Conversely, we could not satisfactorily fit the Arrhenius law to the temperature dependence of 2following Open in a separate window Figure 8 Results of systematic changes in heat and shear rate on binding linear density.Points of similar color were binding linear densities retrieved at identical heat but different shear rate; (a) data of simulated binding linear densities (left axis) plotted against experimental binding linear densities (bottom axis) with model, showing good correlation between rough energy scenery model and experimental data. durations between antigen and antibody, in a range from 0.1 to 10?ms. Under physiologically relevant forces, 2D association is usually 100-fold slower than 3D association as analyzed by surface plasmon resonance assays. Supported by brownian dynamics simulations, our results show that a minimal encounter period is required for 2D association; an energy scenery featuring a rough initial part might be a affordable way of accounting for this. By systematically varying the heat of our experiments, we evaluate roughness at 2during which a receptor interacts with its Molibresib besylate ligand (referred later as encounter period) can be written as Open in a separate window Physique 1 Two option energy landscapes for bond formation.(a) classical energy scenery formed by a free energy peak followed by a free energy well (only the first well of several possible is usually shown, with further parts of energy scenery suggested by dotted collection). Probability of crossing as a function of encounter duration is usually given by and length followed by a free energy well (again, only DAP6 the first well of several possible is usually shown, and further parts of energy scenery are suggested by dotted collection). Probability of crossing the rough part of the energy scenery as a function of encounter duration is usually given by 2. where is the on-rate. Recently, we observed discrepancies between bond formation measurements performed with the laminar circulation chamber and the on-rate model. Probability of bond formation was not proportional to encounter duration: we proposed a bond formation model23,24 based on a rough initial part in the energy scenery (the rough energy Molibresib besylate scenery being a concept first suggested by Zwanzig25 in another context). In this model, the first part of the energy scenery is made of numerous small energy peaks (forming the rough part of the scenery, of length and roughness is usually a phenomenological factor assumed to represent the proportion of properly folded and functional molecules, is the complementary error function, and is a characteristic time of the bond. From a theoretical point a view, recent reports suggest that binding kinetics of membrane attached molecules can be recalculated by accounting for membrane fluctuation and Molibresib besylate roughness26,27,28. However, the molecular intrinsic association rate is not questioned in these studies. In a laminar circulation chamber, receptor-coated microspheres move in a shear circulation on top of a surface bearing ligand molecules. If a receptor binds its ligand, the microsphere stops, while a pressure is usually immediately applied to the bond. During an experiment at a given shear rate, the number of association events and the total distance travelled by microspheres after sedimentation are measured, their ratio being called binding linear density (in m?1). A first simulation work follows to describe the microspheres and ligand and receptor movements responsible for bringing ligand and receptor together prior to their interaction, thus calculating the distribution of the durations during which one ligand may interact with one receptor (or encounter durations) for the experimental condition. A second simulation work uses binding models to retrieve simulated binding linear density, and permits comparison of these models to the experimental binding linear density24,29,30. The distribution of durations during which one ligand may interact with one receptor (or encounter durations) is essential for calculation of kinetic rates30,31. In assays where one of the reactants is in solution such as surface plasmon resonance, this distribution depends solely on diffusion. This distribution is usually directly controlled in a laminar circulation chamber, usually by varying the shear rate23. In the present study, we added two innovative features to the laminar circulation chamber: first, the distance between microsphere and surface was varied by tilting the set-up (observe Fig. 2a,b). This changed the distribution of encounter durations independently of shear, thus independently of applied pressure. This allowed us to obtain a large number of experimental conditions, differing either by shear rate or common microsphere distance to the surface, that were fitted for each binding model with the same set of parameter. This permitted to compare the validity of each binding model, and supported at the same time the validity of the model of microsphere and molecular movement. Second, heat was controlled and systematically varied to obtain quantitative information around the thermodynamics of the process. Besides, to measure kinetics, it is necessary to collect a large number of individual association and dissociation events due to their stochastic nature. We built a new automated laminar circulation chamber set-up in order to maximize data acquisition, used to measure the association and dissociation kinetics of a model antibody-antigen system at the single molecular level. We systematically varied shear rate and tilt angle to put our numerical models to test and to compare two alternative models of binding kinetics. One model was based on one free energy barrier, giving a classical on-rate (is usually minimal with the chamber parallel to the horizontal plane..
