Determining the binding parameters from co-sedimentation assays.

The stoichiometry n and the dissociation constant [Formula: see text] are key binding parameters characterizing the ligand-macromolecule interactions and equilibria. Equilibrium co-sedimentation experiments are performed in varying the concentration of one of the reactant while keeping constant that of the other reactant. The measured observable is the fraction [Formula: see text] of bound ligands when the ligand concentration is kept constant while that of macromolecules is varying whereas it is the macromolecule coverage [Formula: see text] with bound ligands when the ligand concentration is varying while that of macromolecules is kept constant. We have derived general expressions for [Formula: see text] and [Formula: see text] and subsequently showed that those expressions are in perfect agreement with simulations for a system of large ligands binding on macromolecules. Approximations have been developed to derive mathematical simple analytical expressions for [Formula: see text] and [Formula: see text] that can be used to fit the experimental data and thus extract, n and [Formula: see text] within the framework of equilibrium co-sedimentation assays. The method usefulness is illustrated and demonstrated by fitting the data from the literature using the derived formulas to determine the binding parameters.

Elasticity of podosome actin networks produces nanonewton protrusive forces.

Actin filaments assemble into force-generating systems involved in diverse cellular functions, including cell motility, adhesion, contractility and division. It remains unclear how networks of actin filaments, which individually generate piconewton forces, can produce forces reaching tens of nanonewtons. Here we use in situ cryo-electron tomography to unveil how the nanoscale architecture of macrophage podosomes enables basal membrane protrusion. We show that the sum of the actin polymerization forces at the membrane is not sufficient to explain podosome protrusive forces. Quantitative analysis of podosome organization demonstrates that the core is composed of a dense network of bent actin filaments storing elastic energy. Theoretical modelling of the network as a spring-loaded elastic material reveals that it exerts forces of a few tens of nanonewtons, in a range similar to that evaluated experimentally. Thus, taking into account not only the interface with the membrane but also the bulk of the network, is crucial to understand force generation by actin machineries. Our integrative approach sheds light on the elastic behavior of dense actin networks and opens new avenues to understand force production inside cells.

Dynamical decoration of stabilized-microtubules by Tau-proteins.

Tau is a microtubule-associated protein that regulates axonal transport, stabilizes and spatially organizes microtubules in parallel networks. The Tau-microtubule pair is crucial for maintaining the architecture and integrity of axons. Therefore, it is essential to understand how these two entities interact to ensure and modulate the normal axonal functions. Based on evidence from several published experiments, we have developed a two-dimensional model that describes the interaction between a population of Tau proteins and a stabilized microtubule at the scale of the tubulin dimers (binding sites) as an adsorption-desorption dynamical process in which Tau can bind on the microtubule outer surface via two distinct modes: a longitudinal (along a protofilament) and lateral (across adjacent protofilaments) modes. Such a process yields a dynamical distribution of Tau molecules on the microtubule surface referred to as microtubule decoration that we have characterized at the equilibrium using two observables: the total microtubule surface coverage with Tau's and the distribution of nearest neighbors Tau's. Using both analytical and numerical approaches, we have derived expressions and computed these observables as a function of key parameters controlling the binding reaction: the stoichiometries of the Taus in the two binding modes, the associated dissociation constants and the ratio of the Tau concentration to that of microtubule tubulin dimers.

Correcting binding parameters for interacting ligand-lattice systems.

Binding of ligands to macromolecules is central to many functional and regulatory biological processes. Key parameters characterizing ligand-macromolecule interactions are the stoichiometry, inducing the number of ligands per macromolecule binding site, and the dissociation constant, quantifying the ligand-binding site affinity. Both these parameters can be obtained from analyses of classical saturation experiments using the standard binding equation that offers the great advantage of mathematical simplicity but becomes an approximation for situations of interest when a ligand binds and covers more than one single binding site on the macromolecule. Using the framework of car-parking problem with latticelike macromolecules where each ligand can cover simultaneously several consecutive binding sites, we showed that employing the standard analysis leads to underestimation of binding parameters, i.e., ligands appear larger than they actually are and their affinity is also greater than it is. Therefore, we have derived expressions allowing to determine the ligand size and true binding parameters (stoichiometry and dissociation constant) as a function of apparent binding parameters retrieved from standard saturation experiments.