Multiscale Simulation Unravel the Kinetic Mechanisms of Inflammasome Assembly

Abstract

In the innate immune system, the host defense from the invasion of external pathogens triggers the inflammatory responses. Proteins involved in the inflammatory pathways were often found to aggregate into supramolecular oligomers, called ‘inflammasome’, mostly through the homotypic interaction between their domains that belong to the death domain superfamily. Although much has been known about the formation of these helical molecular machineries, the detailed correlation between the dynamics of their assembly and the structure of each domain is still not well understood. Using the filament formed by the PYD domains of adaptor molecule ASC as a test system, we constructed a new multiscale simulation framework to study the kinetics of inflammasome assembly. We found that the filament assembly is a multi-step, but highly cooperative process. Moreover, there are three types of binding interfaces between domain subunits in the ASC^PYD filament. The multiscale simulation results suggest that dynamics of domain assembly are rooted in the primary protein sequence which defines the energetics of molecular recognition through three binding interfaces. Interface I plays a more regulatory role than the other two in mediating both the kinetics and the thermodynamics of assembly. Finally, the efficiency of our computational framework allows us to design mutants on a systematic scale and predict their impacts on filament assembly. In summary, this is, to the best of our knowledge, the first simulation method to model the spatial-temporal process of inflammasome assembly. Our work is a useful addition to a suite of existing experimental techniques to study the functions of inflammasome in innate immune system.

Introduction

During an infection, injured tissues trigger the innate immune response in which molecular patterns expressed by the invading pathogens are recognized by a group of pattern recognition receptors (PRRs) [1, 2] either on membrane surfaces or in cytoplasm. After these receptors detect the existence of danger signals, they can recruit adaptors which further activate the effector such as caspase-1 [3], leading into the production of pro-inflammatory cytokines [4, 5]. It has been reported that proteins involved in this process can aggregate into supramolecular oligomers, called ‘inflammasome’[6, 7], so that the inflammatory cascade can be collectively carried out. More recently, it was found that inflammasomes are assembled into specific filamentous structures through the homotypic interactions between the caspase recruitment domains (CARD) or the pyrin domains (PYD) [8, 9]. These domains belong to the death domain (DD) superfamily which is ubiquitously presented in the receptors, adaptors and effectors of inflammasome [10]. For instance, the filament of PYD domains from the adaptor molecule ASC (Apoptosis-associated Speck like protein containing a Caspase recruitment domain) has been observed by cryogenic electron-microscopy (cryo-EM) at a near atomic resolution [11]. The ASC plays an essential role in converting the inflammatory stimulation into the caspase activation [12]. Therefore, the structural model of ASC^PYD filament greatly advances our knowledge about inflammasome formation. In order to further facilitate the studies on its biological implications and pathological consequence, we need to decode the molecular mechanisms that regulate the kinetics of inflammasome assembly. A quantitative analysis on how this filamentous molecular machinery forms will bring tremendous impacts on the understanding of innate immune system and diseases that result from its malfunctions.

However, it is complicated to experimentally modulate the assembling kinetics of inflammasome. Comparatively, computational simulations can offer mechanistic details of a dynamic process that are currently unapproachable in the laboratory. A mathematical model was constructed to describe the biochemical pathways of ASC-dependent inflammasome [13], instead of the physical process of inflammasome assembly. A large variety of additional simulation approaches have been developed to model the biophysics of protein oligomerization. All-atom molecular dynamic (MD) [14, 15] or Brownian dynamic (BD) [16–18] simulation is the most commonly used method to study the dynamic properties of binding between proteins. Due to the intense consumption for computational resources, current applications of MD or BD simulations are mainly focused on modeling the interactions between two individual subunits in a protein complex. In contrast, coarse-grained (CG) models [19–26] that sacrifice the intramolecular structural details are able to simulate the full assembling processes of large protein oligomers. They have been successfully applied to understand the assembling mechanisms of supramolecular systems such as viral capsids [27–29], cytoskeleton [30], or molecular machines [31]. Unfortunately, it is still not realistic to fully consider the energetic features of interacting molecular components in these simplified methods. In order to overcome the limitations in these different approaches, multiscale modeling is becoming a promising technique to complement the energetic details in MD simulations and computational efficiency in CG models [32–34]. As a result, the implementation of this technique to understand the dynamics of inflammasome polymerization is highly demanded.

In this work, we developed a multiscale framework to simulate inflammasome assembly. The filament formed by PYD domains of adaptor molecule ASC is used as a test system. In the multiscale framework, each domain in the filament was represented by a rigid-body (RB) in a simplified model so that the assembling pathways can be effectively traced with spatial details. The RB model was specifically designed to capture sufficient geometric features in the filamentous structure of the ACS inflammasome. Moreover, the binding rates between each domain were characterized from high-resolution simulations which incorporate structural and energetic information of protein complex. We first found that the phase transition of inflammasome assembly is a multi-step kinetic process regulated by various factors such as concentration and binding strength. As illustrated in the model of ASC^PYD filament, there are three types of binding interfaces between domain subunits. Both RB-based and low-resolution simulations indicate that these three interfaces are not identical, but play distinctive roles in modulating assembly. We further showed that filament formation can be abolished by our simulations in which residues at binding interfaces were computational mutated. Our simulations were validated by the experiments of structure-based mutagenesis in the literatures. Finally, we demonstrate that the efficiency of our multiscale modeling framework allows us to computationally design mutants on a systematic scale and predict their impacts on filament assembly. This is, to the best of our knowledge, the first computational method to simulate the spatial-temporal process of inflammasome assembly. The generality of the multiscale framework also pave the way for its applications to the oligomerization of other supramolecular systems.

Results

Construct the rigid-body-based model for the ASC^PYD filament

Based on the helical symmetry that was obtained by the cryo-EM structure [11], we built a coarse-grained model for the ASC^PYD filament (Figure 1a). In this model, each PYD domain in the filament is represented by a spherical rigid body. This is a reasonable simplification, because PYD domains have a globular structural fold of six-helical orthogonal bundle (Figure 1b). The diameter of each rigid body equals 26.0Å, which is set to fit the size of PYD domains. Rigid bodies are placed next to each other along the filament which has the C3 point group symmetry with 53° right-handed rotation and 14.0Å axial rise per domain. Based on the helical symmetry, the filament can be projected onto a two-dimensional diagram. As shown in Figure 1c, each specific domain in the diagram (the black hexagon in the center) has six structural neighbors, leading to the fact that there are six corresponding binding interfaces for each domain. These interfaces are further classified into three geometric groups. As illustrated in Figure 1c, the interfaces II (between yellow and black hexagons) and interface III (between blue and black hexagons) mostly mediate interactions between domains from different layers, whereas the interfaces I (between red and black hexagons) represents contacts between adjacent domains in the same layer of the filament.

Figure 1:

A coarse-grained model was constructed for the ASC^PYD filament based on the helical symmetry derived from the cryo-EM structure, in which domains are represented by spherical rigid bodies (a). The structural details of these domains and their interactions are shown in (b), with the same color code as the rigid-body model. Further simplification can be made based on the helical symmetry to project the filament onto a two-dimensional diagram (c), in which three types of binding interfaces can be recognized. In this schematic diagram, it is easy to find that each domain in the filament has six structural neighbors through these three types of interfaces. Therefore, six binding sites are assigned on the surface of each domain to delineate the inter-molecular interactions with its neighbors. The index of these binding sites is listed in (d).

These three interfaces are geometrically and structurally distinctive with each other. Therefore, we assign six binding sites on the surface of each rigid body to delineate the inter-molecular interactions. The index of these binding sites is shown in Figure 1d. For instance, through the interface I, the binding site “1” of one domain form contact with the binding site “2” of its neighboring domain in the same layer, while the binding site “2” of the same domain form contact with the binding site “1” of another domain in the opposite direction. Similarly, through the interface II, the binding site “4” of one domain form contact with the binding site “5” of its neighboring domain in the lower layer, while the binding site “5” of the same domain form contact with the binding site “4” of another domain in the upper layer. Finally, the binding sites “3” and “6” mediate the binding through interface III.

The spherical rigid body and the spatial arrangement of six binding sites incorporate the sufficient geometry of the filamentous structure. Followed by the rules of interactions between specific pairs of binding sites, domains can be assembled into helical complex from a random initial configuration, while the assembling kinetics is further determined by the diffusion constant of each domain and binding rates between two domains. Details of the diffusion reaction algorithm used to guide the assembling process are described in the Methods. Based on the helical symmetry, the longest filament can be theoretically formed for a system contains N domains is (N×14.0)/3Å, assuming that all domains are finally assembled together.

Characterize the general dynamics of inflammasome assembly

In order to understand the kinetic mechanism of filament formation, we simulated the assembly of ASC^PYD domains by the RB-based model described above. Specifically, 150 spherical rigid bodies of PYD domains were randomly placed in a 3-dimensional cubic box with a volume of 50×50×50 nm³ as an initial configuration. This gives us the concentration on the level of mM, which is much higher than the experimental concentration that is on the level of μM [11]. As you will see later, this high concentration results in the fact that the timescale of inflammasome assembly in simulations is less than a second, which is much faster than experiments that occurred on the timescale of minutes [11]. And also, the diagonal distance of box is just above the length of the longest filament that can theoretically be formed in the system.

Domains undergo stochastic diffusion in the simulation box. The diffusion constant of each domain equals 10Ų/ns. Different domains will associate into complex if their distance is below the cutoff (10Å), and vice versa, complex can also dissociate into monomers. The probabilities of these reactions depend on the rates of association and dissociation, as described in the Methods. As the first step, the values of both association rate (r_on) and dissociation rate (r_off) for all three binding interfaces were given equally (r_on=0.05ns⁻¹; r_off=0.006ns⁻¹) to characterize the general behavior of filament assembly.

The kinetics profiles of assembly and snapshots from the simulations are plotted in Figure 2. In comparison, a control simulation was carried out, in which only one binding interface instead of three is considered between two domains so that only dimers can be formed. We placed 900 domains in the control simulation to maintain the level of possible interactions as in the filament assembly. All other parameters such as diffusion constant, rates of association and dissociation remain unchanged. Figure 2a shows that the system of dimerization reached equilibrium after 2×10⁷ns. However, the number of interactions in the systems of polymerization grew much more slowly. Despite the slower kinetics, much more inter-domain interactions can be formed in the system of polymerization. There were on average 100 dimers formed when each domain contain one binding interface. In contrast, more than 200 inter-domain interactions were observed during polymerization. This increased number of interactions is due to the reason that a domain can leave a filament only if all three binding interfaces dissociate from its neighboring domains in the filament. The curve of polymerization also shows relatively smaller fluctuations than dimerization. Specifically, we compared the last 10⁷ns trajectories of polymerization simulation with dimerization simulation. The distributions of fluctuations in both simulations were plotted as histograms in Figure S1. The standard deviation of fluctuations in dimerization is 12.14, while the standard deviation in polymerization is 6.71. The lower degree of fluctuations in polymerization suggests that the system of filament assembly is more resistant to external noises. In addition to the total interactions, we plotted the total number of formed polymers and the maximal size of polymers found in the simulations in Figure 2b and Figure 2c, respectively, while the total number of monomeric domains left in the system is plotted in Figure S2 of the Supporting Information. Based on these figures, we suggest that the assembly of inflammasome filament is a multi-step process. The similar mechanism of multi-step assembly has also been observed during the formation of some other protein complex systems [35] such as actin cytoskeleton [36].

Figure 2:

We simulated the assembly of ASC^PYD filament with the rigid-body based model. The kinetics profile of filament assembly is compared with a control system in which there is only one binding interface between two domains so that only dimers can be formed (a). The total number of inter-domain interactions formed during polymerization is plotted as black curve, while the red curve shows the total number of interactions formed in the control simulation. Along with the simulation time, we also plotted the total number of formed polymers (b), the maximal size of polymers found in the system (c). We suggest that there are four stages involved in the assembly. These four stages are indicated by different color panels in the figure. The distribution of various polymer species is traced along the simulation. The histograms of polymer size at some selective time points are plotted in (d) as a function of amount that belongs to the corresponding size. The simulation was started from an initial configuration (e), while some representative snapshots for the second, third and fourth stages of filament assembly are plotted in (f), (g) and (h), respectively. Filaments with the maximal size of more than 40 PYD domains were observed by the end of the simulation.

In detail, we suggest that four stages are involved in the assembly. The first stage is between 0 and 1×10⁷ns, as shown by the red panel. The number of interactions in this stage increases very slowly (Figure 2a). Only dimers or trimers are formed in the system (Figure 2c). After there are enough trimers formed, however, both number and size of polymers increase faster. Therefore, we propose that the first stage is called “seeding” stage in which a small oligomer consisting of at least three interacting domains serves as a seed for the further growth. Following the first stage, more seeds are formed and these stabilized seeds are extended by adding more domains, leading into the second stage, called “growing” stage, as shown by the yellow panel. While the size of polymers keeps growing at the end of this stage (2.5×10⁷ns), the total number of polymers starts decreasing. We thus suggest that this is the new stage, called “converging” stage. In this stage, as shown by the green panel, small polymers are resolved and merged into large polymers. Finally, the growth of polymers becomes slowly after 6×10⁷ns due to the limited number of free monomers left in the system. This is the “saturated” stage, as shown by the blue panel. This multistep assembling mechanism is conformed while we traced the changes of different polymer species along the simulation. The distributions of polymer size at some selective time points are plotted in Figure 2d as a function of polymer abundancy. The figure highlights the process in which the initial formation of small oligomers leads to the condensation and further growth of long filaments. The representative snapshots for the initial configuration, as well as from the second, third and fourth stages of filament assembly are plotted in Figure 2e, Figure 2f, Figure 2g, and Figure 2h, respectively. We found that the longest filament formed at the end of the simulation contains more than 40 PYD domains.

To illustrate the concentration dependence of assembly, we further fixed the size of the simulation box and changed the total number of rigid bodies in the system from 0 to 300. At the end of each simulation, we counted the maximal size of polymers in the system. The correlation between the domain concentration and size of formed polymers is plotted in Figure 3a. The figure indicates that when the total number of domains increases, the system undergoes a phase transition from a state only consisting of small oligomers to a state that domains can be assembled into long filaments. Specifically, when the system contains lower than 60 domains, we can only observe oligomers with less than 10 domains (Figure 3b). However, a small increase of domain number from 50 to 60 led to the assembly of a long filament with 30 domains (Figure 3c). This interesting result suggests that there is a threshold in the formation of inflammasome under high cellular concentration of ASC. Since ASC has the highest expression level in immune cells, this threshold of inflammasome assembly is naturally designed for these immune cells as a response to the external danger signals. When the total domain number further increases, more filaments are assembled, as shown in Figure 3d. More interestingly, under the highest concentration, we observed the branching structures during the growth of filaments, as shown in Figure 3e. We speculate that when density in the simulation box is getting higher, the average distance between neighboring fragments of filaments becomes smaller. As a result, these fragments are easier to merge together and lead into the occurrence of filament branching. The similar threshold-like transition as a function of concentration has also been confirmed by a statistically more robust test in which multiple (10) trajectories were carried out on a relatively smaller system under each specific concentration. The correlation between concentration and sizes of the longest filaments averaged over all the trajectories are plotted in Figure S3 with the error bar.

Figure 3:

We further fixed the size of the simulation box and changed the total number of domains in the system to illustrate the effect of concentration on assembly. The correlation between the concentration and maximal size of formed filament is plotted in (a). We found that only small oligomers can be formed when the system contains 40 domains (b). Interestingly, a small increase of domain number from 50 to 60 led to the assembly of a long filament with 30 domains (c). When the total domain number further increases, more filaments are assembled, as shown by the systems that contain 120 domains (d) and 300 domains (e), respectively. This phase-transition-like behavior indicates that there is a threshold in the cellular concentration to trigger the formation of inflammasome. This threshold is naturally designed as a response to the strength of upstream danger signals.

Altogether, these kinetic features and dynamic properties of filament assembly reveal biological insights to the general functions of inflammasome. Although the multi-step kinetics leads to a slower assembling process, the intrinsic cooperativity between PYD domains makes the polymerization more stable than the dimerization. Consequently, the biological noises can be effectively reduced through the multimeric interactions in the ASC filaments. Additionally, the assembly is highly sensitive to the overall concentration of PYD domains in the system. Only small sizes of oligomers can be formed at low concentration, whereas the polymerization of long filament is facilitated after the concentration of monomers reaches a threshold. This behavior suggests that there is a critical concentration to trigger the filament assembly, corresponding to the situation in which the effective association rate under the increasing concentration finally reaches the point that is greater than the dissociation. The critical concentration in the assembly of ASC^PYD domains was observed by previous in vitro experiment [11, 13]. Finally, the critical concentration of assembly and the high stability of filaments assure that the inflammasome could exhibit an all-or-none binary response only to a persistent and high dose of external stimulation as an inflammatory signal. This robust and threshold-like signal response is functionally important for the innate immune system to remain active in a stochastic environment [37, 38].

Compare the functions of different binding interfaces in the filament

As shown in Figure 1a, the binding interfaces between each domain and its six structural neighbors in the filament are classified into three geometrical groups: the interface I mediates the interactions between domains in the same layers, while the other two types of interfaces mediate the interactions between domains from different layers. In the last section, we investigated the general mechanism of filament assembly by assuming that the values of both association and dissociation rates are identical for all binding interfaces. In order to analyze the functions of three interfaces in regulating the filament assembly, we further changed their rates into different values.

In specific, we tested the functions of association and dissociation separately. We first focused on association by turning off the values of r_on of different binding interfaces. All possible combinations were tested. The control simulation is system in which the rates for all three interfaces are on (r_on=0.05ns⁻¹), while six additional systems were considered. The interface I, II and III were individually turned off in the first three systems. In the fourth system, we turned off both interface II and III, while we turned off both interface I and III in the fifth system. Finally, in the sixth system, only interface III was turned on. In order to achieve both statistical significance and computational accessibility, we carried out multiple trajectories on a relative smaller simulation setup for all seven systems. In detail, 20 trajectories were generated for each system. Each trajectory was 5×10⁷ns long and was started from a random configuration with 100 domains distributed in a 3-dimensional cubic box with a volume of 40×40×40 nm³.

We counted the sizes of filaments formed at the end of all simulations and the distributions are plotted in Figure 4a for each system. The control system is shown in the first column on the left as white bar. The next three columns indicate the systems in which one of the three binding interfaces was turned off, while the three green columns on the right indicate the systems with two binding interfaces off. The information about which interfaces are on is shown by the index at the bottom of Figure 4a. The figure suggests that if any two of the three binding interfaces are turned off, only very few small oligomers can be formed. On the other hand, if only one of the three binding interfaces is turned off, the systems still have the chance to form relatively large size of filament, as shown by the red, grey and striped bars in Figure 4a. Interestingly, by comparing these three bars, we found that turning off the association of interface I (red bar) leads to much lower distribution of filament size than turning off interface II (grey bar) and III (striped bar). Threrefore, we applied one-way ANOVA [39] to test the statistical significance of our results by comparing the distributions among different conditions including the control system. The detailed analysis results can be found in the Figure S4. The ANOVA test shows that the calculated F-statistic score equals 73.5 with a p-value of 0.00001, suggesting that variations in size of polymers caused by turning off different binding interfaces are statistically significant enough. This statistical result suggests that interface I has the most significant impact on filament assembly in terms of regulating the association between domains in the same layer.

Figure 4:

We turned off the association rates of different binding interfaces to test their functions in regulating filament assembly. Seven scenarios were specifically considered. We counted the sizes of filaments formed at the end of simulations for all scenarios. Their distributions are shown in (a) as a box-whisker plot. The average size of filaments is marked as ●, while the maximal and minimal sizes are marked as ×. The box of each distribution in the plot includes the range of polymer sizes from 25 to 75 percentiles, while the whisker indicates the outlier of the distribution with the coefficient equal 1.5. The control simulation is system in which the association rates for all three interfaces are on (black bar). The interface I, II and III were individually turned off in the next three scenarios (corresponding to the red bar, grey bar and striped bar), while both interfaces II and III, I and III, as well as I and II were turned off in last three scenarios (green bars). We further fixed the association rates and changed dissociation rates. The dissociation rates for all three interfaces were first turned into the same value from 0.06ns⁻¹ to 0.0006ns⁻¹ and the maximal size of filaments and total inter-domain interactions are plotted in (b) and (c). Finally, different values of dissociation rates were assigned to different interfaces. Each time we fixed the value of one interface and tested all combinations for the other two. The 2D color contour in (d) gives the longest filament found in the systems with the covariance of dissociation rates between interface II and III. The similar contour plots give the covariance between interfaces I and III (e), as well as the covariance between interfaces I and II (f). The color bar corresponds to the maximal size of filaments found in each system.

In attempt to understand how stability of interactions between domains in a filament affects assembly, we further fixed the rate of association and tuned r_off into different values. A simple test was first carried out in which r_off for all interfaces were assigned to the same value. Five specific values were used, ranging from 0.06ns⁻¹ to 0.0006ns^-1. Each time one of these five values was tried in the simulation. Maximal size of filaments and total inter-domain interactions were calculated at the end of five systems and their results are plotted in Figure 4b and Figure 4c. The figures show that no oligomers can be formed under large values of r_off. Surprisingly, after a small change in r_off from 0.02ns⁻¹ to 0.006ns⁻¹, long filaments suddenly appeared, indicating that there is a threshold in the strength of domain interactions to trigger the phase transition of filament assembly. Moreover, when we further increase the strength of domain interactions by decreasing the values of r_off, both filament size and number of domain interactions start to reduce. We speculate that this could be due to the fact that the growth of filaments is slowed down by the strong interactions between domains.

In the next step, different values of r_off were assigned to all three interfaces. To minimize the number of variables, each time we fixed the value of one interface and tested all combinations for the other two. Figure 4d shows the two-dimensional color contour of the maximal filament sizes found in the systems in which we fixed the r_off of interface I (0.006ns⁻¹) and changed the r_off of interface II (x-axis) and interface III (y-axis). Likewise, Figure 4e and Figure 4f show the contours in which r_off values of interface II and III were fixed (0.006ns⁻¹). Comparing Figure 4d with Figure 4e and Figure 4f, we found that long filaments with more than 45 domains (red in the contours) can only be formed when the r_off of interface I was allowed to change. Moreover, the asymmetric patterns in Figure 4e and Figure 4f indicate that interface I requires lower values of r_off to facilitate assembly than interface II and III. Therefore, our simulation results suggest that interface I plays the most important role in regulating the stability of filaments.

Taken together, we demonstrated that the assembly of inflammasome is a phase transition that is closely regulated by the interactions through three binding interfaces of PYD domains. Without going to the structural and energetic details of domain binding interfaces, the simulations on the topological level show that the functions of these three binding interfaces are not equal. The interface I is the most significant one. It plays a more regulatory role than the other two in mediating both the kinetics and the thermodynamics of assembly. Considering that domains from the same layer in the filament interact through interface I, while domains interact through interface II and III come cross different layers, we therefore speculate that the intra-layer interactions are more important to stabilize the filaments than the inter-layer interactions.

Explore the energetic basis of assembly from high-resolution simulations

We have shown the difference of three binding interfaces in the regulation of filament assembly based on a geometric model. In order to further explore the energetic origin of this difference, higher-resolution atomic simulations were used to evaluate the inter-domain interactions in which the structural details of each domain was presented. Practically, the atomic coordinates of each ASC^PYD domains and their relative orientations in a filament are taken from the PDB id 3J63. We first applied our recently developed residue-based kinetic Monte-Carlo (kMC) method [40] to estimate the association rates of binding between domains. Three systems were built to respectively test: 1) the binding between two ASC^PYD domains through interface I (Figure 5a); 2) the binding between two ASC^PYD domains through interface II (Figure 5b); as well as 3) the binding between two ASC^PYD domains through interface III (Figure 5c).

Figure 5:

Residue-based kinetic Monte-Carlo (kMC) simulation was applied to estimate the association rates between two domains with the structural and energetic details. Three series of simulations were carried out to calculate the association rate through the binding interface I (b), interface II (c) and interface III (d). For each system, two domains were first randomly separated from each other with a distance cutoff d_c. Different values of distance cutoff were tested. For each distance cutoff, the probability that two domains form an encounter complex was calculated from the 10³ simulation trajectories. The relation between distance cutoff and the frequency of forming encounter complexes for all three interfaces is plotted in (d). The all atom MD simulations were further carried out to a system which contains three neighboring domains (e). Based on the average of four independent MD simulation trajectories, the dynamical cross-correlation matrix was plotted (f) to reflect the inter-domain motions through different interfaces. The rates of association and dissociation evaluated by the atomic simulations were integrated into the rigid-body based model to guide filament assembly. Using these parameters, the kinetic profile of the total inter-domain interactions is plotted in (g), with the insertion of the initial and final snapshots.

For each system, 10³ simulation trajectories were generated. In the initial conformation of each trajectory, two domains with residue-based representation were placed with a random position relative to each other in which the distance between their binding interfaces is fallen within a cutoff value d_c. As described in the Methods, the diffusions of two domains during the simulations are guided by their binding energies. The energies contain both hydrophobic effect and electrostatic interactions between two interacting domains. At the end of each trajectory, two domains either form an encounter complex through their pre-defined interface, or diffuse away from each other. Based on the simulation results collected from all the trajectories, we counted the frequency ρ that a dimer can be formed given a specific value of d_c. We systematically tested different values of distance cutoff d_c, ranging from 15Å to 20Å. The relation between d_c and ρ for three interfaces is plotted in Figure 5d.

The figure shows that probabilities of association drop for all three binding interfaces when the distance cutoff increases, suggesting that dimers are more difficult to form if two domains are separated farther from each other in the beginning. More importantly, the comparison of the curves among three binding interfaces indicates that the association rate through interface II is much lower than the other two. This is consistent with the fact that interface II has the lowest electrostatic complementarity [11]. More interestingly, the figure also shows that the binding through interface I has the highest association rate. This provides the energetic basis to our previous results in which we show that interface I plays more significant role in regulating the filament assembly. With the structure-based simulations, here we demonstrated that the fast association between domains through interface I is not only required to geometrically facilitate the assembly of high-order structure with specific helical symmetry, but also is naturally designed in their primary protein sequences. In another word, the sequences of amino acids not only program the energetic landscape of proteins tertiary structures, but also program the kinetic binding between proteins to shape the assembly of protein quaternary structures.

In addition to the rate of association, we also considered the stability of domain interactions on the atomic level. Specifically, molecular dynamic (MD) simulations were carried out to a system which contains three neighboring domains (Figure 5e). As shown in the figure, all three interfaces can be found among the domains. We therefore assume that these neighboring domains are the minimal structural building block that leads to the spatial organization of helical filament. We performed four independent trajectories of 100 nanosecond-long MD simulations to the system using GROMACS [41]. Detailed simulation setups are described in the Methods. The average cross-correlation of motions between all pairs of residues in three domains is calculated and plotted as a matrix in Figure 5f after MD simulations. The figure shows that the overall motions between domain 1 (grey) and domain 2 (red) through interface I have less negative correlations than the motions between domain 1 (grey) and domain 3 (green) through interface III, as well as the motions between domain 2 (red) and domain 3 (green) through interface II. This result, consistent with the kinetic property reflected in Figure 5d, suggests that interface I has stronger inter-domain interactions than the other two interfaces.

We further used DCOMPLEX [42] to calculate the free energies of binding. The calculated binding free energy through interface I is −6.24Kcal/mol, the binding free energy through interfae II is −5.05Kcal/mol, while the binding free energy through interface III is −5.23Kcal/mol. These calculations suggest that the binding of the interface I is the most stable and the interface II is the lease stable. Using the values of association rate and binding free energy as reference, the dissociation rates can be determined. We adopted relatively higher dissociation rates than the calculations but keeping their relative differences. This can assure that the simulation can be computationally accessible and in the meanwhile the kinetics of the assembly process still remains qualitatively unchanged. As a result, the value of r_on for interface I is 0.05ns⁻¹and r_off equals 0.002ns⁻¹; the value of r_on for interface II is 0.001ns⁻¹and r_off equals 0.000125ns⁻¹; and finally the value of r_on for interface III is 0.04ns⁻¹and r_off equals 0.004ns^-1. Using these association and dissociation rate parameters, the dynamics of filament assembly was simulated again by the rigid-body model. The profile of the total inter-domain interactions formed during the simulation is plotted in Figure 5g, with the insertion of the initial and final snapshots. The figure clearly shows that filaments can be formed by giving the binding parameters from the atomic simulations.

Combining the simulations at the atomic and the low resolution scales, we therefore illustrated that the kinetic properties of filament assembly are rooted in the energetics of atomic interactions at the binding interfaces between individual structural domains. More specifically, the interaction through interface I is both kinetically and thermodynamically favored. Compatible with the results on the geometric level, we suggest that this priority of interactions along the same layer of filament facilitates the efficiency and stability of inflammasome assembly.

Computationally regulate the inflammasome growth by mutagenesis

Our multiscale simulation framework further provides us the possibility to testify how variations of residue sequence at domain interfaces affect the kinetic balance of inflammasome assembly. Previous experiments show that mutations of different residues disrupted filament formation and led to more monomeric fractions in the size-exclusion chromatography [11]. Some of these residues were used to test our computational mutagenesis. In detail, the mutations K26E at interface I, F59E at interface II and R41E at interface III were selected. SCRWL4 [43] was applied to reconstruct the sidechains of these mutated residues at their corresponding interfaces.

The residue-based kMC simulation was then used to generate 10³ trajectories under different distance cutoff (d_c) values for these mutation systems. The frequencies of association ρ at d_c=20Å were calculated and compared with the wild-type in Figure 6a. The simulations of association through interface I are plotted as grey bars, while the simulations through interface III are plotted as striped bars. Simulation of binding through interfaces II are not shown because its calculated rate is much lower than the other two interfaces. Relative to the wild-type which is listed at the most left column in the figure, mutation R41E (second left column) shows lower frequencies of association through interface I. In order to further assess the statistical significance of obtained differences between the wild-type and the mutant, we randomly divided the 10³ trajectories into 10 groups for both systems. A student’s t-test was performed to the two datasets. In detail, the average rate of association for the wild-type is 0.28 and the standard deviation is 0.01, while the average rate of association for the mutant is 0.04 and the standard deviation is 0.01. The distributions of both systems are plotted in Figure S5. The null hypothesis that no difference exists between two sets was tested at a 95% confidence interval. Consequently, the calculated t-score equals 18.08 and the corresponding P-value is 0.00001. Therefore, the small P-value for the t-test suggests that we can reject the null hypothesis and accept the alternative hypothesis, i.e., the difference of association rates between the wild-type and the R41E mutant is significant.

Figure 6:

Previous experiments show that mutations of different residues disrupted filament formation. Some of these residues were tested by our computational mutagenesis. The residue-based kMC simulation was used to calculate the frequencies of association for these mutants. The frequencies of association through interface I (grey bars) and interface III (striped bars) are compared with the wild-type (a). The comparison of filament assembling kinetics between mutants and wild-type is plotted in (b). In order to further illustrate that our method is able to design a large scale of mutations and systematically predict their functions, LEU28 was selected as a blind test to artificially mutate its sidechain into 12 other types. The residue is located at the binding interface I between two domains (d) and also partially involved in the interface III (e). The frequencies of association for these mutants were calculated by residue-based kMC (c). The rates were derived from these frequencies and fed into the rigid-body simulations to guide filament assembly. The simulation results for different mutant of LEU28 and their comparison with the wide-type are shown in (f).

It is worth of mentioning that R41E is the mutation at interface I. It is very interesting that association rate through interface III is also drastically reduced due to this mutation. This result therefore suggests that mutations of residues at one interface can indirectly affect the binding through other interfaces. Similarly, mutation K26E (third left column in Figure 6a) also shows remarkably lower frequencies of association through both interface I and interface III, although the residue is located at interface III. Finally, mutation F59E is at interface II. The figure shows that this mutation decreased the association frequency through interface III. Therefore, our simulations give clear evidence that mutations of a single residue can change the energetics around the surfaces of the entire domain and affect its binding through all interfaces.

The association and dissociation rates of these mutants were derived based on above kMC simulations and DCOMPLEX calculations. Using these binding parameters to model the mutated domain interface, together with all the other original parameters, rigid body simulations were carried out to illustrate the impacts of these mutants on filament assembly. Figure 6b shows the simulation results in which 150 mutated domains were included in a 3-dimensional cubic box with volume of 50×50×50 nm³. The black curve is the total number of domain interactions formed along the simulation time in the wild-type system, while the three mutation systems are plotted by other colors as indicated in the figure. Figure 6b shows that mutations R41E (blue) and K26E (green) totally abolished filament formation, while the domain interactions in mutation F59E (red) are also highly weakened. These results are consistent with the experimental measurements and demonstrated that our computationally method is sensitive enough to quantitatively capture the impacts of sequence variations on kinetics of inflammasome assembly.

We also tested the additional mutations that do not completely abolish but weaken filament formation. In specific, the mutations L50A at interface I and E80R at interface II were selected. Moreover, we assume that the mutation R41K will not affect the filament assembly by replacing the positively charged residue with another similar type. We therefore used this benign mutation as a positive control. Our tested results on these mutants and their comparison with the wild-type can be found in Figure S6. We first applied the residue-based kMC simulation to estimate the inter-domain association of these mutation systems. We compared the frequencies of association ρ at d_c=20Å between the mutants and the wild-type (Figure S6a). The benign mutant R41K does not show much difference from the wild-type in association of both interface I and interface II. On the other hand, the mutation L50A leads to slightly lower frequencies of association through interface I, while the mutation E80R shows lower frequencies of association through interface III. With these rate parameters, we further carried out rigid body simulations to illustrate the impacts of these mutants on filament assembly. Figure S6b shows the simulation results in which 150 mutated domains were included in a 3-dimensional cubic box with volume of 50×50×50 nm³. We found that the mutants L50A and E80R slowed down the kinetics of filament assembly at different levels. The kinetics of assembly is marginally affected when the hydrophobic residue Leucine50 is replaced by alanine. Comparatively, the mutation R41K did not cause any effect on the assembly. In summary, we demonstrated that our method is able to predict the effects of mutants that not only abolish the formation of filaments, but also weaken the kinetics of their assembly.

Computational simulation is much less time-consuming and labor-intensive than the traditional experimental approaches. It can be used to design a large scale of different mutations and systematically predict their functions. In order to test this, we randomly selected a residue at surfaces of the domain and artificially mutated its sidechain into many other types. As a result, LEU28 was used in our blind test. It is directly involved in binding interface I between two ASC^PYD domains (Figure 6d) but also close to binding interface III (Figure 6e). Computational mutagenesis was performed to the residue from LEU to 12 other types of sidechain. For each mutation, residue-based kMC simulation was first used to estimate the rate of association. The frequencies of association ρ at distance cutoff d_c=20Å were calculated and compared with the wild-type for these mutants in Figure 6c. The simulations of association through interface I are plotted as grey bars, while the simulations through interface III are plotted as striped bars. Relative to the wild-type which is listed at the most left column in the figure, the figure shows that mutations of LEU28 into the negatively charged sidechains such as ASP and GLU weaken the association through both interface I and interface III, as marked by symbol * in the histogram. In contrast, the positively charged mutations such as L28K and L28R strengthen the association through both interface I and interface III, as marked by symbol ● in the histogram.

The binding rates of these mutants were further fed into the rigid body simulation to guide filament assembly. The simulation results and their comparison with the wide-type are shown in Figure 6f. The wild-type is plotted as the black curve, while the color index for all the 12 mutants is shown by the column right next to the figure. Figure 6f indicates that wild-type is one of the systems that achieved the highest number of domain interactions at the end of the simulations. Interestingly, the positively charged mutations such as L28K and L28R, although increased the association between individual domains, did not collectively enhance the filament assembly. This result suggests that the native sequence of the ASC^PYD domain is naturally optimized through evolution to prefer a filamentous domain arrangement so that its function as a signaling adaptor can be effectively carried out. Additionally, we show that among all designed mutations, filament formation in L28D was significantly affected, as shown by the blue curve in the figure. This mutation disrupts the original hydrophobic interactions, adds unfavorable electrostatic pattern into the native binding interfaces and therefore slows down the kinetics of domain assembly. Comparatively, the filament formation in L28E was only slightly weakened, as shown by the red curve in Figure 6f. This corresponds to the fact that the impact of L28E on reducing the binding rates is not as strong as L28D (Figure 6c). This result indicates that the changes of binding rates should be large enough to significantly affect the assembling kinetics, suggesting there is a tolerance of variations at binding interfaces that assures the robustness in filament formation.

In summary, we testified that through computationally designing and engineering mutations of residues at domain-domain interfaces, assembly of ASC^PYD filaments can be effectively modulated by our multiscale simulations.

Discussions

The innate immune system constitutes the first line of host defense from the invasion of external pathogens [44]. The defense triggers the inflammatory responses, leading into the development of clinical signs such as swelling [45]. Proteins in the death domain superfamily are critical components involved in the inflammatory signaling pathways. Recent studies discovered that these proteins can often assemble into high-order oligomers through the homotypic interaction between their death domains. Surprisingly, most of these oligomers share the similarity of the unique helical symmetry. The oligomer formed by the PYD domains of the adaptor molecule ASC in the ASC-dependent inflammasome is one typical example. The model obtained by the cryo-EM experiment shows that the oligomer has a filamentous structure. Each PYD domain in the filament form interactions with its six structural neighbors through three different interfaces. Based on this structural model, we developed a new multiscale simulation approach to further understand the kinetic mechanisms of how these filaments are assembled. Using a rigid-body based model, we first found that the filament assembly is a multi-step, but highly cooperative process. The functions of three binding interfaces are not identical during this process. Interface I plays a more regulatory role than the other two in mediating both the kinetics and the thermodynamics of assembly. Moreover, combined the simulations at the atomic scale, our results indicate that dynamic properties of domain assembly are rooted in the primary protein sequence which defines the energetics of molecular recognition through different binding interfaces. Finally, our multiscale simulation strategy gives us the opportunity to test the impacts of residue point mutations on the overall dynamics of filament formation. We demonstrated that our method is sensitive enough to computationally design new mutations for residues at domain interfaces that can effectively modulate the assembly of filaments. Our method, for the first time, simulates the biophysical process of inflammasome assembly. The simulation results throw light on the physiological functions of ASC-dependent inflammasome in the signaling of innate immune system.

In spite of these achievements, some pieces of information about the assembling details are still missing in current simulations. For instance, in our model, domains can enter and leave the filaments from both ends. So our simulation does assume that filament growth can proceed from both sides. However, previously studies suggested that nucleated ASC filaments might undergo unidirectional polymerization [46]. It was proposed that this unidirectional polymerization is due to the conformational change which lies in the α2-α3 loop of the domain. Since the intramolecular structural changes were not captured by our coarse-grained model, our simulations cannot reproduce the process of unidirectional polymerization. Future improvement that integrates the intramolecular degrees of freedom will be able to help us address this issue.

Current study also provides the foundation for further extending the model to directly understand the functions of spatial organization in the biochemical pathway of ASC-dependent inflammasome. For instance, the filament formation of the adaptor molecule ASC is triggered by the activation of upstream sensor proteins. Two classes of sensor proteins, ALR (Absent in Melanoma 2[AIM2]-like receptor) and NLR (nucleotide-binding domain [NBD] and leucine rich repeat [LRR]-containing receptor), were identified [46, 47]. Both receptors contain N-terminal PYD domains, same as the adaptor molecule ASC. Due to the reason that PYD domains in different proteins might form homotypic interactions, it was therefore hypothesized that the sensor receptors can also form oligomers after they recognize external signals [48, 49]. These oligomers further serve as a platform to induce the ASC filament assembly. Previous experimental evidences suggested that the nucleation of NLP can increase the local concentration of ASC above a supercritical level [50]. Our simulations here show that the polymerization is very sensitive to the local concentration of ASC monomers. Therefore, our study indirectly supports the mechanism whereas NLP can initiate the ASC polymerization. By extending the multiscale simulation framework developed in the work to a system which contains both PYD domains from the sensor receptor and PYD domains from the adaptor molecule ASC, we will be able to directly simulate the oligomerization of sensor receptors through their PYD domains, and the kinetic correlation between the sensor oligomers and the assembly of ASC filaments.

Furthermore, it was observed that the ASC^PYD filament can convert inactive ASC domains into their active, filamentous form [51]. The single-molecule fluorescence study revealed that during this prion-like polymerization, there is a large conformational change between the PYD domain and the CARD domain in ASC [50]. Along with this conformational change from a close state to an open state, the ASC filament can be assembled above a critical concentration. In order to characterize the dynamics of this prion-like behavior, atomic MD simulations can be applied to capture the conformational transition of the full-length ASC molecule. The rate of this transition can be further integrated into the rigid-body based simulations to discover the role of conformational dynamics in regulating the assembly of ASC filament. This will finally help us understand how signals are passed from ASC adaptor to the downstream effector protein.

On the other hand, the generality of this multiscale framework also opens the door to its applications in the oligomer assembly of other molecular systems that contain death domain superfamily. For an example, the viral RNAs in cells can be detected by proteins called RIG-I-like receptors (RLRs) [52]. The RNA binding of receptors initiates the signaling cascade by interacting with the mitochondrial antiviral-signaling (MAVS) protein [53]. MAVS proteins were found to aggregate on the surface of mitochondria after activation. The reconstructed model from cryo-electron microscopy further shows that the CARD domain (caspase activation and recruitment domain) of MAVS proteins also form a similar filamentous structure [54] as found in the ASC-dependent inflammasome. Each domain in the filament has six structural neighbors, while there are three types of interfaces between domains. Different from the ASC^PYD filament, the MAVS^CARD filament displays a left-handed single-stranded structure with a twist angle of 101.1° and a rise of 5.13 Å [55]. Using these symmetric parameters, we can build a helical model with rigid body representation and simulate the assembling kinetics of MAVS-dependent inflammasome.

Proteins from the death domain superfamily not only form homogeneous oligomers, but can also aggregate into heterogeneous complex. One example is a signaling platform in the NF-κB pathway called Myddosome. In the NF-κB pathway, ligand binding of Toll-like receptors (TLR) on cell surfaces leads to the recruitment of intracellular TIR-containing adaptors MyD88. In addition to its C-terminal TIR domain, MyD88 also contains an N-terminal death domain (DD), which also exists in the downstream molecules, IRAK4 and IRK1/2. MyD88, IRAK4 and IRK1/2 therefore form the signaling platform Myddodome through the interactions between their DDs. The crystal structure of Myddosome shows that the complex possesses of a single stranded left-handed helical symmetry and comprises 6 MyD88, 4 IRAK4 and 4 IRAK2 death domains [56]. The hierarchical assembling pathway of Myddosome can be simulated by our computational methods. In summary, the multiscale simulation approach developed in this work is a useful addition to a suite of existing experimental techniques for the study of inflammasome functions.

Methods

Simulate filament assembly by a rigid-body based diffusion-reaction algorithm

The geometric representation for each domain, the spatial arrangement of binding sites on the surface of each domain and the rules of interactions between domains were described in the Results and Figure 1. Given the model representation, a large number of rigid bodies are generated and randomly distributed in a 3D simulation box (Figure 2e). After the initial set-up, simulations are followed by a diffusion-reaction algorithm [57]. Details of the algorithm were specified in our previous works. In brief, the system undergoes a two-step process within each simulation time step. In the first step, domains are randomly diffused along their three translational and three rotational degrees of freedom. The amplitude of diffusions is determined by the diffusion coefficient.

Diffusions are followed by the reaction scenario in which the kinetics of association and dissociation between domains is simulated. Association will be triggered with the probability P_on = r_on × Δt_RB, if the distance between the specific binding sites of two domains is smaller than the effective distance d_ass. The length of each simulation time step (Δt_RB) is 10 nanosecond, while r_on and d_ass are estimated from the residue-based kinetic Monte-Carlo simulations, as introduce in the next section. If two domains associate together, their orientations will be aligned by rigid-body superposition to fit the helical symmetry of the filament. Consequently, if a domain associate with another domain in an already formed filament, the probability of association at the interfaces between the incoming domain and all the other domains in the filament will be individually calculated to establish additional interactions. After the execution of association, each domain has the probability to dissociate from the rest of a filament within each time step, which is calculated by P_off = r_off × Δt_RB. The values of dissociation rate r_off between two domains were estimated based on the information derived from the high-resolution simulations. Similarly, the probability of dissociation between a domain and its neighbors in a filament through all three interfaces will be individually calculated within each simulation step. This domain will be separated from the filament only if it dissociates with all the neighbors. After separation, the domain monomer will diffuse independently until it encounters with other single domains or another filament in the following simulation steps.

Finally, after the execution of association and dissociation scenario between each pair of domains in the system, those oligomers containing no more than three domains can diffuse together with a relatively low diffusion constant. Filaments with a larger number of domains, on the other hand, can no longer move. This simplification is based on the truth that diffusion constant of a protein oligomer is negatively correlated to its molecular weight. After both diffusion and reaction scenarios are completed within a corresponding time step, the new configuration is updated and the simulation time is proceeded. The kinetics of the system thus evolves in both Cartesian and compositional spaces through this iterative process. The source codes of rigid-body based simulations and the output files from the sample tests are available for download at: https://github.com/wujah/RB-ASCAssembly.

Structure-based estimation of association and dissociation rates between domains

For a given pair of PYD domains, the association rate r_on through a specific binding interface can be calculated by a previously developed kinetic Monte-Carlo (KMC) simulation [40]. A coarse-grained model of domain is used in the simulation. Each residue in the model is represented by two sites; one is the position of its Cα atom, while the other is the representative center of a side-chain selected based on the specific properties of a given amino acid. The simulation starts from an initial conformation, in which two domains are placed randomly and the corresponding binding interface is separated within a given distance cutoff d_c. Following the initial conformation, both domains undergo random diffusions within each simulation step. A physics-based scoring function that includes electrostatic interaction and hydrophobic effect is used to evaluate the energy between two proteins along simulation and guide their diffusions. Based on the calculated energy, the probability to accept the diffusional movements is determined by the Metropolis criterion. At the end of each simulation step, if an encounter complex is formed through the corresponding interface, the current simulation trajectory will be terminated. Otherwise, the simulation continues until it reached the maximal time duration.

In order to effectively estimate the association rate for a given binding interface, simulations were performed under different values of distance cutoff. For a specific distance cutoff d_c, multiple trajectories (10³) are carried out. Each trajectory starts from a relatively different initial conformation, but the initial distances between the corresponding interfaces of two domains in all trajectories are below this d_c. Complexes are successfully formed at the end of some trajectories. In contrast, two domains diffuse far away from each other at the end of other trajectories. Consequently, the value of the association rate r_on and effective distance of association dass are derived from the statistical analysis of these trajectories, as described in our previous study. These effective rate and distance are integrated in the rigid-body based model [58–60] to simulate filament assembly. In order to connect residue based and rigid-body based simulations with the same time-scale, the maximal time duration to terminate each trajectory of residue-based simulations is fixed to Δt_RB, which is the length of time step in the rigid-body simulation. As a result, each trajectory of residue-based simulation consists of 10³ steps and each step is 0.01nanosecond, so that the total simulation time for each trajectory is10 nanosecond, which equals the value of Δt_RB.

The dissociation rates used in the rigid-body simulation of filament assembly were derived based on the above calculations of association rates and the estimation of binding affinity between two interacting domains. The traditional method to calculate free energy of binding based on molecular dynamic simulations requires sophisticated sampling that gradually dissociates a complex and measures the free energy cycle [61]. In comparison, another category of computational approaches predict binding affinity of protein complex based on the statistical analysis [62–73]. We used a method in this second category to estimate the approximate values of binding affinities with high computational efficiency. In detail, DCOMPLEX was implemented into the modeling framework. DCOMPLEX [42] used the structure-derived potential of mean force to rank the stability of protein complexes and thus provide an accurate prediction to their binding affinity. Finally, the dissociation rates in the simulations were rescaled into higher values than the calculations but keeping their relative differences to assure the simulations are computationally accessible and the kinetics of the assembly process remains qualitatively unchanged.

Calculate cross-correlation of inter-domain motions from all atom MD simulations

The all atom MD simulation is carried out using GROMACS with the AMBER99sb-ILDN force-field and the TIP3P water. The initial conformation of the simulation system was adopted from the three neighboring domains in the crystal structure with PDB id 3J63. The protein was solvated with 25890 water molecules, and the box size was approximately 94×94×94 ų. The net charge of the simulation box was neutralized by adding six NA⁺ ions. The system was equilibrated at 310 K and 1 atm to remove unrealistic contacts. A uniform integration step of 2 fs was used for all types of interactions, throughout all simulations. A cutoff of 13 Å was used for van der Waals interactions, and electrostatic interactions were calculated with the particle mesh technique for Ewald summations, also with a cutoff of 13 Å. Temperature (310 K) and pressure (1 bar) are controlled using the v-rescale thermostat and the Parrinello-Rahman barostat, respectively.

After equilibration, we first performed a production run for a total length of 10² nanoseconds. At the end of the simulation, four additional sample runs were further carried out to enhance the statistical significance. The length of each individual run is 10² nanoseconds. Moreover, to mimic the physiological condition, a salt concentration of 150 mM was created in these four systems by including 78 Na+ and 72 Cl-ions. The root mean square deviation (RMSD) was calculated by the spatial changes in protein Cα atoms relative to their initial positions. The RMSD of four sample runs are plotted in Figure S7 as a function of simulation time. The small RMSD and the flat plateaus after 50ns in all four systems indicate the convergence of the simulations. We therefore analyzed the trajectories for the last 50 nanoseconds of these simulations. The relevant parameters used in the MD simulations are summarized in Table S1.

The dynamical cross-correlation matrix of the three-domain complex was built by the Bio3d package in R [74]. Dynamic cross-correlation method is widely used to analyze the atomic fluctuation in the trajectory. The elements of the matrix were defined as:

$$C_{ij}=\frac{\langle \Delta r_i\cdot \Delta r_j\rangle }{\sqrt{\langle \Delta r_i^2\rangle \langle \Delta r_j^2\rangle }}$$ (1)

In above equation, Δr_i and Δr_j are displacement vectors from the mean position of Cα atom i and j, respectively. The angle bracket denotes an ensemble average over the whole trajectory. The values of C_ij are ranged between −1 and +1. The positive values indicate the fluctuations of two residues are correlated, while the negative values indicate anti-correlated motions between them.

Highlights.

• We constructed a new multiscale simulation framework to study the kinetics of ASC inflammasome assembly.

• We show that the filament assembly of ASC inflammasome is a multi-step, but highly cooperative process.

• We found a critical concentration to trigger the inflammasome assembly, which assures that the inflammasome could exhibit an all-or-none binary response only to a persistent and high dose of external stimulation as an inflammatory signal.

• We illustrated that the interaction along the same layer of filament is both kinetically and thermodynamically favored, which facilitates the efficiency and stability of inflammasome assembly.

• The efficiency of our computational framework also allows us to design mutants on a systematic scale and predict their impacts on filament assembly.