Comparative MD analysis of the stability of transthyretin providing insight into the fibrillation...

Comparative MD Analysis of the Stability of Transthyretin ProvidingInsight into the Fibrillation Mechanism

Jesper Sørensen,1,2,3,4,5 Donald Hamelberg,4,5,6 Birgit Schiøtt,1,2,3 J. Andrew McCammon4,5,61 Department of Chemistry, Aarhus University, Aarhus C, 8000, Denmark

2 Center for Insoluble Protein Structures (inSPIN), Aarhus University, Aarhus C 8000, Denmark

3 Interdisciplinary Nanoscience Center (iNano), Aarhus University, Aarhus C 8000, Denmark

4 Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, CA 92093-0365

5 Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, CA 92093-0365

6 Howard Hughes Medical Institute, University of California at San Diego, La Jolla, CA 92093-0365

Received 10 December 2006; revised 8 February 2007; accepted 13 February 2007

Published online 21 February 2007 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/bip.20705

This article was originally published online as an accepted

preprint. The ‘‘Published Online’’ date corresponds to the

preprint version. You can request a copy of the preprint by

emailing the Biopolymers editorial office at biopolymers@wiley.

com

INTRODUCTION

The unique ability of proteins to fold into sequence-

specific functional structures is a key element in all

life processes. When proteins misfold the outcome

can be insoluble aggregates. These aggregates, which

may take the form of amyloid fibrils, accumulate in

tissues or the extra cellular matrix of vital organs. They are

linked to a variety of diseases, some highly debilitating and

some even fatal. The diseases known to be caused or influ-

enced by amyloidogenic proteins among others are Alzhei-

mer’s disease, Type II diabetes mellitus, British familial de-

mentia, and senile systemic amyloidosis (SSA).1 To date, 20

proteins have been identified to have the ability to form these

fibrils. Although all of the fibrils have seemingly similar

ABSTRACT:

Proteins can misfold and aggregate, which is believed to

be the cause of a variety of diseases, affecting very diverse

organs in the body. Many questions about the nature of

aggregation and the proteins that are involved in these

events are still left unanswered. One of the proteins that

is known to form amyloids is transthyretin (TTR), the

secondary transporter of thyroxine, and transporter of

retinol-binding protein. Several experimental results have

helped to explain this aberrant behavior of TTR; however,

structural insights of the amyloidgenic process are still

lacking. Therefore, we have used all-atom MD simulation

and free energy calculations to study the initial phase of

this process. We have calculated the free energy changes of

the initial tetramer dissociation under different

conditions and in the presence of thyroxine. We show that

tetramer formation is indeed only thermodynamically

favorable in neutral pH conditions. We find that binding

of two thyroxine molecules stabilizes the complex, and

that this occurs with negative cooperativity. In addition to

the energetic calculations, we have also investigated the

dominant motions of the TTR and found that only the

dimeric form of the protein could undergo the initial

fibril formation. # 2007 Wiley Periodicals, Inc.

Biopolymers 86: 73–82, 2007.

Keywords: transthyretin; fibrils; amyloid; MD; MM-

PBSA; PCA

Comparative MD Analysis of the Stability of Transthyretin ProvidingInsight into the Fibrillation Mechanism

Correspondence to: Donald Hamelberg; e-mail: [email protected]

VVC 2007 Wiley Periodicals, Inc.

Biopolymers Volume 86 / Number 1 73

structural properties, the proteins from which these fibrils

are formed show no apparent homology. One of the interest-

ing things about amyloid formation is when and where in

the lifetime of a protein this process of misfolding occurs.

There are several sites where this erroneous event could

occur. Misfolding may occur during protein synthesis, during

the transport from the lumen of the endoplamatic reticulum

to the extra cellular space, in the quality control mechanism

of that transport, or perhaps in the extra cellular space or in

the specific tissues where the amyloids appear.2

Transthyretin (TTR) is one of the proteins that can assem-

ble into amyloid fibrils. TTR has been widely studied over

the years and has shown to be the cause of or involved in

SSA.1 Mutant variants of TTR are related to the more severe

illnesses familial amyloidotic polyneuropathy (FAP) and

familial amyloidotic cardiomyopathy (FAC). The pathologi-

cal aspects of the fibrils have not yet been discovered. It is still

unclear whether the amyloids are causing the diseases or if

they are an effect of them,1 although evidence points towards

them being the cause of the disease.3 Studies suggest that in-

termediate states during misfolding may be more cytotoxic

than the amyloid fibril itself.4 It has been shown through au-

topsy studies that 15–25% of the population over the age of

80 years show symptoms of SSA from wild-type TTR.5,6

Although this fact poses a problem as the lifetime of the

human population seems to increase, more disturbing is the

fact that the single-point mutations in the genetic variants

can make the disease much more aggressive and show onset

at a much earlier age, around 30–60 years depending on the

variant.7 Currently, 80 single-point mutations on TTR are

known.8 Of all the single-point mutations, only one shows a

nondisease effect, and even an inhibitory effect on other

point mutations, and that is the T119M mutant.9 Currently,

no clinical treatment for SSA is known, but FAP and FAC

can be cured through liver transplantation, as the majority of

TTR is produced in the liver.1

Since the aberrant nature of protein misfolding is not well

understood, we were prompted to investigate this process

using computational methods. Our investigation is of TTR

as there is already an abundance of experimental data avail-

able.10–13 We look at the stability of TTR in various settings

to determine what is necessary for initial phase of fibrillation.

The effects we investigate are changes in pH, effects of ligand

binding, and the effects of a mutation.

Dissociation Mechanism

TTR is a 55 kDa homotetramer, with each of the monomers

composed of 127 amino acids. The TTR monomers form

dimers by hydrogen bonding between the b-strands f and h

on one monomer (A) to the same strands on another mono-

mer (B) as shown in Figure 1. The dimer (AB) binds to

another dimer (CD), through mostly hydrophobic interac-

tions, resulting in the tetrameric form of TTR having a dimer

of dimers configuration.14 Until recently, the dissociation

mechanism was still speculative, but recent experimental

studies by Foss et al.10 have helped to clarify it. The suggested

mechanism is that the dimer AB dissociates from the dimer

CD (Figure 2). The mechanism was proposed based on ki-

netic measurements, and it clearly disproved other theories,

for example, that the AC dimer dissociating from the BD

dimer or the monomers dissociating one at the time,

although monomer exchange is possible.15 Whether the

dimers need to dissociate into monomers before fibrillation

can occur is still unclear. Mechanisms have been proposed

that require this dissociation before fibrillation can take

place.3,16 NMR studies of TTR by Yeates and coworkers13,17

have found flattening of the dimer and displacement of the

b-strands c and d, which they see as the requirement for the

fibrillation to occur, a mechanism they call ‘‘edge exposure.’’

A recent computational study by Yang et al.18 on the unfold-

ing mechanism of a TTR monomer agrees with the edge ex-

posure mechanism, but does not address possibility of this

mechanism in the dimeric form. Yeates and coworkers19 state

that dissociation to monomers is, to date, not a confirmed

requirement for fibril formation, because they have showed

that fibrillation is possible even when the monomers in the

dimers are cross-linked. We will present data that suggest

that dissociation to monomers is not a requirement.

FIGURE 1 The transthyretin dimer, showing the labeling of the

b-strands a to h in the A monomer. The b-strands are colored

respectively as blue (a), red (b), orange (c), green (d), pink (e), cyan

(f), purple (g), and lime (h) while the rest of the monomer is col-

ored yellow and the entire Bmonomer is colored white.

74 Sørensen et al.

Biopolymers DOI 10.1002/bip

The conditions necessary for tetramer dissociation in vivo

are thought to involve a change in the environment, and in

particular a change in pH.20 The endocytic pathway has been

suggested as a place of this pH change.1 Some studies have

shown that the rate-limiting step in the fibril formation is the

dissociation step from tetramer to monomer.3 One of the

points of our research has been to investigate the dissociation

process of tetramer to dimer in different environments. We

have simulated the wild-type tetramer in two different pH set-

tings: in neutral pH (nWT) and in a strongly acidic (aWT)

environment. In the latter case, all residues that could be

affected by such a pH change have been protonated, which

represents an extreme condition. As explained in the introduc-

tion, mutations also have an effect on the fibril formation and

we have therefore chosen to look at the most common muta-

tion, valine to methionine, at position 30. This mutant variant

has been simulated under the same conditions as with the

wild type, and the simulations will be referred to as nMUT

and aMUT for the neutral and acidic conditions, respectively.

Ligand Binding

TTR is a transport protein. It transports the small thyroid

hormone thyroxine (T4) (Figure 3). TTR acts as the primary

transporter in cerebral spinal fluid, and it is the secondary

carrier in blood plasma.8 Binding of T4 to TTR has been

shown to stabilize the tetramer and thereby prevent dissocia-

tion, and subsequent amyloid formation.3,15 TTR binds two

equivalents of T4. The binding site is at the hydrophobic

interface region between the two dimers AB and CD as

shown in Figure 2. It therefore requires all four monomers to

create the binding pockets. Experimental results show that

binding of T4 is favorable for both ligands because they both

increases the reaction barrier toward unfolding, which is also

the case for most other small molecules tested for binding.3

The binding occurs with negative cooperativity, as the change

in the binding free energy is larger for the first ligand.3 Sev-

eral studies aimed at finding a molecule that will act as an

agonist for TTR have been reported.3 The molecules, which

are being tested, are not supposed to inhibit T4 binding, but

simply prevent the TTR tetramer from dissociating. The

problem so far is finding a molecule that specifically targets

TTR, remembering that there are two other transport proteins

for T4, albumin, and thyroxine-binding-globulin, and further-

more, of these three transport proteins, TTR does not have the

highest affinity for T4.1,3 TTR is additionally the transporter

of retinol-binding-protein, but to our knowledge, this has not

been linked to tetramer dissociation and fibril formation, and

we have therefore not looked further into this issue.

MATERIALS AND METHODSAs a starting structure for our studies, we used the TTR X-ray crys-

tal structure with PDB ID: 2ROX21 from the RCSB Protein Data-

bank22,23 solved at a resolution of 2.0 A. Previously, Hornberg

et al.24 reviewed 23 TTR structures (2ROX included) and concluded

that the discrepancies between the structures were minor and not to

any extent crucial for MD simulations. The structure was missing

residues in the C-terminus end of monomer A and B (residues1–9,

128–136) as well as residues 253–254 in the N-terminus end of

monomer B. We have not inserted these residues as they are too far

away from the binding pocket to have an effect on the affinity of the

ligands, and the flexibility of these residues would only obscure the

principal component analysis (PCA). The XLEAP module in

AMBER 925 was used to solvate the protein and ligands. TIP3P26

water molecules were added within a distance of *8 A around the

protein in a periodic truncated octahedral box. In the dimer simula-

FIGURE 3 The hormone molecule, thyroxine.

FIGURE 2 The transthyretin tetramer shown here in a secondary

structure view, with two thyroxine molecules bound shown in ball

and stick. The AB dimer in red and the CD dimer in blue, L1 in

green, and L2 in orange.

Molecular Dynamics of Transthyretin 75


tions, around 8500 water molecules were added and around 15,000

were added in the tetramer simulations. The systems were neutral-

ized by adding either sodium or chloride ions. In the acidic environ-

ment, the residues Glu, Asp, and His were modeled as fully proto-

nated. In the mutant variants, we mutated the valine in position 30

on each monomer to methionine. We have performed MD simula-

tions on each of the above-mentioned structural variants of

TTR under different conditions for the amount of time shown on

Table I. We have also simulated T4 alone in neutral conditions. This

simulation has been carried out for 50 ns.

All simulations were run using NAMD27 with Duan and cow-

orkers’28,29 AMBER FF03 force field parameters. ANTECHAM-

BER30 was used to generate the force field parameters for the

ligands. To calculate the RESP partial charges, a quantum mechani-

cal optimization of the ligand was performed using Gaussian 0331 at

the HF/6-31G* level of theory. To simulate the neutral environment,

the deprotonated form of the carboxylic group of T4 was used to

calculate the parameters. We changed the iodine atoms on T4 to

bromines, since the basis set is not parameterized for atoms with

very high atomic numbers. We chose bromine as this resembles io-

dine well enough for these molecular mechanics calculations.

The initial solvated structures were relaxed by conjugate gradient

energy minimization in three steps of 5000 iterations each. The whole

of the protein was held fixed, except for the water and ions, in the first

round of minimization. In the second round, only the protein back-

bone was fixed, and finally everything, but the a-carbon atoms of the

protein, was free to move. After this initial relaxation, the system was

heated to 300 K by performing MD simulation for 10 ps with the a-carbons atoms of the protein held fixed. Finally, a 10-ps MD simula-

tion was run with no constraints to complete the equilibration phase.

We simulated the system in the isothermal–isobaric (NPT) en-

semble at 300 K and 1 atm. We used the Nose–Hoover Langevin pis-

ton pressure control32–35 to keep the pressure of the system con-

stant, with the piston target set to 1.01325 bars, the piston period at

200 fs, the piston decay set at 100 fs, and the piston temperature at

300 K. We have used Langevin dynamics to control the temperature

with the dampening coefficient set to 2 ps�1, but not affecting

hydrogens. Periodic boundary conditions were applied and all elec-

trostatic interactions were calculated using the Particle Mesh Ewald

(PME) method.36–38 A cutoff of 10 A was set, and switching was

turned on using a switching distance of 9 A and a pair list distance

of 11 A. All of the hydrogen–heteroatom bond distances were held

fixed using the SHAKE algorithm.39,40 The equations of motion

were integrated every 2 fs using the Velocity Verlet algorithm, and

snapshots were stored every 2 ps.

Free energy calculations were performed using the molecular

mechanics Poisson–Boltzmann solvent accessible surface area (MM-

PBSA) method.53 To perform these calculations, it was necessary to

remove water molecules and ions from the trajectories and this was

done using the Ptraj module in AMBER 9.25 The calculations were

done with the SANDER module in AMBER 9, where each snapshot

was calculated separately using a single-step minimization.25 We fol-

lowed the protocol of Luo and Tan41 as it is implemented in

AMBER 925 (see Ref. 103 in the AMBER 9 manual). All nonbonded

interactions were calculated with no cut-off distance. The Poisson–

Boltzmann equation was solved with the setting proposed by Luo

and Tan as this is optimized for TIP3P water. The dielectric constant

of the solvent was set to 80 and that for the solute was set to one.

The size of the probe for the PB energy grid was 1.6 A, which is also

the r value of the TIP3P water molecule.

The calculations of translational and rotational entropies were

performed using a method developed by Minh et al.,42 which freezes

one part of the protein structure and calculates the motions of the

other part with respect to the frozen part. To get a more correct

number, we held one dimer fixed and calculated the loss of transla-

tional and rotational entropies, and then held the other one fixed

and did the same thing; the average between these two numbers is

the value used in the free energy calculations. The flexible C-termini

residues were removed (residues 123–127, 252–254, 377–381, and

506–508) when performing the entropic calculations and the princi-

ple-component analysis.

RESULTS AND DISCUSSION

Protein Motions

PCA is a mathematical tool to identify patterns in datasets of

large dimensionality.43,44 Particularly, in this case, PCA is

used to analyze the large amplitude motions that are difficult

to visualize from a lengthy MD trajectory due to frequent

small amplitude motions. We have analyzed all of the trajec-

tories in a series of different ways. To compare all the data,

we stripped the trajectories of the tetramers down to the size

of the AB dimer so that they would be identical in the num-

ber of atoms to the dimer simulation. PCA was then per-

formed on the combined trajectory of length 4 3 32 ns. The

index of selectivity only includes the a-carbon atoms as we

are interested in conformational changes involving the back-

bone. It has been reported that the choice of index of selec-

tivity has a great influence on PCA44 and therefore we have

performed a scree test (scree plot) to determine how success-

ful the reduction in dimensionality is. The scree plot shows a

kink after the third eigenvector (data not shown), which

means that the data is highly correlated. To visualize the

dominant motions, we projected the first three eigenvectors

back onto each of the trajectories. We then looked at

Table I Overview of Simulated Structures

nWT (ns) aWT (ns) nMUT (ns) aMUT (ns)

Dim 32 20 20 20

Tw0 32 20 20 20

Tw1 32

Tw2 32

The different TTR systems simulated and the length of each simulation

under different conditions. Dim ¼ dimer, Tw0 ¼ tetramer without ligands,

Twl ¼ tetramer with one ligand, Tw2 ¼ tetramer with two ligand, nWT ¼wild type in neutral conditions, aWT ¼ wild type in acidic conditions,

nMUT ¼ V30M mutant in neutral conditions, and aMUT ¼ V30M mutant

in acidic conditions.

76 Sørensen et al.


two-dimensional (2D) plots of the trajectories to find the dif-

ferent conformations that were sampled. After analyzing

them separately, the plots were overlaid to compare the dif-

ferent simulations as shown in Figure 4.

It is striking to observe that the motion along the third

eigenvector, projected back onto the dimer simulation, sam-

ples an entirely different conformational space (Figure 4)

than in the tetramer. This prompted us to visualize the

motion in a molecular graphics program using VMD45 and

using Interactive Essential Dynamics46 to display the eigen-

vectors as shown in Figure 5. The motion that we see on the

dimer is the movement of the b-strands b, c, and d. The b

strand moves down towards to b-sheet double layer, and

aligns with the other b-strands. To do this, both the c and d

strands are pushed outwards. This conformational change

makes an almost flat b-sheet of strands b, c, e, and f.

This movement is consistent with the movement required

for the ‘‘edge exposure’’ model proposed by Yeates and co-

workers.13 The outward movement of the d strand can prob-

ably be seen when simulating the monomer alone also, as we

have seen in the dimer. To move the b strand, some confor-

mational changes in the loop between the a and b strands

(the ab-loop, residues 19–22 in monomer A and residues

146–149 in monomer B) are also necessary. When TTR is

in its tetrameric form, the ab-loop is interacting with the

ab-loop of the opposing monomer and therefore cannot

undergo the required conformational change. We have plot-

ted the root-mean-square-fluctuation of the nWT dimer and

the AB dimer of the tetramer of the nWT Tw0 simulation as

shown in Figure 6 (in this figure, it is residues 10–13 and

128–131, because of the residues missing in the crystal struc-

ture), and it is clear that in the tetrameric form the motion

FIGURE 4 Showing the projections off the first three eigenvectors from the combined nWT sim-

ulations back onto each nWT trajectory. The color dots show: black ¼ dim, red ¼ Tw0, green ¼Tw1, and blue ¼ Tw2. (a) Eigenvector one on the horizontal axis and eigenvector three on the verti-

cal axis. (b) Eigenvector two and three on the horizontal and vertical axis, respectively.

FIGURE 5 A porcupine plot in stereo showing the TTR dimer with cones signifying the third eigenvectors movements.



of the ab-loop is dampened. We also checked the nWT dimer

against the Tw1 and Tw2 simulations, and the only consistent

difference is the movement of the ab-loop. A recent MD

study by Yang et al.18 also saw the dislodging of the c and d

strands in the single-monomer simulations, but only in the

variant forms V30M and L55P. Their work was done with

implicit solvation and at higher temperatures to enhance

unfolding, so whether their results are comparable to our

study is uncertain. The unfolding motions, we have sampled,

will also likely be present in monomer simulations. What we

can definitively conclude is that the motion is only detected

when the dimer is simulated alone, which clearly suggests

that the tetramer has to dissociate before fibrillation. This

fact is known from experimental results, and this supports

the method employed here as the results are consistent with

those from laboratory experiments.

The next analysis is of the trajectories from the variant

simulations (aWT, nMUT, aMUT). We combined all the

sampled trajectories (4 3 32 ns + 6 3 20 ns) and found the

eigenvectors. The first and second eigenvectors were then

projected back onto the trajectories of the dimers. The plots

from each of these were then overlaid and are shown in Fig-

ure 7. From this figure, it is clear that the acidic and neutral

structures sample different parts of the phase space, strongly

suggesting that there is an effect from the change in environ-

ment going from neutral to acidic.

Energy Calculations

To calculate the free energies of tetramer dissociation and

ligand binding, we have employed MM-PBSA ensemble

energy calculations for the internal energies and solvation-

free energies.53,47 The free energy between different states

does not reveal anything about the kinetics of the reaction

(such as activation barrier). All it reveals is whether the reac-

tion going from one state to another is thermodynamically

favorable or not. From these results, it is possible to discern

whether a reaction seems thermodynamically probable, but

without knowing the kinetics of the reaction it is only sug-

gestive. For all the energy calculations, we have used the reac-

tion scheme shown in Figure 8. For all the variants, we have

calculated the dimer association, and for the nWT case, we

have also investigated the effects of ligand binding.

FIGURE 6 The top panels shows the root-mean-square-fluctuation

of each residue of the AB dimer, from the Dim (solid) and Tw0

(dotted) simulations, each of 32 ns. The lower panel shows the percent-

age difference of each residue between the Dim and Tw0 simulations.

FIGURE 7 Showing the projections of the first and second eigen-

vectors from the combined simulations back onto each of the dimer

trajectories. The color dots show: black ¼ nWT, red ¼ aWT, green

¼ nMUT, and blue ¼ aMUT.

FIGURE 8 The reactions for which we calculate the energies.

78 Sørensen et al.


Entropy Loss

We have employed the method by Minh et al.42 that uses the

quasi-harmonic oscillator approach to calculate the loss of

rotational and translational entropies. This approach has pre-

viously been used to calculate the loss of entropy from ligand

binding.48–50 The quasi-harmonic approach has been

criticized regarding the validity of the approximation that a

single Gaussian can be used to describe the sampled confor-

mations.51 We have therefore, as in the original article, also

calculated the entropic loss using both a single- and a dou-

ble-Gaussian to describe the distribution. The difference

between the methods is that the double-Gaussian consis-

tently finds an entropic loss of about 1–2 cal/mol K less,

which when compared with the internal energies is such a

small number that the extra time spent on the calculations

cannot be justified. In these calculations, we have assumed

that a dimer- and the ligand-simulated alone has free rota-

tion and translation, and we have calculated the loss due to

tetramer formation and ligand binding. It could be argued

that we should assume the monomers as free and then calcu-

late the loss for association to dimers, but we speculate that

dimer formation is a process-occurring during protein fold-

ing and thus we have left this step out of our reaction

scheme. An important concern of entropy calculations is

whether they have converged. Throughout the simulation,

we have calculated the entropic convergence to estimate

when we have collected enough sampling data. Figure 9

shows the convergence for the combined translational and

rotational entropies during the entire simulation. These data

show that the entropies tend to converge after *20 ns. There

are still some small fluctuations, but these are within 1 cal/

mol K. To explore what caused these fluctuations, we split

the translational and rotational energies and plotted their

convergence. The translational entropy converges rather

quickly (*10 ns), and the rotational entropy converges after

around 20 ns, where after there are still small fluctuations.

The results for the nWT loss of translational and rota-

tional entropy are shown in Table II. The results make sense

in that the loss of translational and rotational entropies was

greatest for tetramer formation. Indeed, the net result for

this contribution (TDS & �11.3 kcal/mol) is similar to that

from the dimerization of the FAS2 and ACHE proteins (TDS& �9.0 kcal/mol).42 Results also show that binding of the

first ligand compared to the second gives a greater loss in en-

tropy.

Internal and Solvation Energies

The final step in these free energy calculations is the calcula-

tion of the internal energy of the system, which includes the

solvation free energy. This step has been calculated using the

MM-PBSA methodology as implemented in AMBER 9.25

This method has previously been used on a variety of differ-

ent protein systems.52 The energies were calculated for each

snapshot of the sampled trajectories. Therefore, the energies

reported are the average energies over the ensemble of snap-

shots. The method used was the one-trajectory approach.

The one-trajectory approach involves calculating the energy

from the entire complex and then extracting the different

components of the complex, and calculating the energies

from these parts alone. Originally, this way would be helpful

in that it involves less MD simulation, which is very cost effi-

cient; but in our case, we have had to simulate the compo-

nents alone for use in the PCA, so we did not gain anything

from this effect. Another advantage of the one-trajectory

approach is that it cancels the inherent error in the energy

calculation due to energetic drift during the simulation.47

Last, the only assumption that is required for the calculation

to be valid is that the ligand-binding site remains largely unal-

tered throughout the simulations.48 From visual inspection,

FIGURE 9 The convergence of the translational and rotational

entropy of each of the dimers from nWT simulations. The colors are

as follows: black ¼ Tw0-dimerAB, red ¼ Tw0-dimerCD, green ¼Tw1-dimerAB, blue ¼ Tw1-dimerCD, purple ¼ Tw2-dimerAB, and

orange ¼ Tw2-dimerCD.

Table II Overview of the Free Energy Calculation of nWT

Process Entropy Lossa Internal Energy DG b

Step 1 �37.6 �60.8 6 5.0 �49.5 6 5.0

Step 2 �29.5 �31.76 3.5 �22.9 6 3.5

Step 3 �20.1 �20.06 3.7 �14.0 6 3.7

Each column depicts the different contributions to the free energy, which

is in the last column, of the processes shown in Figure 8. The unit of entropy

is cal/mol K, while that of internal energy and DG is kcal/mol.a Only translational and rotational entropy.b Not including configurational entropy.



this last requirement seems to be upheld throughout all our

simulations. The results from these calculations are shown in

Table II. These results show that dimer association is greatly

stabilized from nonbonding interactions at the interface

between the dimers. The error values included are the stand-

ard errors from the ensemble average calculations.

Gibbs Free Energies

In calculating the Gibbs-free energies for the reactions of the

nWT simulations, we have combined the different contribu-

tions as shown in Table II. The temperature is set to 300 K

for the calculations. The standard error included is the lower

bound of the error, as we have not calculated the errors from

the entropic contribution. The results show that the tetramer

formation is a favorable process, as it is known to be from

experiments. Binding of the two thyroxine molecules is also a

favorable process. Here, it is shown that the binding of the

ligands is negatively cooperative, meaning that the second

ligand does not bind as strongly as the first. The binding

results do not tell us anything about the kinetics of the reac-

tion and whether or not reactions actually do occur is to be

determined through further experiments/simulations. Our

results, although lacking the contribution from the configu-

rational entropy, are in line with experimental results.3

The same procedures were employed to calculate free

energies for the TTR variant simulations. The results for tet-

ramer formation of the variants are presented in Table III.

Again the standard error included is the lower bound of the

error. The results show that changing the pH environment

has a great effect on the energy of the tetramer formation, as

it becomes very unfavorable. These calculated values are

quite unfavorable; this is due to a major change in the proto-

nation state in the acidic environment. We chose to proton-

ate all residues affected by a large drop in pH, which involves

around 76 residues in total. The MM-PBSA calculations are

sensitive to changes in the electrostatic environment and so

these values, although they seem high, should be correct. It is

unlikely that the pH will drop to such a level in vivo, but for

a theoretical purpose, this sets an upper bound of what the

energies will be under such conditions. Our results also show

that tetramer formation is not affected by the V30M muta-

tion in neutral environment, as the free energy change associ-

ated with tetramer formation is similar to that of the nWT.

This result is a little surprising, but it suggests that it is not

the stability of the tetramer that is affected by the mutation;

instead it indicates that it is the reaction barrier that is low-

ered for the dissociation to occur at a faster rate, as has been

shown in experiments.1

CONCLUSIONS AND OUTLOOKIn this study, we have examined the dissociation mechanism

of TTR using MD simulations. We have reported trajectories

of a total of 248 ns in length. The simulations have varied in

pH and genetic variants and have not only been of the tet-

ramer with zero, one, or two ligands, but the dimer alone as

well. Our investigation of the protein motions has revealed

the initial motions toward fibrillation only for the dimer

simulation, which is in line with previous studies.13,16 We are

questioning whether or not the tetramer has to dissociate to

monomers as a requirement for fibrillation, as we see this

predicted motion in the dimer. However, recent studies have

concluded that these motions are also present in the mono-

mer form.18 It thus seems likely that TTR in its monomer

form may also form fibrils, but dissociation to monomers

might not be a requirement for fibril formation.

Another part of our study was to investigate the free

energy change between the different states. It is known that

tetramer formation is favorable and this is exactly what we

see from the simulation of the WT in neutral environment.

We also see that tetramer formation for the genetic variant

V30M is just as favorable, which suggest that the faster rate

of tetramer dissociation, which has been seen in experiments,

then must solely come from a lowering of the energy of the

transition state. Changing the environment to strongly acidic

on the other hand makes tetramer formation very unfavora-

ble, which is in line with previous experimental studies.1

We have calculated binding of the ligands as a two-step

process. Binding of both the two ligands is favorable. The

binding of the ligands occurs with negative cooperativity,

meaning that the free energy change accompanied by binding

the first ligand is larger than the subsequent binding of the

second ligand, which has previously been proven in experi-

ments.3 There are still many questions left to answer with

regards to amyloid formation of TTR. Here, we have given

an insight into the initiation of the fibrillation process. Fur-

ther energy calculations on other variants could also be in-

triguing, e.g., the most lethal variant, L55P, or the nonamy-

loid forming variant, T119M. Studies of TTR in a variety of

Table III Free Energies of Formation of the TTR Tetramer in

Different Environments

Process nWT aWT nMUT aMUT

DGa (step 1) �49.56 5.0 +191.96 6.1 �49.8 6 6.7 +130.0 6 7.5

Free energies of formation of TTR (step 1 in figure 8) under different

conditions in kcal/mol.a Not including configurational entropy.

80 Sørensen et al.


pH environments from neutral to our very acidic condition

could be very interesting.

We thank D. D. L. Minh for providing the program to calculate the

translational and rotational entropies and for discussion of the

results, Dr. J. Gullingsrud for discussions and help with setup of the

simulations and Dr. T. Jain for helpful discussions of the configura-

tional entropies. We gratefully acknowledge support from NSF,

NIH, CTBP, NBCR, and SDSC. J. S. greatly appreciates Danske

Bank, the Faculty of Science at Aarhus University and the Hakon

Lund Foundation for financial support during his stay at UCSD. J.

S. is very thankful of Professor McCammon for allowing him to

come and work in his laboratory.

REFERENCES1. Sacchettini, J. C.; Kelly, J. W. Nat Rev Drug Disc 2002, 1, 267–

275.

2. Dobson, C. M. Trends Biochem Sci 1999, 23, 329–332.

3. Johnson, S. M.; Wiseman, R. L.; Sekijima, S.; Green, N. S.;

Adamski-Werner, S. L.; Kelly, J. W. Acc Chem Res 2005, 38,

911–921.

4. Klein, W. C.; Kraft, G. A.; Finch, C. E. Trends Neurosci 2001,

24, 219–224.

5. Cornwell, G. G., III; Murdoch, W. L.; Kyle, R. A.; Westermark,

P.; Pitkanen, P. Am J Med 1983, 75, 618–623.

6. Westermark, P.; Sletten, K.; Johansson, B.; Cornwell, G. G., III.

Proc Natl Acad Sci USA 1990, 87, 2843–2845.

7. Jacobson, D. R.; Pastore, R. D.; Yaghoubian, R.; Kane, I.; Gallo,

G.; Buck, F. S.; Buxbaum, J. N. N Engl J Med 1997, 336, 466–

473.

8. Jiang, X.; Buxbaum, J. N.; Kelly, J. W. Proc Natl Acad Sci USA

2001, 98, 14943–14948.

9. Hammerstrom, P.; Schneider, F.; Kelly, J. W. Science 2001, 293,

2459–2462.

10. Foss, T. R.; Wiseman, R. L.; Kelly, J. W. Biochemistry 2005, 44,

15525–15533.

11. Kelly, J. W. Structure 1997, 5, 595–600.

12. Kelly, J. W. Curr Opin Struct Biol 1998, 8, 101–106.

13. Serag, A. A.; Altenbach, C.; Gingery, M.; Hubbell, W. L.; Yeates,

T. O. Nat Struct Biol 2002, 9, 734–739.

14. Wiseman, R. L.; Powers, E. T.; Kelly, J. W. Biochemistry 2005,

44, 16612–16623.

15. Wiseman, R. L.; Green, N. S.; Kelly, J. W. Biochemistry 2005, 44,

9265–9274.

16. Kelly, J. W. Curr Opin Struct Biol 1996, 6, 11–17.

17. Laidman, J.; Forse, G. J.; Yeates T. O. Acc Chem Res 2006, 39,

576–583.

18. Yang, M.; Yordanov, B.; Levy, Y.; Bruschweiler, R.; Huo, S. Bio-

chemistry 2006, 45, 11992–12002.

19. Serag, A.; Altenbach, C.; Gingery, M.; Hubell, W. L.; Yeates, T.

O. Biochemistry 2001, 40, 9089–9096.

20. Lashuel, H. A.; Lai, Z.; Kelly, J. W. Biochemistry 1998, 37,

17851–17864.

21. Wojtczak, A.; Cody, V.; Luft, J.; Pangborn, W. Acta Crystallogr

D 1996, 52, 758.

22. Berman, H. M.; Westbrook, J.; Feng, Z.; Gilliland, G.; Bhat, T.

N.; Weissig, H.; Shindyalov, I. N.; Bourne, P. E. Nucleic Acids

Res 2000, 28, 235–242.

23. www.pdb.org.

24. Hornberg, A.; Eneqvist, T.; Olofsson, A.; Lundgren, E.; Sauer-

Eriksson, A. E. J Mol Biol 2000, 302, 649–669.

25. Case, D. A.; Darden, T. A.; Cheatham, T. E., III; Simmerling, C.

L.; Wang, J.; Duke, R. E.; Luo, R.; Merz, K. M.; Pearlman, D. A.;

Crowley, M.; Walker, R. C.; Zhang, W.; Wang, B.; Hayik, S.;

Roitberg, A.; Seabra, G.; Wong, K. F.; Paesani, F.; Wu, X.; Bro-

zell, S.; Tsui, V.; Gohlke, H.; Yang, L.; Tan, C.; Mongan, J.; Hor-

nak, V.; Cui, G.; Beroza, P.; Mathews, D. H.; Schafmeister, C.;

Ross, W. S.; Kollman, P. A. AMBER 9, University of California,

San Francisco, 2006.

26. Jorgensen, W. L.; Chandraserkhar, J.; Madura, J. D.; Impey, R.

W.; Klein, M. L. J Chem Phys 1983, 79, 926–935.

27. Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid,

E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kale, L.; Schulten, K. J

Comput Chem 2005, 26, 1781–1802.

28. Duan, Y.; Wu, C.; Chowdhury, S.; Lee, M. C.; Xiong, G.; Zhang,

W.; Yang, R.; Cieplak, P.; Luo, R.; Lee, T. J Comput Chem 2003,

24, 1999–2012.

29. Lee, M. C.; Duan, Y. Proteins 2004, 55, 620–634.

30. Wang, J.; Wang, W.; Kollman, P. A.; Case, D. A. J Mol Graph

Model, 2006, 25, 247–260.

31. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.;

Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven,

T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.;

Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.;

Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.;

Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.;

Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.;

Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo,

J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.;

Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Moro-

kuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzew-

ski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.;

Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.;

Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.;

Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.;

Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.;

Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.;

Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03,

Revision C. 02, Gaussian, Inc., Wallingford CT, 2004.

32. Hoover, W. G. Phys Rev A 1985, 31, 1695–1697.

33. Nose, S.; Klein, M. L. Mol Phys 1983, 50, 1055–1076.

34. Martyna, G. J.; Tobias, D. J.; Klein, M. L. J Chem Phys 1994,

101, 4177–4189.

35. Feller, S. E.; Zhang, Y.; Pastor, R. W.; Brooks, B. R. J Chem Phys

1995, 103, 4613–4621.

36. Ewald, P. Annalen der Physik 1921, 64, 253–287.

37. Darden, T.; York, D.; Pedersen, L. J Chem Phys 1993, 98, 10089–

10092.

38. York, D. M.; Wlodawer, A.; Pedersen, L. G.; Darden, T. A. Proc

Natl Acad Sci USA 1994, 91, 8715–8718.

39. Ryckaert, J. P.; Ciccotti, G.; Berendsen, H. J. C. J Comp Phys

1977, 23, 327–341.

40. Weinbach, Y.; Elber, R. J Comp Phys 2005, 209, 193–206.

41. Tan, C.; Luo, R. in preparation.

42. Minh, D. D. L.; Bui, J. M.; Chang, C.; Jain, T.; Swanson, J. M. J.;

McCammon, J. A. Biophys J 2005, 89, L25–L27.



43. Eriksson, L.; Johansson, E.; Kettaneh-Wold, N.; Wold, S. Multi-

and Megavariate Data Analysis: Principles and Applications;

Umetrics Academy, Umea, 2001; Chapter 2–3.

44. Stein, S. A. M.; Loccisano, A. E.; Firestine, S. M.; Evanseck, J. D.

Annu Rep Comp Chem 2006, 2, 233–261.

45. Humphrey, W.; Dalke, A.; Schulten, K. J Mol Graphics 1996, 14,

33–38.

46. Mongan, J. J Comp-Aided Mol Design 2004, 18, 433–

436.

47. Golhlke, H.; Case, D. A. J Comput Chem 2004, 25, 238–

250.

48. Swanson, J. M. J.; Henchman, R. H.; McCammon, J. A. Biophys

J 2004, 86, 67–74.

49. Luo, H.; Sharp, K. Proc Natl Acad Sci USA 2002, 99, 10399–

10409.

50. Carlsson, J.; Aqvist, J. J Phys Chem B 2005, 109, 6448–6456.

51. Chang, C.; Chen, W.; Gilson, M. K. J Chem Theory Comput

2005 1, 1017–1028.

52. Kollman, P. A.; Massova, I.; Reyes, C.; Kuhn, B.; Huo, S.; Chong,

L.; Lee, M.; Lee, T.; Duan, Y.; Wang, W.; Donini, O.; Cieplak, P.;

Srinivasan, J.; Case, D. A.; Cheatham, T. E., III. Acc Chem Res

2000, 33, 889–897.

53. Srinivasan, J.; Cheatham, T. E., III; Cieplak, P.; Kollman, P. A.;

Case, D. A. J Am Chem Soc 1998, 120, 9401–9409.

Reviewing Editor: Kenneth Breslauer

82 Sørensen et al.


Comparative MD analysis of the stability of transthyretin providing insight into the fibrillation...

Documents

Transcript of Comparative MD analysis of the stability of transthyretin providing insight into the fibrillation...