Can a bulky glycocalyx promote catch bonding in early integrin adhesion? Perhaps a bit

Many types of cancer overexpress bulky glycoproteins to form a thick glycocalyx layer. The glycocalyx physically separates the cell from its surroundings, but recent work has shown that the glycocalyx can paradoxically increase adhesion to soft tissues and therefore promote the metastasis of cancer cells. This surprising phenomenon occurs because the glycocalyx forces adhesion molecules (called integrins) on the cell’s surface into clusters. These integrin clusters have cooperative effects that allow them to form stronger adhesions to surrounding tissues than would be possible with equivalent numbers of un-clustered integrins. These cooperative mechanisms have been intensely scrutinized in recent years; a more nuanced understanding of the biophysical underpinnings of glycocalyx-mediated adhesion could uncover therapeutic targets, deepen our general understanding of cancer metastasis, and elucidate general biophysical processes that extend far beyond the realm of cancer research. This work examines the hypothesis that the glycocalyx has the additional effect of increasing mechanical tension experienced by clustered integrins. Integrins function as mechanosensors that undergo catch bonding – meaning the application of moderate tension increases integrin bond lifetime relative to the lifetime of integrins experiencing low tension. In this work, a three-state chemomechanical catch bond model of integrin tension is used to investigate catch bonding in the presence of a bulky glycocalyx. This modeling suggests that a bulky glycocalyx can lightly trigger catch bonding, increasing the bond lifetime of integrins at adhesion edges by up to 100%. The total number of integrin-ligand bonds within an adhesion is predicted to increase by up to ~60% for certain adhesion geometries. Catch bonding is predicted to decrease the activation energy of adhesion formation by ~1–4 kBT, which translates to a ~3–50× increase in the kinetic rate of adhesion nucleation. This work reveals that integrin mechanic and clustering likely both contribute to glycocalyx-mediated metastasis.


Introduction
Many metastatic carcinomas -such as recurrent glioblastoma multiform, which is invariably lethal 1,2 -overexpress bulky glycoproteins to form a thick (~10s-100s of nanometers [nm]) glycocalyx layer [3][4][5][6] . This glycocalyx imposes a physical separation between the cancer cell and its surroundings that is much wider than the typical length of adhesion proteins such as integrins (~20 nm). Recent work by Paszek, Weaver, and others has shown (perhaps counterintuitively) that this glycocalyx can increase adhesion to soft tissues and therefore promote the invasion of metastatic cancer cells by forcing integrin receptors into kinetic traps. Within these traps, the integrins assemble into high-strength focal adhesions (FAs) with the extracellular matrix (ECM) [6][7][8] (Figure 1). FA formation and maturation is critical to invasion, survival, and growth of cancer cells; in addition to mechanically coupling the cytoskeleton and cell membrane to the ECM, FAs recruit signalling molecules that produce biochemical outputs 9,10 including growth factor signalling upregulation 11,12 , which is also crucial for cancer proliferation [13][14][15][16] . In GBM (and potentially in similar types of soft-tissue cancer), integrin activation upregulates glycocalyx expression, leading to a feedback loop that further promotes cancer cell adhesion, survival, and growth 3 . Beyond GBM, glycocalyx upregulation is a common feature in metastatic and circulating cancer cells 4,6,[17][18][19][20] , and therapies that de-bulk the glycocalyx have proven promising in vivo [21][22][23] .
While recent work has illuminated the role that the glycocalyx plays in integrin clustering, much remains unknown about integrin mechanics in this context. Mechanical tension is critical to integrin function; integrins display catch-bond behavior, meaning that their adhesiveness increases under piconewton (pN)-scale tension 24 . Tension also promotes integrin structure-switching from an inactive conformation into an active conformation that promotes heightened intracellular signaling [25][26][27] . Furthermore, recent studies have shown that integrins generally behave as orientation-dependent mechanosensors 25,[28][29][30] , meaning that the geometry of glycocalyx-mediated FAs may play a unique role in mediating integrin activation that is separate from clustering. The role that the glycocalyx plays in modulating the magnitude and orientation of tension experienced by integrins, and the effect that such modulation will have on integrin catch bonding, has not been directly investigated.
It recent years, it has been suggested on numerous occasions that a bulky glycocalyx can impose tensile forces on integrins 31,32 , which could potentially drive catch bonding and integrin structure switching. This hypothesis of glycocalyx mediated integrin tension -that is, the hypothesis that resistance from a bulky glycocalyx on the plasma membrane can increase the tension experienced by integrin receptors binding to extracellular ligands -has not (to this author's knowledge) been investigated experimentally or computationally. However, this prediction can be derived from a simple force-balance analysis of integrin adhesion (Figure 1); if compression of the glycocalyx is counter-balanced by tension on integrin-ligand bonds then the edges of adhesions, where the plasma membrane slopes away from the underlying surface, should exhibit increased integrin tension due to increased distance between the plasma membrane and the surface.
Several computational models of integrin adhesion have incorporated mechanical considerations of the glycocalyx 7,33-36 . Other computational models have incorporated consideration of integrin catch bonding [37][38][39][40][41] . In this work, the mechanics of both glycocalyx compression and integrin catch bonding are considered together to understand how these phenomena interact to influence early integrin adhesion. Chemomechanical modeling 42,43 is used to address these questions.
The results of this analysis suggest that a bulky glycocalyx can trigger a small amount of catch bonding, increasing the bond lifetime of integrins at adhesion edges by up to 100%. This increase in integrin lifetime can increase the total number of integrin-ligand bonds within an adhesion by up to ~60% (depending on adhesion geometry). Finally, the ability of integrins to form catch bonds (instead of slip bonds) is predicted to decrease the activation energy of adhesion formation by ~1-4 k B T, which translated to a ~3-to ~50-fold increase in the kinetic rate of adhesion nucleation. While these values may not be quantitatively accurate due to assumptions that were made in the construction of the model used in this work, the general conclusion of this study is that glycocalyx repulsion and integrin catch bonding may interact to impose a small -but non-negligible -increase in adhesiveness and the rate of integrin adhesion formation. Following initial adhesion, glycocalyx-mediated integrin clustering and intracellular signaling, as described previously 3,6,7,16 , can trigger positive feedback loops to promote endurant adhesion and tissue invasion. This work contributes to our understanding of the mechanical role of the glycocalyx in early cancer adhesion.
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Methods
In the model used for this work, interactions are simulated between integrins on a plasma membrane and ligands on an underlying planar surface. The ligands are fixed in position, but the integrins can diffuse freely across the plasma membrane. The values of all parameters used in this study are listed in Table 1.

Kinetic and mechanical models of integrins
In line with prior work 7 , integrin ligand bonds in this work are modelled as linear springs with stiffness = 2 / ( Figure 2C). Accordingly, the relationships between bond force, , mechanical strain energy ( ), and bond extension ( ) are described by the relationships: Integrin catch bonding is represented in this work using a three-state model, wherein the integrin-ligand pair undergoes force-dependent transitions between the unbound state and two distinct bound states (bound 1 and bound 2 ) as shown in Figure 2A 37,44 . Kinetic rate constants for transitions between states are modelled with Bell model 33 -type equations: where is the prefactor parameter, Δ is the distance to the transition state parameter, and = 4.114 is thermal energy at room temperature. Specifically, transitions from . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted March 17, 2023. ; bound 1 to bound 2 and vice-versa ( and , respectively) and from bound 1 and bound 2 to unbound ( , and , , respectively) are described by: where the 8 Bell model parameters ( Figure 2D) were optimized to recreate the average lifetime ( ) vs. plot from Asaro, Lin, and Zhu 37 as shown in (Figure 2E). To assess the importance of catch bonding in this work, results were also compared to results obtained using slip bond kinetics, represented with the equation: . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made  . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted March 17, 2023. ; . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made

Physical representation of the plasma membrane
The plasma membrane is approximated as a square grid, centered on the origin, with 1 nm lateral spacing and zero thickness. The plasma membrane is assumed to have a Gaussian profile (this shape was chosen because it resembles known profiles and can be described simply with 3 parameters). The z-height of the gridpoint, , , can thus be described by: . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made

Steady-state calculation
To calculate the steady-state number of integrin-ligand bonds at a given surface position, total rate constants were first calculated by integration. The rate constant for total association at the j th substrate gridpoint was calculated by numerically integrating between the substrate gridpoint and all plasma membrane gridpoints within a lateral cutoff of 50 nm: , , = , # (7) where , is calculated with as the distance between the j th substrate gridpoint and the i th plasma membrane gridpoint, is the surface density of ligands on the planar surface, is the surface density of active integrins on the plasma membrane ( Figure 3A, C). is the area of the i th gridpoint, which is can be approximated by: where and are the x-and y-components of the gradient of the plasma membrane surface.
Each of the other rate constants for the j th gridpoint was also calculated: . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made where is the fraction of time that an integrin paired to the ligand at the j th substrate gridpoint spends at the i th plasma membrane gridpoint ( Figure 3B).
was calculated using a partition function: Once all total rate parameters are calculated, an Eulerian Markov matrix, , was constructed: . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made  . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made

Initial representative calculation
Initial steady-state calculations of integrin adhesion were performed (using parameters from previous work 7 ) with ℎ = 165 , = 27 , and Δ = 16 . For comparison as a glycocalyx-free control, steady-state adhesion to a flat plasma membrane was also simulated ( = 27 and Δ = 0 ) (Figure 4A,B). The flat plasma membrane resulted in a high degree of adhesion across the surface, with ≈ 0, , ≈ 0.55, and , ≈ 0.45 ( Figure 4C). In contrast, binding to the curved plasma membrane was highly positiondependent; increased from 1 far away from the center of the adhesion to ~0 close to the center of the adhesion ( Figure 4D). Notably, the bound 2 state (the tightly bound state) was higher at the edge of the plasma membrane contact zone (peaking at ~0.85) than at the center of the contact zone.
The substantial increase in the tightly bound state observed for the curved plasma membrane provides support for the hypothesis that the glycocalyx promotes catch bonding. To better assess the catch bond-mediated lifetime increase, the average bond lifetime at each surface gridpoint was calculated be re-arranging the equilibrium constant equation: While was low for the flat plasma membrane (~0.93 s), increased up as high as 2 seconds at the edge of the contact zone. The ratio of with a flat plasma membrane to with a curved plasma membrane, , which is equivalent to the increase in bond lifetime that is driven by the presence of a bulky glycocalyx, increases as high as 2.5 ( Figure 4F). However, these high . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The catch binding-mediated percent-increase in binding across the entire adhesion, , can be calculated through integration by weighting according to the bound fraction at each surface gridpoint: For this initial calculation, = 27.7% which is a moderate increase in adhesion due to catchbonding and the presence of a bulky glycocalyx.
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Binding enhancement with different adhesion geometries
Calculations of were next performed across a range of adhesion geometries.
Specifically, was varied from 20 nm (representing very close contact) to 40 nm (representing a complete lack of binding). Width was varied from 5 nm to 240 nm. For all conditions, the maximum plasma membrane height, + Δ was held fixed at = 43 . In addition, the total number of integrin-ligand bonds, was calculated by numerical integration: For this initial set of calculations, the maximum ligand density simulated by Paszek et al. 7 was used ( = 2,500 ). Across all values, increased superlinearly with adhesion width, while increased slightly with increasing width and levelled off around ℎ ≈30 nm ( Figure 5A). In contrast, decayed to zero and increased superlinearly with increasing across all ℎ values (Figure 5B). To summarize, depends strongly on both and ℎ ( Figure 5C), but depends primarily on ( Figure 5D).
As before, the largest is observed at conditions that have the least amount of binding (e.g. at higher ). This finding suggests an overall limit to the enhancement effect. Indeed, at conditions with 1 − > 0.001 (that is, when < 30 ), the frontier of the vs.
scatterplot (black line, which occurs at ℎ = 236 , Figure 5E)   The process of initial adhesion formation is characterized primarily by decreases of (e.g., the tip of adhesion coming into close contact with the substrate). The process of adhesion growth is characterized by increasing ℎ. The impact of catch binding on both processes can be analysed separately. The results of the previous paragraph show that during the adhesion growth process, catch bonding continues to play an important role in increasing binding at the adhesion edge. However, as the adhesion grows, the total fraction of integrin-ligand bonds that exhibit catch binding decreases (because bonds that are not close to the adhesion edge experience lower intrinsic forces).
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Effect of catch bonding on adhesion formation
To assess the dynamics of initial adhesion formation, the system energetics were considered by summing the energies of glycocalyx compression (Figure 6A, B), membrane bending (Figure 6C), and adhesion ( Figure 6D) (see Methods subsection "Energetics"): A phase plane analysis was then applied to the vs. ℎ vs. surface (Figure 7A), which contained one saddle point. Gradient descent was used to determine that the energy surface exhibits two regions: One region wherein adhesion growth is favored, and one region wherein adhesion shrinkage is favored. At moderate and high ℎ (i.e. >~70 nm), the dividing line (i.e. the separatrix, blue line in Figure 7A) between these two regions occurs at = 30 to 35 .
Very narrow-width adhesions are energetically disfavoured due to high plasma membrane bending energy, and so the separatrix shifts towards ≈ 25 at low ℎ.
This energy surface was then used to calculate the activation energy of adhesion formation. To accomplish this, the ensemble average energy at each value was calculated using the partition function: Calculating ⟨ ⟩ at each value yields a collapsed energy vs. curve (Figure 7B) representing the process of initial adhesion formation. In a manner resembling the energy surface, the collapsed curve exhibits a single maximum that separates the adhesion shrinkage and adhesion growth regimes. In order to assess the role of catch bonding in promoting adhesion formation, . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted March 17, 2023. ; https://doi.org/10.1101/2023.03.16.532909 doi: bioRxiv preprint this process was also repeated with integrins that exhibit slip-bonding ( Figure 7B). A 1.5 nm shift in the location of the energy maximum, as well as a Δ ≈3 k B T decrease in the height of the maximum, can be seen in the resulting energy vs. curve. This change in the activation energy barrier for adhesion formation translates to an exp(3) ≈ 20-fold change in the kinetic rate of adhesion formation.
. CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made  . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made  . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made To conclude this study, this process was repeated to compute ΔE at lower ligand densities ( , ranging from 250 to 2,500 ) and different bond stiffnesses ( ) (Figure 8).
Lower bond densities are expected to be more physiologically relevant than what was originally simulated, while lower bond stiffness can serve as an approximation for adhesion with compliant materials (such as soft tissue). This analysis suggests that Δ is independent of ( Figure   8A) but depends nearly linearly on the ( Figure 8B). In other words, this analysis suggests that the role of integrin catch bonding in early adhesion is independent of ligand density, but dependent on bond stiffness. The Δ values in this analysis ranged from 1.5 to 3.5 k B T, corresponding to a 4.5× to 33× increase in the rate of adhesion formation.
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Conclusion
This study suggests that catch bonding may perform a small role in promoting integrin adhesion due to intrinsic stress applied by the glycocalyx. Simulations in this work show that integrin catch bonding at the edges of curved adhesions can increase integrin-ligand bond lifetime by ~2fold (Figure 4) and can increase the total number of integrin-ligand bonds by ~15-50% ( Figure   5). Compared to hypothetical integrins with slip bond kinetics, integrins with catch-bond kinetics are predicted to form with a decrease in activation energy on the order of 1-4 k B T, corresponding to a 2.7-55× increase in the kinetic rate of adhesion formation. As with any computational study, numerous assumptions and simplifications were made that could alter these quantitative results.
Nonetheless, the interaction between catch bond kinetics and a bulky glycocalyx in integrin function has not yet been investigated. This initial study suggests that catch bonding likely plays a small-but-notable role in early integrin adhesion in the presence of a bulky glycocalyx.

Acknowledgments
This work was supported by the United States National Cancer Institute F99/K00 fellowship, grant number F99CA245789 / K00CA245789. . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted March 17, 2023. ; https://doi.org/10.1101/2023.03.16.532909 doi: bioRxiv preprint