Multiscale Simulations to Discover Self-Assembled Oligopeptides: A Benchmarking Study

Abstract

Peptide self-assembly is critical for biomedical and material discovery and production. While it is costly to experimentally test every possible peptide design, the computational assessment provides an affordable solution to evaluate many designs and prioritize synthesis and characterization. Following a theoretical investigation, we present a systematic analysis of all-atom and coarse-grained simulations to predict peptide self-assembly. Benchmarking studies of two model dipeptides allow us to assess the impacts of intrinsic properties (like amino acids and terminal modifications) and external environments (like salinity) on the simulated aggregation. Further examination of 20 oligopeptides containing two to five amino acids shows a good agreement among our theory, simulations, and prior experimental observations. The success rate of our prediction is 90%. Therefore, our theory, simulation, and analysis together can be useful to identify peptide designs that can self-assemble and predict the potential nanostructures. These findings lay the ground for future virtual screening of peptide-assembled nanostructures and computer-aided biologics design.

Introduction

Guided mostly by intermolecular interactions, the self-assembly of a peptide reflects the information coded in the sequence (e.g., α-, β-, or γ-sidechain location; L- or D-configuration; hydrophobicity or hydrophilicity, etc.). Many natural or manmade peptides have the potentials to arrange into ordered, discrete nanostructures spontaneously.^1–4 Such processes could be modulated by external factors⁵ (e.g., solvent,⁶ heat,⁷ salt,⁸ pH,⁹ and voltage¹⁰), and thus allow sophisticated control during the fabrication of the self-assembled nanostructures. At present, typical self-assembled peptide nanostructures include nanofibrils, nanofibers, nanobelts, nanosheets, nanotubes, nanorods, nano doughnuts, nanovesicles, nanomicelles, and supramolecular hydrogels.^{2–5,11–13} An important application of these nanomaterials is targeted drug delivery. For example, Arg-α,β-dehydrophenylalanine nanoparticles, when loaded with an anticancer compound, showed higher cellular uptake and an enhanced tumor regression than the native form.¹⁴ Another study showed that an amphipathic peptide, which self-assembles to a nanocarrier system, can control drug release in gene therapy.¹⁵ There is also emerging interest in using self-assembled peptide nanostructures for tissue engineering and regeneration.^16,17

Despite these research efforts in self-assembled peptide nanostructures, rational design remains a significant hurdle, presumably owing to the lack of effective theoretical and computational tools to predict detailed structures and properties.^18–20 Few peptide nanostructures except amyloid^21,22 and collagen^23,24 have been characterized to the atomistic level,^21,25 while computational studies using all-atom (AA) modeling are limited by relatively small time and space scales.^26–28 Further, it was suggested that one should sacrifice atomistic details and use reduced models to simulate the peptide aggregation processes.¹⁹ For example, coarse-grained (CG) models with the Martini force field²⁸ have successfully studied the self-assembly of di- and tri-peptides.^29,30 Studies showed that in the coarse-grained models, peptides first form oligomers and subsequently assemble into larger aggregates of peptides.³¹ Our prior studies showed that the performance increased by a factor of two to four using a top-down approach to observe the self-assembly of melittin.³² However, over-aggregation of this 26-residue cationic peptide was observed,³³ presumably caused by an underestimation of the inter-molecular repulsion. Considering the accuracy-efficiency tradeoff, it is critical to carry out systematic studies of AA and CG simulations of peptide self-assembly to minimize or even close the gaps between the experimental and computational determinations.

In this work, we first developed the theory of peptide self-assembly using the aggregation propensity metrics and validated our theory with two model dipeptides using AA and CG simulations. After systematically optimizing the setups and conditions, we performed an extended examination of 20 peptides with known self-assembled nanostructures. Our results provide benchmarking evidence for computational models and methods to predict, under a given condition, (1) the aggregation behavior of a peptide and (2) the stable nanostructure which a peptide aggregates into. Rather than investigating the self-assembly processes and mechanisms, we focus on the development and validation of an accurate computational approach for large-scale studies of many peptide candidates. Our ultimate goal is to establish affordable computational approaches toward the virtual screening and computer-aided design of biologics and biomaterials.

Results

1. Metrics of Peptide Self-Assembly.

The aggregation propensity (AP), first defined by Frederix et al.²⁹ has been used as a critical metric for simulated peptide aggregation. It is the ratio of the initial and final solvent accessible surface areas (SASA) of all the peptides in a simulation. It has been widely used as a simple score to study the self-assembly behaviors of oligopeptides.^{29,30,34–37}

$$A{P}_{\mathit{\text{SASA}}}=\frac{SAS{A}_{\mathit{\text{initial}}}}{{\langle \mathit{\text{SASA}}\left(t\right)\rangle }_{\mathit{\text{final}}}}$$ (Eq. 1)

Specifically, we calculated the initial SASA from our starting configuration, which contains a targeted number (N) of oligopeptides. These peptides were built to adopt an extended structure and placed arbitrarily in the simulation box without contacting each other. Thus, the initial SASA in Eq. 1 was equivalent to N times the SASA of a single, extended peptide. The final SASA was computed with the last 10 ns of the simulation trajectory, which was justified based on prior studies,^32,33,38 and the comparison between the last 10- and 50-ns windows (Table S1). The AP scores were calculated with at least two simulation replicas.

Overall, an AP_SASA score close to 1.0 (like the glycine-glycine dipeptide, or GG) indicates subtle changes in the SASA after the simulation and thus a low tendency to self-assemble. In contrast, a high AP_SASA score (like the phenylalanine–phenylalanine dipeptide, or FF) results from the significantly reduced SASA in the simulation, indicating a high likelihood of peptide aggregation. AP_SASA is often straightforward to compute for short peptides (e.g., < six amino acids in length), because the reduction of SASA is mainly due to the formation of peptide-peptide contacts, rather than peptide folding. However, longer peptides are more likely to adopt secondary structures, and thus the reduction of SASA can be caused by folding, aggregation, or both. We present an alternative AP — AP_contact — to separate folding and aggregation based on intermolecular contacts. The definition of AP_contact is as follows.

For a trajectory frame at time $t$ containing $N$ peptides, we formulate the calculation as the maximization of a scoring function $\left(f\right)$ over an input set $\left(\left\{P_{i\in N}\right\}\right)$ containing $\left(N-1\right)$ elements drawn from an interpeptide distance matrix in Angstroms $\left(D\right)$ that represent a path drawn from an initial to a final peptide that visits each peptide exactly once. The scoring function is simply a (nonlinearly) weighted sum of the elements in the input set (Eqs. 2a–b). The details of the optimization, justification of weighting function, and constructions of the matrix $D$ and the input set $\left\{P_i\right\}$ are discussed in the Supporting Information (SI).

$$f\left(P_i\right)=\frac{1}{N-1}\sum _{j=1}^{N-1}w\left(p_i^j\right)$$ (Eq. 2a)

$$w\left(x\right)=\{\begin{array}{cc}1& x<4\text{\hspace{0.17em}Å}\hfill \\ \text{exp}\left(-\left(x-4\right)\right)& 4\le x\le 12\text{\hspace{0.17em}Å}\hfill \\ 0& x>12\text{\hspace{0.17em}Å}\hfill \end{array}$$ (Eq. 2b)

Like AP_SASA, we report AP_contact as the average score over the last 10 ns of each simulation (Eq. 2c).

$$A{P}_{\mathit{\text{contact}}}=\langle \underset{i}{\text{max}}{\left[f\left(P_i\subset D\left(t\right)\right)\right]\rangle }_{t \in \mathit{\text{last}} 10 ns}$$ (Eq. 2c)

Although AP has been previously applied to identify self-assembled peptides from large-scale CG simulations,^29,37 we also investigated the connections between AP_SASA, AP_contact, and assembly structures using a theoretical model (Figure 1), which approximates each peptide as a sphere of radius r (or the so-called unit radius). This model considers the total number of N spheres to self-assemble into a cylinder. We assume that the maximum number of spheres packing on one layer is a, and the assembly structure has N/a layers as in simple packing. With a fixed number of N, the value of a is associated with the assembly structure in this model: low a and N/a >> a indicates a long cylinder or a nanorod, while high a indicates a nanosheet; comparable a and N/a likely lead to the structure to resemble a nanosphere. With these assumptions, we can readily calculate the surface areas or the contacts and further the AP scores. Thus, we can correlate the values of AP with different assembly structures. Fortunately, a two-dimensional solution — circles packing into a circle — has been previously solved.^39–43 Key in the solution is the value of a coefficient M: the enclosing circle’s radius is r/M (Figure 1). Using known values of M, we can estimate the theoretical values of AP_SASA and AP_contact with various pairs of a and N (Table 1).

Figure 1.

Cartoon illustration of our theoretical model to establish the connection between aggregation propensity and potential assembly nanostructures. The small yellow circles are called unit circles. M is the ratio of the unit circle radius over the radius of the enclosing circle.

Table 1.

AP_SASA estimated with N = 100, 300, 500, 1000, and 2000.

a	M	Ref.	aM	a/M	AP (N=100)	AP (N=300)	AP (N=500)	AP (N=1000)	AP (N=2000)
10	0.26	38	2.6	38.1	1.90	2.33	2.44	2.53	2.57
20	0.20	39	3.9	102.4	1.93	2.91	3.24	3.54	3.71
30	0.16	40	4.8	186.0	1.69	2.99	3.53	4.08	4.43
40	0.14	40	5.6	284.9	1.46	2.88	3.58	4.37	4.92
50	0.13	40	6.3	397.5	1.26	2.71	3.50	4.50	5.25
75	0.10	41	7.8	725.4	-	2.27	3.16	4.49	5.69
100	0.09	41	9.0	1108.7	-	1.92	2.80	4.28	5.80
200	0.06	42	12.9	3091.2	-	-	1.80	3.16	5.08

$$SAS{A}_{\mathit{\text{initial}}}=4\pi r^2\cdot N$$ (Eq. 3a)

$$SAS{A}_{\mathit{\text{final}}}\approx 4\pi {\left(\frac{r}{M}\right)}^2+2\pi \cdot \left(\frac{r}{M}\right)\cdot \left(\frac{N}{a}\right)\cdot 2r$$ (Eq. 3b)

$$A{P}_{\mathit{\text{SASA}}}=\frac{SAS{A}_{\mathit{\text{initial}}}}{SAS{A}_{\mathit{\text{final}}}}=\frac{NaM}{\frac{a}{M}+N}$$ (Eq. 3c)

By definition, AP_contact is always 1.0 as all the spheres are packed with direct contacts, regardless of a and N. In contrast, AP_SASA is a function of a and N (Eq. 3c and Table 1). With N = 500, for example, AP_SASA is 2.4 for a nanorod or a nanofiber (a = 10), 2.8 for a nanosheet or a nanotape (a = 100), and above 3.5 for a nanosphere (a between 30 and 50). Our theoretical model also suggests a size dependence of AP_SASA on the simulation size N (Eq. 3c). For nanosheets of the same thickness (N/a = 2), AP_SASA is 1.26 (N = 100, a = 50, M = 0.13), 1.50 (N = 500, a = 250, M = 0.058⁴⁴), and 1.59 (N = 1000, a = 500, M = 0.041⁴⁵). Similarly, for nanofibrils with low a (e.g., a = 10), AP_SASA is 1.90 at N = 100 and increases significantly above 2.33 at N > 300. Therefore, the finite size of a simulation may impact AP_SASA: too few peptides (e.g., < 100 in the simulation box) can be inaccurate to predict the self-assembly behavior.

The surface area of a real peptide can be more complex than a sphere in our theoretical model, but AP_contact can still be readily calculated without complicated wrapping. AP_contact is also useful to identify peptides that can self-assemble into nanostructures, as the calculation of AP_contact is insensitive to system size and peptide folding. On the other hand, AP_SASA appears to increase along the order of nanofibers, nanosheets, and nanospheres. Thus, it can be used to estimate the assembly structure from simulations by comparing the relative values with a fixed system size. To further validate the theory, we carried out AA and CG simulations of two model dipeptides by varying the system size, the capping, and the salinity, before extending to simulations of 20 oligopeptides of various lengths. Compared with prior experimental characterizations, the tests of our theoretical model and extensive simulations may gain valuable knowledge for multiscale modeling of peptide self-assembly and future design studies.

2. Impact of the System Size on Peptide Self-Assembly Simulations.

With the peptide concentration fixed at 0.13 ± 0.01 M, we further validated the finite-size effect of peptide self-assembly by varying the number of peptides (N = 64, 125, 216, 343, and 512 of FF or GG) in MD simulations. As CG models of 300 dipeptides were previously reported to aggregate within 100 ns,^29,33 we chose to run 100-ns CG simulations and 400-ns AA simulations, estimated with the four-to-one mapping rule in the Martini force field.⁴⁶ Generally, in these simulations, the surface area of FF decreased in the first 25 ns with the CG model and in the first 150 ns with the AA model (Figure 2), while the surface area of GG remained unchanged. Despite large uncertainty in the analysis, we obtained a significantly lower diffusion coefficient of FF calculated with the last 10 ns compared to the first 10 ns (Figure S2), indicated by both AA and CG models. The convergence of our simulations was confirmed by the small fluctuation of SASA and AP_SASA in the last 10 ns (Figure S2), as well as the similar averaged AP_SASA in the last 10 and 50 ns (Table S1). Thus, our data analysis focuses on the last 10-ns stage of each simulation.

Figure 2.

Simulated peptide aggregation showed some dependence on the number of peptides. (A) Bar charts to compare AP_SASA of FF and GG using the all-atom and coarse-grained models. The number of simulated peptides ranges from 4³ = 64 to 8³ = 512. These peptides had no contact in the initial construct before the simulations. (B) The final snapshot of 216 GG dipeptides was shown. (C) Scatter plot to compare AP_SASA and AP_contact of all-atom (green markers) and coarse-grained (golden markers) models of FF. Two final snapshots were shown from the all-atom simulations of 64 and 512 FF dipeptides, respectively. All the simulations were performed for 100 ns for CG and 400 ns for AA with peptides of neutral caps.

Overall, while no assembly of GG was observed (AP_SASA ~1.0, Figure 2B), FF in our simulation displayed a strong tendency to aggregate into a rod-like structure (AP_SASA > 2.9, Figure 2C), in good agreement with prior results of Frederix et al.²⁹ To compare the assembled nanostructures, the radius of gyration (R_g) was computed using the final frame of FF simulations (Table S3): R_g is 17.2 Å (N = 64) and 43.5 Å (N = 512) in the AA models; R_g is 18.8 Å (N = 64) and 41.0 Å (N = 512) in the CG models. Similar to the radius of gyration analysis, our principal axes analyses of FF simulations with AA and CG models also agree on forming a nanotube (Table S4). Therefore, general agreements were observed between AA and CG modeling in both AP_SASA values and assembly structures.

A noticeable impact of system size on AP_SASA was observed in our simulations (Figure 2), as it increased from 2.9 (N = 64) to 4.7 (N = 512) in our AA simulations of FF dipeptides, as well as from 2.5 (N = 64) to 3.1 (N = 512) in our CG simulations. While this trend agrees with our theory, we also found that CG models are less sensitive to the system size than the AA models. Distinct from AP_SASA, AP_contact did not vary with the system size, as suggested in our theory. The numerical difference of AP_contact between the AA (~ 0.9) and CG models (~ 0.7) for FF simulations stems from the larger inter-peptide distances in the CG models but the same distance cutoff using in the function w(x) of Eq. 2b. In general, our results showed the consistency between the theoretical model and molecular simulations at the AA and CG resolutions.

3. Impact of Terminal Capping on Peptide Self-Assembly Simulations.

Given the finite size effect, we continued more tests with the 216-peptide systems for terminal capping and salinity. We next examined how terminal charges impact simulated peptide self-assembly with the FF and GG dipeptides. Frederix et al.²⁹ showed that using neutral (rather than zwitterionic) peptides drastically decreases the time needed for peptides to aggregate in CG simulations.³⁰ To systematically study the impact, three terminal caps (zwitterionic, neutral, and methyl caps) were tested in our AA and CG simulations (Figure 3). We modelled the neutral GG or FF dipeptide with the standard MARTINI backbone bead (P5), and zwitterionic peptides with charged beads (the anionic Q_a and the cationic Q_d). CG models with methyl capping were not tested, due to the similarity to neutral caps on the CG level. In general, we found that terminal capping impacted our AA simulations but not the CG simulations (Figure 3)

Figure 3.

Simulated peptide aggregation was slow with zwitterionic peptides. (A) Bar charts to compare AP_SASA of FF and GG using all-atom and coarse-grained models of different terminal shown in (B) with their chemical structures. The capped peptides had methyl caps in both the N and C termini. (C) Scatter plot to compare AP_SASA and AP_contact of all-atom (green markers) and coarse-grained (golden markers) models of FF in our simulations. Two final snapshots were shown from the simulations of neutral capping. All the simulations were performed for 100 ns for CG and 400 ns for AA with 216 peptides.

In our simulations, the formation of a nanorod was observed for FF with neutral and methyl capping, as indicated by AP_SASA at ~4.0 with AA models and ~2.9 with CG models. While the zwitterionic FF showed aggregation at the CG resolution with slightly lower AP_SASA at 2.5, we did not see an apparent aggregation of zwitterionic FF in the AA simulations, given AP_SASA at 1.0 and AP_contact at 0.2. Presumably, this can be attributed to unfavorable electrostatic repulsion (for example, between two cationic N termini or anionic C termini) that needs to be overcome for aggregation to take place in the AA models. Such repulsion is eliminated in the peptide models with neutral and methyl capping or underestimated in the CG model. A long simulation is likely needed to show aggregation with the AA models of zwitterionic FF.

Furthermore, the CG models are less sensitive to the capping and still provide consistent assembly structures (Figure 3B). The radius of gyration (R_g) of the structure predicted by CG simulation is 29.8 Å and by AA simulation is 29.4 Å, suggesting the agreement between the two resolutions with neutral capping. Although the zwitterionic peptides represent a more accurate chemical description under the neutral pH, the neutral peptides with uncharged termini are good approximations for larger-scale simulation studies to predict peptide self-assembly.

4. Impact of Salinity on Peptide Self-Assembly Simulations.

Peptides and proteins have been well known to aggregate in salt solutions depending on the concentrations.^47,48 While there is a rich body of prior related studies that have shown that high salt concentration leads to ordered aggregations,^47,48 we specifically compared the AA and CG models in an affordable setting: 216 natural peptides for 100 ns (CG) and 400 ns (AA) in 0, 100, 500, or 1000 mM of NaCl. While the non-assembly GG seems to be indifferent to the salinity in the environment, FF shows a generally higher AP_SASA at higher salinity.

The AA models of FF displayed a minimum AP_SASA at 100 mM NaCl, while the CG models show a maximum AP_SASA at 0 mM NaCl (Figure 4B). Protein aggregation has been long known as a function of the surrounding salt concentrations.⁴⁹ It seems that the AA model provides a more consistent description of the experimental salting out effect with a maximum protein solubility. Furthermore, we compared the time evolution of AP_SASA at 0 and 1000 mM NaCl. The AA models show a faster assembly at higher salinity while the CG models show the opposite (Figure 4C). Overall, the AA model provides a clearer picture of the thermodynamics and kinetics of peptide self-assembly than the CG models. CG models lack such sensitivity and should be used with caution, especially for assembly dynamics.

Figure 4.

Different salinity dependents were shown in the AA and CG models. (A) Bar charts to compare AP_SASA of FF and GG using all-atom and coarse-grained models in different salinity (0 to 1000 mM NaCl). (B) Scatter plot to compare AP_SASA and AP_contact of all-atom (green markers) and coarse-grained (golden markers) models of FF in our simulations. (C) Time evolution of AP_SASA in all-atom and coarse-grained simulations (neutral capping) at 0 and 1 M NaCl. Final snapshots were shown from the simulations of FF with neutral capping at 1 M NaCl. All the simulations were performed for 100 ns for CG and 400 ns for AA with 216 neutral peptides.

5. Self-assembly Simulations of 20 Oligopeptides.

Based on the systematic examination of model dipeptides GG and FF, we believe that 100-ns CG simulations of 300 peptides in the Martin 2.1 force field are suitable for extended studies of general oligopeptides. Despite little impact from the peptide capping and salinity on the CG models, we chose zwitterionic peptides without additional salt. 20 oligopeptides were selected based on prior simulations and experiments: some of these oligopeptides, as negative controls, do not aggregate in the solution, like GG, ECG, and DFN, while others are known to form regular nanostructures, like CFF and FFF. From our CG simulations, our calculated AP scores agree well with AP_SASA from prior simulation studies (Table 2); our simulated structures resemble most experimental assembly structures (Table 2 and Figure 5). Specifically, we did see the aggregation for FE, ECG, or DFN, but a clear formation of fiber-like structures for KFG, FW, WY, and IF, all consistent with prior experiments. With the same force field and similar setup (like 300 peptides), our CG simulations reproduced previously reported AP_SASA of dipeptides, pentapeptides, and part of tripeptides (Table 2). Tripeptides CFF and FFF appear to have greater AP_SASA values in our simulations than in prior ones, but these values (AP_SASA > 3.0) are better in line with the experimentally found nanosphere and nanofiber structures.

Table 2.

Summary of oligopeptide aggregation. The AP scores were computed using two metrics, AP_SASA and AP_contact. All the simulations were performed with the CG models (300 peptides, 100 ns, and 0 M NaCl). The predictions were made based on the AP scores, principal axis final assembly structures.

Peptide	APSASA (this work)	APSASA (Literature)	APcontact	Nanostructure (Prediction)	Nanostructure (Experiment)
ECG	1.01	1.0130,50	0.13	None	None
GG	1.04	1.0029	0.09	None	None
FE	1.17	1.1029	0.38	None	None
DFN	1.38	1.1730,51	0.49	None	None
KFG	1.82	1.5630,52	0.63	Fiber/Tube	Tube/sphere52
RWDW	1.91	-	0.70	Hydrogel	Hydrogel53
WY	2.01	2.2029	0.65	Fiber/Tube	-
VKVFF	2.24	1.9535	0.67	Fiber	Fiber35
FKIDF	2.28	2.0335	0.71	Fiber	Needle Fiber35
SYCGY	2.30	2.4235	0.68	Fiber	Needle Fiber35
IF	2.31	2.3029	0.60	Fiber/Tube	Fiber54
KFFFE	2.46	1.9535	0.75	Tape	Sheet/Tape35
SHFF	2.54	-	0.74	Tape	Hydrogel55
FW	2.97	3.5029	0.73	Tube	Tube56
FFV	3.01	2.0330,57	0.72	Fiber	Fiber57
VFF	3.05	2.3330,57	0.70	Sphere	Tape57
FF	3.16	3.2029	0.72	Tube	Tube56/Vesicle56,58
LFF	3.25	2.0730,59	0.71	Fiber	Fiber59
CFF	3.26	2.0530,60	0.69	Sphere	Sphere60
FFF	3.41	2.2226,30,34	0.76	Sphere	Sphere/rod34

Figure 5.

AP_SASA and AP_contact of six dipeptides, eight tripeptides, two tetrapeptides and four pentapeptides. Final snapshots of our CG simulations with aggregated nanostructures.

Discussion

While our and prior simulations²⁹ support that AP scores from CG simulations are helpful to identify self-assembly peptides, AP_SASA is quite accurate to indicate the potential assembly structures of given peptides. With N = 300, peptides with low AP scores (AP_SASA < 1.5 or AP_contact < 0.5) are less likely to aggregate, such as GG, FE, ECG, and DFN. Peptides with higher AP scores (AP_SASA > 1.5 or AP_contact > 0.5) are more likely to assemble into nanospheres, nanofibers, or nanorods, with examples like FF, CFF, and FFF. Further, we can use a simple rule based on the AP scores to predict the potential assembly structures: nanofibers, nanotubes, or hydrogel if 1.5 < AP_SASA < 2.3; nanotapes if 2.3 < AP_SASA < 3.0; nanosphere or nanovesicle if AP_SASA > 3.0. It must be noted that there is some ambiguity in distinguishing nanofibers and nanotubes (like IF), as well as nanospheres and nanovesicles (like FF). In addition, CG simulations likely overestimate AP_SASA for VFF, FFV, and LFF. The success rate of our prediction is 90% (17 out of 19). Still, the CG simulations provide a good accuracy to guide future experiments.

An empirical approach to designing self-assembly peptides highly relies on the hydrophobicity/polarity of amino acids and the secondary structure propensity.³⁵ It is often thought that peptides with hydrophobic residues (like VFF, FFV, and CFF) promote the aggregation that is shown by high AP scores; peptides consist of small or charged amino acids even with hydrophobic residues (like GG, FE, ECG, and DFN) has a lower tendency to aggregate. Our study may fill the gap that the earlier studies left, as we found that aggregation propensity is not only the polarity of each amino acid but also the polarity of the entire peptide. Beyond the empirical estimate, simulations of CG models offer a rational guide to understanding the self-assembly behaviors and even the chemical details. Given the high efficiency (20 minutes/peptide on NVidia A100) and accuracy (90% success rate), the CG simulation with both AP_SASA and AP_contact calculations can be a useful tool for the virtual screening of self-assembly peptides for desirable nanostructures.

Comparing the AA and CG model resolutions, AA models provide more accurate electrostatic interactions but require much longer sampling to study peptide aggregation. Our data suggest that CG models may be sufficient to study most oligopeptides (< 6 residues), as the AA and CG simulations showed comparable assembly structures for peptides of four or five amino acids (Figure 6). When folding becomes more significant for longer peptides, it is possible to combine AA and CG models in a top-down simulation³¹ — to capture both inter- and intra-molecular interactions for aggregation and folding. For the screening studies of many peptides, it is also viable to first perform CG simulations to reduce the number of peptide designs and then AA simulations to refine the selection for experimental validation. Finally, recently Sankaranarayanan and coworkers successfully used the decision trees model combined with CG simulations to predict pentapeptide aggregation.³⁵ Our findings, complementary to the machine learning approach, may provide novel physical insights needed for predictions of longer peptide self-assembly and co-assembly.

Figure 6.

Comparison of AP_SASA of tetra- and penta-peptides from AA (green markers) and CG (golden marker) simulations. Both the simulation results depict the similar morphology of the tetra- and pentapeptide.

Conclusions.

In this work, we have developed a theoretical model for peptide self-assembly and systematically simulated oligopeptides of two to five amino acids, using both AA and CG models. With collaborative theoretical, simulation, and experimental data, our results provide important evidence that modeling peptide aggregation with CG simulations can identify peptides that aggregate to regular nanostructures. The aggregation propensity scores, based on either surface area or interpeptide contacts, are good indicators of various nanostructures like nanorods, nanosheets, nanospheres, etc. We tested several simulation conditions and setups and suggested the optimal ones for future screening of the self-assembly of peptides prior to experimental studies. We show confidence in multiscale simulations of peptide self-assembly regarding whether a peptide may self-assemble or not, as well as what assembly structure will be potentially obtained. These findings can serve as a practical guide — for future studies of simulation-guided design or virtual screening of peptide-assembled nanostructures — toward biomedical and material applications.

Methods and Models

Model Preparation.

We have developed an in-house software program called Peptide BACon (Build, Assembly, and Construct) to build peptide models for large-scale simulations and screening studies. Peptide BACon is an in-house Python program to set up, run, and analyze simulations with Schrödinger software release mostly 2021–2 and Gromacs 2020.2. Peptide BACon is available to download via https://github.com/jianingli-purdue/Peptide-BACon.git.

Simulation Setting.

To further study and develop the Aggregation Propensity (AP) metric presented by Tuttle et al. in their investigation of CG peptide systems^29,30 similar systems, represented with MARTINI 2.1 or 2.2 CG beads, were assembled by randomly scattering 300 peptides in a cubic box such that no peptide was closer than 3 Å to any other peptide. Peptide systems were solvated with MARTINI water, sodium, or chloride counter ions. Using GROMACS 2020.2,⁶¹ a steepest descent minimization was conducted on each system with a convergence threshold of 20 kJ mol⁻¹ nm⁻¹ for every bead and a maximum length of 5000 steps. GPU-accelerated MD simulations consisted of varying numbers of 25 fs timesteps in the NPT ensemble using the V-rescale⁶² thermostat and Berendsen barostat to maintain a temperature of 303 K and a pressure of 1.0 bar⁶³. The VDW potential switch distance was 0.9 nm, and the VDW/Electrostatic cutoff was 1.2 nm. The dielectric constant was 15.

For comparison, AA systems were prepared with Schrödinger 2021–2. Maestro/Desmond tools. The first step was to create an AA representation of each peptide in a β-sheet-like conformation and to translate copies of it into a cubic grid arrangement with 4 to 8 peptides per side such that 15 Å separated identical atoms on adjacent peptides. Then, some peptides were rotated slightly without altering their conformation to ensure that the grids were not periodic. Next, the model systems were solvated using the system-builder utility included with Desmond. The system-builder tiles a pre-equilibrated box of SPC water to cover the simulation box.⁶³ Water molecules too close to atoms in the solute are removed, and some randomly chosen water molecules are converted into Cl⁻ or Na⁺ ions as needed to neutralize the net charge. Each system was then subjected to the Desmond relaxation protocol, which involves a series of restrained and unrestrained GPU-accelerated simulations during which the temperature is raised to the target temperature and the simulations switch from initially using the NVT ensemble to using the NPT ensemble.⁶⁴ Finally, GPU-accelerated simulations were conducted in the NPT ensemble with the MTK barostat at 300 K, and a pressure of 1.0 atm for 400 ns, and Particle Mesh Ewald technique was used for electrostatic interactions. We used the center of geometry of the water molecule for the position of the corresponding CG water site, which has a mass equivalent to that of a water molecule.³³

Data Analysis.

Data analysis was carried out with the Schrödinger Python API and Gromacs command line tools, through Peptide BACon wrapper scripts. The AP of the last 10 ns of the simulation was averaged, and the standard deviation is represented here as an error bar. Model visualization was done, and aggregated structures were made in PyMOL programs.⁶⁵ Figures were made using the python matplotlib module.⁶⁶ The principal axis was computed using the principal axis module from Gromacs.⁶¹ The radius of gyration was calculated using VMD.⁶⁷