Computer simulations of amyloidosis


Malcolm McLean (Homepage)


Abstract


Some proteins form fibrillar structures known as amyloid. They are important theoretically as another stable conformation of protein, and medically as they are associated with a wide range of serious diseases. They are also an attractive target for computer modeling, because short peptides of tractable size will form fibrils in vitro. A single structure has been solved by crystallography, but generally fibrils will not crystallize. Oligomers, rather than mature fibrils, are probably the toxic species, and those of different sequence are sensitive to antibodies in common. Simulations have attempted to find structures for dimers and higher, but even the basic question of whether bonding is parallel or a mixture of parallel and anti-parallel is unresolved. Reduced representations and evolutionary search algorithms may potentially determine the gross stable low-energy conformations, full atom models have a role to play in refining the putative structures.


Introduction


Amyloid deposits are composed of long fibrils of protein, made of repeats of identical peptides, with a cross beta-sheet internal structure and a characteristic beaded appearance under atomic force microscopy (Figure 1). They are insoluble, and immune to attack by most if not all protein-degrading enzymes (see [1] for a partial exception). They are implicated in several human diseases, including Alzheimer's and Creutzfeldt-Jakob disease (CJD). These structures have attracted a lot of interest from computer modelers, both because of their medical importance, and because they represent a real system related to, but different from, the general protein-folding problem.


Amyloid fibrils are very difficult to crystallize, and currently we only have one crystal structure (Nelson, 2005 [2]). Since they are insoluble, they are also unsuitable for solution NMR. Solid-state NMR studies have been done [3-5], but they produce only constraints, not full coordinate sets. One goal of computer modeling is therefore to predict the structure. Just as important is to understand the physical forces that are holding the fibrils together, to help in rational drug design, and to understand the dynamics of fibril formation, because it may be intermediate oligomers rather than mature fibrils which are causing the medical problems in the degenerative brain disorders [6].









Figure 1. Fibrils of the SH3 domain, showing beaded characteristics. A is Atomic Force Microscopy, C an electron micrograph. The scale bar is 100nm. The apparently greater width of the fibril in A is an artifact of the imaging method. A cross-section profile for A is shown in panel B. (image from Chamberlain, 2000 [50] )















The History of Amyloid


The word “amyloid” was coined by Mathias Schlieden (1838) [7] from the Greek “amylon”, or “starch”, to describe the normal starchy constituents of plants. Rudolph Virchow (1854) [8] used the term to denote macroscopic human tissue abnormalities, including the corpora amylacea in the brain, and “lardaceous” deposits found in the liver, that stained blue with a solution of weak iodine and strong sulphuric acid. Virchow erroneously believed that he had demonstrated the existence of a cellulose-like material in vertebrates, important because biochemical theory of the time held that only plants could perform anabolis [9]. However Carl Friedreich and August Kekule (1856) showed that amyloid in the spleen is protein, now known to be the main constituent of all amyloid, except the corpora amylacea, which were indeed polyglucosan in character, and are not now termed “amyloid” [10]


Figure 2 An amyloid liver (bottom) compared with a normal liver (top) showing lardaceous deposits described by Virchow.

Image from

http://www.swissweb.ch/pathopic/e/getpic-fra.cfm?id=2857

(Labels switched on website.)


Some 70 years after Virchow's description, Divry and Florkin (1927) [11] recognized that the amyloid deposits showed apple-green birefringence when specimens stained with Congo red were viewed under polarized light.


With the advent of electron microscopy, Cohen and Calkins (1959) [12] first recognized that all forms of amyloidosis demonstrated a non-branching fibrillar structure. The base fibrils are approximately 60-130 angstroms thick, 1000-16,000 angstroms long. Eanes and Glenner (1968) [13] did the first X-ray diffraction studies, and determined that the structure was a repeated beta-sheet-like aggregation, with the beta strands perpendicular to the major axis of the fibril. The final milestone was when Nelson et al (2005) [2] produced the first high-resolution crystal structure of an amyloid fibril.


Amyloid deposits are implicated in several human diseases, including Alzheimer's disease, Parkinson's disease, type 2 diabetes, Creutzfeldt-Jakob disease, Huntington's disease, congestive heart failure, and dialysis-related amyloidosis (see table 1). Of great recent interest was the appearance of a transmissible form in British cattle, Bovine Spongiform Encephalitis (BSE). Amyloid fibrils also appear in yeast, where they appear to have an adaptive function [42]. Fowler (2006) [14] found an amyloid structure in mammals, which appears to synthesise melanin, the first non-pathological amyloid known in animals.


There is no agreed definition of amyloid [15]. Most proteins can be induced to form fibrils under very harsh, denaturing conditions [16]. Staining with Congo Red is used in clinical practice as the diagnostic, but the alpha-synuclein structures in the Lewy bodies, found in Parkinson's disease, are an exception, and do not always stain [17]. There are also many short artificial peptide sequences which are amyloidogenic under physiological type conditions (see table 2). However often pH has to be reduced to about 2 to enable fibrils to form in vitro.



Table 1 naturally-occuring amyloid proteins in humans



Amyloid Protein

Precursor

Systemic or Localised

Syndrome or involved tissues

AL

Immunoglobulin light chain

S, L

Primary Myeloma-associated

AH

Immunogloblin heavy chain

S, L

Primary Myeloma-associated

Ab2M

b2-microglobulin

S (L?)

Hemodialysis-associated (joints)

ATTR

Transthyretin

S (L?)

Familial Senile Systemic (Tenosynovium)

AA

(Apo)serum AA

S

Secondary, reactive

AApoAI

Apolipoprotein AI

S, L

Familial, Aorta

AApoAII

Apolipoprotein AII

S

Familial

AApoAIV

Apolipoprotein AIV

S

Sporadic, associated with aging

AGel

Gelsolin

S

Familial (Finnish)

ALys

Lysozyme

S

Familial

AFib

Fibrinogen a-chain

S

Familial

ACys

Cystatin C

S

Familial

ABri

ABriPP

S

Familial dementia, British

ADan*

ADanPP

L

Familial dementia, Danish

Ab

Ab protein precursor

L

Alzheimer's disease, aging

APrp

Prion protein

L

Spongioform encephalopathies

ACal

(Pro)calcitonin

L

C-cell thyroid tumors

AIAPP

Islet amyloid polypeptide

L

Islets of Langerhans insulomas

AANF

Atrial natriuretic factor

L

Cardiac atria

APro

Prolactin

L

Aging pituitary prolactinomas

Alns

Insulin

L

latrogenic

AMed

Lactadherin

L

Senile aortic, media

AKer

Kerato-epithelin

L

Cornea, familial

ALac

Lactoferrin

L

Cornea

A(tbn)**

tbn

L

Odontogenic tumors





#Proteins are, when possible, listed according to relationship. Thus, apolipoproteins are grouped together, as are polypeptide hormones;

*ADan comes from the same gene as ABri; **A(tbn), to be named. The designation is waiting for a protein name.


(from Westermark [15] )



Table 2, Amyloidogenic short sequences




Sequence

Researcher

Details

STVIIE

de la Paz [41]

designed

GNNQQNY

Nelson [2], Lipfert [42]

Yeast prion

KLVFFAE

Oakley [33]

Alzheimer's

LMVGGVVIA

Oakley [33]

Alzheimer's

AGAAAGA

Oakley [33]

CJD prion

SIRELEXRIRELEXRIG

Kammerer [43]

X = Ala, Leu, Met

KLKLKLELELELG

Khurana [44]


EDVAVYYCHQYYS

Khurana [44]


NFLNCYVSGFH

Nishino [45]

Beta-2 microglobulin

KFFE

Mousseau [26] Melquiond [37] Tjernberg [46]

designed

KFFEAAAKKFFE

Makin [47]

designed

NHVTLSQ

Ivanova [48]

Beta-2 microgloblin

NFGIAL

Mousseau [26]

Islet

YTIAALLSPYS

Jarionec [49]

Transthyretin

CPLMVKVLDA

Chamberlain [50]

Transthyretin




Outstanding issues


Amyloidogenic peptides are of tractable size; one sequence (KFFE) is only four residues long.


Some of the natural amyloids are also small, for instance Alzheimer's ABeta is 42 residues long. However since amyloid is a function of quaternary structure, several peptides are needed in the model. The sequence KLVFFAE, from the centre of the amyloidogenic sequence, may represent the core of the Alzheimer's amyloid fibril, the “amyloid stretch” hypothesis [18]. However the 40-residue sequence, missing the last two residues, is much less amyloidogenic than the 42. The two C terminal residues, isoleucine and alanine, are obviously playing some important role in the structure.


Amyloid fibrils do not form large crystals, and so cannot be solved crystallographically, except with the special narrow beam X-ray equipment used by Nelson [2]. Her structure, of the peptide GNNQQNY, from yeast sup35 prion protein , showed two beta sheets, made of parallel, in register peptides, which were held together with a very close interdigitation of side chains, excluding all water from the interface between the sheets (Figure 3). It is not known whether this is a general property of amyloid fibrils.



Figure 3 Nelson's [2] structure for GNNQQNY. Water, represented by corsses, is entirely excluded from the dry interface. The parallel beta sheets run perpendicular to the page.


When amyloid fibrils are formed with gentle agitation, the morphology is different to fibrils formed in quiescent peptides (figure 4). The differences then propagate to daughter fibrils, seeded with nuclei from the old [19]. Solid-state NMR studies (Gregory, 1998 [3], Balbach 2000 [4], Petkova 2006 [5]), produce only constraints, not full structures. The results tend to be contradictory – Gregory obtained parallel and Balbach anti-parallel structures for a similar Alzheimer's AB fragment, residues 10-35 and 16-22 respectively. It is possible that these researchers were working with fibrils of different morphology.

Figure 4 Alzheimers AB42 fibrils formed with no agitation (top) and gentle agitation (bottom).

From Petkova (2005) [19].



Aggregation is not the same as amyloid formation. Amyloid fibrils show a very clear, fibrous structure, whilst many proteins will simply aggregate in an amorphous mass. Most residues with a propensity form to amyloid also have a propensity to aggregate, however the amyloidogenic property is more sensitive to position, whilst most sequences of predominantly hydrophobic residues will aggregate [20]. The question is how to distinguish the early stages of amyloid from simple aggregation, given that the computer modeler can only include a few strands in his simulation.


Immunological studies may give us an answer to this. Kayed [21] discovered that antibodies to Alzheimers Abeta42 oligomers, which did not react with soluble, low molecular weight AB42, nor to the mature fibrils, also reacted to a wide range of other amyloid oligomers, including alpha synuclein, human insulin, lysozyme, prion protein, and polyglutamine. In each case, species below 8-mers, and mature fibrils, did not react. This tells us that the oligomers of a large number of types of amyloid have some commonality in structure, which the antibody is recognising.


Amyloid aggregation is therefore an attractive target for computer simulations. The problem is at about the limits of the capabilities of modern computers to handle, and there are many important questions which computer models can help us answer.


Box 1


Are all amyloid fibrils parallel, or are some anti-parallel?


Does the “amyloid stretch” from the core of the fibril?


Are dry interfaces between beta sheets a common characteristic of amyloid fibrils?


Why does morphology differ when fibrils are grown with agitiation?


What is the common element in amyloidogenic oligomers?


How does the mature fibril assemble?


Why are the oligomers toxic, and how can we prevent them from forming?




Computational tools


Homology modeling is impossible, because we have only one solved structure, and amyloidogenic sequences have no discernible homology anyway, so the problem must be tacked with ab initio methods. All current ab initio methods work by applying a forcefield to a proposed model. Commonly-used forcefields include AMBER [22], CHARMM [23], GROMOS [24] and OPLS [25].


A major issue for any forcefield is how to handle the solvent. Explicit solvent is expensive to model, and in fact we still don't have a good model of hydrogen bonding in water. Furthermore, steric clashes with solvent molecules can artificially frustrate the model, unless so many simulations are run that solvent effects average out. Implicit solvent avoids these problems, but means that hydrophobic effects, the dominant force in protein folding, are no longer based on physical fundamentals. The hydrogen bonds that the water forms with the protein are also modeled in a different way to protein to protein hydrogen bonds.


Full atom models run in O(N2) time, since each atom enters into a relationship with every other. By uniting hydrogens with the main atoms, runtime can be reduced disproportionately. Some forcefields go even further, by constraining atoms to lie on a lattice, and representing amino acid sidechains as beads. The OPEP (Optimised Potential for Efficient Peptide structure prediction) [26] represents all backbone atoms, but models side chains as a single bead. The Miyazawa-Jernigan [27] or MJ potential calculates empirical pairwise interactions between all 20 residue types, and is thus very simplified.


The RAFT forcefield [28] also sacrifices theoretical accuracy for speed. The protein backbone torsion angles are constrained to be within a set of six in Ramachandran space. Thus there is no need for a torsion term, all allowed torsions are equally favourable. The sidechains have no degrees of freedom, and are modelled by polar / non-polar spheres. The backbone is modelled by hydrogen donor / acceptor spheres, and a backbone sphere (Figure 5). Hydrogen donor and hydrogen acceptor spheres attempt to overlap, modelling hydrogen bonds, whilst non-polar spheres attempt to stick together, modelling hydrophobic effects. Despite its crudeness, the forcefield is quite good at representing local secondary structure [29].






Figure 5: The reduced representation of residues in the RAFT forcefield. The backbone spheres are green, the non-polar spheres blue, and the polar spheres red. Image from Gibbs N (PhD thesis, Bristol 2000)



Given a forcefield, the modeler can either trace the forces on the atoms through time, in molecular dynamics, or try to predict the lowest energy structure by searching conformational space.


Molecular dynamics requires time steps of around a femtosecond, meaning that simulations are confined to the order of a few nanoseonds to a microsecond. Amyloid fibrils aggregate in a few hours, so it is obviously impossible to trace the process of aggregation. However a proposed structure can be run through a molecular dynamics simulation, to assess whether it is stable.


The Levinthal [30] paradox states that a protein has 4.7 degrees of freedom per residue, obtained by modelling the peptide on a lattice. This gives an enormous number of states, 4.7^N, more than can be visited with the age of the universe for a modest-sized protein. The resolution is that the states are ordered. To find “Smith JS” in a telephone directory ranked by number, we need to read through on average half the entries. To find Smith in an alphabetically ordered directory, we simply do a binary search, eliminating half the entries on each access. The algorithm is thus O(log2 N) or for our problem O(log 4.7 ^ N), or O(N). Real proteins are not completely ordered, but not completely random either. Each free energy value has a strong correlation with the states to it, producing an “energy landscape”


If the lowest energy state is required, a good search strategy is simulated annealing [31]. A temperature t is steadily reduced, and mutants are accepted if either more favourable, or with the Metropolis [32] probability of exp(-diff/t). As a search strategy, it has the advantage that at higher temperatures the solution jumps out of local minima. Theoretically, it has the advantage that the Boltzmann distribution of the moves represents the real distribution of a molecule at a given temperature, assuming an unbiased move set.



Recent work on computer simulation of amyloid


Oakley (2005) [33] did a systematic evaluation of search alogithms on amyloidogenic peptides, using the MJ potential as the forcefield. He used Monte Carlo (constant temperature [32], Simulated Annealing [31], Replica Exchange (several parallel Monte Carlo runs at different temperatures, occasionally exchanging states,[34, 35]), Tabu search (do not revisit old conformations [36]), and a combined MonteCarlo / Tabu list search. The Replica Exchange method performed the best, with Simulated Annealing a close second. The Tabu search method seemed to be best at searching local areas of conformational space.


Mousseau (2005) [26] used a strategy called the activation-relaxation technique (ART). A local minimum is found by gradient descent, then a saddle point, representing the lowest intermediate ridge between two adjacent minima, is found. The conformation is then pushed to the new minimum, using the Metropolis criterion for acceptance.


Using the OPEP potential, Mousseau [26] predicted an anti-parallel structure for Alzheimer's AB16-22, with both in-register and out of register sheets. An alternating structure satisfied Balbach's (2000) [4] NMR constraints. They found a 6-chain barrel like structure for the fragment KFFE. In earlier work [37] they found that 4-chain sheets of KFFE form, but are not stable in a GROMOS forcefield with explicit solvent.


Gnanakaran (2006) [38] ran KLVFFAE under the AMBER forcefield in explicit solvent, at different temperatures. Dimers were found to have six energy basins, including in-register and out-of-register parallel and anti-parallel strands, and also cross conformations.


Lei (2006) [39] used the AMBER forcefield to investigate the formation of NHVTLSQ dimers, using molecular dynamics in explicit and implicit solvent. They found that an anti-parallel structure was most stable, but results were affected by the choice of solvent. The strands were restrained to be in Beta sheet conformation. When this restraint was removed, the peptides did not form beta strands within the runtime of the simulation.


Fernandez (2005) [40] ran Nelson's [2] structure under OPLS with explicit solvent, to try to determine the nature of the inter-sheet bonding. From visual inspection it would appear that the structure is held together by van der Waal's forces, and the exclusion of solvent. He found that the van der Waals forces between sheets were minimal, and did not contain the thermal energy. However the structure was stabilized by wrapped hydrogen bonds, that is, hydrogen bonds with non-polar groups within 6 Angstroms excluding solvent.


Future Directions


The basic question of whether fibrils are formed of parallel or anti-parallel cross-beta structures still has not been answered by simulations. However we know that amyloidogenic peptides have two forms, the native or folded state, and the amyloid. We also know that the amyloid fibrils themselves adopt different morphologies, given different conditions. Therefore it is not sufficient to produce a low-energy conformation, and declare it to be the structure. Methods that can find a series of metastable states are necessary.


A metastable state is one which is not the lowest in free energy, but from which there is no accessible pathway to a lower-energy structure. Therefore both the thermodynamic energy minimisation approach, to find the energy minima, and molecular dynamics, to see whether the structures are maintained, can be used. Unfortunately, starting a molecular dynamics run from a putative structure may tell us more about the forcefield than about the structure. The close interdigitation of sidechains in our one solved structure [2] is not something that is commonly seen in general proteins, and is thus not easy for a semi-empirical forcefield to model.


There is a tradeoff between the size of system that can be modeled and accuracy. Though initially it is useful to find putative structures of small peptide dimers and trimers, the basic unit of an amyloid fibril is somewhat larger, and is distinguished from aggregation by a fibrillar structure. With the exception of very short amyloidogenic peptides like KFFE, any feasible model must be simplified if we are to handle oligomers of eight peptides or higher. This can be done by adding restraints, or by using a reduced atom representation. For rational drug design of amyloid inhibitors, or of inhibitors of the oligomers, it will however be necessary to use a full atom representation. Thus the successful approach will probably use a reduced model to obtain the basic structure, and then refine it with a full atom model.


It is also important to attempt to falsify hypotheses. This may be done by predicting which peptide sequences will form amyloid and which will not, with the crucial requirement that the experimental observations are made after the computer model has been run.





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