Exploring the Sulfatase 1 Catch Bond Free Energy Landscape using Jarzynski's Equality

Abstract

In non-covalent biological adhesion, molecular bonds commonly exhibit a monotonously decreasing life time when subjected to tensile forces (slip bonds). In contrast, catch bonds behave counter intuitively, as they show an increased life time within a certain force interval. To date only a hand full of catch bond displaying systems have been identified. In order to unveil their nature, a number of structural and phenomenological models have been introduced. Regardless of the individual causes for catch bond behavior, it appears evident that the free energy landscapes of these interactions bear more than one binding state. Here, we investigated the catch bond interaction between the hydrophilic domain of the human cell surface sulfatase 1 (Sulf1HD) and its physiological substrate heparan sulfate (HS) by atomic force microscopy based single molecule force spectroscopy (AFM-SMFS). Using Jarzynski's equality, we estimated the associated Gibbs free energy and provide a comprehensive thermodynamic and kinetic characterization of Sulf1HD/HS interaction. Interestingly, the binding potential landscape exhibits two distinct potential wells which confirms the recently suggested two state binding. Even though structural data of Sulf1HD is lacking, our results allow to draft a detailed picture of the directed and processive desulfation of HS.

Figure 1

Flat representation of free energy landscapes of slip and catch bonds, respectively. Here, the reaction coordinate is the path along which the system evolves under the impact of an external force. In the experiment this is measured as the molecular extension. (A) Exemplary single well free energy landscape of a molecular slip bond. The black curve depicts the binding potential of a molecular complex without external force. In contrast, the potential is distorted (lowering of the transition state) when the complex is subjected to an external force (red curve). (B) Double well free energy landscape as proposed for catch bond interaction. The occupancy of the states S1 and S2 governed by equilibrium thermodynamics. Without an external force (black plot) solely S1 is occupied. By increasing the force S2 is successively populated. Within the transition (catch) regime both S1 and S2 are populated. The estimated complex life time therefore is a superposition of the individual life time of both states. (C) Characteristic force life time plots of a slip and catch bond, respectively. The plots exhibit the complex life time of Sulf1HD bound to heparosan N-sulfate lacking 6-O-sulfates (left panel) and Sulf1HD’s physiological substrate HS (right panel). The catch regime (gray) marks the transition between two individual slip bond states S1 (dashed red) and S2 (dashed green).

Figure 2

(A) Typical disaccharide units of heparan sulfate S-regions. Disaccharide units of highly sulfated heparan sulfate S-regions consist of an uronic acid (either iduronic acid: X¹ = H and X² = COOH or glucuronic acid: X¹ = COOH and X² = H, with or without 2-O-sulfation (dark grey)) 1-4 linked to a modified glucosamine. Up to 8 consecutive disaccharide units were shown to have the depicted structure, where N-sulfation (light grey) is uniform and 6-O-sulfation (magenta) of the glucosamine residue is predominant. Regions of heparan sulfate with di- or tri-sulfated disaccharide units are the primary substrate of Sulf1 and 6-O sulfation is required for binding by the hydrophilic domain of Sulf1. (B) Hypothetical model of heparan sulfate 6-O-desulfation by Sulf1. The hydrophilic domain (HD) of Sulf1 (dark blue) binds to 6-O-sulfated sites (magenta) in highly sulfated S-regions of heparan sulfate (HS, yellow). Additional contacts between heparan sulfate and the catalytic domain (CAT-D) and the C-terminal domain (CTD) of Sulf1 may be formed. The 6-O-desulfation at the active site of Sulf1 (orange) could induce a shift to a tensed state in which HD and HS are interacting with high affinity. Although structural details are unknown, an associated conformational change could potentially facilitate progression of Sulf1 to the next 6-O-sulfated residue within highly sulfated regions of HS. N-sulfate groups (light grey dots) and 2-O-sulfate groups (dark grey dots) of HS are indicated. (C) Typical AFM setup to probe the dissociation forces of molecular complexes. HS polymers (yellow, 6-O-sulfates magenta circles) are covalently immobilized to a gold AFM tip via PEG-NHS ester disulfite linkers (green). MBP-HD fusion proteins (HD blue, MBP red) are bound to the gold substrates using the same linker.

Figure 3

(A) Dissociation force histograms acquired at different pulling speeds. The histograms evolve from double-peaked distributions at low and medium velocities to single peaked distributions. The occurrence and height of the peaks corresponds to the occupancy of the individual states S1 and S2. At a pulling velocity of 1000 nm s^-1 (blue plot) the low force peak referring to dissociation from S1 vanished completely. (B) A set (n = 50) of molecular force extension curves approximated to a worm like chain curve (solid red) l_p = 0.4(0.1) nm and L₀ = 15(1) nm. (C) Work distributions for different velocities. (D) Evolution of the Jarzynski equality. The exponentially averaged work W_n plotted versus the number of dissociation events n. (E) Estimated differences in free energy ΔG⁰ at various pulling velocities. Within the catch (transition) regime (gray) S1 is successively depleted whereas S2 becomes continuously populated. (F) Proposed free energy landscape (not to scale) for Sulf1HD/HS interaction. Here, the low force (S1) and high force binding state (S2) are shown in one potential landscape. Depending on the conformational state Sulf1HD could either bind in the low or high force state. In the mechanically relaxed state Sulf1HD binds only partially to the HS substrate (S1). When subjected to an external force Sulf1HD is stretched such that it can cross the transition state and establish additional bonds to the HS strand (S2).