Bidirectional allostery mechanism of catch-bond effect in cell adhesion

We conducted MD simulations starting from the HA-bound T state (low binding-strength) with a tensile force applied between the Cter of CD44 and the HA ligand. The CD44-HA bond was considered ruptured if the binding energy became zero. By repeating the simulations independently, we calculated the lifetime and survival probability of the CD44-HA complex (Appendix B and Supplementary Text). At zero tensile force, one can observe successful rupture of CD44-HA bond for $\sim$60$\%$ of the MD trajectories within the simulation length(Fig. S2). The distribution of survival probability of CD44-HA bond shows an exponential-like decay feature (Fig. 1e, red). The overall average lifetime was estimated to be $\sim 2.2\times 10^{9}$ MD steps based on a maximum likelihood approach (Fig. 1f). This lifetime value, after calibrated by protein conformational dynamics (Supplementary Text) [44], is close to the experimentally measured range of the CD44-HA bond (200-250s) at the force-free case [49]. In comparison, much fewer rupture events were observed at moderate tensile forces, which leads to long-lived CD44-HA bond. For example, with the tensile force of $\sim$10.4pN, only $\sim$20$\%$ of the MD trajectories show rupture events and the lifetime distribution becomes wider compared to that of the force-free case (Fig. S2). In addition to the prominent distributions at small lifetime range, the events with much longer lifetime have also been significantly populated, and the overall average lifetime was estimated to be $\sim 6.2\times 10^{9}$ MD steps(Fig. 1f). Such results suggest that applying appropriate tensile force alters the CD44-HA interactions, leading to observations of more stabilized CD44-HA bond.

With increasing tensile force, both the survival probability and average lifetime of the CD44-HA bond show intriguing nonmonotonic changes (Fig. 1e, f). In the small tensile force range (0-5.2 pN), the lifetime decreases with tensile force, while the survival probability decays more rapidly. Such results are in accordance with the conventional slip-bond scenario as described by Bell law [11]. When the tensile force exceeds a certain threshold ($\sim$5.2 pN), the lifetime and survival probability of the CD44 bond increase with the applied tensile force, demonstrating a typical catch-bond effect. With the further increasing of the tensile force ($>$12.1 pN), the lifetime starts to decrease, recovering to slip-bond behavior (Fig. 1f). Overall, the above results not only reproduce the catch-bond effect observed in experiments [23, 42, 36] but also identify a previously unrecognized slip-catch-slip triphasic pattern for the force responses of the receptor-HA bond. The success of the dynamic energy landscape model in describing the experimentally observed catch-bond effect enables in-depth investigation of the underlying molecular mechanism.

To reveal the underlying molecular mechanism of the observed enhancement of the CD44-HA bond after applying tensile forces, we investigated the conformational dynamics of the HA-bound CD44-core. The trajectories at zero force load show that the CD44-core hops between two conformational states, i.e., the T state ($\chi<0$) and R state ($\chi>0$) (Fig. 2a; see Appendix C for the definitions of reaction coordinates). The two-dimensional free energy profile along the reaction coordinates $Q_{C}$ (which ranges from 0 to 1 and describes the folding event of Cter) and $\chi$ (which describes the conformatonal change of CD44-core) shows that the relative stabilities of the two conformational states can be modulated by the structure of Cter (Fig. 2b). When Cter is largely folded (larger $Q_{C}$), both the T and R states can be significantly populated. In contrast, the CD44-core dominantly stays in the high binding-strength R state after Cter unfolds and detaches from the CD44-core (smaller $Q_{C}$). The one-dimensional free energy profile also demonstrates switching of the relative stabilities of the two conformational states with folding/unfolding of Cter (Fig. 2c). These results demonstrate that Cter acts as a latch regulating the conformational states of the CD44-core, which is in line with previous experimental observation that appropriate conformational plasticity of CD44 is essential for stable cell rolling under fluid shear stress [36]. Because the T and R conformations have different HA binding-strengths, conformational switching modifies the CD44-HA interactions. As shown in Fig. 2d, when the CD44-core switches from the T conformation to the R conformation, the distribution of the ligand binding energy $E_{bind}$ is shifted, with the mean value increasing by $\sim$2.0 kcal/mol.

We further calculated the free energy landscape along the reaction coordinates $\chi$ and binding energy $E_{bind}$ (which characterizes the ligand dissociation). The conformations with $E_{bind}\geq$-0.0 kcal/mol is considered as dissociated state. One can see that after the CD44-core switches from T to R state, which is coupled to the unfolding of the Cter, the free energy barrier of ligand dissociation increases from $\sim$6.0 kcal/mol (megenta arrow) to $\sim$9.0 kcal/mol (blue arrow) (Fig. 2e), demonstrating the tight interplay between the folding state of the force-sensing Cter and the binding strength of ligand HA.

The above results suggest that unlocking of the force-sensing C-terminal latch under tensile forces tends to trigger the conformational switching of the CD44-core to the high binding-strength state via allosteric coupling, which can then contribute to the observed catch-bond effect. These findings directly demonstrate the crucial role of allosteric coupling, which is in line with the allosteric mechanism implicated in a number of previous catch-slip models [13, 14, 15, 16, 17, 29, 32, 35, 38].

To further understand the unusual triphasic force-response profile, we constructed the pathways of CD44-HA dissociation using MD trajectories under different pulling forces. The pathways were assigned based on the conformational state of the CD44-core (T or R), folding state of Cter (folded (F), detached (D), or partially folded intermediate (I)), and binding state of HA (bound (B) or unbound (U)) (Supplementary Text, Figs. S3 and S4). For example, “TFB” indicates that the CD44-core adopts the low-affinity T conformation, Cter is fully folded, and HA is bound. Strikingly, depending on the applied tensile force, we can observe three major dissociation pathways: 1) partial unfolding of Cter and T to R switching of the CD44-core first occur simultaneously, followed by full unfolding of Cter and then rupture of the CD44-HA bond from the high binding-strength R conformation (Fig. 3a-d); 2) conformational switching from the T to R state occurs simultaneously with full unfolding of Cter, and the CD44-HA bond ruptures from the high binding-strength R state (Fig. 3c, Fig. S4b); and 3) CD44-HA rupture occurs directly from the low binding-strength T state with Cter well folded (Fig. 3c, Fig. S4c). Both pathways 1 and 2 contribute to long-lifetime events.

Because the structure of the Cter latch, which is the key force-sensing element, can modulate the relative stabilities of the T and R conformations (Fig. 2b,c), the time scale of the conformational switching and the CD44-HA dissociation pathways are expected to be regulated by the strength of the applied tensile forces. In the small force range ($<5.2$ pN), the time scale of conformational switching is insensitive to the force strength (Fig. 3e), and HA tends to dissociate from the low binding-strength T conformation. Consequently, CD44-HA dissociation dominantly occurs following the pathway 3 (Fig. 3g). In this case, the major effect of the applied tensile forces is to reduce the barrier height of the CD44-HA rupture step, as described by the classic Bell law, demonstrating slip-bond behavior [11]. With a further increase in the tensile force (5.2-12.1 pN), the T to R conformational switching becomes increasingly accelerated due to the force-induced unfolding of the force-sensing Cter latch (Fig. 3e) such that more CD44-HA rupture events occur in the high binding-strength R conformation following the pathways 1 and 2 (Fig. 3g). The increased populations of the high binding-strength pathways lead to elongation of the average lifetime of the CD44-HA bond, exhibiting the catch-bond effect. It is worth noting that the CD44-core may switch back to the low binding-strenth T state after the T to R conformational transition before ligand dissociation (Fig. S5). Such T$\rightarrow$R$\rightarrow$T transition loop does not affect the relative populations of the slow and fast pathways, and therefore was omitted from the trajectory in constructing the pathways shown in Fig. 3c. With the increasing of tensile force, the reversal R to T transition becomes slower (Fig. 3e), which also tends to increase the probabilities of the high binding-strength pathways. At forces larger than a critical value ($\sim$12.1 pN), the relative population of the pathways 1 and 2 reached its maximum, and becomes less sensitive to the increasing of the tensile force. Consequently, the kinetics of the CD44-HA rupture recover to the slip-bond behavior. These results clearly demonstrate a force-induced multi-pathway repartitioning mechanism of the above observed slip-catch-slip triphasic pattern in the force-response behavior of the CD44-mediated adhesion bond.

Due to the coexistence of multiple dissociation pathways with different rates at relatively large tensile forces, the observed survival probability deviates from single-exponent trend and show piecewise linear decays with distinct slopes in the semi-log plots (Fig. 3f, Fig. S6). The fast decay phase and slow decay phase are dominantly contributed by the dissociation events following the fast pathway 3 (Fig. 3f, red dots) and the slow pathways 1 and 2 (Fig. 3f, blue dots), respectively. The lifetime distributions for the dissociation events following the above two sets of pathways can be separately fitted by single-exponential functions with different time constants (Fig. S6). Such results are consistent with the force-induced multi-pathway repartitioning mechanism discussed above.

The above results show that unlocking of the C-terminal latch tends to trigger the conformational switch of the CD44-core to the high binding-strength R state, which therefore contributes to enhanced CD44-HA binding. However, before Cter unfolding, the CD44-core mostly stays in the low binding-strength T conformation as discussed above, and applying tensile force also tends to promote rupture of such low strength CD44-HA bond. Apparently, developing the catch-bond effect requires that there are a sufficient number of events in which force-induced unfolding of the Cter occurs prior to CD44-HA rupture. Consequently, a natural question that arises is what strategy the CD44 uses to meet the above required specific kinetic control over a wide range of tensile forces, which is the key aspect for understanding the molecular mechanism of the catch-bond effect but still remains unresolved.

To answer the above question, we characterized the force response behavior of the C-terminal latch, which is the force-sensing element of the CD44. Firstly, we performed constant-velocity pulling simulations with the pulling force applied between the CD44-core and the C-terminal residue and extracted the unfolding forces of the Cter latch (Fig. 4a). By repeating multiple simulations with and without HA binding, we calculated the distributions of the unfolding forces. One can see that HA binding dramatically modifies the force response behavior of the C-terminal latch (Fig. 4b). Without HA binding, the C-terminal latch shows high mechanical stability with the mean value of the unfolding force of $\sim$17.0 pN, which is much higher than the typical force range showing catch-bond effect (5.2pN-12.1pN, Fig. 1f). In contrast, after HA binding, the mean value of the unfolding force becomes $\sim$9.0 pN, which is within the force range of the catch-bond phase. Similar results can be observed when different force acting points were used in the pulling simulations (Fig. S7).

In the above constant-velocity pulling simulations, the used pulling velocity needs to be very high in order to observe a successful unfolding event within reasonable simulation time, which tends to overestimate the unfolding force. Therefore, we also performed constant-force pulling simulations at different tensile forces and calculated the free energy profiles. The pulling force at which the folded state and unfolded state have equal population is defined as unfolding force. The results show again that HA binding significantly reduces the unfolding force (Fig. 4c,d and Fig. S8). In the absence of HA, the unfolding force is between 10.4 pN and 12.1 pN. In the presence of HA, the unfolding force becomes $\sim$ 6.9 pN. The free energy profile along the reaction coordinate $Q_{C}$ at zero force load also showed that the free energy barrier height for Cter unfolding was significantly lowered upon HA binding (Fig. S3). All these results suggest that the binding of the ligand HA significantly decreases the stability and unfolding force of the C-terminal latch, although the HA binding site is spatially distant from the Cter, demonstrating typical allosteric coupling behavior. Therefore, the above results indicate that CD44 is able to utilize the allosteric coupling from the HA binding site to the force-sensing element Cter to promote the detachment of the otherwise stably folded C-terminal latch with a much lowered threshold force. Consequently, it may enhance the force sensitivity of the C-terminal latch and enable the force-induced conformational switching to occur before the bond rupture from the low binding-strength state which is a basic prerequisite for catch-bond formation.

The above results suggest a bidirectional allosteric coupling mechanism of force-enhanced cell adhesion. In this mechanism, HA binding allosterically promotes the mechanical unfolding of the distant force-sensing Cter before bond rupture (i.e., forward allostery), which in turn activates the CD44-core and leads to force-enhanced CD44-HA binding via backward allostery (Fig. 4e). Such bidirectional allosteric coupling enables the catch-bond effect to occur under a wide range of tensile forces and therefore may favor efficient rolling adhesion of cells.

To further demonstrate the role of bidirectional allostery for catch-bond formation, we constructed a minimalist kinetic model (Fig. 4f). The unfolding rate of Cter under tensile force F can be estimated as

Here, $k_{1}^{0}$ represents the unfolding rate of Cter at zero-force without considering the forward allostery, $\Delta x_{1}$ represents the transition distance for unfolding, and $\beta=1/k_{B}T$. When the effect of forward allostery is considered, the barrier height for the Cter unfolding is decreased by $\Delta\Delta G$. According to the simulation result (Fig. S3), $\Delta\Delta G\sim$ 2kcal/mol. The unfolding rate is then written as following

The Cter unfolding is reversible with the folding rate given by $k_{2}^{0}e^{-\beta F\Delta x_{2}}$. HA may dissociate either from the Cter-folded state or Cter-unfolded state, with the rates being roughly estimated by $k_{3}^{0}e^{-\beta F\Delta x_{3}}$ and $k_{4}^{0}e^{-\beta F\Delta x_{4}}$, respectively. Here $k_{2}^{0}$, $k_{3}^{0}$, $k_{4}^{0}$, $\Delta x_{2}$, $\Delta x_{3}$, and $\Delta x_{4}$ represent the corresponding rates and transition distance at zero-force. The backward allostery, as implicated in most catch-bond models, requires $k_{3}^{0}>k_{4}^{0}$, such that unfolding of the force sensor Cter elongates the CD44-HA lifetime. By appropriately optimizing the parameters (Tab. S1), the above bidirectional model can reasonably describe the slip-catch-slip triphasic behavior observed in the simulations (Fig. 4g, orange). In comparison, when the forward allostery is not considered ($\Delta\Delta G=0$), the catch-bond effect becomes much weaker (Fig. 4g, blue). Such results clearly demonstrates that the forward allostery plays crucial role for the catch-bond formation, supporting the bidirectional allostery mechanism.

As a complementary characterization of the bidirectional allostery mechanism, we further conducted two sets of all-atom MD simulations, i.e., “ligand-bound” simulations and “ligand-free” simulations. In order to avoid introducing new force field parameters, the ligand HA was considered implicitly in the “ligand-bound” simulations (Appendix D, Supplementary Text). Initiating from the ordered structure with the Cter being well folded, we conducted five independent simulations for each case under force-free condition. We then performed energy decomposition analysis to investigate the allosteric coupling[50]. The calculated contact energies between the residues of the Cter and the CD44-core showed that binding of HA significantly weakens the key interactions stabilizing the Cter (Fig. 5b). Particularly, the interface interactions involving the Tyr161 of the Cter, which has the most prominent contribution to the interface interactions between the Cter and the CD44-core, were much weakened upon ligand binding (Fig. 5c-f). For the ligand-free case, the Tyr161 forms stable contacts with the CD44-core with the average contacting energy of $\sim$ -13.5 kcal/mol. For the ligand-bound case, the Tyr161 hops between a strongly contacting state ($\sim$ -13.5 kcal/mol) and a weakly contacting state ($\sim$ -7.9 kcal/mol). Apparently, such ligand binding induced destabilization of the interface interactions between the CD44-core and Cter would reduce the threshold force for the Cter unfolding. All these all-atom MD simulation results and the energetic decomposition analysis suggest that the allosteric coupling from the HA binding site to the Cter is significant, further supporting the bidirectional allostery mechanism. We also conducted all-atom MD simulations and energy decomposition analysis for the PSGL-1 receptor P-selectin, which is another key receptor mediating rolling adhesion of cells along vessel walls during the inflammatory response [12, 35, 29, 4], and similar results were observed (Fig. S9).

In the above discussions, the protein model was calibrated to satisfy the experimental restraints on the conformational equilibrium, therefore corresponding to wild-type (WT) CD44 (Supplementary Text). The conformational equilibrium is related to the energy landscape dictating the conformational switching of CD44-core between the T and R states, and is controlled by the global energy gap parameter $\Delta V$ of the double-basin energy function given by Eq. 2 (Fig. 6a, Appendix A). To demonstrate the crucial role of appropriate conformational equilibrium in the observed catch-bond effect, we also conducted simulations by designing a number of CD44-mutant models, in which the protein conformational equilibrium was altered by tuning the parameter $\Delta V$. For the CD44-mutant models with an extremely T- or R-biased conformational equilibrium, the lifetime of the CD44-HA bond monotonically decreases with increasing tensile force (Fig. 6b), lacking the catch-bond effect. Nevertheless, one can observe obvious catch-bond effect for the parameter range around the WT model (Fig. 6b, c). These CD44 models exhibiting catch-bond effect have two key features, which may represent the essential thermodynamic and kinetic requirements for the receptor protein to shape a catch-bond. First, both the T and R conformations are accessible with significant probabilities in the zero force case, and applying a tensile force can modulate the conformational distribution through force-induced unfolding of the Cter(Fig. 6d). Therefore, the relative stability between the two conformational states should not be too large, such that the conformational dynamics of the CD44-core can be sensitively modulated by the Cter unfolding. Second, the time for the reverse conformational switching from the R to T state can be significantly prolonged by applying a tensile force due to force-induced Cter unfolding, such that the receptor has higher probability to be locked in the high binding-strength conformation before bond rupture (Fig. 6e), demonstrating the crucial role of kinetic effect of tensile forces for catch-bond formation.

The above results demonstrate that the CD44 models with appropriate conformational equilibrium tend to exhibit more prominent catch-bond effect, possibly because these protein models can better satisfy the above thermodynamic and kinetic requirements for bidirectional allosteric coupling. These results may suggest that WT CD44 has well evolved to optimize the conformational equilibrium and thereby develop the catch-bond effect, which is essential for its biological function to mediate rolling adhesion of cells. Such a tight interplay between the appropriate conformational equilibrium and force-response behavior of adhesion bonds has significant implications for drug design targeting cell adhesion receptors.

At physiologically relevant range of shear stresses, the circulating tumor cells or leukocytes may behavior diversely[51, 52]. Part of the cells undergo rolling adhesion, and other cells may undergo firm adhesion or directly flow away with the fluids. The relative importance of these different outcomes varies with the cell lines and the shear stress. In a previous experimental work by Suzuki and coworkers [36], two CD44 mutants respectively over-stabilizing the high binding-strength conformation (R) and the low binding-strength conformation (T) were introduced. Their results showed that for the mutant biasing to high binding-strength conformation (Y161A), the rolling of the cells is much less efficient. Whereas for the mutant biasing to the low binding-strength conformation (by introducing a disulfide bond between T47 and N164), the adhesion becomes much weaker and rolling adhesion is rare. These mutagenesis studies suggested that mutations altering the conformational equilibrium of the CD44 may affect the biological function, which supports the key role of conformational equilibrium of receptor protein for the catch-bond formation revealed above.

In addition to the conformational equilibrium of receptor protein, the force response behavior of the CD44-HA bond could also be modulated by the variations of the ligand HA. In this work, the key feature of HA as a native ligand of CD44 is considered by appropriately assigning the interaction strength with CD44. The coefficient $\lambda\epsilon_{LP}$ in Eq. A2 controls the interaction strength between HA and CD44. In order to investigate the effect of the variations in HA on the observed force-response behavior of the CD44-HA bond, we performed additional simulations with varied interaction strengths $\lambda\epsilon_{LP}$. The value of $\lambda$ less (larger) than 1.0 represents that the varied HA has weaker (higher) binding strength with the CD44, by which we can effectively model the effect of variations in HA on the force-response behavior of CD44-HA bond. The results showed that for wide range of interaction strengths, we can observe the catch-bond effect. However, when CD44-HA interactions become extremely weak or strong, applying tensile force does not enhance the lifetime of the CD44-HA bond (Fig. S10), and therefore the catch-bond effect becomes weak.