Molecular-level observation of the self-assembly of a virus-like particle

Protein self-assembly is crucial for biological function, enabling emergent properties such as structural stability, cooperativity and dynamic response that proteins cannot achieve individually. Driven by a set of non-covalent homo- and hetero-interaction principles^2,15, self-assembly spans several scales and dimensions¹⁶, from soluble oligomers to surface-associated clusters on membranes. In solution, it underpins the dynamic organization of the cytoskeleton, the formation of bacterial microcompartments, viral capsids and membraneless organelles^5,17,18,19, whereas on membranes, it mediates signalling, immune recognition and virus–host interactions^{20,21,22,23,24}. Studying and quantifying assembly across spatial and temporal scales is thus essential for explaining how structure, symmetry and dynamics are coupled to enable biological function, how they are dysregulated in disease^3,4 and how they may be used for therapeutic intervention.

An archetypal example for biomolecular self-assembly processes are simple spherical viruses, in which identical protein subunits interact to form multivalent building blocks that further assemble into highly regular symmetric, closed capsid structures, encapsulating the viral genetic material^6,7,25,26. This process showcases self-assembly dynamics finely tuned to distinct phases of the viral life cycle, yet capable of proceeding spontaneously with high yield, enabling its recapitulation in relatively simple in-vitro experimental systems across several viruses¹³. Acquiring pathway-level understanding of the underlying molecular dynamics is critical for the rational design of new artificial capsid-like protein nanocages^9,10, as well as the design and development of antiviral treatments^27,28.

The fundamental challenge of visualizing the molecular details of simple spherical capsid assembly comes down to two factors. First, the self-limiting free energy landscape results in a well-defined, finite and closed complex and involves weak and reversible pairwise interactions. These properties make assembly stochastic, whereas key intermediates are typically short-lived and of low abundance^{29,30,31,32,33}. Second, the involvement of tens to thousands of subunits results in an exponentially increasing number of molecular assembly paths and a high degree of heterogeneity in solution^34,35. As a result, ensemble-based approaches have struggled with this heterogeneity, relying on complex analysis or modelling^{29,34,36,37,38,39}.

Single-molecule approaches have been applied to overcome such heterogeneity: charge detection mass spectrometry and resistive pulse sensing provide ensemble-averaged snapshot observations of a subset of stable intermediates but struggle with the temporal resolution required to capture dynamics, with charge detection mass spectrometry additionally not operating in solution^40,41,42. Single-molecule fluorescence yields dynamics but struggles in quantifying the degree of oligomerization^43,44, whereas atomic force spectroscopy reveals structure and interactions at the protein subunit scale only in 2D, in which full capsids cannot assemble^45,46. In terms of monitoring capsid assembly, interferometric scattering microscopy has been used to monitor the formation of capsids on an RNA template⁴⁷, yielding information on nucleation and elongation at the single-particle level. This study, however, did not have the temporal resolution and sensitivity required to reveal molecular-level details of the assembly process. As a result, despite decades of dedicated study, no experimental approach has been successful in visualizing the molecular mechanism underlying capsid assembly¹³. Thus, although theoretical and computational models for assembly are established^{48,49,50,51,52}, fundamental questions remain, such as how assembly navigates  a highly heterogeneous configurational space, what molecular mechanisms lead to or avoid kinetic traps and what sequence of molecular events result in capsid polymorphism.

Overcoming these limitations requires a new experimental framework. Such a framework must be able to: (1) quantify the thermodynamic and kinetic parameters that govern the fundamental, pairwise interactions between multivalent subunits; (2) monitor particle assembly dynamics at the ensemble level; (3) identify transient intermediates and map their relative abundances as a function of time; (4) monitor the assembly progression of single complexes by capturing the sequence of microscopic states and the transition rates between them. Here we establish such a framework by combining MP¹⁴ with a single-molecule trapping approach⁵³, enabling complete, molecular-level characterization of the assembly process of a VLP.

To enable an analytical understanding of the stoichiometries and topologies involved in the assembly pathway of empty VLPs, we selected an engineered, self-assembling VLP (mi3-VLP (ref. ⁵⁴); Methods) under evaluation at present as a multivalent vaccine platform^12,55. The mi3-VLP consists of 60 identical mi3-monomers, hierarchically assembled into a dodecahedron from 20 homotrimeric building blocks (mi3-trimers), yielding a particle with 12 pentagonal faces, sharing molecular similarity with T = 1 icosahedral native viral capsids (Fig. 1a). Although the geometry is dodecahedral rather than the triangulated icosahedral lattice found in viruses, we expect that the fundamental biophysical principles governing the assembly of empty capsids are conserved. The exact capsid and assembly mechanism, symmetry and local conformations, however, will govern the specific pattern of locally stable intermediates (Fig. 1a), the degeneracy values of microstates and the exact dynamics of how assembly pathways branch^31,38.

We begin by characterizing the assembly process in solution using standard MP, in which individual proteins and complexes bind non-specifically from solution to a glass surface. At 58 nM total mi3-monomer concentration, the solution distribution is dominated by mi3-monomers and mi3-trimers at 38 ± 2 kDa (see also Supplementary Fig. 1) and 108 ± 1 kDa, respectively (Fig. 1b, top and Supplementary Figs. 2 and 3). Plotting the mass distribution on a logarithmic scale (Fig. 1b, middle) shows the extremely low abundance of intermediates in the 150–500-kDa mass range, as well as particles near the measured mass of complete mi3-VLPs (2,030 ± 10 kDa; Supplementary Note 1 and Supplementary Fig. 2b). Conversion of particle abundances into mass fractions (Fig. 1b, bottom, in which each species was weighted according to its oligomeric state) shows that mi3-monomers are predominantly found in trimeric form (65 ± 4%), followed by fully assembled VLPs (15 ± 4%), monomers (11 ± 3%) and small oligomers (9 ± 3%) (Fig. 1b, bottom). At a higher total monomer concentration (350 nM), most of the monomers are now found in assembled VLPs (82 ± 5%, at 1,982 ± 25 kDa) (Fig. 1c). The small deviation of the average mass of assembled VLPs (1,982 versus 2,030 kDa) could be caused by a fraction of particles missing one trimeric subunit owing to slow kinetics associated with capsid closure⁵⁶. By globally fitting the law of mass action across several total protein concentrations, we can convert these relative abundances of the three dominant molecular states (mi3-monomer, mi3-trimer and VLP) into the affinities governing the assembly process^34,50 (Fig. 1d and Supplementary Note 2), namely, \({K}_{{\rm{D}}}^{(1)}=1.3\pm 0.4\,{\rm{\mu }}{\rm{M}}\) and \({K}_{{\rm{D}}}^{(2)}=2.5\pm 0.4\,{\rm{\mu }}{\rm{M}}\) (Fig. 1d, bottom). The key pairwise interactions are thus weak relative to the pseudocritical concentrations needed for assembly (about 50 nM), which emphasizes the importance of multivalency in stabilizing these interactions.

A notable challenge for characterizing self-limiting assembly in solution is the low abundance of assembly intermediates. In our case, intermediate states are those originating from assembly of mi3-trimers into larger oligomers, on-path to the full VLP. One approach to make higher-order assembly more favourable is to reduce the entropic penalty associated with complex formation. Here we achieve this by tethering hexahistidine-tagged (6xHis-tag) trimeric subunits to supported lipid bilayers (SLBs), where they are able to freely diffuse in two dimensions (Methods). In this 2D configuration, rotational degrees of freedom are constrained, pre-aligning trimers for oligomerization, thus increasing the interaction free energy gain per interaction^57,58. Furthermore, surface confinement results in an increased effective concentration and therefore promotes assembly (Fig. 2a). We validated that mi3-subunits do not interact with the SLB in the absence of a tag (Supplementary Fig. 5) and therefore we expect that tethering to the 2D surface maintains the solution structure and conformation.

In contrast to the experiments shown in Fig. 1, in which we characterize solution distributions from non-specific binding of proteins to a glass surface, the data now consist of individual proteins diffusing in 2D on an SLB^21,59,60 (Fig. 2b). Different oligomers of mi3-trimers appear at their respective mass multiples (Fig. 2c) and are resolvable by mass even at the raw frame rate of our measurement (270 Hz). In analogy to a solution-based experiment, in which increasing the solution concentration leads to a higher fraction of assembled capsids (Fig. 1c), raising the surface density of mi3-trimers increases the abundance of higher-order oligomers (Fig. 2d). We observe the expected exponential decay in higher oligomer abundance with the exception of the pentamer of mi3-trimers, which is stabilized by the further interaction associated with ring formation, as observed also for T = 1 icosahedral capsids⁶¹. Larger assemblies are not formed, as the concentration of mi3-subunits in solution is well below the pseudocritical concentration for assembly (<5 nM), whereas surface tethering prevents out-of-plane interactions. In this way, we arrest the assembly and characterize the formation of the smallest stable intermediate, a pentagonal face of mi3-trimers.

Resolving the oligomeric distribution while directly measuring the mi3-trimer surface density allows us to construct a complete thermodynamic model for the 2D assembly. Here we require only one parameter: the pairwise, standard 2D association free energy change, \(\Delta {G}^{0}(2{\rm{D}})\) (Supplementary Note 3.1 and Supplementary Fig. 6). Fitting the oligomeric occupancies as a function of surface density (Fig. 2e) yields a 2D interaction free energy gain of 6.75 ± 0.2 k_BT per contact that corresponds to \({K}_{{\rm{D}}}^{2{\rm{D}}}=0.74\pm 0.15\,{{\rm{\mu }}{\rm{m}}}^{-2}\) for mi3-trimeric subunits.

We can now use the ratio of the 2D and 3D dissociation constants, which defines a characteristic confinement length \(h=\frac{{K}_{{\rm{D}}}(2{\rm{D}})}{{K}_{{\rm{D}}}(3{\rm{D}})}\), to reveal the origin of affinity enhancement on surface confinement (Supplementary Note 3.2). In our case, h = 0.5 ± 0.1 nm, falling within the estimated values for enhancement arising from restricted translational and rotational degrees of freedom in two dimensions⁵⁸. By contrast, a substantial membrane-induced enthalpic stabilization would result in values that are orders of magnitude smaller. Therefore, we conclude that, thermodynamically, our surface-based measurement is representative of measurements in solution, the only exception being a different scaling originating from the reduction in dimensionality.

Thermodynamic analysis (Figs. 1d and 2e) suggests that the formation of this pentagonal face on the SLB, and the formation of the complete VLP in solution, are consistent with a single trimer–trimer contact free energy. Accordingly, we expect that any transiently stabilized intermediates or variability in transition times between states are unlikely to arise from cooperativity or alternative conformations, which would result in different fundamental interaction parameters. Instead, any assembly heterogeneity is topology driven: as assembly proceeds, the local coordination (number of intertrimer contacts per subunit) increases and ring closure adds further stabilization, thereby governing intermediate lifetimes and transition kinetics.

SLB tethering of subunits enables continuous monitoring of the molecular masses, positions, mobilities and interactions between individual subunits (Extended Data Fig. 1a,b), a measurement that cannot be performed in solution owing to rapid diffusion. Simultaneous tracking of molecular mass and position allows each association and dissociation event to be identified directly, providing both the reaction coordinate and the molecular state. We measured the average dissociation dwell times for the dimers and trimers of mi3-trimers, with transition times of 0.65 ± 0.05 s and 0.36 ± 0.04 s, respectively (Fig. 2f, Extended Data Figs. 1 and 2 and Supplementary Note 4). The factor of 2 between the dissociation times strengthens the suggested independence between the pairwise interactions (Extended Data Fig. 1d). Combining these measurements with the measured mobilities (Supplementary Fig. 8) and the equilibrium constant obtained from our thermodynamic analysis yields the complete elementary reaction dynamics governing the formation of the pentameric face, including the bimolecular association rate constants (Extended Data Fig. 1e,f and Supplementary Note 3.3). The values obtained show that association between the trimeric subunits is essentially diffusion-limited (Extended Data Fig. 1f), with no appreciable energetic barriers for association, and, as a result, that sampling the correct orientation between the two trimeric subunits is most likely the limiting factor.

By separating the assembly process into two phases, solution and SLB (Fig. 3a), we can create a modest driving force for assembly, while keeping the assembly conditions close to equilibrium. We achieve this by producing an equilibrated surface mixture of oligomers that contains closed pentameric rings, which serve as a nucleus for assembly. They represent the smallest stable oligomeric state with a higher probability to elongate than to dissociate. In solution, untagged mi3-subunits form an equilibrated mixture in which mi3-monomers, mi3-trimers and complete VLPs coexist (Fig. 1d). Because each phase by itself is equilibrated, there is no net driving force for assembly within each phase. However, coupling the two equilibrated systems introduces a chemical potential difference between the pentagonal ring and the complete VLP, mediated by the pseudocritical concentration of free mi3-trimers. In this coupled configuration, the chemical potential difference (Extended Data Fig. 3 and Supplementary Note 5) between the surface pentameric rings and the complete VLPs is constant, because the bulk concentration is effectively constant.

The resulting small driving force (about 15 k_BT), together with diffusion-limited and reversible inter-mi3-trimer interactions, result in a slow assembly reaction, enabling near-equilibrium sampling of the assembly propagation pathway. Notably, subunits in solution lack the histidine tag and therefore do not interact with the SLB (Supplementary Fig. 5). Any observed mass additions thus arise from subunits from solution binding to SLB-bound pentamers (Fig. 3b and Supplementary Figs. 10–18). Therefore, the assembly propagation is dictated by the 3D, solution free-energy landscape. Repeating the experiment at decreasing solution concentrations slows down the assembly timescale, ranging from about 10 min for complete assembly at 88 nM to about 20 min at 44 nM (Fig. 3b) and 40 min at 29 nM (Extended Data Fig. 4 and Supplementary Figs. 10–17). Although the timescales differ, the intermediate states (indicated in Fig. 3b, black vertical lines) are consistent across different concentrations. Averaging distributions across technical repeats during time periods in which relatively little change in intermediates is observed improves the statistics and reveals well-resolved peaks and valleys as a function of mass (Fig. 3c and Extended Data Fig. 5).

Overlaying the calculated free energy landscape of the lowest free energy path between the mi3-trimeric subunit and the complete VLP reveals the driving force for assembly following the formation of the pentagonal ring (Fig. 3c, top). It also shows that oligomeric states that accumulate along the assembly reaction match local minima in the free energy landscape, whereas low abundances correspond to local maxima (Fig. 3c and Extended Data Fig. 5). Examining the associated stoichiometries shows that stable intermediates are those corresponding to closed pentagonal faces (or closed rings), stabilized by a larger average trimer–trimer coordination number. It is important to note that the equilibrated grand canonical free energy landscape, representing the equilibrated solution, does not change when the two systems are coupled, only the starting point for assembly. Therefore, the measured distribution of oligomeric species on the SLB propagates in time according to the molecular transitions governed by the equilibrated underlying free energy potential.

Population-level measurements highlight overrepresented states and thus hint at key assembly intermediates. From an ergodic standpoint, repeated measurements of one complex should converge to the ensemble probability distribution. However, the ensemble does not provide information on the sequence of steps or the transition dynamics. We therefore combined MP with a single-molecule confinement approach⁵³ to observe the real-time assembly dynamics of VLPs at the level of individual complexes with molecular resolution. To achieve this, we create circular SLBs of 5 µm diameter by lithographic removal of a dense poly-L-lysine polyethylene glycol (Fig. 4a, top) layer. Any species bound to the SLB are now confined and can thus be observed and mass measured for extended periods of time (Extended Data Fig. 6).

We form SLB-bound pentameric rings by adding 6xHis-tagged mi3-subunits as before but now to SLB traps, followed by approximately 30 min of equilibration (Methods). Subsequently, we add an equilibrated solution of untagged mi3-subunits at total protein concentrations between 88 and 100 nM. Mi3-trimeric subunits from solution bind to tethered pentameric rings, which we monitor in real time by continuous mass measurement (Fig. 4a and Supplementary Video 2). The resulting mass traces reveal the oligomeric states that are populated for extended time periods, separated by sharp mass changes. Intermediate masses match those of topologically closed structures (red lines), which also accumulate in ensemble experiments (Fig. 3c). We observed these features irrespective of assembly rate, for which both slower (Fig. 4a, top) or faster (Fig. 4b, black curve) molecular mass trajectories exhibited similar features.

Superimposing multiple trajectories (Fig. 4b) confirms these observations, for which the normalized distribution exhibits features similar to the ensemble results (Fig. 3c), linking the single complex dynamics experiments (Fig. 4b) to population mass distributions (Fig. 3c). Although the rapid off-rate combined with the small mass change (108 kDa) associated with pairwise trimer–trimer interactions (Fig. 1) is beyond the capabilities of our present experimental approach, we can observe and identify the key states with longer dwell times, that is, those representing closed structures. Notably, we do not observe disassembly in any of the measured trajectories.

When evaluating the lifetimes associated with different intermediates (Supplementary Figs. 19 and 20), the pentameric ring exhibited the longest dwell time, whereas other species showed broadly similar dwell times (Fig. 4c and Extended Data Fig. 7a). This is readily explained from a molecular perspective: transitioning from the pentagonal ring to the next stable state (8-mer) requires binding of three weakly interacting mi3-trimers to form an extra topological face before any of them dissociates. The subunit concentration in solution determines the collision frequency and therefore the probability that three subunits bind in the correct configuration before unbinding. By contrast, for subsequent transitions up to the 14-mer, closing each new face requires only two more subunits, leading to shorter transition times. Using the measured dwell times (Fig. 4c), we simulated the expected time-dependent oligomeric distribution of the closed configurations at a mi3-monomer concentration of 88–100 nM. The resulting population evolution is in good agreement with the independently measured population-level distribution acquired at a comparable concentration (Extended Data Fig. 7b,c), showing a direct connection between the stochastic dynamics of individual assembly trajectories and the behaviour of the ensemble. We note that the reported pentamer dwell time may be affected by the approximately 20 s gap between subunit addition and the start of acquisition, as well as the maximum observation time of 300 s (Supplementary Fig. 22). Because the 14- and 15-mers are both closed structures, we report the cumulative dwell time (top of Fig. 4c).

Our measurements reveal the molecular, energetic and kinetic details of a topology-driven, self-limiting, VLP assembly pathway (Extended Data Fig. 8a). Trimeric subunits engage in weak pairwise interactions (K_D ≈ 2 μM) allowing for reversible encounters, which stochastically explore molecular configurations until a topologically closed stable arrangement is reached. Notably, the short lifetime of individual interactions prevents the persistence of loosely connected structures. Once a subunit attains a coordination number ≥2, the associated stabilization results in a much slower off-rate than the on-rate for new subunits arriving. Repetition of this process throughout the growth of the dodecahedron enables an efficient and well-defined assembly process.

Our results provide a molecular-level explanation to the kinetic origin of the difference between nucleation and elongation, the hallmark of a two-state assembly process (Fig. 1) and characteristic of many capsids and VLPs^32,33,62, for which the nucleus was suggested to be a small polygon intermediate⁴⁸. Here the smallest stable intermediate is a pentagonal ring, formed after four trimer additions. The subsequent transition (5-mer to 8-mer) requires three additions, whereas later steps up to 14-mer require only two. Our measurements (Fig. 2) suggest that the interactions are independent and therefore we expect that the corresponding reaction rates scale with the fourth, third and second powers of the mi3-trimer concentration, respectively (Extended Data Fig. 8a). Owing to the irreversibility of the closed topologies, transitions between these configurations can be viewed as a series of first-passage stochastic events. Because the first-passage time is highly sensitive to the number of additions, formation of the first pentagonal face is the critical step: once formed, it enables propagation of the entire assembly process, with sequentially increasing rates. The distinction between nucleation and elongation thus arises directly from the difference in the number of subunits required to complete topological rings, corresponding to a sequence of first-passage events.

Observation of single VLP assembly events shows that, within the timescale of assembly, the reaction proceeds through a sequence of irreversible, specific steps. This creates an apparent contradiction between microscopic irreversibility that predicts total consumption of mi3-trimeric subunits, whereas our solution data (Fig. 1) shows coexistence between subunits and complete VLPs, consistent with the law of mass action^63,64. Key here is that, although specific states can be considered as irreversible, the pairwise interactions leading to these states are weak and reversible. Thus, while the assembly reaction proceeds and the concentration of free subunits decreases, the timescale for creating the pentameric intermediate rapidly increases. At the pseudocritical monomer solution concentration, which is eventually reached independent of the starting concentration as VLPs are assembled, this timescale becomes either so long that assembly is practically irrelevant or comparable with the timescale of ring disassembly (longer than our observation window). In both cases, experimentally, the result complies with the expected observation of the law of mass action, in which subunits and complete VLPs coexist in solution.

We can now understand the assembly process in full detail, represented by a simple stochastic kinetic simulation (Supplementary Note 7). At sufficiently low concentrations, lower or equal to the pseudocritical mi3-trimer concentration (17 nM; Fig. 1d), the probability of five trimers coming together before at least one of them departs becomes vanishingly low. As a result, the pentagonal ring is never formed and thus, also, no VLPs (Extended Data Fig. 8b, left). If, however, we skip this low-probability initial pentagonal ring formation step, here by lowering the barrier using an SLB, assembly does become possible at the same solution concentration (Extended Data Fig. 8b, middle and Fig. 3). Finally, at concentrations that result in a high assembly yield, the timescale difference between ring formation and subsequent propagation makes intermediates so transient that, at equilibrium, only free subunits and complete VLPs will coexist (Extended Data Fig. 8b, right and Fig. 1b,c).

Our work provides experimental access to fundamental assembly mechanisms of empty VLPs, showing how weak, reversible, multivalent interactions lead to nucleation-like behaviour through a restricted set of highly coordinated, productive intermediates. Further regulatory factors, including conformational regulation and shell elasticity are nevertheless expected to further shape assembly pathways of native capsids and capsid-like structures. These have been proposed to play important roles in capsid polymorphism⁶⁵ and in affecting assembly outcomes in response to small-molecule assembly modulators²⁷ and will be the subject of future work using our approach. Beyond the implications for our understanding of the fundamental principles driving and controlling self-assembly, our approach represents a framework for studying biomolecular assembly and dynamics more broadly. The approach of characterizing pairwise interactions, quantifying equilibrium distributions and monitoring individual assembly events and dynamics is general: here it was applied to a simple, homo-oligomeric analyte, but owing to the universality of mass measurement, our approach can be applied to a broad range of multimolecular systems, opening up new avenues for studying biomolecular dynamics and mechanisms in the context of biological function and regulation.

Expression and purification of SC003-mi3 VLP

The mi3-VLP (also known as SC003-mi3) was derived from i3-01 (ref. ⁶⁶) by introducing two mutations that remove surface-exposed cysteines to prevent aggregation and by genetically fusing a SpyCatcher domain to the N-terminus to enable plug-and-play attachment of SpyTagged proteins⁵⁴. The plasmid pET28a-SpyCatcher003(SC003)-mi3 (gift from Professor Mark Howarth, Cambridge University) was transformed into Escherichia coli BL21(DE3) RIPL cells (Agilent) and plated on Luria-Bertani (LB) agar supplemented with 50 µg ml⁻¹ kanamycin. After incubation for 16 h at 37 °C, a single colony was used to inoculate 10 ml LB media containing 50 µg ml⁻¹ kanamycin and grown overnight at 37 °C with shaking at 200 rpm. This starter culture was transferred into 1 l LB medium with the same antibiotic and incubated at 37 °C, 200 rpm, until the OD600 reached about 0.6. Protein expression was then induced with 0.42 mM IPTG and cultures were grown for a further 16 h at 22 °C with shaking (200 rpm). Cells were collected by centrifugation at 4,000 × g for 15 min. Cell pellets were resuspended in 40 ml lysis buffer (20 mM Tris-HCl, 300 mM NaCl, pH 8.5 at 4 °C) containing 0.1 mg ml⁻¹ lysozyme, cOmplete EDTA-free protease inhibitor cocktail (Roche, 1 mg ml⁻¹) and 1 mM PMSF. The suspension was passed through a high-pressure homogenizer (Constant Systems) at 30,000 psi, with 2–3 passes on ice. The lysate was clarified by centrifugation at 35,000 × g for 45 min at 4 °C and the supernatant was collected. Ammonium sulfate was then added at 170 mg/ml of lysate and the mixture was incubated at 4 °C for 1 h with agitation (220 rpm) to precipitate the particles. Following centrifugation at 30,000 × g for 35 min at 4 °C, the pellet was resuspended in 8 ml buffer (25 mM Tris-HCl, 150 mM NaCl, pH 8.0 at 4 °C) and passed through 0.22-µm filters (Croning). The filtrate was dialysed overnight against a 500-fold excess of the same buffer at 4 °C. Dialysed material was centrifuged at 17,000 × g for 30 min at 4 °C to remove insoluble aggregates and filtered again (0.22 µm). Purification was completed by size-exclusion chromatography on a HiPrep Sephacryl S-500 HR 16/60 column (GE Healthcare) equilibrated in 25 mM Tris-HCl, 150 mM NaCl, pH 8.0 at 4 °C, using an ÄKTA Pure 25 system (GE Healthcare). Elution was performed at 1 ml min⁻¹, collecting 1-ml fractions. Fractions containing SpyCatcher003-mi3 nanoparticles were pooled, concentrated and dialysed into TBS 25 mM Tris-HCl, 150 mM NaCl, pH 8.0 at 4 °C using a 100-kDa MWCO centrifugal filter (Millipore) and stored at −80 °C. Final protein concentration was determined by BCA assay (Pierce, Thermo Fisher Scientific).

Solution self-assembly experiments

It was shown previously⁶⁶ that mi3-VLPs can reversibly disassemble and reassemble at guanidinium thiocyanate concentration of 2.5 M. To perform the assembly experiments, we started with a solution containing purified mi3-VLPs (Supplementary Fig. 1) at an mi3-monomer concentration of 84 μM and disassembled the VLPs using 2.5 M of guanidinium thiocyanate at varying mi3-monomer concentrations ranging from 35 to 5.8 μM. Following an incubation time of 30 to 60 min at room temperature, assembly was initiated by rapidly diluting the protein solution 100-fold in assembly buffer (20 mM HEPES pH 7.4, 138 mM NaCl) to a final mi3-monomers concentration ranging between 350 and 58 nM. The assembly reactions equilibrated at room temperature for an extra 30 min. We quantified the distribution of masses of the reassembled VLPs at the chosen concentrations using a standard MP landing assay.

MP measurements in solution

The equilibrated assembly reactions (Fig. 1 and Supplementary Figs. 2 and 3) were measured using a commercial mass photometer (TwoMP, Refeyn Ltd.) using an imaging field of view of 4.3 × 10.9 μm². Measurements were conducted on microscope glass coverslips (24 × 50 mm, Menzel Gläser, VWR 630-2603) that were pre-cleaned by three consecutive 5-min cycles of bath sonication in acetone, 50% isopropanol in Milli-Q water (18.2 MΩ cm) and Milli-Q. Cleaned coverslips were then dried using nitrogen flow and 3-mm silicone gaskets (GBL103250, Grace Bio-Labs) were attached to the coverslip surface. The gasket was prefilled with 15 μl of buffer and the focus position was adjusted for maximum contrast before adding 5 μl of protein solution. Measurements were performed at a frame rate of 500 Hz followed by frame binning of 2, resulting in an effective frame rate of 250 Hz. We analysed data using DiscoverMP v2024R1 (Refeyn Ltd.), in which rolling ratiometric videos were generated using an averaging window size of 20 frames (80 ms). Threshold parameters for particle detection were set to the default values of 1.5 (threshold 1) and 0.25 (threshold 2). For each dataset, a calibration of ratiometric contrast to mass was performed using a protein standard while using the same acquisition parameters, similar to a previously reported procedure^60,67.

SLB preparation

SLBs were prepared using a similar procedure as previously reported, with small modifications²¹. In short, phospholipid stocks in chloroform were mixed to form a 5 mM stock solution with a molar composition of 0.05 mM DGS-NTA, 0.1 mM 18:1 PEG550 and 4.85 mM POPC. The stock solution was stored at −20 °C. Before use, 50 μl of the lipid stock solution was added to 200 μl of chloroform in a clean glass tube. The chloroform was evaporated by manually rotating the tube while applying a weak flow of nitrogen, followed by 1 h of evaporation under vacuum. Lipids were hydrated by adding 0.5 ml of buffer (20 mM HEPES pH 7.4, 150 mM KCl), followed by two cycles of 20-min incubation in a 40 °C water bath, mixing between each cycle. The sealed tube was left at ambient room temperature for at least 2 h or overnight. The hydrated lipids were tip-sonicated in a 1.5-ml Eppendorf tube using a 2-mm tip probe at 30% power and 1 s pulse duration separated by 3 s waiting time for a total of 10 min sonication time (Vibra-Cell, Sonics & Materials). During sonication, the tube was kept in ice water. The sonicated lipids were centrifuged at 21,130 × g for 30 min at 4 °C, before taking 0.4 ml of the supernatant. Cleaned coverslips were treated with oxygen plasma for 5 min at 40% power and 0.6 mbar oxygen pressure (Zepto plasma cleaner, Diener Electronic). Immediately after plasma cleaning, a silicon gasket (GBL103280, Grace Bio-Labs) was placed at the centre of the coverslip and 30 μl of buffer (20 mM Tris pH 7.8, 150 mM NaCl, 2 mM MgCl₂) followed by 20 μl of lipids were added and thoroughly mixed in the gasket and SLB formation was allowed for about 20 min. After examining the SLB integrity, excess vesicles were washed from the surface with assembly buffer.

Preparation of the histidine tag mi3-VLPs for measurements on SLB

Spytag-polyhistidine peptide (Spy-hist) at a concentration of 270 μM in DPBS was mixed with an 84-μM solution of mi3-VLP (total mi3-monomer concentration) at a volume ratio of 2:1, resulting in a large excess of the Spy-hist peptide (180 μM versus 27 μM) and the mixture was incubated on ice for 3 h. Following incubation, the solution was filtered through a 4-ml, 100-kDa MWCO centrifugal filter (Amicon) at 4,000 × g eight times to remove the excess peptide. For each round of centrifugation, the 4-ml initial solution was concentrated to 0.1 ml. This resulted in an estimated dilution factor for the excess of Spy-hist peptide of 10⁹. To tether the subunits to the SLBs, the tagged VLPs were disassembled by diluting 1 μl of the tagged VLP solution into 50 μl of 2.5 M of guanidinium thiocyanate. After about an hour, the disassembled VLPs were rapidly diluted 100-fold into 20 mM HEPES pH 7.4, 138 mM NaCl (assembly buffer). The final concentration of tagged mi3-monomers is estimated to be 5 nM, which is much lower than the critical concentration for VLP formation. MP measurements validated the existence of only mi3-monomers and mi3-trimers in solution, before addition as a solution on top of the SLBs.

Dynamic MP acquisition and data analysis (Figs. 2 and 3)

Data acquisition. Dynamic MP measurements of the two-dimensional assembly reactions of the pentagonal face were performed on a commercial mass photometer (OneMP, Refeyn Ltd.). We used the ‘medium’ field of view (6.3 × 9.9 μm²) at the maximum frame rate of 540 Hz and a metapixel size of 77.35 nm after 4 × 4-pixel binning. After frame averaging (two frames), the effective frame rate was 270 Hz. Following the formation of the SLB, 2 nM of tagged subunits were added to the gasket. Through different incubation times, the density of trimeric mi3-subunits was controlled. When the desired density of particles was obtained, the solution was replaced with assembly buffer at least five times, washing away soluble mi3-subunits, and the system was allowed to equilibrate for 30 min. For characterizing the thermodynamics (Fig. 2), after equilibration, between 3 and 15 60-s-long MP videos were acquired to collect enough statistics of particle trajectories, depending on the particle surface density. Each video was recorded at a different area of the SLB. Before each acquisition, the microscope stage was adjusted to the optimal focus position. Before the acquisition of each dataset, a protein standard was measured to calibrate the contrast to mass conversion using the same acquisition parameters.

Image analysis. Videos were analysed using a custom-written Python package modified from a previously published version²¹. In short, video processing is divided into three steps: image processing, particle detection and contrast fitting. For image processing, each frame of the 60-s video at 270 Hz was normalized to the total detected photoelectron count. To detect the local reflectivity changes originating from light scattered by the diffusing proteins on the SLBs, we subtracted the constant background of the underlying glass roughness by applying a moving median ratiometric imaging analysis approach^21,60. We chose a 2.2-s time window for the moving median, suitable for the expected masses and diffusion coefficients of the tethered proteins. To suppress low-spatial-frequency intensity modulations, originating from rapid laser scanning of the imaged area, we convoluted each frame with a spatial median kernel of size 15 × 15 pixels and divided the ratiometric frame accordingly. The results of these image-processing operations are images similar to the representative frame in Fig. 2b. For particle detection, individual particles were detected above the intrinsic noise of the SLB by cross-correlating each frame with a 13 × 13-pixel kernel of the experimentally obtained point spread function (ePSF) of individual proteins. The ePSF was calculated by averaging individual PSFs of multiple glass binding events of a monodisperse protein solution. Template detection was applied using the match_template function from the scikit-image Python package. A cut-off value for template matching was set to 0.4. Only pixels whose value was higher than the cut-off values and that were identified as local maxima within a spatial window of 4 × 4 pixels were considered as detection events. For contrast fitting, each candidate pixel then serves as the centre of a region of interest (ROI) of size 11 × 11 pixels and the initial guess for the fitting procedure. The contrast of the detected particle was extracted by fitting the x,y coordinates of the centre of the experimentally normalized (to 1) interpolated ePSF. The x,y positions were found by minimizing the square difference between the defined ROI around the detected particle and the ePSF shifted to the x,y position. The minimized function is given by

in which i,j are the indices of the ijth pixel of the ROI and c(x,y) is a scaling factor of the normalized ePSF that minimizes the R² value at a given x,y position. c_min(x_min,y_min) is the reported measured contrast of the protein/complex. The best fitted contrast at each iteration is given by

Generating a trajectory from consecutive localizations. Individual successful and consecutive fitting events across adjacent frames were connected into a single molecular trajectory using the same code published and explained previously²¹ using the trackpy Python package.

Segmenting trajectories using step detection. To segment each molecular trajectory to its specifically sampled oligomeric states, separated by 120 kDa, for better mass resolution on the histogram level, characterization of the thermodynamic (Fig. 2) and for calculation of the average transitions kinetics, we implemented a step detection algorithm⁶⁸. We combined this implementation with a step size threshold of 50 kDa, which is much lower than the known steps of approximately 120 kDa owing to trimer additions and is slightly higher than the noise introduced by the bilayer interface (about 40 kDa standard deviation at 270 Hz). Specifically, the extra mass threshold introduced was used to avoid detection of small mass changes that result from lateral movement of particles during frame acquisition, leading to different blurring of the PSF and therefore to small contrast variations. Given the intrinsic bilayer noise level of about 40 kDa at a frame rate of 270 Hz and our interest in resolving transitions between known measured masses at raw frame rate, we found this threshold to be suitable. This was confirmed by simulated data of a known transition rate (Extended Data Fig. 2). Only trajectories longer than 20 frames (74 ms) were considered for segmentation, for which shorter trajectories (<20 frames) were considered without segmentation. The minimum segment was restricted to three frames (11 ms).

Extraction of oligomeric mass and diffusion coefficient. For calculation of the diffusion coefficient, all detected trajectories and molecular segments were considered similarly. The diffusion coefficient was calculated as previously reported²¹, for trajectories longer than ten frames (37 ms). For shorter trajectories, we did not include a measure of the mobility. The molecular mass of each trajectory or segment was calculated by the median value of the mass trajectory. For a given diffusion coefficient, the assigned mass was corrected to take into account the motion blur that smears the detected and fitted PSF. This smearing effect lowers the fitted contrast by several percent, depending on the diffusion coefficient of the protein and the mass. The blur correction was validated both experimentally and with simulations for different masses, diffusion coefficients and acquisition parameters, as described previously^21,60. The masses of molecular trajectories to which a diffusion coefficient was not assigned were not corrected.

Plotting mass histograms and calculating surface molar fractions. To calculate the surface densities of different oligomeric species, we generated weighted mass histograms from the trajectory dataset. To avoid noise detection at lower masses, we considered only trajectories longer than ten frames (37 ms); short segments of long trajectories were included even if their length was shorter than ten frames. The contribution of each mass trajectory or segment was weighted by its length and the final histogram was divided by the total number of frames per video and by the detected area. This results in a mass histogram in which the y-axis represents the average number of detected molecular species per detected area (or surface density). The histograms (Fig. 2) were then fitted to a series of five Gaussian functions for the five oligomeric species, from one mi3-trimer to the pentagonal ring. The surface density of each oligomer was multiplied by the number of its trimeric subunits and the total surface density of trimers was calculated by the sum of all oligomers. Following normalization, the molar fraction of mi3-trimers in each oligomeric state is given by

in which X_n is the molar fraction of mi3-trimers in an oligomer of size n trimers and ρ_n is the surface density of this oligomer.

Measurements and detection of mass changes. To quantify the dissociation rate constant of the dimer and trimer of mi3-trimers (\({k}_{{\rm{off}}}^{{\rm{dimer}}},{k}_{{\rm{off}}}^{{\rm{trimer}}}\)), we performed three dynamic MP experiments at trimer surface densities of 0.25, 0.34 and 0.72 μm⁻². The experiments were performed as described above, by adding 2 nM of hist-tag mi3-subunits on top of the SLB. Following an equilibration time of 30 min and for each bilayer, we consecutively measured 30 different areas on the SLB, each area of dimensions roughly 6.3 × 9.9 μm², for 1 min and at an effective frame rate of 270 Hz. The detected molecular trajectories were analysed and segmented as described above. Following segmentation, segments attributed to dimeric and trimeric oligomers were defined as all mass traces whose median mass falls within the experimental range given by the overall mass distribution of the corresponding oligomer. Dissociation events for dimers or trimers were defined as any mass change during the molecular trajectory in which the final mass is lower than the initial mass and that the absolute mass change is larger than 50 kDa. Theoretically, direct analysis of the resulting distribution of dwell times before dissociation will provide information on the dissociation constant. However, this analysis is prone to several statistical and experimental biases, including: early termination of trajectories owing to particles leaving the field of view, termination of molecular trajectories owing to identity switching (wrong trajectory linking results from close proximity of particles below the diffraction limit) and mass fluctuations resulting from close proximity of particles that do not interact. We therefore focus our analysis on the calculation of the average observed transition rate. Here <r_ij> is the average transition rate from an oligomeric state i to any oligomeric state j, in which m_j < m_i, and m is the measured mass. Taking the inverse of this rate, τ_ij = <r_ij>⁻¹, represents the average characteristic timescale for disassembly of oligomer, i, or the average dwell time before disassembly. Calculation of the average dissociation rate for the ith oligomer, <r_i> follows

Here N_ij is the number of detected transitions from state i to state j, in which m_j < m_i, and t_i,k is the total observation time of the kth segment of state i. Therefore, the average is given by the total number of disassembly events, \({N}_{{\rm{diss}}.}^{(i)}\), divided by the total observation time, \({T}_{{\rm{total}}}^{(i)}\). An example of the calculation for a representative trace is shown in Extended Data Fig. 3. The average dissociation rate was calculated for the dimeric and trimeric states for each 1-min dynamic MP video and converted to the average lifetime, τ_i = <r_i>⁻¹. A distribution of the 30 measured average lifetimes for the two oligomers is shown in Supplementary Fig. 5. The average lifetimes across different surface densities are shown in Fig. 2 (inset). Also, because for two-dimensional reactions the rate constant depends on the local distribution of proteins, the ratio of the average lifetimes of the dimer and trimer per video was calculated as well, as shown in Extended Data Fig. 2.

Dynamic MP measurements (Fig. 3)

Data acquisition. Dynamic MP measurements of solution bulk assembly kinetics from tethered pentamers (Fig. 3) were performed on the same commercial mass photometer (OneMP, Refeyn Ltd.). Here acquisition used a custom field of view of size 15.4 × 13.2 μm² to allow maximum statistics and a frame rate of 250 Hz for maximum temporal resolution. Each measurement corresponds to acquiring a 60-s video. No further averaging was applied. Following the formation of the SLB and washing excess vesicles from the surface, 2 nM of tagged subunits were added to the gasket. The density of mi3-trimers was controlled by the incubation time. The solution of the tagged mi3-subunits was replaced with assembly buffer at least five times, washing away subunits in solution, and the system was allowed to equilibrate for 30 min to allow formation of pentamers on the surface. The initial mass distribution was measured and the assembly reaction was initiated by adding an equilibrated solution of the reassembled, untagged-mi3-VLPs at total protein concentrations of 88, 44 and 29 nM. The added solution of equilibrated VLPs does not contain the histidine tag modification and therefore particles do not bind the SLB (Supplementary Figs. 5 and 18) and bind surface-assembled pentamers instead. The assembly process of surface pentamers into fully assembled VLPs was monitored by acquiring consecutive 1-min videos, each at a different area of the SLB and for approximately 40 min per technical repeat. At each assembly condition, we repeated the experiment three times. For each repeat, a new SLB was formed and the above procedure was followed. Each repeat of assembly measurements represents a kinetic measurement of approximately 1,000 particles (about 20–30 particles per measurement multiplied by approximately 30–40 time points).

Analysing trajectories to extract mass distributions. Mass histograms of the dynamic MP experiments shown in Fig. 3 and Supplementary Figs. 10–17 were processed in the same way as described above, with only one extra step. The approximately four times larger field of view used here to increase statistics results in small optical contrast inhomogeneities across the imaged field of view. To quantitatively correct these small variations (several percent), we performed a standard MP experiment (similar to the procedure described above for a landing assay on a glass surface) using citrate synthase protein, a monodisperse protein calibrant with a known mass. Using this calibrant, we constructed a two-dimensional map of relative variations of the measured mass as a function of the x,y position across the imaged field of view (Supplementary Fig. 9). Following the fitting stage, we used this map to correct each measured particle contrast according to its fitted x,y position. Because the corrected mass is a constant function related to the microscope, the same correction was used for all of the measurements that correspond to the same size of the field of view. The experimentally calibrated relative contrast variation is shown in Supplementary Fig. 9.

Single-complex assembly experiments

Coverslip preparation and photolithography. Confined SLBs were prepared using a previously published protocol^69,70, with modifications as detailed in ref. ⁵³. Briefly, glass coverslips were cleaned as described above. Following plasma cleaning, the coverslips were rinsed with Milli-Q water, dried with nitrogen and fitted with silicone gaskets. The gaskets were filled with 50 µl of 2 µg ml⁻¹ PLL(20)-g[3.5]-PEG(2) (SuSoS Surface Technologies) and incubated for 30 min at room temperature. After incubation, the coverslips were rinsed with Milli-Q water, dried with nitrogen and exposed to deep ultraviolet light using a mask aligner (Suss MJB4, HgXe 500 W source) for 60 min through a custom-made chrome photolithography mask containing an array of 5-µm-diameter circles. Finally, the coverslips were rinsed with Milli-Q water, dried with nitrogen and stored at −20 °C for up to three months before use.

Data acquisition. Patterned supported SLBs were prepared using the photolithographically patterned glass coverslips and the SLB preparation procedure. Formation of surface pentamers confined to the SLB followed a similar protocol as described above. For assembly from pentamers to full VLPs, an equilibrated solution of preassembled untagged-mi3-VLPs at total mi3-monomer concentrations of 88 or 100 nM was added on top of the confined pentamers. The focus position was then found and the confined SLBs were measured for 5 min from the time of solution addition using a OneMP with a field of view of size 15.4 × 13.2 μm².

Data analysis. We carried out data analysis in the same manner as for standard dynamic MP analysis (see above), with an extra step for correcting long tracking of single assembled VLPs in the case in which more than one pentagonal ring complex was confined in the same trap. After automatic trajectory linking, resulting trajectories were further manually examined and linked using frame, position and contrast values. In several cases, slower mobility of particles close to the edge of the trap affected the ratiometric contrast, owing to the median background subtraction, and we manually found periods in which the VLPs did not move and reanalysed these with a modified version of ratiometric analysis in which the background is estimated using interpolation of the raw images from 250 frames before immobilization to 250 frames after immobilization. For longer immobilization periods, in which the modified ratiometric analysis could not overcome sample drift, we did not consider the mass measurements from the corresponding frames (Supplementary Fig. 21). The contrast values of the initial pentameric rings were converted to mass by aligning the initial contrast values (first 10 s) to the expected pentamer mass, following calibration of the mass to contrast conversion for the same acquisition settings.

Mass trajectories analysis. We performed dwell times analysis using the same step detection procedure described above to identify transitions between molecular states, with a threshold of 70 kDa. The resulting trajectories are shown in Supplementary Figs. 19 and 20. The molecular states were defined according to their expected masses (Supplementary Fig. 19, projected histograms) with a possible error of up to 5% owing to variations in the contrast to mass conversion as a result of variation in focus position. The trajectories and molecular transitions were also examined manually to validate the transition times between stable intermediates. In cases where a molecular state was not detected in a particular mass trace, its dwell time was set to 0.

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Author notes

1. These authors contributed equally: Roi Asor, Dan Loewenthal

Authors and Affiliations

1. Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, Oxford, UK

   Roi Asor, Dan Loewenthal & Philipp Kukura

2. Kavli Institute for Nanoscience Discovery, University of Oxford, Oxford, UK

   Roi Asor, Dan Loewenthal & Philipp Kukura

3. MRC Translational Immune Discovery Unit, Weatherall Institute of Molecular Medicine, University of Oxford, Oxford, UK

   Diana Melnyk & Tiong Kit Tan

4. Chinese Academy of Medical Sciences Oxford Institute, Nuffield Department of Medicine, University of Oxford, Oxford, UK

   Tiong Kit Tan

Contributions

R.A., D.L., T.K.T. and P.K. conceptualized the study. R.A., D.L., T.K.T. and P.K. designed the research. R.A. and D.L. performed the experiments and analysed the data. R.A. wrote the analysis software and performed the modelling and simulations. D.M. and T.K.T. expressed, purified and characterized the mi3-VLPs. R.A. and P.K. supervised the research. R.A., D.L. and P.K. wrote the original draft and all of the authors contributed to writing, reviewing and editing the paper.

Corresponding authors

Correspondence to Roi Asor or Philipp Kukura.

Competing interests

P.K. is a non-executive director, shareholder of and consultant to Refeyn Ltd. R.A., D.L. and P.K. have applied for a patent for confined diffusion mass photometry (N432337GB). The other authors are not aware of any affiliations, memberships, funding or financial holdings that might be perceived as affecting the objectivity of this manuscript.

Peer review information

Nature thanks Bogdan Dragnea, Charlotte Uetrecht and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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