A Condensation-Ordering Mechanism in Nanoparticle-Catalyzed Peptide Aggregation
[['With the advent of nanoscience much interest has arisen about the ways in which nanoparticles interact with biological systems , because of their potential applications in nanotechnology and effects on human health [1]–[7] .', 'When nanoparticles are introduced in a living organism they may interact with a variety of different cellular components with yet largely unknown pathological consequences .', "These concerns have been articulated particularly in the case of misfolding disorders with increasing evidence , for example , about an association between exposure to heavy metals and an enhanced risk of developing Parkinson's disease [8] .", 'Such misfolding diseases are caused by the aberrant association of peptides and proteins [9] , which result in fibrillar aggregates that share a common structure of intertwined layers of [9] .', 'Although is well known that such aggregates are formed in a nucleation-dependent manner [9] , [10] and that very often nucleation phenomena are known to be triggered by external factors [11] , experimental reports on protein aggregation in heterogeneous systems have only begun to emerge [12]–[15] .', 'These studies are important , since peptides and proteins in vivo often interact with a variety of potential seeding agents such as macromolecular complexes or membranes , which may strongly influence their aggregation behaviour .', 'Indeed , it is well known that colloids [12] , [14] , [15] , lipid bilayers [16] , and liquid-air , liquid-solid or liquid-liquid interfaces [17] , [18] can have significant effects in promoting amyloid formation .', 'It has also been recently shown that , in vivo , nanoparticles are often covered by peptides and proteins that determine their behaviour in the cell [13] , [15] .', 'Despite these observations , the detailed processes underlying the association of proteins on surfaces or nanoparticles have so far remained elusive .', 'In this work we use molecular dynamics simulations to investigate the molecular mechanism of peptide self-assembly in the presence of spherical nanoparticles .', 'Although computational studies using full atomistic models have provided considerable insight into the role of fundamental forces in promoting the self-assembly of polypeptide chains , they are restricted to relatively small systems of peptides and short timescales [19]–[29] .', 'Coarse-grained models have proven capable of following the evolution of systems composed of larger numbers of peptides over longer timescales .', 'The most tractable models are confined to a lattice [30]–[32] , although in these cases the structural details used to represent polypeptide chain conformations are necessarily limited .', 'Off-lattice protein models used to simulate protein aggregation include two-state models in which the protein can adopt , in addition to a native state , a state that is prone to formation [33] , [34] , two-bead models , in which each amino acid is represented by two spheres with a knowledge-based potential [35] , and fine-grained models with explicit representation of the side chains in combination with a phenomenological force field [36]–[39] .', 'The more detailed is the protein model , the higher is the computational cost and the larger is the number of parameters required to specify the force field [40] .', 'The studies mentioned above have investigated the process of protein self-assembly in homogeneous systems in which external factors such as nanoparticles or other molecules are absent .', 'Only very recently , Friedman et al . investigated the process of assembly of amphiphatic peptides in the presence of lipid vescicles [41] .', 'In the present work , we adopted an off-lattice protein model [42]–[45] , in which the protein backbone is represented as tube that embeds a chain of atoms subject to interactions that are common to all polypeptide chains , including excluded volume constraints , hydrophobic attractions , bending rigidity , and cooperative hydrogen bonds ( see Materials and Methods ) .', 'The major strength of the model is its ability to reproduce rather accurately secondary structure elements through the excluded-volume effects due to the tube geometry [42]–[45] , which enables the use of a relatively simple force field and thus is very efficient computationally .', 'By using this type of model , we already provided insight into the early stages of the aggregation process , to establish the existence of a general condensation-ordering transition for protein aggregation [46] , [47] , and to reveal a self-templated nucleation mechanism [48] that is able to explain a key feature observed in protein aggregation - the coupling between the initial formation of oligomeric assemblies and their subsequent rearrangement into a highly ordered structures .', 'In this work , we show the feasibility of simulating hundreds of peptides over several milliseconds , and we characterise in detail the molecular mechanism of self-assembly of the peptides at the surface of nanoparticles .', 'This process takes place in two steps - at first the peptides associate on the surface thus increasing their local concentration and subsequently they undergo a process of reordering into sheet structures , which is driven by the tendency to form hydrogen bonds .'], ['We have characterised the process of nanoparticle-catalysed peptide aggregation in terms of a condensation-ordering mechanism and investigated its dependence on the nanoparticle diameter and the strength of the nanoparticle-peptide interactions .', 'A similar mechanism of aggregation has already been observed in the absence of catalysing factors [46]–[48] , [52] , suggesting that the process of aggregation is driven in both cases by the intrinsic tendency of polypeptide chains to associate by forming ordered networks of hydrogen bonds [53] , [54] .', 'In the case that we have studied here , the initial condensation of peptides is initiated by nanoparticle surfaces to form small disordered oligomeric structures that subsequently re-order into as their size increases .', 'Although this mechanism will be modulated by specific sequence-dependent interactions for more complex amino acid sequences , our findings are consistent with recent experiments on seeded fibrillation [12] .', 'These results therefore suggest that the process of protein aggregation can be speeded up by the presence of factors capable of increasing the local concentration of proteins and thus promoting the formation of disorder oligomeric assemblies whose presence in turn facilitates the conversion of soluble proteins into highly ordered fibrillar structures .'], ['We used a modified version of the tube model [42] .', 'In this model , residues are represented by their atoms , which are connected into a chain with a distance of 3 . 8±0 . 2 Å between neighbouring atoms .', 'The tube geometry is approximated by assigning a diameter of 3 . 8 Å to the atoms .', 'Neighbouring atoms are not allowed to interpenetrate .', 'Bond angles are restricted between 82° to 148° , and an analogue of bending rigidity is introduced by means of an energetic penalty , , for values of bond angles lower than 107 . 15°; these are the same criteria used previously [42] .', 'The introduction of is useful to mimic the constraints placed on local conformations by the presence of side chains , as usually visualised by Ramachandran plot .', 'Hydrophobicity enters through a pairwise-additive interaction energy of ( positive or negative ) between any pair of residues and that approach closer than 7 . 5 Å .', 'The quasi-cylindrical symmetry of the tube is broken by the geometric requirements of hydrogen bonds .', 'These geometrical requirements were deduced from an analysis of 500 high resolution PDB native structures [55] , from which we computed the normalised histograms of distances between atoms involved in backbone-backbone hydrogen bonds which are shown in Fig . 4 .', 'The distances we used to define the hydrogen bonds at the atom level are summarised in Table 1 .', 'Our definitions distinguish between hydrogen bonds that belong to a helix , parallel or anti-parallel sheets .', 'We emphasise the fact that there is not a full correspondence with the real hydrogen bonds formed between amide and carboxyl backbone groups .', 'For instance , there are two different kinds of residue pairs facing each other in nearby anti-parallel .', 'In the first kind , the two hydrogen bonds are formed between the two residues , whereas in the second kind , no hydrogen bond is formed between them .', 'The two kinds alternate along the pair of nearby strands .', 'In our definition of hydrogen bonds based on atoms , we will say that for both kind of pairs one hydrogen bond is formed between the two .', 'Yet , we keep track of the peculiar geometry of hydrogen bonds within anti-parallel by using two different sets of distances , which we call anti-parallel 1 and anti-parallel 2 , as the distances between consecutive pairs facing each other on nearby do indeed alternate .', 'Furthermore , we request that one residue cannot form more than two hydrogen bonds , and that the first and last atoms of a peptide do not at all .', 'Hydrogen bonds may form cooperatively between residues and [or and for anti-parallel hydrogen bonds] , thereby gaining an additional energy of .', 'The distance criteria for cooperative hydrogen bonds within are obtained from Fig . 4F and summarised in Table 1 .', 'The energy of hydrogen bonds was set to , where is the thermal energy at room temperature and is the Boltzmann constant .', 'This energy correspond to the experimental one ( 1 . 5 kCal/mol at room temperature [56] ) .', 'Values of the hydrophobicity and stiffness parameters , and , are given in units of and the reduced temperature is .', 'In all our simulations we set and .', 'The ratio of a hydrogen bonding energy to hydrophobic energy is .', 'As the number of hydrophobic contacts within an oligomer is usually about one order of magnitude larger than the number of hydrogen bonds , our choice ensures that these interactions provide similar contributions to the potential energy of the oligomer [47] .', 'For this set of model parameter the peptide folds into a native state below the folding temperature .', 'is the parameter which determines the strength of the interaction energy between atoms representing the peptide molecules and the seed particle .', 'The range of the peptide seed interaction is set to 10 Å from the nanoparticle surface .', 'We performed discontinuous molecular dynamics ( DMD ) simulations [57] , which is a fast alternative to standard molecular dynamics simulations .', 'The main difference is that in DMD simulations the system evolves on a collision by collision basis , and requires the calculation of the collision dynamics and the search for the next collision .', 'In the simulations we used a cubic box , of side 633 Å , and applied periodic boundary conditions .', 'The implementation of our definition for the hydrogen bonding requires some additional consideration .', 'In order to prevent that one residue forms three hydrogen bonds we treat the associated collision as fully elastic .', 'In order to implement and consider cooperative hydrogen bonding we keep and update a list of all hydrogen bonds formed in the system at all times .', 'Note that a recalculation of the hydrogen bonds formed in the system without considering this list can lead to a different result .', 'Independent starting configurations were generated at and rapidly cooled down to at the beginning of each simulation run .', 'We performed all our simulation in the NVT ensemble using an Anderson thermostat .', 'In order to associate the number of collision steps performed in our simulation to a real time we measured the long time self-diffusion coefficient of our model peptide , , and matched it to experimental data .', 'We took from the literature the value for the self-diffusion coefficient , , which was measured for lysozyme [43] .', 'The Einstein relation for the diffusion coefficient together with the Stokes law yield where is the Boltzmann constant , is the radius of the diffusing object , and is the viscosity .', 'The latter can be evaluated through kinetic theory as , where is the density of the viscous medium in which diffusion takes place and is the mean flight time between collision with solvent molecules setting the time scale [15] .', 'The resulting expression for the diffusion coefficient allows us to get picoseconds as an estimate of the real time corresponding to one collision step in our molecular dynamics simulations .', 'We use as an estimate of for lysozyme , whereas we take as the average radius of gyration of the peptide as found in our simulations .', 'Hence , the total number of collision steps , 4×109 , performed in every simulation corresponds qualitatively to 0 . 78 milliseconds .']]
['Introduction', 'Results and Discussion', 'Materials and Methods']
['Nanoparticles introduced in living cells are capable of strongly promoting the aggregation of peptides and proteins .', 'We use here molecular dynamics simulations to characterise in detail the process by which nanoparticle surfaces catalyse the self-assembly of peptides into fibrillar structures .', 'The simulation of a system of hundreds of peptides over the millisecond timescale enables us to show that the mechanism of aggregation involves a first phase in which small structurally disordered oligomers assemble onto the nanoparticle and a second phase in which they evolve into highly ordered as their size increases .']
["Protein misfolding and aggregation are associated with a wide variety of human disorders , which include Alzheimer's and Parkinson's diseases and late onset diabetes .", 'It has been recently realised that the process of aggregation may be triggered by the presence of nanoparticles .', 'We use here molecular dynamics simulations to characterise the molecular mechanism by which such nanoparticles are capable of enhancing the rate of formation of peptide aggregates .', 'Our findings indicate that nanoparticle surfaces act as a catalyst that increases the local concentration of peptides , thus facilitating their subsequent assembly into stable fibrillar structures .', 'The approach that we present , in addition to providing a description of the process of aggregation of peptides in the presence of nanoparticles , will enable the study of the mechanism of action of a variety of other potential aggregation-promoting agents present in living organisms , including lipid membranes and other cellular components .']
['biophysics', 'computational biology']