# Interaction Patterns for Staggered Assembly of Fibrils from Semiflexible Chains
## 3 Results
### Langevin Dynamics Simulations
Real systems such as helical peptides and proteins are polar. A possible domain structure for a generic polar interaction pattern for driving staggered assembly into a hexagonal lattice immediately follows from the non-polar case of Figure 8b, and is shown in Figure 8c. It is a sequence of three polar domains, \(\alpha\), \(\beta\) and \(\gamma\). Staggered assembly into a hexagonal lattice will ensue if interactions of the domains are such that the individual parallel \(\alpha\), \(\beta\) and \(\gamma\) domains form a hexagonal sheet with a pattern of alternating \(\alpha\), \(\beta\) and \(\gamma\) domains. This will happen, for example, if the only attractive interactions are \(\alpha\)-\(\beta\), \(\beta\)-\(\gamma\) and \(\gamma\)-\(\alpha\). The most likely experimental system for which interaction patterns on semiflexible chains such as those we discussed here can be realized are collagen-like proteins. Indeed, short collagen-like peptide sequences have already been designed, that make use of the kind of charge complementarity that we also discuss here, for driving staggered fibrillar assembly [17; 18]. Our results suggest that a fruitful starting point for designing novel self-assembling collagen-like proteins would be the design  
Figure 8: Generalization of the patterned chain. (**a**) For chains with the \(S_{0}\) sequence, which have the simple staggered \(P_{1}\) lattice as their lowest interaction energy state, the sequence is composed of two polar \(\alpha\)-domains and a non-polar \(\beta\)-domain, separated by inert gap sequences (\(\beta\)). (**b**) The non-polar \(\beta\)-domain interacts with two of the polar \(\alpha\)-domains, in the opposite orientation, forming a two-dimensional hexagonal lattice (**c**) generalization to polar chains with \(\alpha\), \(\beta\), \(\gamma\) domains putatively assembling into hexagonal staggered \(P_{1}\) lattices if there is a preference of the \(\alpha\), \(\beta\), and \(\gamma\) domains for assembly in a two-dimensional hexagonal lattice in which the \(\alpha\), \(\beta\) and \(\gamma\) domains alternate. of sets of short collagen-like helices with controlled mutual interactions. These can then be used as elements in longer collagen-like helices to drive self-assembly. This is very similar to the notion of sets of orthogonal coiled coil-peptides and other peptide building blocks [27; 28], that are being used to construct larger assemblies [29; 30]. Successful de-novo design of self-assembling collagens is currently also hampered by our limited understanding of the thermal stability of collagen triple helices, such that a priori we do not know which G-Xaa-Yaa sequences will give stable triple helices and which will not. Only limited data and models are available, and are based on the substitution of single Xaa or Yaa residues in sequences that are otherwise composed of only G-P- or G-O-P triplets [31; 32; 33]. These models fail to predict the stability of collagen-like triple helices for which the majority of triplets are not G-P-P or G-O-P, such as for example, collagen-like triple helices found in bacteria [34; 35]. Given this limitation, a reasonable starting point to start exploring the atomistic-level computational design of self-assembling collagen-like proteins with current protein design software such as Rosetta [36], would therefore be to fix a triple-helical main-chain conformation, and to focus on Xaa and Yaa side-chain choice and conformation in designing sets of short collagen-like helices, with well-defined interaction interfaces. G-Xaa-Yaa triplets could, for example, be chosen to be those that are most frequent in natural collagen-like helices. These shorter sequences can then be used to drive self-assembly in longer designed collagen-like helices. Conceptualization, R.d.V. ; methodology, C.S., investigation, A.J. and R.d.V. ; writing-original draft, R.d.V. ; All authors have read and agreed to the published version of the manuscript. This research received no external funding. Acknowledgments.R.d.V. acknowledges [PERSON] for useful discussions.