Self-Templated Nucleation in Peptide and Protein aggregation

0.4 MB·English

by  Stefan Auer

Self-templated nucleation in peptide and protein aggregation
Stefan Auer,1 Christopher M. Dobson,2 Michele Vendruscolo,2 and Amos Maritan3
1Centre for Self Organising Molecular Systems, University of Leeds, Leeds LS2 9JT, United Kingdom
2Department of Chemistry, University of Cambridge,
Lensfield Road, Cambridge CB2 1EW, United Kingdom
3Dipartimento di Fisica, Universit´a di Padova, INFN and CNISM, Via Marzolo 8, 35131 Padova,Italy
(Dated: January 13, 2009)
Peptides and proteins exhibit a common tendency to assemble into highly ordered fibrillar ag-
gregates, whose formation proceeds in a nucleation-dependent manner that is often preceded by
the formation of disordered oligomeric assemblies. This process has received much attention be-
cause disordered oligomeric aggregates have been associatedwith neurodegenerative disorders such
as Alzheimer’s and Parkinson’s diseases. Here we describe a self-templated nucleation mechanism
thatdeterminesthetransitionbetweentheinitialcondensationofpolypeptidechainsintodisordered
assembliesandtheirreorderingintofibrillarstructures. Theresultsthatwepresentshowthatatthe
molecularlevelthistransitionisduetotheabilityofpolypeptidechainstoreorderwithinoligomers
into fibrillar assemblies whose surfaces act as templates that stabilise the disordered assemblies.
9
0 Thereare two fundamentalquestions that onecan ask helices and β-sheets [4], and a wide range of different
0
about the general phenomenon of formation of ordered proteins can assemble into highly ordered fibrillar aggre-
2
structures by atoms and molecules. The first concerns gates [5]. Although the amino acid sequences of these

n the type of assembly that the given particles can form, proteins are often unrelated, the structures of amyloid
a
andthesecondthekineticpathsthattheparticlesfollow fibrils show a common characteristic cross-β structure in
J
in order to reach a stable structure. The answer to the which themainaxis ofindividualmolecules runsorthog-
3
firstquestion, atleastinthecaseswhentheparticlesare onal to the direction of the filaments. It has thus been
1
rigid,isthatinnaturethereexistsonlyasmallnumberof suggested that the inherent ability to form fibrillar as-

] possiblecrystalstructures,correspondingtothe230crys- semblies is a feature common to polypeptide chains [6].
M
tallographic space groups [1]. The extraordinary power
B of this result, which is based on symmetry and geome- In order to explain why this process takes place de-
. try arguments, is that the answer is independent of the spite the remarkable resistance of native states of pro-
o
i specific particles and of their mutual interactions. The teins to aggregation, a “nucleated conformational con-
b specific particle properties merely determine which type version” mechanism has been proposed in which the for-
-
q ofcrystalstructureisthemoststable. Theanswertothe mation of highly dynamic oligomeric assemblies facili-
[ second question is generally more difficult, and involves tates the further conversion of polypeptide chains into

a nucleation and growth mechanism [2]. In this mech- ordered fibrillar structures [7]. Evidence in favour of
1
v anism the atoms first need to come together to form a this mechanism has been provided through experimental
6 critical nucleus (nucleation phase), before they can grow [8, 9, 10] and theoretical studies [11, 12, 13, 14, 15, 16].
4 (elongation phase). The probability Pc that a sponta- In this work we exploit the ability of computer simu-
8 neousfluctuationwillresultintheformationofacritical lations to provide a description of molecular process at
1
. nucleus depends exponentially on the free energy ∆Fc very high resolution - an ability that has proven invalu-
1 required to form such a nucleus: Pc = exp(−∆Fc/kT), able in defining nucleation processes in atomic and col-
0
where T is the absolute temperature and k is the Boltz- loidal systems [3, 17]. In the case of polypeptide chains
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mannconstant. Inatomicsystemstheactivationbarriers we have recently shown that it is possible to follow the
0
: are usually very high, and the probability of observing aggregation process on a time long enough to include
v
nuclei is very small; even when they form, their lifetime both the initial condensation into disordered oligomeric
i
X is fleetingly short, so that up to now there is no clear assemblies and their subsequent reorganisation into fib-
r experimental observation of critical nuclei in atomic sys- rillar structures [18], and that the nucleated conforma-
a tems, and computer simulations have become a major tional conversion mechanism can also be described as
tool to investigate this phenomenon [3]. a “condensation-reordering” mechanism (Fig. 1). Here
An additional problem arises when the particles form- we investigate a self-templated nucleation mechanism,
ingtheorderedstructuresarenotrigid,butflexible,asis which determines the coupling between the assembly of
the case of peptides and proteins. Individual molecules polypeptidechainsindisorderedoligomersandthetrans-
of this type have often an intrinsic tendency to fold into formationintohighlyorderedcross-β structures. Atem-
ordered structural patterns, which may either favour or plate model by which misfolded prions induce the con-
hindertheirintermolecularassemblyprocess. Thisprob- version of nearby native prions to the misfolded state
lem constitutes an entirely new chapter in the study has already been proposed [19], and described for SH3
of ordering that has very great significance for biology [20] and ccβ [21]. In particular, in the latter case it was
and biotechnology. Indeed biomolecules such as DNA shown that β-sheets with exposed hydrophobic surfaces
and proteins have recurrent structural motifs such as α- and unsaturated hydrogen bonds accelerate the conver-
2
(a) have been shown experimentally to form amyloid assem-
blies. Inalloursimulationstheenergyofhydrogenbonds
was set to e = −3kT , a value close to experiments
HB o
(1.5kCal/mol at room temperature [29]). Here kT is a
o
referencethermalenergyandthereducedtemperatureis
T∗ = T/T . The hydrophobic and stiffness energy are
o
set to e = −0.15kT and e = 0.9kT respectively.
HP o S o
The ratio e /e = 20 is such that these interactions
HB HP
(b) provide similar contributions to the potential energy of
the oligomer. With this choice of parameter the pep-
tidesformanαhelicalnativestructurebelowthefolding
temperature T∗ ∼0.6, and a random coil above.
f
Inordertoillustratethecondensation-reorderingtran-
sition (Fig. 1) we set the peptide concentration to c =
12.5mM and the reduce temperature to T∗ = 0.66, to
FIG.1: Condensation-reorderingmechanismatc=12.5mM
keep the lag time prior to aggregation very short. Low-
and T∗ =0.66 above the folding temperature. Peptides that
ering the concentration, while keeping the temperature
do not form interchain hydrogen bonds are shown in blue,
those forming interchain hydrogen bonds are assigned a ran- constant, results in a dramatic increase of the lag time.
dom colour. Peptides within the same β-sheet are assigned At c = 1mM the peptides remain monomeric on the
thesamecolour. (a)Initially,att≤1000,thepeptidesarein timescale that we have been able to follow, although
amonomericstate(leftpanel). Theprogressvariabletisthe the aggregated state is likely to be much more stable
number of Monte Carlo moves performed in the simulation,
than the monomeric state. In this concentration regime
and one unit of t is a block of 105 Monte Carlo moves. As
(c = 1mM to c = 12.5mM) the monomeric state is
the simulation progresses, a hydrophobic collapse causes the
metastable with respect to the aggregated state, and the
formation of a small disordered oligomer (t = 15000, right
panel). (b) Enlarged view of a disordered oligomer which aggregation of polypeptide chains follows a nucleation
subsequentlyordersintoaprotofilamentstructure: t=15000 mechanism [30]. Under such conditions we calculated
(left), t=19000 (middle), t=30000 (right). thenucleationbarriersassociatedwiththecondensation-
reordering transition.
A prerequisite for such a calculation is the ability to
sion from native α-helices to β-sheets. describequantitativelytheformationofsmalloligomeric
The computational strategy that we follow is based assemblies. Byusingastandardclustercriterion,i.e. any
on the attempt to reproduce simultaneously two com- two peptides whose centre of mass distance is less than
mon aspects of proteins, their ability to form secondary 5˚A belong to the same oligomer, it is possible to define
structural motifs [22], and their propensity to form or- the oligomer size n, that corresponds to the number of
dered fibrillar aggregates [5]. Recently it has be shown peptides within the oligomer. At the same time it is
that motifs such as α helices, β sheets and cross-β struc- possible to measure the β-sheet content of the oligomer.
turesarenaturalformsofamarginallycompactphaseof As the formation of β-sheets is driven by interchain hy-
matter characteristic of flexible polymers [23, 24]. The drogen bonding, we use m, the number of interchain hy-
descriptionofproteinsintermsofflexibletubescaptures drogen bonds formed within an oligomer, as a structural
in a simple way the main symmetry of chain molecules. observable. In order to calculate the joint equilibrium
In this approach a polypeptide chain is represented by probability P(n,m) for the formation of an oligomeric
a C chain of finite thickness, which approximately en- assembly consisting of n peptides with m interchain hy-
α
velopsthebackboneatoms. Thehydrophobiceffectsdue drogen bonds we performed biased Monte Carlo simula-
to the water are considered by a pairwise additive inter- tions[17,18]inthecanonicalensembleusingcrankshaft,
action between different C atoms, with an energy e , pivot, reptation, rotation, and translation moves. As a
α HP
when they are close. The sequence independent defini- biasingpotentialweincludedanadditionalparabolicen-
tion for hydrogen bonding is obtained by an analysis of ergy term, W = α(m − m )2, in the energy function,
0
the geometric properties of hydrogen bond forming C whereαandm areparameters,thatcanbeusedtocon-
α 0
atoms from the Protein Data Bank and assigned an en- troltherangeofmvaluessampledinthesimulation. The
ergy e . Steric constraints due to side chains are im- calculationofP(n,m)wassplitinto28independentsim-
HB
posed by local bending stiffness with energy e (for a ulationsfordifferentm values,andfinallycombinedinto
S 0
detailed description of the model see [18, 25]). Based one by a multi-histogram technique. The corresponding
on the hypothesis that the formation of amyloid fibrils nucleation free-energy landscape, apart from an additive
is a common feature of all polypeptide chains, which de- constant,isgivenbyF(n,m)=−kT∗ln[P(n,m)].Arep-
pendsmainlyonthegenericpropertiesoftheirbackbone resentative calculation of such a free energy landscape
[26, 27], we investigated the behaviour of a representa- obtained at c = 1.2mM and T∗ = 0.51 (i.e. below T∗)
f
tive model system consisting of 80 weakly hydrophobic is shown in Fig. 2a. The succession of local minima in
12-residuehomopolymers. Systemsofhomopolymers[28] this landscape reveals the central result of this work -
3
(a) (b) 25
25
20
*
30 T
20 (0,4) (3,7) (5,8) 2205 (m) / k1105 n b =3 n b =6
1
F
15 5
15
n =8
10 b
n 00 10 20 30 40 50 60 70 80
5 m
10 0 (c) 20
*
5 (0,4) (1,5) (2,6) (3,7) (5,8) ) / kTmax1105 n b < 3n b < 4
m
(0,3) n,
0 (2 5
F
0 10 20 30 40 50 60 70 80
m 0
0 5 10 15 20 25
n
FIG. 2: (a) Contour plot of the nucleation barrier F(n,m) calculated at concentration c=1.2mM and reduced temperature
T∗ = 0.51, which is below the folding temperature. The black circles indicate the minima on the free energy surface, and
the black line indicates a possible path that connects them. The labels (n ,n ) of the minima describe the structure of the
α β
oligomer, where n and n are, respectively, the number of peptides in a α-helical and β-strand structure, and n=n +n .
α β α β
In the inset we show snapshots of the oligomers associated with the minima. (b) Nucleation barrier for β-sheet formation,
F (m),asafunctionofthenumberofinterchainhydrogenbondsmthatareformedwithintheoligomer. (c)Nucleationbarrier
1
F (n,m ) for the formation of an oligomer of size n that can at most form m interchain hydrogen bonds: m = 10
2 max max max
(n <3) (black line), m =20 (n <4) (red line), all m values included (green line).
β max β
the presence of a coupling between the oligomer size n β-sheetconformationcanformatmostteninterchainhy-
and the number of hydrogen bonds m in the states of drogen bonds with each other, each maximum of F (m)
1
minimal free energy for the oligomers. To clarify the na- corresponds to the addition of a new peptide to the ex-
ture of this coupling we analysed the structure of the isting β-sheet structure within the oligomer. After the
oligomers formed in the local minima of the free en- first few interchain hydrogen bonds are formed, the free
ergy landscape. As an example, we show in the inset energy decreases until an optimal number of hydrogen
of Fig. 2a that the oligomer corresponding to the mini- bondsisformed,correspondingtoalocalminimum. The
mum (n = 13,m = 68) consists of n = 8 peptides in elongation barrier for β-sheet nucleation corresponds to
β
a β sheet conformation and n = 5 in a helical confor- the free energy needed to transform a peptide from its
α
mation. Here we define two peptides to be part of a α-helical conformation to the extended structure it has
β-sheet if they form more than four interchain hydrogen in its β-sheet conformation. The elongation barrier is
bonds with each other. Since the peptides within the a quantitative measure for the aggregation propensities
oligomer are either in a α-helical or β-strand conforma- of proteins, andcanbe measured experimentally[27]. In
tion,n=n +n ,welabelledeachminimumbythepair ourcalculationadimerformedbytwoβ-strandsisalways
α β
(n ,n ). Typical configurations of other oligomers are unstableanddisassemblessoonafteritforms;thecritical
α β
also shown in the inset of Fig. 2a. We further analyse size of the β-sheet is a tetramer, at least in the range of
this coupling in Fig. 3, where we plot, for the states cor- concentrations and temperatures that we considered.
responding to the minima of the free energy, the number Next we investigated how the nucleation barrier for
nα of peptides in an α-helical conformation within an the formation of an oligomer depends on its internal
oligomer as a function of the number nβ of peptides in a structure, i.e. if a β-sheet is present or not. The
β-sheet conformation. The essentially linear relationship structural average over m is obtained by resorting to
indicatesthattheprobabilityofoligomericassembliesin- the marginal distribution function P(n,m ≤ m ) ≡
max
creases with the size of the ordered β-sheet structures. (cid:80)mmaxP(n,m) and the corresponding free-energy pro-
m=0
Torevealthemolecularbasisofthiscoupling, wehave file is given by F (n,m )=−kT∗lnP(n,m≤m ).
2 max max
analyzed the nucleation barrier for β-sheet formation in- Here F (n,m ) is the nucleation barrier for forming
2 max
dependentofthenumberofpeptidesinaα-helicalconfor- anoligomerofnpeptides, withatmostm interchain
max
mation. The average over n is achieved by the marginal- hydrogen bonds. This upper limit to the number of in-
isation of P(n,m) with respect to n, and its correspond- terchain hydrogen bonds is introduced in the projection
ing free-energy profile is F (m)=−kT∗ln[(cid:80) P(n,m)]. operation with the goal of unveiling the role of the β-
1 n
ThecalculationsindicatethatF (m)iscomprisedofase- sheet structure formed within the oligomer in the dy-
1
ries of component barriers, each separated by ∆m = 10 namical evolution of the aggregation process. If we do
(Fig.2b). Sinceeachpairofpeptidesconsideredhereina not allow the formation of β-sheets consisting of more
4
(a) 10 should lead to an increasing ability to modulate the
growth of peptide and protein aggregates, and it should
8
play an important role in the development of therapies
for conditions such as Alzheimer’s and Parkinson’s dis-
6
α
eases [31].
n
4 We thank A. Aggeli, E. Paci, P. Olmsted, and J. R.
Banavar for illuminating discussions. Corresponding au-
2 thors: [email protected] and [email protected]
0
2 3 4 5 6 7 8 9
n
β
(b)
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2
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