A Rough Energy Landscape to Describe Surface-Linked Antibody and Antigen Bond Formation

Antibodies and B cell receptors often bind their antigen at cell-cell interface while both molecular species are surface-bound, which impacts bond kinetics and function. Despite the description of complex energy landscapes for dissociation kinetics which may also result in significantly different association kinetics, surface-bound molecule (2D) association kinetics usually remain described by an on-rate due to crossing of a single free energy barrier, and few experimental works have measured association kinetics under conditions implying force and two-dimensional relative ligand-receptor motion. We use a new laminar flow chamber to measure 2D bond formation with systematic variation of the distribution of encounter durations between antigen and antibody, in a range from 0.1 to 10 ms. Under physiologically relevant forces, 2D association is 100-fold slower than 3D association as studied by surface plasmon resonance assays. Supported by brownian dynamics simulations, our results show that a minimal encounter duration is required for 2D association; an energy landscape featuring a rough initial part might be a reasonable way of accounting for this. By systematically varying the temperature of our experiments, we evaluate roughness at 2kBT, in the range of previously proposed rough parts of landscapes models during dissociation.


Supplementary information on the automated laminar flow chamber set-up:
The laminar flow chamber device: the laminar flow chamber device is a block of brass, 75x25x12 mm 3 with several machined features. First, nine vertical cylindrical holes (diameter 6mm, one per individual chamber) are filled with PMMA rod to form illumination windows. Second, one entry hole on one side of each PMMA window and one exit hole on the other side are drilled, then brass tubing is glued to form connections for flow chamber PDMS piping. Third, two horizontal holes (diameter 4mm, length 75mm) are drilled on the outer side of the entry and exit holes, along the whole length of the device. Both extremities of both holes are filled with machined brass rod that are tin-welded to the brass block. Vertical holes (diameter 4mm) are then drilled at each extremity, with brass piping glued for connection to temperature control PDMS piping. An automated vinyl cutter (Graphtec, Japan) cuts nine rectangular holes (10x2 mm²) in a 75x25mm² rectangle of 75µm thick self-adhesive vinyl film. Two such layers are glued to the bottom of the machined brass block, forming nine individual 10x2x0.15mm 3 chambers.
The temperature control system: The heating resistor of a bath heater (Thermo-Fisher, France) and the compressor, radiator, and whole coolant piping of an ice-cube machine are set in a plastic box (RS Components, France) with the heating resistor and cube-forming part of the ice-cube machine both set in an insulated plastic container of approximatively 3 liter volume, filled with water. PDMS piping is connected to the insulated container, then to a low-voltage water pump (RS Components, France), then to the flow chamber thermoregulation inner piping, then back to the water container. A microcontroller (Arduino Uno, Arduino, Italy) receives signal from a thermistor and controls both the heating resistor and the cooling compressor through relays. The microcontroller is programmed to regulate the container water temperature according to one of 10 pre-programmed settings, chosen through a rotating selector, and to pump the water at will in the chamber through temperature control PDMS piping.
The agitation device: A rectangular piece is machined in polyacetal (POM-C); a standard hobby servomotor (Hitec, Japan) is bolted to it with rubber bushing allowing some play, while its base is bolted to the microscope stage. A clamp able to hold the reservoir is machined in POM-C and bolted to the rotor of the servomotor. A vibrating electrical DC engine, identical to what is found in mobile phones, is fitted to the clamp. The reservoir itself is machined in a PMMA cylinder (diameter 20mm, length 50mm).

The laminar flow chamber automaton:
The control device is based on a microcontroller (Arduino Mega, Arduino, Italy) that controls directly the servomotor and vibrating motor of the agitation device, the microscope illumination through a relay, and controls the syringe pumps stepper motors through dedicated stepper motors control boards (model A4983, Pololu, USA) with micro-step resolution. Both syringe pumps are made from the frame and lead-screw of former single-speed syringe pumps (Razel, USA) and equipped with stepper motors (Crouzet, France).
Experimental sequence and movies post-processing: Prior to data acquisition, microsphere reservoir is filled with microsphere suspension, injection syringe, flow syringe, piping and one chosen chamber are filled with PBS with 0.2% bovine serum albumin. Thermoregulation bath is connected to the chamber and its temperature selected. The operator launches a movie acquisition by the camera software, then the operator turns the automaton on. What follows is fully automated: microsphere reservoir is agitated by rotation and vibration, then 200µl of microsphere suspension are injected in the chamber by the injection syringe pump, then the flow syringe pump is actuated. Microscope illumination is then turned on by the controller, and a movie with microspheres displacements and arrests is recorded. Then the illumination is turned off, and the whole cycle is repeated with a different shear rate. The operator turns off the automaton and movie acquisition when all shear conditions have been measured. The operator may then either disconnect the current chamber to connect one of the remaining eight, change the temperature, or change the set-up angle, then record a new movie and re-launch the automaton. This method produce one initial movie containing several sequences (one for each shear rate), separated by non-illuminated (black) sequences. Post-processing is done by a plug-in written in Java for ImageJ that cut the initial movie when illumination is off, get rid of non-illuminated sequences, and create separate movies for each shear stress. Theses sequences are then saved in a folder named after the initial movie, then particle detection and trajectory retrieving follows automatically.