The staphylococcal biofilm protein Aap forms a tetrameric species as a necessary intermediate before amyloidogenesis

The accumulation-associated protein (Aap) from Staphylococcus epidermidis is a biofilm-related protein that was found to be a critical factor for infection using a rat catheter model. The B-repeat superdomain of Aap, composed of 5 to 17 B-repeats, each containing a Zn 2+ -binding G5 and a spacer sub-domain, is responsible for Zn 2+ dependent assembly leading to accumulation of bacteria during biofilm formation. We previously demonstrated that a minimal B-repeat construct (Brpt1.5) forms an antiparallel dimer in the presence of 2-3 Zn 2+ ions. More recently, we have reported the presence of functional amyloid-like fibrils composed of Aap within S. epidermidis biofilms and demonstrated that a biologically relevant construct containing five and a half B-repeats (Brpt5.5) forms amyloid-like fibrils similar to those observed in the biofilm. In this study, we analyze the initial assembly events of the Brpt5.5 construct.


Introduction
The human skin commensal, Staphylococcus epidermidis, has been referred to as the 'accidental pathogen' (1). Its primary virulence factor is its apt ability to form biofilms on a variety of surfaces (2). It is this feature that has allowed S. epidermidis to take its place as a leading cause of hospital-acquired infections (3), and specifically, as the primary culprit in device-related infections (4). Biofilms are well-organized bacterial communities that offer a high degree of mechanical and chemical resistance to its constituent cells (5). Biofilm formation begins with the attachment of bacteria to a biotic (e.g., corneocytes or collagen-coated implant) or abiotic surface (e.g., catheter or artificial joint). Following attachment, the accumulation of bacteria is mediated by protein-protein interactions and/or secretion of the extracellular polysaccharide, poly-N-acetyl glucosamine (PNAG). As the biofilm matures, its characteristic 3-dimensional structure takes shape. Eventually, cycles of dispersal of planktonic bacteria from the biofilm occurs, allowing for the cycle to begin again with establishment of biofilms and infection at locations distal to the original site (2).
One of the key determinants of biofilm formation, specifically in the context of infection, is the expression of accumulation-associated protein (Aap) (6)(7)(8)(9). This protein is anchored to the peptidoglycan layer of the staphylococcal cell wall at its C-terminus. Starting at the N-terminus is a series of short A-repeats, followed by a lectin domain flanked by proteolytic cleavage sites, the Brepeat superdomain containing up to 17 B-repeats composed of Zn 2+ -binding G5 domains and spacer regions, and, lastly, a highly extended proline/glycine-rich stalk region ( Figure 1) (10). Although the A-repeats and/or lectin domain are required for Aap's role in staphylococcal attachment to a surface, removal of these regions via cleavage by SepA or other proteases is required for the accumulation of bacteria in the biofilm via B-repeat self-assembly (11,12). Biophysical and crystallographic studies on minimal B-repeat constructs containing one and a half B-repeats (Brpt1.5; a full B-repeat containing a G5 domain and spacer region, plus a C-terminal G5 domain) have shown that B-repeats are highly extended, rich in β-sheet and random coil secondary structure, and are monomeric in the absence of Zn 2+ (9,(13)(14)(15)(16). When Zn 2+ is present, Brpt1.5 dimerizes in a mostly overlapping, anti-parallel fashion with no observable change in secondary structure. In the crystal structure, a Zn 2+ ion is bound to each G5 domain and interacts with both protomers ( Figure  1) (15). The residues involved in Zn 2+ binding have been identified by crystallography and mutagenesis (15). Our lab has also shown that Cu 2+ can support assembly of B-repeats, while Mn 2+ , Co 2+ , and Ni 2+ can bind, but do not support assembly (16).
Another important feature is that while the Brepeats are 89-100% identical, each Aap B-repeat exists as one of two subtypes. These two subtypes differ in eight residues in the G5 domain that swap in and out as a "cassette" of residues. These residues are located near the Zn 2+ -binding site, dimer interface and hydrophobic "stack" in the Brpt1.5 dimer structure. Interestingly, the variant B-repeats with the less common cassette show weaker Zn 2+dependent dimerization, but higher thermal stability, compared to the more common consensus repeats in Brpt1.5 constructs (13).
While the Zn 2+ -dependent assembly of Brpt1.5 constructs has been well explored, Aap is believed to require at least 5 B-repeats to support biofilm formation, given results observed in its S. aureus ortholog, SasG (17). Our lab has previously sought to characterize the Zn 2+ -dependent assembly of longer, more biologically relevant constructs (namely a Brpt5.5 construct), and we identified the formation of larger, Zn 2+ -induced species leading up to the formation of functional amyloid-like fibrils. The presence of amyloid fibrils in S. epidermidis biofilms was demonstrated, and we also showed the fibrils are composed primarily of proteolytically processed Aap. These fibrils are likely to offer physical resilience to the biofilm, as well as resistance to chemical insults: for example, the Brpt5.5 amyloid fibrils, but not oligomers, resist disassembly by the Zn 2+ chelator DTPA or by acidic pH. In contrast, addition of DTPA completely inhibits Brpt5.5 assembly in solution and inhibits initial biofilm formation (but has no effect on mature, pre-formed biofilms) (18).
In this report, we first focus on characterizing the initial, reversible assemblies formed by Brpt5.5 in the presence of Zn 2+ using analytical ultracentrifugation. Our analyses demonstrate the formation of a Brpt5.5 dimer and tetramer, in contrast to Brpt1.5 constructs, which only form dimer (9,13,15,19). By analysis of the linked equilibria between Zn 2+ -binding and Zn 2+ -mediated B-repeat assembly, we report the number of Zn 2+ ions bound upon dimerization and tetramerization. We utilized chemical modifications and sitedirected mutagenesis to narrow down our search for residues in the tetramer interface and Zn 2+coordination sites, resulting in the development of a tetramer-negative mutant. Native Brpt5.5 undergoes a temperature-dependent conformational change in the presence of Zn 2+ that correlated with rapid aggregation; however, the tetramer-negative mutant did not undergo this conformational change or the subsequent aggregation, suggesting that formation of the tetramer is a critical step in amyloidogenesis of tandem B-repeats. Finally, we propose models of the dimer and tetramer assembly states formed by Brpt5.5.

Brpt5.5 exhibits monomer-dimer-tetramer equilibrium
To initiate our investigation into the assembly of Brpt5.5, we performed sedimentation velocity analytical ultracentrifugation (AUC) experiments at increasing ZnCl2 concentrations at a constant Brpt5.5 concentration (Figure 2A, Supplemental Figure S1). In the absence of ZnCl2, Brpt5.5 is monomeric at all concentrations tested (Supplemental Figure S2) with a frictional ratio of 3.33 (Table 1), indicating a highly elongated conformation (compact, globular proteins have a frictional ratio of approximately 1.2-1.4 (20,21)). We observed an increase in the sedimentation coefficient as the ZnCl2 concentration was increased. As expected, based on the dimerization of shorter B-repeat constructs (9,13,15,16,19), the distribution shifted, rather than showing independent peaks locked at specific s* values which change only in intensity. The shifting or sliding of distributions upon assembly is characteristic of a reversible equilibrium exhibiting fast kinetics on the timescale of the sedimentation velocity experiment (22-25). Also, a shift from ~2.2 S to ~6.5 S is unexpectedly large for a monomerdimer assembly (Brp1.5 dimerization resulted in a shift from ~1.5 S to ~2.7 S (9,13)). Based on our previous observations of higher-order assembly of Brpt5.5 in the presence of Zn 2+ (18), we interpreted the sedimentation velocity results as suggesting assembly beyond a dimer. Figure 2B shows the relationship between the weight-average sedimentation coefficient (s̅ ) and the Zn 2+ concentration. At 8 mM ZnCl2, there is significant loss of protein due to aggregation prior to running the experiment, but no further shift in s̅ compared to the 7 mM ZnCl2 condition. Experiments performed at 2-and 3-fold higher protein concentrations showed only a minor increase in sedimentation (Supplementary Figure S3), indicating we are observing a true species, rather than a reaction boundary between two species. Given that the 8 mM ZnCl2 data essentially describe a single species (the largest soluble species before aggregation), we can estimate the frictional ratio of the terminal species at 1.44: less elongated than the monomer, but still indicative of an elongated, nonglobular shape ( Table 1).
In order to better define the species present during Zn 2+ -dependent assembly, a sedimentation equilibrium AUC experiment was performed at 3 mM ZnCl2, where all species should be populated to an observable degree, based on the sedimentation velocity data. A global fit was performed using nonlinear least squares analysis on data at three different protein loading concentrations and at least three speeds. The data were best fitted by a monomer-dimer-tetramer (1-2-4) equilibrium, compared to 1-2, 1-3, 1-4, 1-2-3, and 1-3-4 (Supplementary Table S1). Figure 2C shows the raw data and species fits for the middle concentration of 1.9 µM (0.15 mg/ml) sample, with residuals shown in the upper plot. Higher and lower ZnCl2 concentrations also showed a 1-2-4 equilibrium (see data in Figure 3, as well as Supplementary Figure S4). This is the first data confirming formation of a tetramer by tandem Brepeats. A species plot derived from the experimentally fitted association constants ( Figure  2D) revealed overlapping populations of the monomer, dimer, and tetramer forms of Brpt5.5. Species plots at other Zn 2+ concentrations show a similar trend (Supplementary Figure S4).
While we have previously reported that there is no change in the secondary structure of Brpt1.5 upon dimerization (9), we tested for the presence of any changes that might occur in the secondary structure of Brpt5.5 upon assembly. In the presence of 5 mM ZnCl2, where Brpt5.5 should exist as a mix of dimer and tetramer, there was little to no change in the secondary structure by CD (Supplemental Figure  S5). This indicates there is likely no major local conformational change throughout this reversible assembly. In the context of Brpt1.5, we infer the lack of secondary structure changes and the relatively minimal contact area between the two protomers in the crystal structures as meaning there is little difference, structurally, between the protomers in the monomer and dimer state. The shared coordination of Zn 2+ between the two protomers in the dimer is likely the dominant stabilizing force (15).

Analysis of linked equilibria indicates that Brpt5.5 and shorter constructs share similar assembly mechanisms
We previously analyzed the linked equilibria between Zn 2+ -binding and Zn 2+ -mediated Brpt1.5 and Brpt2.5 dimerization, revealing that dimerization was linked to the binding of ~2 Zn 2+ ions; this is consistent with the X-ray crystal structure of Brpt1.5, which forms an anti-parallel dimer around two Zn 2+ ions (no structural data is available for Brpt2.5) (9,15,19). Sedimentation equilibrium AUC experiments were performed with Brpt5.5 at fifteen ZnCl2 concentrations and the dimerization and tetramer assembly constants were determined. For the dimerization association constant, K12, the slope of the log-log Wyman Plot indicated that 8.1 (±1.0) Zn 2+ ions are bound upon dimerization ( Figure 3A). A comparison of the number of Zn 2+ ions bound during dimerization as a function of the number of G5 domains for Brpt5.5, Brpt2.5 and Brpt1.5 (9,19) revealed an apparent linear trend, with a slope of 1.3 Zn 2+ ions bound per G5 domain, consistent with the 1-2 Zn 2+ ions per G5 domain previously reported (9,19) ( Figure 3B).

Formation of the tetramer requires additional Zn 2+ ions
We then produced a Wyman Plot for the overall tetramerization constant, K14, ( Figure 3C) determined in the linked equilibrium analysis, along with the stepwise dimer-tetramer assembly constant, K24, ( Figure 3D). The slope of the K14 Wyman plot was 24.2 (± 1.7), and that of the K24 Wyman Plot was 5.4 (± 1.6). These data indicate that while dimerization of Brpt5.5 requires 7 to 9 Zn 2+ ions, 4-7 additional Zn 2+ ions are required for the two dimeric species to assemble into a Brpt5.5 tetramer.

Chemical modification to probe the tetramer surface interface
To probe surface residues of Brpt5.5 required for tetramer formation, we chemically modified residues expected to be outside of the dimer interface, based on the Brpt1.5 dimer crystal structure solved ( Figure 4) (15). Because our analysis of linked equilibria suggested a similar dimerization mechanism across these B-repeat constructs, we expect this to be a useful representation of the repeating units of the Brpt5.5 dimer. We performed chemical modifications of tyrosine and arginine residues, primarily due to the relatively gentle conditions required to perform these modifications. One arginine and two tyrosine residues are present in every B-repeat of Brpt5.5 (Supplementary Figure S6). Acetylation of tyrosine residues using 1-N-acetylimidazole ( Figure 4, orange residues) resulted in a significant decrease in the sedimentation coefficient in the presence of Zn 2+ , compared to that of the unmodified Brpt5.5 ( Figure 5). Addition of a bulky, hydrophobic group to arginine residues ( Figure 4, purple), which flank the tyrosine residues on the opposite face of the Zn 2+ -binding site involved in dimerization, also resulted in a shift toward lower sedimentation coefficients, though to a slightly lesser extent than Tyr modification ( Figure 5). Modification of both types of residues resulted in a sedimentation profile very similar to tyrosine modification alone ( Figure  5). Based on the location of these residues, it seems likely that the tetramer is formed via a side-by-side mechanism as opposed to an end-to-end mechanism. This is also supported by the large decrease in the frictional ratio observed for the tetramer compared to the monomer (Table 1).

Site-directed mutagenesis to define the Zn 2+coordination site in the tetramer
After determining from the Wyman plots that 4-7 additional Zn 2+ ions are required for tetramer formation, we began searching for another Zn 2+binding site. Figure 4 (inset) shows a potential Zn 2+binding site that contains a His (H85) and several negatively charged residues (D87, E100, D122) that could coordinate a Zn 2+ ion. These residues are present in each B-repeat spacer region (Supplementary Figure S6). This hypothesized Zn 2+ -binding is located near Y126, one of the residues that decreased tetramer formation upon chemical modification ( Figure 5). We chose the histidine in position 85 (H85) of each B-repeat spacer region for further investigation, due to the importance of His residue H75 in dimerization (15) and the general prevalence of His residues in Zn 2+ coordination sites (26).
To test our hypothesis that H85 is required for Zn 2+dependent tetramerization, we produced a Brpt5.5 pentamutant containing a H85A mutation in each spacer region of Brpt5.5 (i.e. H85A, H213A, H341A, H469A, and H597A), which we will refer to as Brpt5.5 5xH85A for simplicity. Note that there are only 5 spacer regions, while there are 6 G5 domains in Brpt5.5, since the C-terminal halfrepeat is a final G5 domain. The 5xH85A mutant revealed similar secondary structure to the native Brpt5.5 construct by far-UV CD, but showed an 8 °C decrease in thermal stability, likely due to the involvement of the H85 residues in a hydrogen bonding network and electrostatic interactions in each spacer region (Supplemental Figure S7 and S8).
We performed a series of sedimentation velocity experiments examining Zn 2+ -dependent assembly of Brpt5.5 5xH85A ( Figure 6A). In the absence of ZnCl2, 5xH85A was monomeric with a similar sedimentation coefficient and frictional ratio for 5xH85A as observed for WT (Table 1, Supplementary Figure S2). Along with the previously mentioned CD results, these data suggest the H85A mutations do not significantly disrupt local secondary structure or global conformational preferences. With increasing ZnCl2 concentrations, 5xH85A displays an increase in the weight-average sedimentation coefficient (s̅ ) values up to a maximum of ~4 S compared to ~6.5 S for WT ( Figure 6B and Supplementary Figure S3). Individual distributions comparing 3.50 mM ZnCl2 and 8 mM ZnCl2 clearly show significant inhibition of assembly by the 5xH85A mutant ( Figure 6B, inset). Furthermore, the apparent single sigmoidal transition in the 5xH85A weight-average sedimentation coefficient data suggests only a monomer-dimer equilibrium is present.
Equilibrium AUC experiments performed with Brpt5.5 WT and 5xH85A in the presence of Zn 2+ revealed very little change in the dimerization constants ( Figure 6C, Table 2). However, under conditions in which the WT construct predominantly assembled into tetramer, no tetramer species was detectable for 5xH85A ( Figure 6D). Equilibrium assembly constants from global fitting of the AUC data for WT Brpt5.5 and 5xH85A are shown in Table 2. These data suggest that H85 in the spacer region is absolutely critical for tetramer formation but is not involved in dimerization.

H85-dependent Zn 2+ -coordination is required for Brpt5.5 aggregation
Because we did not observe aggregation at high Zn 2+ concentrations during initial characterization of the Brpt5.5 5xH85A construct, we were interested in testing the ability of Brpt5.5 5xH85A to form Zn 2+ -induced amyloid-like fibrils. With WT Brpt5.5 in the presence of 5 mM ZnCl2, we observe a major change in the far-UV CD spectrum at ~225 nm as temperature is increased ( Figure 7A, left panel). Interestingly, Brpt5.5 5xH85A under the same conditions appears to simply unfold as the temperature is increased ( Figure 7A, right panel). The strong minimum observed near 40 °C for WT is likely representative of major rearrangement or twisting of β-sheets (27) into a nucleating species on the pathway to amyloidogenesis, as the appearance of the minimum at 225 nm was immediately accompanied by heavy aggregation in the cuvette and loss of CD signal. We have previously shown that Brpt5.5 under these conditions forms fibers which could be detected by the anti-amyloid OC antibody and amyloid-or aggregation-detecting dyes (18). Furthermore, upon cooling the sample at the end of the experiment, Brpt5.5 5xH85A refolded to its native secondary structure, whereas Brpt5.5 WT exhibited virtually complete irreversibility and failed to regain its native structure ( Figure 7A, black line).
We evaluated the ability for Brpt5.5 5xH85A to form Zn 2+ -induced aggregates via two other methods as well. We monitored light scattering as ZnCl2 was titrated into a cuvette of Brpt5.5 WT or Brpt5.5 5xH85A ( Figure 7B), and we observed a sigmoidal transition with a midpoint near 15-20 mM ZnCl2 for WT. For Brpt5.5 5xH85A, we instead observed a very gradual transition that required higher ZnCl2 concentrations for turbidity. Based on these data alone, we cannot say with certainty if this observed turbidity is related to a very weak propensity for amyloid-like aggregation, or if this is non-ordered or non-specific aggregation.
We used a third complementary technique, dynamic light scattering (DLS), to measure Brpt5.5 particle size in the presence of Zn 2+ as a function of temperature. This approach, in parallel with CD measurements, can provide us with two unique perspectives -local secondary structure changes and global aggregation. In good agreement with our CD observations ( Figure 7A), we observe aggregation by DLS of Brpt5.5 WT near 37 °C, consistent with the appearance of the ~225 nm minimum and subsequent loss of signal by CD ( Figure 7C). In the case of Brpt5.5 5xH85A, there is instead a significant decrease in the hydrodynamic radius (Rh) which is mirrored by the unfolding to random coil observed by CD near 50 °C ( Figure 7D). Due to the highly elongated nature of the B-repeats, unfolding of Brpt5.5 5xH85A to a random coil is expected to be described by a decrease in Rh, contrary to the unfolding of a compact, globular protein. We therefore conclude that the H85 residue and its equivalent residues in each spacer subdomain are critically linked to Zn 2+induced B-repeat amyloidogenesis, due to their role in formation of an obligatory tetrameric intermediate state.

Discussion
Based on the results presented in this study, we can propose models for the Brpt5.5 dimer and tetramer assembly. Linkage equilibria studies suggested a consistent mechanism of dimerization between minimal Brpt1.5 constructs, a Brpt2.5 construct, and Brpt5.5 presented here. The number of Zn 2+ ions bound upon dimerization was found to be a consistent 1-2 Zn 2+ ions per G5 domain. X-ray crystallography structures for Brpt1.5 (15) show an "overlapping," anti-parallel dimer, where there are sufficient Zn 2+ -dependent contacts to accommodate the appropriate number of Zn 2+ ions. We propose Brpt5.5 assembles into a similar "overlapping" dimer ( Figure 8 middle, right) as opposed to a more offset dimer (Figure 8 middle, left). This model for Brpt5.5 dimerization is also consistent with the Brepeat subtype pattern found in Aap from this strain of S. epidermidis (RP62A); Brpt5.5 contains one N-terminal variant repeat, followed by four consensus repeats. The "overlapping" model predicts that all four consensus (more assembly-competent) Brepeats can make contact, while the variant (less assembly-competent) B-repeat overlaps with the half-repeat cap.
Due to the number of B-repeats, one could imagine a variety of orientations or configurations for the tetramer (a dimer of dimers). In Figure 8, we evaluate the plausibility of different configurations of each assembly state. Based on our hydrodynamic data from sedimentation velocity AUC experiments (Table 1), the frictional ratio decreases from monomer to tetramer for WT Brpt5.5. Because we cannot isolate the dimer using WT Brpt5.5, we cannot accurately estimate the frictional ratio of this species. However, using the 5xH85A mutant which dimerizes similarly to WT, we can in fact saturate the dimer population, giving us a frictional ratio smaller than that of the monomer (i.e., slightly less elongated). The "overlapping" dimer we proposed based on linkage studies would indeed exhibit a smaller frictional ratio than the monomer, as it is essentially twice as thick in the z-direction, but similar along the other two axes. Importantly, in the "offset" dimer model, there would not be enough Zn 2+ -binding sites in contact to satisfy our observation of 1-2 Zn 2+ ions bound per G5 domain upon dimerization.
The transition from the overlapping dimer to the tetramer is accompanied by a further decrease in the frictional ratio. If dimers attached end-to-end to form the tetramer, there would be a significant extension along the x-axis, while the other axes would be unchanged. This would result in a much higher frictional ratio of the tetramer compared to the dimer. Another option for the tetramer is a "side-by-side" dimer of dimers. There could be several arrangements fitting this description, but each variation presented in Figure 8 would be expected to yield a lower frictional ratio than the dimer, as was observed. A tilted or twisted side-byside dimer of dimers could also be plausible, given that our linked equilibrium result suggests that as few as 4 additional Zn 2+ ions may be required for formation of the tetramer (suggesting not all Brepeats would need to overlap). The "side-by-side" models are also more reasonable than the "end-toend" model in a biological sense, as adjacent copies of cell wall-anchored Aap extending outward from the opposing staphylococcal cell surfaces would be available to interact with neighboring Aap molecules after the initial dimerization event occurs.
Our previous demonstration of the ability of the Brepeats of Aap to form a functional amyloid in the presence of Zn 2+ was an early indication that tandem B-repeats (longer than the Brpt1.5 construct) have the ability to assemble into higherorder oligomers (18). This study revealed Brpt5.5 exhibits a monomer-dimer-tetramer reversible equilibrium in the presence of Zn 2+ . In fact, we found that inhibiting formation of the tetramer through mutation of predicted Zn 2+ -binding sites also prevented a conformational change associated with amyloidogenesis. This raises the intriguing possibility that the tetrameric species acts as a nucleating species for amyloidogenesis and may represent a target for future therapeutics designed to inhibit formation of functional amyloid in S. epidermidis biofilms -a component that appears to confer a high degree of physical strength and chemical resistance to the biofilm.

Protein expression and purification
Brpt5.5 WT cloning, expression, and purification was performed exactly as described previously (18). The Brpt5.5 5xH85A mutant was produced via the Agilent QuikChange II Site-Directed Mutagenesis Kit. Mutated residues include H85, H213, H341, H469, and H597, all of which were mutated to alanine. Primers used for mutagenesis are listed in Supplementary Table S2. Brpt5.5 5xH85A was purified using the same procedures as Brpt5.5 WT.

Analytical ultracentrifugation
A Beckman Coulter XL-I analytical ultracentrifuge was used for AUC experiments. For sedimentation velocity experiments, two-sector epon-charcoal 1.2 cm centerpieces were used with sapphire windows. Data were collected via absorbance optics at ~236 nm (interference optics in the case of chemical modification experiments) at 48,000 rpm at 20 °C in an An-60 Ti rotor. Unless specified otherwise, all sedimentation velocity experiments were performed using 0.50 mg/ml Brpt5.5 WT or 5xH85A. Experiments were run overnight, usually around 20 hours at which point all protein was sedimented. Data were analyzed using SEDFIT's continuous c(s) distribution model (28), SEDANAL's wide distribution analysis (WDA) (29), or DCDT+ version 2.4.3 (30,31).
Sedimentation equilibrium experiments were performed using protein dialyzed into the specified ZnCl2 concentration in 50 mM MOPS pH 7.2, 50 mM NaCl. After dialysis, protein concentrations were adjusted to approximately 0.50, 0.15, and 0.05 mg/ml and loaded into a six-channel 1.2 cm centerpiece. Samples were centrifuged at 10,000, 13,000, 17,000, 24,000, and 37,000 rpm for 24 hours each, which provided ample time for equilibration of the monomer species to occur at each speed. Raw data were trimmed using WinReedit V0.999 and then fit using WinNonlin V1.080. Data from at least three speeds and three loading concentrations were used for analysis of each Zn 2+ concentration. Partial specific volumes were estimated using SEDNTERP (32). Buffer density and viscosity was unavailable for MOPS, so default values were used in SEDFIT, DCDT+, and SEDANAL. As a result, distributions are plotted against the apparent sedimentation coefficient (s*) instead of s20,w values adjusted for temperature, density, and viscosity. Weight-average sedimentation coefficients (s̅ ) were calculated from 0 -15 s* in SEDFIT. For DCDT+, dc/dt was computed using the "auto adjust" function to select which scans should be used. The (s̅ ) values were calculated from integration over the entire distribution of s* for each dataset. For SEDANAL's WDA, the range of integration for calculating (s̅ ) was from 1 -20 s*.
To determine the number of ligand molecules bound or released upon a ligand-dependent equilibrium event, the following equation was used (33): To convert the logK14 values to logK24 values, the following equation was used: Where K14 is the overall association constant for formation of the tetramer from the monomer, K12 is the (stepwise) association constant for the formation of the dimer from the monomer, and K24 is the (stepwise) association constant for the formation of the tetramer from the dimer.
Error propagation for logK24 was calculated according to Equation (3).

(Equation 3) = 3(2 × ) , + ( ) ,
Where ẟQ is the standard deviation in logK24 and ẟa and ẟb are the standard deviations in logK12 and logK14, respectively.
The standard deviations for logK24 and logK14 were determined from the WinNonlin 95% confidence intervals using Eq. (4).

(Equation 4)
Where ̅ is the sample mean, σ is the sample standard deviation, and n is the sample size (831). The critical t-value, t, was calculated at Wolfram|Alpha.com. The input was "StudentTDistribution[831]" which reported a value of 1.96282 for the 97.5 th percentile for a onetail t-test. This is equivalent to a 95 th percentile for a two-tail t-test. After propagating error for logK24, the 95% confidence interval could be determined using Eq. (4). Because 95% confidence intervals for logK12 and logK14 determined in WinNonlin are asymmetric, we assumed two distributions are present and defined a standard deviation based on the lower confidence limit and another standard deviation based on the upper confidence limit. We used the average standard deviation to determine the variance used for weighting. For logK24, we propagated errors based on the standard deviations from the lower limit and upper limits from logK12 and logK14 to get two separate 95% confidence intervals. We then averaged the lower limits from the two confidence intervals to get an average lower confidence limit, and then used to same process to estimate the upper confidence limit. The linear regression performed on the logK24 plot was also weighted based on 1/variance.

Chemical modification
Arginine chemical modification was performed using p-hydroxyphenylglyoxal, HPG (G-Biosciences). HPG was dissolved in water at 100 mM. Brpt5.5 at 1 mg/ml was dialyzed into 50 mM MOPS pH 7.2, 50 mM NaCl overnight, then diluted to 0.50 mg/ml in a solution containing 20 mM HPG (final concentration). The reaction was incubated at room temperature for 3 hours before loading AUC cells and allowing the samples to equilibrate to 20 °C for 1 hour before starting the sedimentation velocity experiment. The Zn 2+ -containing samples had 5 mM Zn 2+ added before loading the AUC cells.
The unmodified sample was treated identically, but with addition of water instead of HPG.
Tyrosine modification was performed using a final concentration of 2 mM 1-N-acetylimidazole (Sigma-Aldrich). Brpt5.5 was prepared in the same way as with arginine modification. 1-Nacetylimidazole was dissolved in water at 100 mM. The reaction was incubated at room temperature and protected from light for 2 hours before adding 5 mM ZnCl2 and performing the sedimentation velocity analysis. For the double modification, both HPG and 1-N-acetylimidazole were added at 20 mM and 2 mM final concentrations, respectively. The reaction was protected from light and incubated at room temperature for 2 hours before starting the AUC experiment.

Circular dichroism
Circular dichroism (CD) experiments were performed on an Aviv 215 CD spectrophotometer equipped with an Aviv peltier junction temperature control system and using a 0.5 mm quartz cuvette (Hellma Analytics). For temperature wavelength scans, a single wavelength scan was recorded at 10 °C intervals from 20 °C to 90 °C and back to 20 °C. Scans were taken from 300 nm to 190 nm in 1 nm steps, with a 3 second averaging time. The cuvette was not removed in between scans, and a macro was used to perform the experiments sequentially. Protein concentrations were 0.50 mg/ml (6.5 µM) and were dialyzed into 50 mM MOPS pH 7.2, 50 mM NaCl, then ZnCl2 was added to a final concentration of 5.00 mM before loading the cuvette. To convert the machine units, θ, to mean residue ellipticity, [θ], Eq. (5) was used. Mean residue weight, MRW, was calculated based on amino acid sequence by ExPASy's ProtParam (34) for Brpt5.5 and Brpt5.5 5xH85A separately, l was 0.05 cm, and concentration, c, was in mg/ml.

(Equation 5)
[ ] = × 10 × × For temperature-dependent experiments (Figure 7), the protein concentration was 1.00 mg/ml and samples were dialyzed in 50 mM MOPS pH 7.2, 50 mM NaCl containing 3.50 mM ZnCl2. A temperature equilibration time of 2 minutes, averaging time of 3 seconds, and 0.5 °C interval was used, which resulted in a similar time duration compared to the DLS experiments. Figure S7B) were performed with 20 µM Brpt5.5 WT or 5xH85A in 50 mM MOPS pH 7.2, 50 mM NaCl. The data were converted to mean residue ellipticity and were fitted in SigmaPlot 12.5 (Systat Software, Inc). The data were fitted to a two-state transition between a folded and unfolded monomer, correcting for pre-and post-transition linear changes as a function of temperature. The fitting assumed no change in the heat capacity between the folded and unfolded states (35).

Turbidity assay
A BioMate 3S UV-Vis Spectrophotometer was used to record the absorbance (or light scattering) at 280, 400, and 700 nm. Protein concentrations were confirmed using the 280 nm absorbance reading before Zn 2+ additions. A 200 µl sample of 0.50 mg/ml (6.5 µM) Brpt5.5 or Brpt5.5 5xH85A, which had been dialyzed in 50 mM MOPS pH 7.2, 50 mM NaCl, was added to a quartz microcuvette. 500 mM ZnCl2 was titrated in 1 µl additions, gently shaking the cuvette between each addition and reading.

Dynamic light scattering
To follow temperature-induced aggregation, 200 µl of protein dialyzed into 50 mM MOPS pH 7.2, 50 mM NaCl, 3.50 mM ZnCl2 was filtered and added to a low-volume quartz microcuvette. Temperature experiments were performed on a Malvern Zen 3600 Zetasizer Nano, using 2 °C intervals with 120 seconds of equilibration time, and 3 measurements at each temperature with an automatic measurement duration. The temperature-dependent changes in viscosity were accounted for within the Zetasizer software.

Data availability
All data described are presented either within the manuscript or in the Supporting Information. All values determined from data collected at 0.50 mg/ml (6.5 µM) protein at 20 °C in 50 mM MOPS pH 7.2, 50 mM NaCl (with the addition of the specified ZnCl2), except for Brpt5.5 WT tetramer, where 1.50 mg/ml protein was used to ensure as much saturation of the tetramer as possible (Supplementary Figure  S3). The weight-average sedimentation coefficient (s̅ ) and weight-average frictional ratio (f/f0) are from SEDFIT's c(s) analysis. Values are not reported for Brpt5.5 WT dimer, as this species can neither be isolated nor highly enriched under these conditions. For Brpt5.5 WT tetramer and 5xH85A dimer, minor amounts of monomer and/or dimer are present, therefore, the reported values are only approximations. Data were collected at 20 °C. Data were collected at 20 °C.     4FUN). Tyrosine residues are colored orange, arginine residues are colored magenta, and hypothesized Zn 2+ -binding residues important in tetramer formation are colored red. The dimer interface surface is colored blue. Image (A) is rotated 90° along the y-axis compared to (B), which is turned 75° to create a view looking down along the side of the dimer. The bottom left inset (C) shows higher detail in the region within the black square from (B). The red arc in the bottom right image (D) represents where we would expect a second dimer to interface with the presented dimer. These images were generated using PyMOL (The PyMOL Molecular Graphics System, Version 1.8, Schrödinger, LLC).  Single experiments have also been performed at 3.50 mM, 5.00 mM, and 8.00 mM ZnCl2 at least twice and provided results within 0.5 S of the presented data. Panel (C) shows sedimentation equilibrium AUC data for Brpt5.5 WT and 5xH85A at the lowest protein loading concentration (0.05 mg/ml). At this loading concentration, WT produces very little tetramer (blue line), but significant amounts of dimer (red line). Comparing the left (WT) and right (5xH85A) halves of this panel show how similar the dimerization behavior is between the two proteins. Panel (D), however, is at 0.50 mg/ml Brpt5.5 -a condition producing significant tetramer in WT (left). Under the same conditions, 5xH85A (right) showed only monomer and dimer. Empty black circles are raw absorbance data, grey lines are the fits for total signal, and black, red, and blue lines show monomer, dimer, and tetramer species fits.  The C-terminal half-repeat is a G5 domain that behaves similar to the G5 domain in consensus Brepeats. Based on the results of this study, we can eliminate several models of assembly based on biophysical data. However, we will require additional data to distinguish between the "side-by-side" tetramer configurations.