Transcript Self-Organizing Bio

Self-Organizing Biostructures
NB2-2007
L.Duroux
Lecture 6
1. Protein Folding
(Proteins 2nd 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?
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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.
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.
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.
What causes mad cow?
To illustrate the concept of protein
folding we chose villin, a protein which
exists in the stomach and intestine of
animals (including homo sapiens).
Why do proteins fold?
What causes mad cow disease?
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Bovine epidemic in UK (1986): 170 000 cows died
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Symptoms: “mad”, aggressive, nervous,
spongiform encephalopathy
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Other examples: scrapie (sheep), CreutzfeldJacob Disease (humans)
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S. Prusiner (1982): Infectious agent are
“proteinaceous infectious particles” = prions
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Prions: proteins found in the nerve cells of all
mammals. Abnormally-shaped prions found in
BSE-infected cows
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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.
2.
Native
Infectious
Contamination: Ingestion / Genetics
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
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Villin headpiece sub-domain: a study
case
for
protein
folding
Villin’s function:
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structure to intestinal villi
stabilizes bundles of actin filaments
folds recognized by specific receptor point of actin filaments
Folding
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Simulated by distributed dynamics (Folding@home)
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.
The structure corresponds to the state with the lowest free
energy of the protein-solvent system. (Anfinsen’s dogma)
If we can calculate the energy of the system precisely, it is
possible to predict the structure of the protein!
Anfinsen experiment: Spontaneous
renaturation of Ribonuclease A
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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
3100 = 515377520732011331036461129765621272702107522001
≒ 5 x 1047
If 100 psec (10-10 sec) were required to convert from a conformation to
another one, a random search of all conformations would require
5 x 1047 x 10-10 sec ≒ 1.6 x 1030 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
Permeation of an ion in Porin
channel
Elastic vibrations of proteins
α-Helix folding
β-Hairpin folding
Bond stretching
Protein folding
10-15
10-12
10-9
10-6
10-3
100
(fs)
(ps)
(ns)
(μs)
(ms)
(s)
Time
Forces Involved in the Protein Folding
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Electrostatic interactions
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van der Waals interactions
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Hydrogen bonds
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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
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The next few slides show four different protein
folding mechanisms currently known
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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
Diffusion/Collision
•
First form secondary
structure by
diffusion/collision
•
Hierarchical: form helices &
hairpins, then microdomains,
decrease entropy
unfolded state
formation of
microdomains
diffusion and collision of
microdomains
native state
Nucleation
unfolded state
Nucleation
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Form nucleus of structure,
then grow (ala 1st order phase
transition)
formation of a
nucleus
native state
Collapse
Collapse first
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Hydrophobically driven:
remove water to form
hydrogen bonds
unfolded state
collapse
native state
Topomer search
unfolded state
Form rough native shape
first (topomer search)
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"topomer"
Find the right “topology”
first, then pack side chains
native state
Evolution will use any mechanism
that works!
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No single mechanism is observed, different
examples appear in nature
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Form secondary structure first (BBA5)
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Collapse first (protein G Hairpin)
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Hierarchical: form alpha-helices & beta-sheets
Hydrophobically driven: remove water to form
hydrogen bonds first
Form rough native shape first (Villin)
1c. Energetic
Considerations
Importance of kinetic factors during folding
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Observed folded conformation not necessarily
the most thermodynamically stable
Folded conformation = the most kinetically
accessible
Not necessarily a pathway to lowest potential
energy
Energy landscapes in protein folding
pathways
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Many paths lead to the lowest energy state that
represents the native protein.
Protein folding
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dictated by primary
structure
Multiple intermediate
steps
Important driving
forces:
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Hydrophobic effect
Hydrogen bonding
Van der Waals
Charge-charge
The pathways for protein folding
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On these pathways, the protein molecules would pass through welldefined partially structured states, some of which could be transient,
but others would be populated significantly
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Similar to Reaction of small molecules: specific pathway and small
region of conformational space, so Levinthal paradox is avoided
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Supported existence of partially folded intermediates formed both
during folding and under partially denaturing conditions
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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
Energy Surfaces, Energy Landscapes
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Based on A description of statistical ensembles and emphases the difference
between the folding reactions
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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
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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
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The enthalpies difference of the denatured and folded protein are on the order
of 30-100kcal/mol
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1eV=22.9kcal/mol=96.32kJ/mol~11560K;
H-bond 20kJ/mol
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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
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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.
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Observed for many protein under both
equilibrium and non-equilibrium
conditions.
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By contrast, for fast folding proteins
without intermediates, the search for a
core or nucleus is likely to be the ratedetermine step; once the core is formed,
folding to the native state is fast
A Unified Mechanism of Protein Folding?
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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
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The overall folding behavior can be changed drastically by relatively
small changes in the model parameter
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Simulations shows that:
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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 shortrange initiation and long range contacts lead to efficient folding. (In fact, helical protein
tend to fold faster than b 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
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
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1d. Molecular
Chaperones
A case of natural kinetic control in
protein folding
Molecular chaperones
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Increase the rate of correct
folding of nascent
polypeptide chains
Aid in the assembly of
multisubunit proteins
Protect proteins from
stress-induced damage (eg.
Heat shock)
Chaperonin
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GroEL/GroES
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Chaperonine from E. coli
Multisubunit protein comples
GroEL – cis and trans ring
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
GroES – dome like hectameric
ring
GroEL/GroES – assists only sa
subset of protein folding
these proteins contains /b
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:
d ri t 
2
mi
dt
2
 Fi t ,
(i  1, 2,  , N ).
(1)
Here, ri and mi represent the position and mass of atom i and Fi(t) is the force on
atom i at time t. Fi(t) is given by
Fi  iV r1 , r2 ,  , rN ,
(2)
where V（r1, r2, …, rN) is the potential energy of the system that depends on the
positions of the N atoms in the system. ∇i is
i  i



j
k
x
y
z
(3)
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,
 
 

1 
1 
2
3
4
ri t  t   ri t   ri t t  ri t t  ri t t  O t ,
2
6



1
1 
2
3
4
ri t  t   ri t   ri t t  ri t t  ri t t  O t .
2
6
The sum of two equations is

 
ri t  t   ri t  t   2ri t   ri t t  O t .
2
4
(4a)
(4b)
(5)
Using eq. (1), the following equation is obtained:
ri t  t   2ri t   ri t  t  
 
1
2
4
Fi t t  O t .
mi
(6)
We should calculate eq. (6) iteratively to obtain trajectories of atoms in the
system (Verlet algorithm).
Energy Functions used in Molecular
Simulation
Φ
r
Θ
Bond stretching
term
Angle bending
term
Vtotal 
Dihedral term
 K r  r    K       K 1  cosn   
2
b
2

0
bonds
angles
dihedrals
 Cij Dij 
 12  10  


 van der Waals
r
Hbonds rij
ij

 i , j pairs


H-bonding term
O
r
H

0
 Aij Bij 
qi q j
 12  6  
r
 electrosta tic r
r
ij
ij

 i , j pairs ij

Van der Waals term
r
The most
time
demanding
part.
Electrostatic
term
＋
r
ー
System for MD Simulations
Without water molecules
With water molecules
# of atoms: 304
# of atoms: 304 + 7,377 =
7,681
MD Requires Huge Computational Cost
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Time step of MD (Δt) is limited up to about 1 fsec (10-15 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 10-14 sec, are the fastest motions in the system for biomolecular
simulations, Δt is usually set to about 1 fsec.
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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
Permeation of an ion in Porin
channel
Elastic vibrations of proteins
α-Helix folding
β-Hairpin folding
Bond stretching
Protein folding
10-15
10-12
10-9
10-6
10-3
100
(fs)
(ps)
(ns)
(μs)
(ms)
(s)
MD
Time
It is still difficult to simulate a whole process of a protein folding using the
conventional MD method.
To perform MD simulations
parallelization is the key
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Special-purpose computer
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Calculation of non-bonded interactions is performed using the special
chip that is developed only for this purpose.
For example;
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MDM (Molecular Dynamics Machine) or MD-Grape: RIKEN
MD Engine: Taisho Pharmaceutical Co., and Fuji Xerox Co.
Parallelization
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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.
Brownian Dynamics (BD)
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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
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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
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BD method is suitable for long time simulation.
The folding of Villin headpiece
subdomain
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Solved using
Molecular Dynamics
simulations with
massively parallelized
computation:
distributed dynamics
with Folding@home
2. Protein Quaternary
Structures
Levels of protein structure
Primary
Secondary
Tertiary
Quaternary
Quaternary structure
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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
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Can have more than two
subunits
Subunits are individual
polypeptides
Pyruvate dehydrogenase complex:
60 subunits!
The flagella assembly of Salmonella
sp.