Kinetics of conformational changes 4 Folding Petr Louša Conformation, allostery 16. 11. 2017 3 / 28 Introduction Conformation of proteins constitution topology of molecule – isopropanol, n-propanol configuration bond arrangement – cis/trans, R/S conformation 3D structure – rotation around single bonds Petr Louša Conformation, allostery 16. 11. 2017 4 / 28 Allostery Outline 1 Introduction 2 Allostery 3 Kinetics of conformational changes 4 Folding Petr Louša Conformation, allostery 16. 11. 2017 5 / 28 Allostery Allostery Change of conformation after ligand binding. ⇒ Change of Kd for other ligands. Typical example hemoglobin. Often multimeric proteins with more equivalent active sites. Petr Louša Conformation, allostery 16. 11. 2017 6 / 28 Allostery Types of allostery By type of Kd change: positive – Kd decreases – next substrate binds more easily – activation negative – Kd increases – next substrate binds more poorly – inhibition Petr Louša Conformation, allostery 16. 11. 2017 7 / 28 Allostery Types of allostery By type of Kd change: positive – Kd decreases – next substrate binds more easily – activation negative – Kd increases – next substrate binds more poorly – inhibition By type of substrate: homotropic – more same ligands bind to protein – e.g. hemoglobin heterotropic – activator/inhibitor differs from next bound substrate – e.g. strychnine inhibits glycine receptor (inhibitive neurotransmitter) Petr Louša Conformation, allostery 16. 11. 2017 7 / 28 Allostery Types of allostery By type of Kd change: positive – Kd decreases – next substrate binds more easily – activation negative – Kd increases – next substrate binds more poorly – inhibition By type of substrate: homotropic – more same ligands bind to protein – e.g. hemoglobin heterotropic – activator/inhibitor differs from next bound substrate – e.g. strychnine inhibits glycine receptor (inhibitive neurotransmitter) Non-regulatory allostery protein needs other component for its function, but is not regulated by it – e.g. ions, vitamins Petr Louša Conformation, allostery 16. 11. 2017 7 / 28 Allostery Hill equation I Quantification of cooperativity R + L RL K (1) d RL + L RL2 K (2) d ... RLn−1 + L RLn K (n) d Constants K (i) d differ – system is cooperative. Petr Louša Conformation, allostery 16. 11. 2017 8 / 28 Allostery Hill equation II Assumption – [RL]i = 0 Only one equation remains ⇒ Hill analysis. R + nL RLn ˆKd (1) ˆKd = [R][L]n [RL]n (2) ˆKd = (Kd)n (3) Petr Louša Conformation, allostery 16. 11. 2017 9 / 28 Allostery Analysis of experiment Measure fraction of bound receptors and linearize: y = [RL]n [Rtot] (4) log y 1 − y = n log[L] − log ˆKd (5) Petr Louša Conformation, allostery 16. 11. 2017 10 / 28 Allostery Microskopic models I – MWC model I Monod, Wyman, Changeux Two-state receptor system – can “switch” only in free form. Form A is dominant in free form. [A] [B] Affinity to B is significantly larger. Assumes change of protein structure after binding – “locking” in B state. Petr Louša Conformation, allostery 16. 11. 2017 11 / 28 Allostery Microskopic models I – MWC model II Assumes constant microscopic Kd. A B A + L AL B + L BL AL + L AL2 BL + L BL2 Ligand binds preferentially to B and shifts the equilibrium of free forms. Problem? Petr Louša Conformation, allostery 16. 11. 2017 12 / 28 Allostery Microskopic models II – KNF model Koshland, Nemethy, Filmer Generalization of MWC model. Assumes different B constants for sequential equilibria. Kd constants are free parameters for fitting. Each ligand binding changes the binding site for other ligands. Disadvantage? Petr Louša Conformation, allostery 16. 11. 2017 13 / 28 Allostery Microskopic models II – KNF model Koshland, Nemethy, Filmer Generalization of MWC model. Assumes different B constants for sequential equilibria. Kd constants are free parameters for fitting. Each ligand binding changes the binding site for other ligands. Disadvantage: too many free parameters (Kd constants) – better for experiment fitting than for predictions. Petr Louša Conformation, allostery 16. 11. 2017 13 / 28 Kinetics of conformational changes Outline 1 Introduction 2 Allostery 3 Kinetics of conformational changes 4 Folding Petr Louša Conformation, allostery 16. 11. 2017 14 / 28 Kinetics of conformational changes Kinetic view to allostery Ligand binding changes equilibrium between two “states” (MWC model). After binding, structural ensemble changes – B forms dominate. Caused by changes of kinetic parameters of the transition. Petr Louša Conformation, allostery 16. 11. 2017 15 / 28 Kinetics of conformational changes Processivity vs. Stochasticity Processivity Ability to run irreversibly in one direction. E.g. ATP synthase, motor proteins, polymerases Free energy decreases in larger jumps – irreversibility. Source of energy needed – ATP, GTP, proton gradient. ATP – ca 20kBT of energy. Petr Louša Conformation, allostery 16. 11. 2017 16 / 28 Kinetics of conformational changes Processivita vs. Stochasticity Stochasticity Many reversible steps. E.g. glycolysis. Reversibility – ∆G ≈ kBT Even many reversible steps can lead to irreversible event – ∆G adds up. Petr Louša Conformation, allostery 16. 11. 2017 17 / 28 Folding Outline 1 Introduction 2 Allostery 3 Kinetics of conformational changes 4 Folding Petr Louša Conformation, allostery 16. 11. 2017 18 / 28 Folding Fundamental questions 1. What structure does given sequence of amino acids take? 2. How does the protein fold? Petr Louša Conformation, allostery 16. 11. 2017 19 / 28 Folding Fundamental questions 1. What structure does given sequence of amino acids take? Homology modeling Prediction de novo Global minimum search ∆G MD of stretched chain Folding@home, Foldit Evolution covariation – requires hundreds of homologous sequences 2. How does the protein fold? Petr Louša Conformation, allostery 16. 11. 2017 19 / 28 Folding Fundamental questions 1. What structure does given sequence of amino acids take? Homology modeling Prediction de novo Global minimum search ∆G MD of stretched chain Folding@home, Foldit Evolution covariation – requires hundreds of homologous sequences 2. How does the protein fold? Folding process Kinetics Transit states Intermediates Petr Louša Conformation, allostery 16. 11. 2017 19 / 28 Folding Can proteins fold on their own? Sometimes. Petr Louša Conformation, allostery 16. 11. 2017 20 / 28 Folding Can proteins fold on their own? Sometimes. Spontaneous folding Small proteins often fold without any help. Often capable of multiple de- and renaturation. Anfinsen experiment – renaturation of ribonuclease A. Can be simulated by computers. Petr Louša Conformation, allostery 16. 11. 2017 20 / 28 Folding Can proteins fold on their own? Sometimes. Spontaneous folding Small proteins often fold without any help. Often capable of multiple de- and renaturation. Anfinsen experiment – renaturation of ribonuclease A. Can be simulated by computers. “Almost” spontaneous folding Folding starts already during translation. Tranlation takes long time – up to 10 seconds. Can not fold spontaneously – order is important. Folding in membrane. Petr Louša Conformation, allostery 16. 11. 2017 20 / 28 Folding Can proteins fold on their own? Sometimes. Spontaneous folding Small proteins often fold without any help. Often capable of multiple de- and renaturation. Anfinsen experiment – renaturation of ribonuclease A. Can be simulated by computers. “Almost” spontaneous folding Folding starts already during translation. Tranlation takes long time – up to 10 seconds. Can not fold spontaneously – order is important. Folding in membrane. Only with “helpers” – chaperons. Hydrophobic boxes. Proteins can search through the configuration space more easily. Petr Louša Conformation, allostery 16. 11. 2017 20 / 28 Folding Folding as conformation change Folding follows the same physics as other structural changes. Differences: Large ranges of equilibrium and nonequilibrium conditions. De-/renaturation can go very slowly and reversibly or “immediately”. “Unfolded state” is not a state. Many different substates – difficult to characterize. Differ also in the denaturation process – temperature, pH, chemical agents,... Petr Louša Conformation, allostery 16. 11. 2017 21 / 28 Folding Overall folding rate Unfolded protein can have multiple substates. Only some allow transition to folded state. Depends on particular rate constants. Depends on substate populations. Population can differ based on the denaturation process. Petr Louša Conformation, allostery 16. 11. 2017 22 / 28 Folding Φ values analysis Alan Fersht Influence of individual residues on folding and transient states. Compare ∆G profiles for wild type and mutant. ∆∆Gij = ∆Gij(mut) − ∆Gij(wt) (6) ΦF = ∆∆GD‡ ∆∆GDN (7) ΦF = 0 residuum is unfolded in transient state. ΦF = 1 residuum is folded in transient state. Petr Louša Conformation, allostery 16. 11. 2017 23 / 28 Conformation, allostery – exercise Petr Louša 16. 11. 2017 Petr Louša Conformation, allostery – exercise 16. 11. 2017 24 / 28 Hill equation 1. Draw Hill plot for case of negative cooperativity. Petr Louša Conformation, allostery – exercise 16. 11. 2017 25 / 28 Hill equation 1. Draw Hill plot for case of negative cooperativity. Petr Louša Conformation, allostery – exercise 16. 11. 2017 25 / 28 Free energy differences Assume free energy differences between states A and B of: 1. 1 kBT 2. 5 kBT 3. 20 kBT Calculate ratio of forward and backward reaction. Think, whether it is processive or stochastic process. Petr Louša Conformation, allostery – exercise 16. 11. 2017 26 / 28 Free energy differences – solution ∆G = −RT ln K (8) ln K = ∆G RT (9) K = kon koff = exp ∆G RT (10) 1. 1 kBT ⇒ K = 2.7 2. 5 kBT ⇒ K = 150 3. 20 kBT ⇒ K = 4.85 · 108 Petr Louša Conformation, allostery – exercise 16. 11. 2017 27 / 28 References Zuckerman, Daniel M. Statistical Physics of Biomolecules. An Introduction Atkins, Peter; de Paula, Julio. Physical Chemistry Kodíček, Milan; Karpenko, Vladimír. Biofysikální chemie Petr Louša Conformation, allostery – exercise 16. 11. 2017 28 / 28 References Zuckerman, Daniel M. Statistical Physics of Biomolecules. An Introduction Atkins, Peter; de Paula, Julio. Physical Chemistry Kodíček, Milan; Karpenko, Vladimír. Biofysikální chemie Wikipedia Petr Louša Conformation, allostery – exercise 16. 11. 2017 28 / 28