Tools for studying protein dynamics
The goal of this lecture is to frame protein dynamics in the conceptual framework of
protein conformational energy landscapes and to discuss the tools we can use to
determine the shape of these landscapes.
Charting conformational energy landscapes
As I pointed out during last class our understanding of protein dynamics and its role in
protein function is still in its early infancy. All tools currently available to the study of
protein dynamics have serious flaws. There is no single technique that allows us to get a
full picture of protein motion. In a way we are similar to early cartographers that
generated geographic maps by combining direct observations with indirect measurements
and educated guesses. For example, old cartographers used to judge the minimal size of a
landmass based on the size of rivers and the number and type of bird species they could
observe from their boats. If the rivers were big and land birds dominated, then the
cartographer would draw a very large land mass even though they had never actually set
foot on the land.
The protein dynamics equivalent of a perfect topographic map would be a perfect map of
the protein energy landscape. We are currently far from such a perfect map and so we are
stuck like the early explorers with rough sketches of energy landscapes that represent a
combination of experimental observations with a lot of conjecture. However, we know
that a protein energy landscape exists and that knowing its shape will tell us everything
there is to know about protein dynamics. So get used to thinking about protein dynamics
in terms of energy landscapes.
To get you started, here are three energy landscapes. What are the dynamic properties of
the molecules that posses these landscapes?
A
B
C
The energy landscape of molecule A is quite flat. There are many different local minima
that all have about the same energy and the barriers between them are rather small. As a
result molecule A would be quite “floppy” or “unstructured”; i.e. molecule A would not
have one dominant structure, but would rapidly exchange between many different
conformations in a diffusion-like manner.
The energy landscape of molecule B has one global energy minimum and this minimum
is much lower in energy than all other conformations. As a result in a population of typeB molecules the vast majority of molecules will adopt a very similar and well-defined
conformation. Most molecular motions of B will be restricted to small structural
fluctuations around the energy minimum. A population of molecule of type C will show
three sub populations of molecules with potentially significant differences in their
structure as well as their biological properties. Because the energy barriers between the
multiple minima are relatively large, the rate with which these populations exchange will
be quite slow.
Now that you are hopefully a little more comfortable with the concept of conformational
energy landscapes lets think about ways to determine the shape of these landscapes.
Two approaches to studying protein dynamics
There are basically two techniques for studying protein dynamics in bulk (i.e. using nonsingle-molecule techniques). One way is to study equilibrium dynamics. That is we look
at a population of molecules that explore a conformational energy landscape and this
energy landscape stays the same throughout the entire experiment.
The second approach is often referred to as the perturbation-relaxation approach. In this
technique we introduce a perturbation to our population of molecules that transiently
changes the shape of the conformational energy landscape. As a result we change the
distribution of molecules in our energy landscape. As we remove the perturbation, we can
now follow the process in which the distribution of conformations re-equilibrates to the
unperturbed state.
Techniques for studying protein dynamics
Below I will introduce two techniques, which have been used extensively to study
conformational energy landscapes of proteins. I will not have time to cover these
techniques in detail, so I will just give you a quick overview of these techniques.
Two other techniques, X-ray diffraction and NMR spectroscopy will receive their own
lectures.
Hole burning spectroscopy
The study of protein conformational energy landscapes has been dominated by one
protein and one experimental technique. The protein is myoglobin, the oxygen carrier in
your muscles, and the technique is hole burning spectroscopy. Outside this very specific
field, hole burning spectroscopy has not seen much use in the lifesciences, but the
technique is ideally suited to explain the idea of conformational energy landscapes so I
will spend some time explaining it to you.
The UV-visible absorption bands of light-absorbing ligands bound to protein molecules
–generally referred to as chromophores- are usually quite broad. The reason for this is
that the protein’s constant conformational fluctuations continuously alter the
chromphore’s molecular environment and thereby alter the energetic difference between
the chomophore’s electronic ground state and its electronically excited state. If a
particular conformational state the electronic ground state but disfavors the electronically
excited state, then the energy difference between the two electronic states is higher, so the
photon energy that promotes this transition will be greater and the absorption band will
be shifted towards the blue.
If this is unclear to you, you may want to go back and have a look at a book on UVvisible spectroscopy. The main thing you have to understand for hole-burning
spectroscopy is that conformational changes in the protein alter the molecular
environment of the chromophore and that these change in the chromophore’s molecular
environment cause a corresponding shift in its absorption spectrum. In other words the
absorption spectrum we observe for a solution containing many molecules is really the
sum of the absorption spectra contributed by a protein’s different conformational states.
Each energy minimum in the conformational energy landscape on the right corresponds
to a slightly different protein conformation providing a slightly different molecular
environment for the chromophore and therefore resulting in a slightly different absorption
spectrum. So the overall absorption spectrum reflects the conformational variability of
the conformational energy landscape.
Hole burning spectroscopy exploits this very close relationship between the absorption
spectrum and the conformational energy landscape.
By illuminating a sample with very intense light in a very narrow wavelength band we
deplete the population of molecules that adopt the specific conformational state that
dominates absorption the absorption spectrum at that wavelength. There are two physical
processes through which this depletion can be achieved. One way is that the energy
delivered by the photon provides the protein with enough kinetic energy to jump into a
different conformational sub state. The other mechanism is the selective photochemical
degradation of those chromophores that absorb at the wavelength with which we
illuminate the sample.
Either way the result will be a hole in the absorption spectrum –hence the name of the
technique. If we now leave the sample alone, the conformational states of the molecule
will re-equilibrate and the absorption spectrum will go back to its original shape – the
hole will disappear. It is important to realize that this equilibration process not only
involves those conformational states that neighbor the depleted state, but all
conformational states. By following the temperature dependence of the rate with which
the hole disappears we can then learn about the distribution of the heights of the energy
barriers that separates all conformational states of our system. The analysis of the
recovery kinetics is rather complicated, so I will not go into it here. Instead I will simply
mention the overall picture of conformational energy landscapes obtained from this
technique. Energy landscapes, according to the results of hole-burning experiments, are
hierarchical. Major conformational states, separated by high energy barriers, are each
comprised of a series of minor conformational states separated by smaller energy barriers
and these minor conformational states are in turn subdivided into conformational
substates separated by even smaller energy barriers and so on.
The main strength of the hole burning technique is that we probe the entire energy
landscape, so we get information of the system as a whole. At the same time, the fact that
we probe the entire landscape is also the major disadvantage of the technique. Certain
protein motions will certainly be more relevant for protein function than others. There are
probably networks of concerted motions similar to the networks of energetically coupled
residues revealed by Ranganathan and co-workers and discussed in a previous class. By
probing the whole system at once, our observations are probably dominated by the
generic –i.e. boring– motions of the bulk of the protein and prevent us from observing the
really interesting motions that shape a protein’s function.
Molecular dynamics simulations
Molecular dynamics simulation is an incredibly useful tool for the study of protein
dynamics, but keep in mind, they are simulations and to some degree you get back what
you put into your simulation.
The basic idea of molecular dynamics is to iteratively solve Newton’s equation of motion
for each atom in a molecule. To start we assign all atoms an initial, random velocity and
we then extrapolate where each of those atoms will be after a period of time Dt. We then
calculate what forces are acting on the atom in its new position and calculate the
acceleration the atom will experience as a result. We then let the atoms fly like a
Newtonian particle for another Dt. Below is the formula we would use to calculate the
location x of our atom at time t based on its starting location x0 its initial speed v0 and the
acceleration “a” it experiences. This acceleration can be calculated from the mass of the
atom and the positional gradient of the conformational energy.
1
x t = x 0 + v 0 ⋅ Dt + a ⋅ Dt 2
2
where
1 dE
a=m dx
With the starting location given by an experimental structure (for example a crystal
structure) and initial velocity given by the temperature all we need to calculate the
location of all our atoms after a given time interval Dt is the dependence of each atom’s
potential energy as a function of its x, y and z coordinates.
We can calculate this potential energy with the help of what is called a force field (though
“energy field” would be the more correct term). In mathematical terms a force field
might look like this:
†
E total =
ÂK
bonds
†
2
bond
(b - bequi. ) +
ÂK
angle
2
angle
(q - q equi. ) +
ÈA
B
qq ˘
K
ij
(1+ cos(nf - g )) +
Í 12
- ij6 + K coulomb. i j ˙
Â
D ⋅ rij ˙˚
rij
Î rij
dihedral 2
non- bonded pairs Í
Â
The total potential energy is the sum of a number of components. The first one is the
potential energy for the stretching of atomic bonds. If the distance between a given atom
and its bonded neighbor is shorter or longer than the ideal bond length then the bond will
push or pull on the atom i.e. accelerate it. The same is true for bond angles and dihedral
angels and of course for non-bonded interactions like van der Waals forces and
coulombic forces.
So how long can Dt be? Well, the Dt in this type of calculation has to be extremely short,
much shorter than the time it takes the atoms to travel their mean free path length of
about a tenth of an Ångstrom. If Dt were any longer, atoms would happily fly through one
another, bond-length would double or approach zero and other physically impossibilities
would occur. As a consequence we have to perform the calculation of the potential
energy function for each atom in our molecule once every femto-second or so. This
makes molecular dynamics simulations computationally costly. Remember we have to
perform this calculation for every atom in our molecule. Performing simulations that take
much longer than a few nanoseconds takes a long time even with the fastest available
computers. So the types of conformational changes that can be studied by molecular
dynamics simulations are very fast compared to conformational changes that can be
observed experimentally. Closing this gap between the timescales of protein motions that
can be studied experimentally and those that can be studied by simulation is one of the
central challenges for the study of protein dynamics.
Also when you use molecular dynamics simulations or use conclusions reached from
such simulations, remember that the potential energy function that are at the heart of
these simulations is only an approximation. For example we have to assume a dielectric
constant to calculate the coulombic term of the potential energy function. Getting this
constant right is quite difficult. We also have to include water molecules in our
simulation and currently there simply is no molecular model of water that describes all
water properties correctly.
To overcome these problems the researchers who have developed molecular dynamics
simulations have come up with a set of computational tricks and approximations and
tweaked the parameters used in their calculations to make their simulations selfconsistent. In other words parameters are adjusted until simulations correctly predict
certain experimentally measurable properties that can be derived from a molecule
dynamics simulation. However, self-consistent does not necessarily mean physically
correct. For example, when we compare different molecular dynamics force fields we
find that the parameters for atom diameters, bond-strength etc. differ substantially. So
take molecular dynamics simulations with a grain of salt, they are very useful, but they
are simulations.