Parametrising a PRIME20-like model

The PRIME20 model provided non-bonded interaction specifications between side- chain beads, allowing peptides composed of all 20 amino acids to be simulated. Our work with the PRIME20-like model additionally includes an update on the universal bond fluctuation tolerance, which was modified from = 2% [Voegler Smith and Hall, 2001] to = 2.375%, a value which “produces a more realistic Ramachandran plot” [Nguyen et al., 2004].

Section 3.1 explains that we have been unable to obtain multiple essential parameters from the original authors. The hydrogen bond well diameter has been updated, but its value has been provided subsequently [Cheon et al., 2012]. The side-chain bead masses are missing, but these do not a↵ect ensemble averages. The simple approach used here is to set side-chain bead masses to the sum of the textbook masses of the constituent atoms. Later PRIME20 publications suggest that the same was done for PRIME20 [Cheon et al., 2011; Wagoner et al., 2011; Cheon et al., 2012]. A more nuanced approach which could be useful to study dynamics accurately would be to include mass contributions from bound water. Other solvent e↵ects on dynamics which are not strictly inertial contributions may be best captured via the damping coefficient of a Langevin thermostat, equation (1.11).

This leaves the set of parameters governing backbone to side-chain interac- tions, including hard sphere diameters, well radii, bond lengths and pseudo-bond lengths. Following the lead of the PLUM model [Bereau and Deserno, 2009], set- ting these interactions the same as alanine (in the PRIME2001-like model) may be an acceptable simplification, and is certainly more time-efficient than separately parameterising each residue’s set via its impact on the Ramachandran plot.

Therefore, we set bond and pseudo-bond lengths to 2.44 ˚A, 1.531 ˚A and 2.49 ˚A for NH, CH and CO, respectively. We set all non-bonded bead diameters

d to values which result from mixing the alanine bead size of 5.0 ˚A with the

PRIME2001-like backbone bead sizes. Well diameters are set somewhat arbitrarily to 1.5 d, which brings their ranges to similar values to the non-bonded side-chain

to side-chain interaction ranges.

PRIME20 implementation details

The PRIME20-like model was implemented in the event-driven simulation package DynamO [Bannerman et al., 2011]. DynamO is a FOSS (free and open source) pro- gram distributed under the terms of the GPL version 3 license [gpl, 2007]. Its source code is written in modern C++11 and is fully object-oriented. The PRIME20-like

model was implemented with great help from the primary developer, Marcus Ban- nerman. The completed implementation comes to 1356 lines of C++ code. Along with smaller tools to set up simulations in the model, the completed work is now available for the public for use.

The A20 system

The PRIME20 model features an extended range for the hydrogen bond interaction in order to allow for larger side-chains, and the A20 peptide in the PRIME20-like model was found to form far more stable↵-helices than the PRIME2001-like model, in which the side-chain is expanded to 5.0 ˚A, but the hydrogen bond range is not adjusted accordingly. This is plotted in fig. 3.2; unfortunately, no comparable data for the canonical PRIME20 model is known to be available. This result leads to the conclusion that the hydrogen bond interaction strength should be left at 1.0 for the PRIME20-like model.

The 48-peptide A 16 22 system

An opportunity to compare our PRIME20-like model to the canonical model exists due to a published study using the PRIME20 model on residues 16 to 22 of the - amyloid (A ) protein [Cheon et al., 2011], which is linked to Alzheimer’s disease. 48 peptides of the corresponding sequence, KLVFFAE, known as A 16 22, are placed in

a simulation box and aggregation occurs, governed by -sheet secondary structure. The original authors simulate the systems at reduced temperatures T⇤ ₂

{0.1, 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.197, 0.20, 0.205_}, at con- centrations 10mM and 20mM, for 5 or 10 runs each.

It was infeasible to recruit a matching level of computational brawn to study this large system in the present project, but trial runs on the system were conducted atT⇤ = 0.17 andT⇤ = 0.20 at 20mM, to check that aggregation occurs as expected and results are similar. Each system ran for 5.0_⇥1010 _{events. Both systems pro-}

ceeded to aggregate into layered -sheets, as in the reference work. Fig. 3.4 shows the structures which were observed at the end of each run.

The reference work defines a test of parallel or anti-parallel structure. The orientation of two bound peptides is measured by the angle✓between vectors down each chain, measured from the second C↵ atom to the second-from-last. The con-

dition for parallel is ✓ < 60 , and the condition for anti-parallel is ✓ >120 . The current work takes two peptides to be bound in -structure when they share four or more hydrogen bonds. The simulations carried out here ended with averages of

72.6% and 70.0% anti-parallel structure for T⇤ = 0.20 andT⇤ = 0.17, respectively. These are slightly weaker preferences for anti-parallel structure than the reference work, whose ranges are approximately 90% to 100% forT⇤ = 0.20, and 72% to 90% forT⇤ = 0.17, over five runs.

The original study observes that, rather than perfectly anti-parallel -sheets coming together when the peptides first aggregate, “parallel strands that formed early in the simulation switch to an anti-parallel orientation by a continuous stochas- tic process”, and that this is most likely immediately below the fibrilization tran- sition temperature. Therefore, one possible source for the discrepancy in observed -structure, especially atT⇤ = 0.20, would be a small change in the transition tem- perature caused by di↵erences from the reference model. Another cause may be the lower run time in the present study; the original study had runs of up to 2.68_⇥1011

events, compared to 5.0_⇥1010 here.