do proteins fold

1
do proteins fold ?
Why
Robert Glen Dmitry Nerukh
Rimini 2005
2
Proteins.

• (Some) Fold into complex 3-dimensional shapes
  that are reproducible
• Have amino acid sequences that combined with the
  dynamics of their motion in water implicitly
  contain information about their observed 3D
  structure
• By a dynamic process in solution, discover these
  folded forms efficiently (Levinthall paradox)
• What is peculiar about the dynamics of such
  protein sequences (good folders) how do they
  know how to fold ?

3
Protein dynamics

• Can be thought of as a system with emergent
  properties the structure we observe emerges
  from the dynamics of the protein in solution
• What we want to know what dynamic processes can
  we analyse that allow insight into the folding
  process, particularly the role of solvent?

4
Complex systems the property of emergence

• Seemingly random systems have the capacity to
  generate structured behaviour
• e.g. lots of ants that are similar, communicate
  locally, yet develop complex communities and
  these look surprisingly alike
• an ECG pattern from different hearts is similar
  yet is the result of many interacting cells - a
  complex rhythm develops
• The interaction between the units, each other
  and their environment is creating new information
• This emergent behaviour can now be quantified
  and analysed for our purposes, we can quantify
  the emergence of structure in a protein from
  dynamics

5
Examples of emergence in simple systems

• The software package StarLogo (from the Media
  Laboratory, MIT, Cambridge, Massachusetts, free)
  allows simple systems of self organisation to be
  constructed.
• A couple of examples.
• 1. Each turtle follows two simple rules (1) it
  tries to keep a certain distance from each of its
  two "neighbors", and (2) it gently "repels" the
  group as a whole, trying to move away from the
  other turtles. With these two rules, the turtles
  arrange themselves into a circle.
• 2. This project explores a simple ecosystem made
  up of rabbits and grass. The rabbits wander
  around randomly, and the grass grows randomly.
  When a rabbit bumps into some grass, it eats the
  grass and gains energy. If the rabbit gains
  enough energy, it reproduces. If it doesn't gain
  enough energy, it dies. The population of rabbits
  and grass develops an attractor predator/prey
  balance.

6
What do we do that is different ?

• Contemporary physics can measure order (e.g.
  temperature) or randomness (e.g. entropy,
  thermodynamics).
• There are no tools to address problems of
  innovation, or the discovery of patterns since
  there are no physical principles that define and
  dictate how to measure natural structure.
• Measuring the computational capabilities of the
  system is the only way to address such questions
• We utilise methods for discovering and
  quantifying emergence, pattern, information
  processing and memory capacity in quantitative
  units.

Nerukh D., Karvounis G., Glen R. Complexity of
classical dynamics of molecular systems Part
1. methodology. J. Chem. Phys. 117, 9618
(2002) Nerukh D., Karvounis G., Glen R.
Complexity of classical dynamics of molecular
systems Part 2. Finite statistical complexity of
a water-Na system. J. Chem. Phys. 117, 9611
(2002) Dmitry Nerukh, George Karvounis, and
Robert C. Glen, Quantifying the complexity of
chaos in multi-basin multidimensional dynamics of
molecular systems, Complexity, 10(2), 40-46
(2004)
7
How to quantify complexity

• We have used a method called computational
  mechanics (Crutchfield)
• An Information based method using computation
  theory (Shannon entropy and Kolmogorov
  complexity)
• Discovers dynamical patterns
• Emergence is computed from the ability of the
  system to process information which means.

J. P. Crutchfield and K. Young, Phys. Rev.
Lett., 63, 105 (1989)
8
What does it really do ?

• When analysing a trajectory from the past to the
  future, patterns emerge. To quantify the
  information in the system, we work out how
  complex a model is required given the past
  trajectory, to predict future trajectories the
  memory of the system bigger memory, bigger
  complexity
• This can be quantified by something called an
  e-machine
• Below, are two e-machines from transitions
  observed as a small peptide undergoes a
  conformational transition one analysis of the
  dynamics is obviously more complex than the
  other

9
How do we calculate complexity of real systems ?
Firstly, the dynamic trajectory (could be moments
of particles, dipole orientation of water etc.)
is converted from a time-based signal to a
symbolic sequence The we form equivalence
classes
00000Future with probability 0.1
01000Future with probability 0.7
Past01010
11101Future with probability 0.2
(Shannon entropy)
Calculating complexity
Where K is a number of equivalence classes,
P(Li) is a probability of the i equivalence class
We look at the probability of going from one
state to another, using the expectation
probability, called the surprise in
probability theory, and calculate the memory
requirements of an e-machine that would be
required to describe the process. This approach
is called computational mechanics (Crutchfield
et. al ). The finite statistical complexity is
calculated as
10
Why use complexity?

• You are probably familiar with a free energy
  funnel this is misleading its not 2D!
• The complexity approach is designed to quantify
  the self-organisation in dynamic systems which is
  multi-dimensional the funnel is also
  multi-dimensional and represents not so much an
  energy funnel, but a description of transitions
  that utilise quasi-periodic dynamics

Theodore L. Brown, Making Truth. The Roles of
Metaphor in Science
11
Calculating the complexity of real systems
How do we make sense out of this
oxygen atom motions from water close to the
protein trajectory
12
Trajectories, dynamics

• This is a cartoon of the global system
• In reality, its a High-dimensional phase space
• Our expectation was that in transitioning from
  one state to another, complexity would change
• Here we are talking about the change in the
  dynamic behaviour (could be the protein or
  solvent for example) of the system
• Like two guitar strings E moves differently
  from A.

13
What about an example of some simple molecular
dynamics showing different dynamic regimes e.g.
two water molecules going from chaotic to
quasi-periodic motion
14
2 waters
Initial conditions chaotic motion Evolve into
quasi-periodic motion This is an atractor, a
state into which the dynamic system approaches
having a single basin of attraction
15
2 waters
Change in dynamic regime
Orientation of Dipole
Oxygen Coordinates

• 6 degrees of freedom (for one molecule)

16
2 waters
Orientation of Dipole
Notice the change in Complexity of two hydrogen
atoms of a water molecule as the simulation
progresses and goes from chaotic to
quasi-periodic motion
17
Trajectories, dynamics

• Back to a cartoon of the global system
• Do the transitions happen in a similar
  concerted fashion, with a decrease in
  complexity of dynamics?

18
Looking at the complexity of a transition from an
extended conformation of a small peptide to form
a b-turn- Leu Enkephalin
19
leu-enkephalin X-ray structure
(Leu-enkephalin, Karle, I.L., Karle, J.,
Mastropaolo, D., Camerman, A., Camerman, N.
(1983) Acta Cryst., B39, 625-637.)
Enkephalins are Small molecule pentapeptides,
found in the brain, have opioid activity.
Tyr-Gly-Gly-Phe-(Leu/Met). From nmr data, some
structure is seen in solution. We were interested
in possible stabilisation of intermittent b-turn
motifs. Similations using Gromacs in explicit
water (SPC) revealed several turn-like events.
Water network dynamics at the critical moment of
a peptides b-turn formation a molecular dynamics
study. George Karvounis, Dmitry Nerukh and Robert
C. Glen, J. Chem. Phys. 2004, 121, 4925 .
20
b-turn form
open form
How does complexity change for the peptide and
for the water?
21
(No Transcript)
22
enkephalin
Formation of a b-turn
23
An example of peptide Dynamic regimes
An example of a transition (fast) from one
minimum to another for this dihedral angle
24
Complexity analysis of peptide/water molecules
during the folding event
turn event
turn event
Topological complexities of the peptides atoms.
The symbolisation alphabet of size 8 and history
length of 3 ps were used. The ?-turn transition
is at 1657 ps
Topological complexities of the waters atoms.
A symbolisation alphabet of size 32 and history
length of 4 ps were used. The ?-turn transition
is at 1657 ps
25
Topological complexities of the peptides atoms.
The symbolisation alphabet of size 8 and history
length of 3 ps were used. The ?-turn transition
is at 1657 ps
Topological complexities of the waters atoms.
A symbolisation alphabet of size 32 and history
length of 4 ps were used. The ?-turn transition
is at 1657 ps
26
Whats happening - ? The dynamics of the states
between the transitions is significantly chaotic
while at the moment of the transition it becomes
semi-chaotic or quasi-regular i.e. the system
can maintain approximate constants of motion and
possess fully deterministic dynamics. We
hypothesise that the effect is the manifestation
of this phenomenon. The low complexity value in
this case corresponds to less chaotic motion. As
a simplified illustration of the dynamics, the
transition can be visualised as passing through a
narrow tunnel connecting two states. In this
situation the phase-space flow should
straighten in order to be transferred from one
basin to the other. How tight is the tunnel ?
27
Sensitivity of folding transitions to small
perturbations of the solvent or peptide

• A larger system. Chignolin, 10 amino acids

GLY-TYR-ASP-PRO-GLU-THR-GLY-THR-TRP-GLY
Simulated for 1ns and transitions in conformation
analysed.
28
chignolin, showing a b-turn
nmr-structure 1UAO
29
Chignolin showing how a small perturbation
(lower) to the velocity of one atom prevents a
transition (upper)
Perturbation applied here transition
doesnt happen! This can be applied to a
water molecule 15? away from the peptide! So, the
tunnel is very tight. The whole system is in
concerted motion at this time
30
Conclusions

• Why proteins fold can be viewed as a phenomenon
  of the dynamics of the system
• Complexity analysis can provide a different
  perspective
• Folding transitions follow very tight concerted
  motions
• Small perturbations can disrupt transitions
  even up to 15? away.
• Caveat all the dynamics simulations were
  performed using Gromacs and the results are
  obviously subject to how accurately the
  methodology reflects protein dynamics.

31
Acknowledgements

• George Karvounis, Herman Berendsen, Makoto Taiji
• Unilever, the Newton Trust, the EPSRC.
• Gromacs
• H. J. C. Berendsen, D. van der Spoel and R. van
  Drunen, GROMACS A Message-passing Parallel
  Molecular Dynamics Implementation, Comp. Phys.
  Commun. , 91, 43-56 (1995) GROMOS W. R. P. Scott,
  P. H. Hunenberger , I. G. Tironi, A. E. Mark, S.
  R. Billeter, J. Fennen, A. E. Torda, T. Huber, P.
  Kruger, W. F. van Gunsteren, The GROMOS
  Biomolecular Simulation Program Package, J. Phys.
  Chem. A, 103, 3596-3607 (1999)

32
(No Transcript)
33
(No Transcript)