Building block aspect ratio controls assembly, architecture, and mechanics of synthetic and natural protein networks

Fibrous networks constructed from high aspect ratio protein building blocks are ubiquitous in nature. Despite this ubiquity, the functional advantage of such building blocks over globular proteins is not understood. To answer this question, we engineered hydrogel network building blocks with varying numbers of protein L domains to control the aspect ratio. The mechanical and structural properties of photochemically crosslinked protein L networks were then characterised using shear rheology and small angle neutron scattering. We show that aspect ratio is a crucial property that defines network architecture and mechanics, by shifting the formation from translationally diffusion dominated to rotationally diffusion dominated. Additionally, we demonstrate that a similar transition is observed in the model living system: fibrin blood clot networks. The functional advantages of this transition are increased mechanical strength and the rapid assembly of homogenous networks above a critical protein concentration, crucial for in vivo biological processes such as blood clotting. In addition, manipulating aspect ratio also provides a parameter in the design of future bio-mimetic and bio-inspired materials.


𝜙 =
•    =     Where vp is the volume of the cylindrical particular and va is the available volume per particle.We can say that a cylindrical particle is able to freely rotate about its centre of mass if  < √  Equating both sides would yield the critical point beyond which the cylindrical particle is no longer able to freely rotate without colliding with another cylindrical particle.

Determination of Fibrin Protofibril Aspect Ratio
The critical length of fibrin protofibrils is between approximately 20-25 monomer units of fibrin 1 .Considering 45 nm monomer length and the double-stranded structure, protofibril length for 20-25 monomers is 450-563 nm while protofibril width is 10-13 nm, taking into account the 8 nm distance between the parallel molecular axes of protofibrils 2 and the 2-5 nm monomer width of fibrin monomers 3 .These ranges give an average length and width of fibrin protofibrils of 506.5 nm and 11.5 nm, respectively, which would correspond to an average aspect ratio for fibrin protofibrils of 44.

Supplementary Tables
Protein L construct Scattering Length Density in 100% D2O (x10

Dynamic Light Scattering (DLS)
DLS measurements of pL7 at varying protein concentrations were conducted using a 3D Photo-correlation Spectrometer (LS Instruments) with a laser excitation wavelength of 660 nm.The samples were placed into 5mm diameter glass tubes and scattered light was detected at scattering angles, θ, between 30-135o in intervals of 5o, at a temperature of 25°C.The intensity autocorrelation functions, g2, were calculated from the dependent scattered intensities and then subsequently converted to field autocorrelation functions, g1, using the Siegert relation: Here, σ is the set-up dependent coherence factor, ~0.95 for our spectrometer.The g1 data show two contributions: we attribute the faster process to the scattering from individual proteins and the slower to the scattering from aggregates.Thus, the data were fit using a sum of two stretched exponentials of the form: where ai are the amplitudes, βi are the stretching parameters, and τi are the characteristic timescales of the two contributions.The b parameter is the baseline amplitude.
The relaxation rate, Γ=1/τ is related to the self-diffusion coefficient, Γ=Dq 2 , where q = 4πn/λ sin(θ/2), λ is the laser excitation wavelength and θ is the scattering angle.The D parameter for different concentrations of the pL polyprotein 7-mer could be determined through linear fits of the Γ vs q 2 data for the faster process observed in the autocorrelation functions.pL7 at varying protein concentrations were conducted on a LS Spectrometer Variable Multi-Angle Light Scattering (LS Instruments).The samples were measured over multiple angles between 30-135 o in intervals of 5 o , and help at 20 o C.

Code Repositories
BioNet simulations (Fig. 1c) were performed using BioNet, a software package in development at the University of Leeds.Kinetic lattice simulations were performed using a bespoke software also developed at the university of Leeds.Access to the code repositories can be found at https://doi.org/10.5518/1344.

pL polyprotein sequences
Below are the residue sequences for each of the pL polyprotein sequences.

3 i 3
.e. the length of the rod is shorter than the length of the cubic voxel of available volume.Substituting   = Here we define the aspect ratio as AR = L/d, substitute L = AR•d and rearrange  2 <  4 Hexa-Histag (for purification) TEV cleavage site (not used in this study) Protein L Folded Domain Linker Regions (unstructured protein L amino acids)

Table 2 :
Fitted parameters with associated fit error from equation 4, extracted from the storage modulus vs AR data in figure1b.Additionally the reduced chi-squared values of these fits are listed.

Table 3 :
The protein and water volume fraction of protein L construct hydrogels as a function of pL construct aspect ratio and at varying protein concentrations in mg•ml -1 , equivalent to those show in figure1b,d and 2d.

Table 4 :
The concentrations in mg•ml -1 of Protein L 7-mer and Fibrinogen used in the lag time measurements (Fig.3), with the corresponding protein and water volume fraction.heatingto 200 o C at a rate of 5 o C/min and finally held isothermally at 200 o C for 2 mins.The percentage weight loss was calculated using the equation below,