Self-Organizing Bio- structures NB2-2007L.Duroux

Lecture 6 1. Protein Folding (Proteins 2 nd Ed., T.E. Creighton) 2. Protein Quaternary Structure

1. Protein Folding Another case of essential self-assembly process

Protein folding is essential to life

Why is the “ Protein Folding ” so Important? Proteins play important roles in living organisms. Proteins play important roles in living organisms. Some proteins are deeply related with diseases. And structural information of a protein is necessary to explain and predict its gene function as well as to design molecules that bind to the protein in drug design. Some proteins are deeply related with diseases. And structural information of a protein is necessary to explain and predict its gene function as well as to design molecules that bind to the protein in drug design. Today, whole genome sequences (the complete set of genes) of various organisms have been deciphered and we realize that functions of many genes are unknown and some are related with diseases. Today, whole genome sequences (the complete set of genes) of various organisms have been deciphered and we realize that functions of many genes are unknown and some are related with diseases. Therefore, understanding of protein folding helps us to investigate the functions of these genes and to design useful drugs against the diseases efficiently. Therefore, understanding of protein folding helps us to investigate the functions of these genes and to design useful drugs against the diseases efficiently. In addition to that, the understanding opens the door to designing of proteins having novel functions as new nano machines. In addition to that, the understanding opens the door to designing of proteins having novel functions as new nano machines.

1a. Examples

Protein (mis)folding can lead to fatal diseases Mad cow disease, or bovine spongiform encephalopathy (BSE), is a fatal brain disorder that occurs in cattle. Abnormal protein folding is considered crucial to the onset of the disease. To illustrate the concept of protein folding we chose villin, a protein which exists in the stomach and intestine of animals (including homo sapiens). What causes mad cow? Why do proteins fold?

What causes mad cow disease? Bovine epidemic in UK (1986): cows died Bovine epidemic in UK (1986): cows died Symptoms: “mad”, aggressive, nervous, spongiform encephalopathy Symptoms: “mad”, aggressive, nervous, spongiform encephalopathy Other examples: scrapie (sheep), Creutzfeld- Jacob Disease (humans) Other examples: scrapie (sheep), Creutzfeld- Jacob Disease (humans) S. Prusiner (1982): Infectious agent are “proteinaceous infectious particles” = prions S. Prusiner (1982): Infectious agent are “proteinaceous infectious particles” = prions Prions: proteins found in the nerve cells of all mammals. Abnormally-shaped prions found in BSE-infected cows Prions: proteins found in the nerve cells of all mammals. Abnormally-shaped prions found in BSE-infected cows The difference in normal and infectious prions may lie in the way they fold The difference in normal and infectious prions may lie in the way they fold Brain surface of CJD patient on autopsy showing sponge-like appearance

Prions, infection and folds. 1. Contamination: Ingestion / Genetics 2. Bloodstream  nervous system. 3. Molecular interaction Infectious / Native  change in conformation of native (  Infectious) 4. Accumulation of Infectious form in fibrillates (self-assembly) 5. Internalization/vesicles  clogging  cell death 6. Release Infectious form 7. Large, sponge-like holes : spongiform encephalopathy Native Infectious

Villin headpiece sub-domain: a study case for protein folding Villin’s function: Villin’s function: structure to intestinal villi structure to intestinal villi stabilizes bundles of actin filaments stabilizes bundles of actin filaments folds recognized by specific receptor point of actin filaments folds recognized by specific receptor point of actin filaments Folding Folding Simulated by distributed dynamics Simulated by distributed dynamics one and only one way of folding is the correct way. one and only one way of folding is the correct way.

1b. Folding mechanisms

Proteins Can Fold into 3D Structures Spontaneously The three-dimensional structure of a protein is self-organized in solution. If we can calculate the energy of the system precisely, it is possible to predict the structure of the protein! The structure corresponds to the state with the lowest free energy of the protein-solvent system. (Anfinsen’s dogma)

Anfinsen experiment: Spontaneous renaturation of Ribonuclease A Primary structure contains sufficient information to allow formation of secondary and tertiary structures Primary structure contains sufficient information to allow formation of secondary and tertiary structures Fig. 4.29

Levinthal Paradox We assume that there are three conformations for each amino acid (ex.  -helix, β-sheet and random coil). If a protein is made up of 100 amino acid residues, a total number of conformations is = ≒ 5 x If 100 psec ( sec) were required to convert from a conformation to another one, a random search of all conformations would require 5 x x sec ≒ 1.6 x years However, folding of proteins takes place in msec to sec order. Therefore, proteins fold not via a random search but a more sophisticated search process. Is it possible to watch the folding process of a protein using molecular simulation techniques?

Time Scales of Protein Motions Time (s) (fs) (ps) (μs)(ns) (ms) Bond stretching Permeation of an ion in Porin channel Elastic vibrations of proteins α-Helix folding β-Hairpin folding Protein folding

Forces Involved in the Protein Folding Electrostatic interactions Electrostatic interactions van der Waals interactions van der Waals interactions Hydrogen bonds Hydrogen bonds Hydrophobic interactions (Entropy driven, role of water) Hydrophobic interactions (Entropy driven, role of water)

Protein folding hierarchy a)Formation of secondary structure elements b)Hydrophobic colapse – molten globule – compact intermediate with high content of secondary structure elements c)Native contacts formation d)In case of multi-domain proteins: interdomain organization. e) Out of pathway intermediates: misfolded proteins – formation of nonative disulfide bonds - Proline cis-> isomerisation:

Protein folding mechanisms The next few slides show four different protein folding mechanisms currently known The next few slides show four different protein folding mechanisms currently known These mechanisms describe different possible sequences and paths, shown with arrows, that the chains of amino acids can follow to go from the unfolded state to the final protein form, called the native state These mechanisms describe different possible sequences and paths, shown with arrows, that the chains of amino acids can follow to go from the unfolded state to the final protein form, called the native state

unfolded state formation of microdomains diffusion and collision of microdomains native stateDiffusion/Collision First form secondary structure by diffusion/collision First form secondary structure by diffusion/collision Hierarchical: form helices & hairpins, then microdomains, decrease entropy Hierarchical: form helices & hairpins, then microdomains, decrease entropy

Nucleation Nucleation Form nucleus of structure, then grow (ala 1 st order phase transition) Form nucleus of structure, then grow (ala 1 st order phase transition) unfolded state formation of a nucleus native state

Collapse Collapse first Hydrophobically driven: remove water to form hydrogen bonds Hydrophobically driven: remove water to form hydrogen bonds unfolded state collapse native state

Topomer search Form rough native shape first (topomer search) Find the right “topology” first, then pack side chains Find the right “topology” first, then pack side chains unfolded state "topomer" native state

Evolution will use any mechanism that works! No single mechanism is observed, different examples appear in nature No single mechanism is observed, different examples appear in nature Form secondary structure first (BBA5) Form secondary structure first (BBA5) Hierarchical: form alpha-helices & beta-sheets Hierarchical: form alpha-helices & beta-sheets Collapse first (protein G Hairpin) Collapse first (protein G Hairpin) Hydrophobically driven: remove water to form hydrogen bonds first Hydrophobically driven: remove water to form hydrogen bonds first Form rough native shape first (Villin) Form rough native shape first (Villin)

1c. Energetic Considerations

Importance of kinetic factors during folding Observed folded conformation not necessarily the most thermodynamically stable Observed folded conformation not necessarily the most thermodynamically stable Folded conformation = the most kinetically accessible Folded conformation = the most kinetically accessible Not necessarily a pathway to lowest potential energy Not necessarily a pathway to lowest potential energy

Energy landscapes in protein folding pathways Many paths lead to the lowest energy state that represents the native protein. Many paths lead to the lowest energy state that represents the native protein.

Protein folding dictated by primary structure dictated by primary structure Multiple intermediate steps Multiple intermediate steps Important driving forces: Important driving forces: Hydrophobic effect Hydrophobic effect Hydrogen bonding Hydrogen bonding Van der Waals Van der Waals Charge-charge Charge-charge

The pathways for protein folding On these pathways, the protein molecules would pass through well- defined partially structured states, some of which could be transient, but others would be populated significantly On these pathways, the protein molecules would pass through well- defined partially structured states, some of which could be transient, but others would be populated significantly Similar to Reaction of small molecules: specific pathway and small region of conformational space, so Levinthal paradox is avoided Similar to Reaction of small molecules: specific pathway and small region of conformational space, so Levinthal paradox is avoided Supported existence of partially folded intermediates formed both during folding and under partially denaturing conditions Supported existence of partially folded intermediates formed both during folding and under partially denaturing conditions Recent studies: Recent studies: the behavior of different proteins often appears quite distinct: some involves well-defined compact intermediates, whilst others are effectively a two-state reaction the behavior of different proteins often appears quite distinct: some involves well-defined compact intermediates, whilst others are effectively a two-state reaction

Energy Surfaces, Energy Landscapes Based on A description of statistical ensembles and emphases the difference between the folding reactions Based on A description of statistical ensembles and emphases the difference between the folding reactions A major distinguishing feature of PF is the extreme heterogeneity of reaction and the complex interplay between the entropic and elthalpic contributions to the free energy of system A major distinguishing feature of PF is the extreme heterogeneity of reaction and the complex interplay between the entropic and elthalpic contributions to the free energy of system Denatured protein usually resembles a “random coil”, in which local interactions dominate the conformational behavior. Extremely heterogeneous, both globally and at the level of individual residues. Nearly Levinthal Paradox Denatured protein usually resembles a “random coil”, in which local interactions dominate the conformational behavior. Extremely heterogeneous, both globally and at the level of individual residues. Nearly Levinthal Paradox The enthalpies difference of the denatured and folded protein are on the order of kcal/mol The enthalpies difference of the denatured and folded protein are on the order of kcal/mol 1eV=22.9kcal/mol=96.32kJ/mol~11560K; H-bond 20kJ/mol 1eV=22.9kcal/mol=96.32kJ/mol~11560K; H-bond 20kJ/mol

A schematic energy landscape for protein folding. The surface is derived from a computer simulation of the folding of a highly simplified model of a small protein. The surface 'funnels' the multitude of denatured conformations to the unique native structure. The critical region on a simple surface such as this one is the saddle point corresponding to the transition state, the barrier that all molecules must cross if they are to fold to the native state. Superimposed on this schematic surface are ensembles of structures corresponding to different stages of the folding process. The transition state ensemble was calculated by using computer simulations constrained by experimental data from mutational studies of acylphosphatase. A schematic energy landscape for protein folding. The surface is derived from a computer simulation of the folding of a highly simplified model of a small protein. The surface 'funnels' the multitude of denatured conformations to the unique native structure. The critical region on a simple surface such as this one is the saddle point corresponding to the transition state, the barrier that all molecules must cross if they are to fold to the native state. Superimposed on this schematic surface are ensembles of structures corresponding to different stages of the folding process. The transition state ensemble was calculated by using computer simulations constrained by experimental data from mutational studies of acylphosphatase.

Molten Globule An intermediate state in the folding of protein pathway of a protein that has some secondary and tertiary structure, but lacks the well packed amino acid side chains that characterize the native state of a protein. An intermediate state in the folding of protein pathway of a protein that has some secondary and tertiary structure, but lacks the well packed amino acid side chains that characterize the native state of a protein. Observed for many protein under both equilibrium and non-equilibrium conditions. Observed for many protein under both equilibrium and non-equilibrium conditions. By contrast, for fast folding proteins without intermediates, the search for a core or nucleus is likely to be the rate- determine step; once the core is formed, folding to the native state is fast By contrast, for fast folding proteins without intermediates, the search for a core or nucleus is likely to be the rate- determine step; once the core is formed, folding to the native state is fast

A Unified Mechanism of Protein Folding? The mechanism developed by considering the free energy surfaces for reaction provide immediate insight into how the Levinthal paradox is overcome. Each folding trajectory is different: depending both on starting point and on the stochastic nature of the folding process The mechanism developed by considering the free energy surfaces for reaction provide immediate insight into how the Levinthal paradox is overcome. Each folding trajectory is different: depending both on starting point and on the stochastic nature of the folding process The overall folding behavior can be changed drastically by relatively small changes in the model parameter The overall folding behavior can be changed drastically by relatively small changes in the model parameter Simulations shows that: Simulations shows that: Fast 2-states folding can occur when collapse involves only a small subset of highly stabilizing native contacts in a core region or nucleus Fast 2-states folding can occur when collapse involves only a small subset of highly stabilizing native contacts in a core region or nucleus for large protein, long range contacts are important; cooperativity between the short- range initiation and long range contacts lead to efficient folding. (In fact, helical protein tend to fold faster than  sheet protein) for large protein, long range contacts are important; cooperativity between the short- range initiation and long range contacts lead to efficient folding. (In fact, helical protein tend to fold faster than  sheet protein) A core in large systems may occur independently in different regions, resulting additional complexities in folding, including the formation of partially structured intermediates and the possibility of extreme heterogeneity in the folding kinetics A core in large systems may occur independently in different regions, resulting additional complexities in folding, including the formation of partially structured intermediates and the possibility of extreme heterogeneity in the folding kinetics Uniform (Hydrophobic) residues often rapidly collapse to a disorganized globule with the slow step in folding corresponding to reorganization events within a compact ensemble of states, especially in large lattices. Uniform (Hydrophobic) residues often rapidly collapse to a disorganized globule with the slow step in folding corresponding to reorganization events within a compact ensemble of states, especially in large lattices. Some core residues are important and have been conserved during evolution Some core residues are important and have been conserved during evolution

1d. Molecular Chaperones A case of natural kinetic control in protein folding

Molecular chaperones Increase the rate of correct folding of nascent polypeptide chains Increase the rate of correct folding of nascent polypeptide chains Aid in the assembly of multisubunit proteins Aid in the assembly of multisubunit proteins Protect proteins from stress-induced damage (eg. Heat shock) Protect proteins from stress-induced damage (eg. Heat shock) Chaperonin

GroEL/GroES GroEL/GroES Chaperonine from E. coli Chaperonine from E. coli Multisubunit protein comples Multisubunit protein comples GroEL – cis and trans ring GroEL – cis and trans ring 7 fold symetry, cis ring binds 7 molecules of ATP 7 fold symetry, cis ring binds 7 molecules of ATP Cis ring hydrolyses ATP and undergoes conformatinal changes resulting in increase of cis ring cavity Cis ring hydrolyses ATP and undergoes conformatinal changes resulting in increase of cis ring cavity GroES – dome like hectameric ring GroES – dome like hectameric ring GroEL/GroES – assists only sa subset of protein folding GroEL/GroES – assists only sa subset of protein folding these proteins contains  /  secondary structures these proteins contains  /  secondary structures

Gro ES Gro EL Cis-ring Gro EL Trans-ring

Molecular chaperones assist protein folding

Mechanism of chaperon action 1.ATP molecules and misfolded protein binds to chaperonin through hydrophobic interactions 2.GroES binds to GroEL resulting in changes of GroEL cis ring structure, changes in misfolded protein- cavity interactions 3.Hydroglyses 7 ATP molecules 4.Binding 7 ATP to trans ring and concomitant release of folded protein, ADP molecules and GroES from cis ring, binding of misfolded protein to trans ring 5.Cis ring becomes trans ring and cycle can repeat

1e. Protein folding predictions

Molecular Dynamics (MD) In molecular dynamics simulation, we simulate motions of atoms as a function of time according to Newton ’ s equation of motion. The equations for a system consisting on N atoms can be written as: Here, r i and m i represent the position and mass of atom i and F i (t) is the force on atom i at time t. F i (t) is given by where V （ r 1, r 2, …, r N ) is the potential energy of the system that depends on the positions of the N atoms in the system. ∇ i is (1) (3) (2)

Integration Using a Finite Difference Method The positions at times (t + Δt ) and (t − Δt ) can be written using the Taylor expansion around time t, The sum of two equations is Using eq. (1), the following equation is obtained: We should calculate eq. (6) iteratively to obtain trajectories of atoms in the system (Verlet algorithm). (4a) (4b) (6) (5)

Energy Functions used in Molecular Simulation Electrostatic term H-bonding term Van der Waals term Bond stretching term Dihedral termAngle bending term r Φ Θ ＋ ー O H r r r The most time demanding part.

System for MD Simulations Without water molecules With water molecules # of atoms: 304 # of atoms: ,377 = 7,681

MD Requires Huge Computational Cost Time step of MD (Δt) is limited up to about 1 fsec ( sec). ← The size of Δt should be approximately one-tenth the time of the fastest motion in the system. For simulation of a protein, because bond stretching motions of light atoms (ex. O-H, C-H), whose periods are about sec, are the fastest motions in the system for biomolecular simulations, Δt is usually set to about 1 fsec. Time step of MD (Δt) is limited up to about 1 fsec ( sec). ← The size of Δt should be approximately one-tenth the time of the fastest motion in the system. For simulation of a protein, because bond stretching motions of light atoms (ex. O-H, C-H), whose periods are about sec, are the fastest motions in the system for biomolecular simulations, Δt is usually set to about 1 fsec. Huge number of water molecules have to be used in biomolecular MD simulations. ← The number of atom-pairs evaluated for non-bonded interactions (van der Waals, electrostatic interactions) increases in order of N 2 (N is the number of atoms). Huge number of water molecules have to be used in biomolecular MD simulations. ← The number of atom-pairs evaluated for non-bonded interactions (van der Waals, electrostatic interactions) increases in order of N 2 (N is the number of atoms). It is difficult to simulate for long time. Usually a few tens of nanoseconds simulation is performed.

Time Scales of Protein Motions and MD Time (s) (fs) (ps) (μs)(ns) (ms) Bond stretching Permeation of an ion in Porin channel Elastic vibrations of proteins It is still difficult to simulate a whole process of a protein folding using the conventional MD method. MD α-Helix folding β-Hairpin folding Protein folding

To perform MD simulations parallelization is the key Special-purpose computer Special-purpose computer Calculation of non-bonded interactions is performed using the special chip that is developed only for this purpose. Calculation of non-bonded interactions is performed using the special chip that is developed only for this purpose. For example; For example; MDM (Molecular Dynamics Machine) or MD-Grape: RIKEN MDM (Molecular Dynamics Machine) or MD-Grape: RIKEN MD Engine: Taisho Pharmaceutical Co., and Fuji Xerox Co. MD Engine: Taisho Pharmaceutical Co., and Fuji Xerox Co. Parallelization Parallelization A single job is divided into several smaller ones and they are calculated on multi CPUs simultaneously. A single job is divided into several smaller ones and they are calculated on multi CPUs simultaneously. Today, almost MD programs for biomolecular simulations (ex. AMBER, CHARMm, GROMOS, NAMD, MARBLE, etc) can run on parallel computers. Today, almost MD programs for biomolecular simulations (ex. AMBER, CHARMm, GROMOS, NAMD, MARBLE, etc) can run on parallel computers.

Brownian Dynamics (BD) The dynamic contributions of the solvent are incorporated as a dissipative random force (Einstein’s derivation on 1905). Therefore, water molecules are not treated explicitly The dynamic contributions of the solvent are incorporated as a dissipative random force (Einstein’s derivation on 1905). Therefore, water molecules are not treated explicitly Since BD algorithm is derived under the conditions that solvent damping is large and the inertial memory is lost in a very short time, longer time-steps can be used Since BD algorithm is derived under the conditions that solvent damping is large and the inertial memory is lost in a very short time, longer time-steps can be used BD method is suitable for long time simulation. BD method is suitable for long time simulation.

The folding of Villin headpiece subdomain Solved using Molecular Dynamics simulations with massively parallelized computation: distributed dynamics with Solved using Molecular Dynamics simulations with massively parallelized computation: distributed dynamics with

2. Protein Quaternary Structures

Levels of protein structure Primary Secondary Tertiary Quaternary

Quaternary structure Quaternary structure refers to the organization and arrangement of subunits in a protein with multiple subunits Same physical forces involved than in intramolecular interactions in monomeric proteins (also disulfides, metal coordination...)

Quaternary structure Can have more than two subunits Can have more than two subunits Subunits are individual polypeptides Subunits are individual polypeptides Pyruvate dehydrogenase complex: 60 subunits!

The flagella assembly of Salmonella sp.