Nicolas Destainville

Confined Diffusion Without Fences of a G-Protein-Coupled Receptor as Revealed by Single Particle Tracking

Single particle tracking is a powerful tool for probing the organization and dynamics of the plasma membrane constituents. We used this technique to study the micro -opioid receptor belonging to the large family of the G-protein-coupled receptors involved with other partners in a signal transduction pathway. The specific labeling of the receptor coupled to a T7-tag at its N-terminus, stably expressed in fibroblastic cells, was achieved by colloidal gold coupled to a monoclonal anti T7-tag antibody. The lateral movements of the particles were followed by nanovideomicroscopy at 40 ms time resolution during 2 min with a spatial precision of 15 nm. The receptors were found to have either a slow or directed diffusion mode (10%) or a walking confined diffusion mode (90%) composed of a long-term random diffusion and a short-term confined diffusion, and corresponding to a diffusion confined within a domain that itself diffuses. The results indicate that the confinement is due to an effective harmonic potential generated by long-range attraction between the membrane proteins. A simple model for interacting membrane proteins diffusion is proposed that explains the variations with the domain size of the short-term and long-term diffusion coefficients.

Microscopic Mechanism for Experimentally Observed Anomalous Elasticity of DNA in Two Dimensions

By exploring a recent model in which DNA bending elasticity, described by the wormlike chain model, is coupled to basepair denaturation, we demonstrate that small denaturation bubbles lead to anomalies in the flexibility of DNA at the nanometric scale, when confined in two dimensions (2D), as reported in atomic-force microscopy experiments. Our model yields very good fits to experimental data and quantitative predictions that can be tested experimentally. Although such anomalies exist when DNA fluctuates freely in three dimensions (3D), they are too weak to be detected. Interactions between bases in the helical double-stranded DNA are modified by electrostatic adsorption on a 2D substrate, which facilitates local denaturation. This work reconciles the apparent discrepancy between observed 2D and 3D DNA elastic properties and points out that conclusions about the 3D properties of DNA (and its companion proteins and enzymes) do not directly follow from 2D experiments by atomic-force microscopy.

Comment to the Article by Michael J. Saxton: A Biological Interpretation of Transient Anomalous Subdiffusion. I. Qualitative Model ☆

In a recent article (1), Michael J. Saxton proposes to interpret as anomalous diffusion the occurrence of apparent transient subdiffusive regimes in mean-squared displacement (MSD) plots, calculated from trajectories of molecules diffusing in living cells and acquired by single particle (or molecule) tracking techniques (SPT or SMT). The demonstration relies on the analysis of both three-dimensional diffusion by Platani et al. (2) and two-dimensional diffusion by Murase et al. (3). In particular, the data reported by Murase et al. cover extremely large timescales and experimental conditions: video rate but also high-speed SPT and single fluorescence molecule imaging. This is an exciting opportunity to address the question of anomalous diffusion because the experiments cover timescales ranging from 33 μs up to 5 s, i.e., a range of more than five orders of magnitude(Fig. 1 b). n n n nFIGURE 1 n nLog-log plots of experimental mean-square displacements divided by time (MSD/t) versus time t, where normal diffusive regimes are characterized by a constant value whereas apparent subdiffusivity is revealed by quasi-linear regimes with negative slopes: ... n n n nAs pointed out by M. J. Saxton, anomalous diffusion (4) arises from an infinite hierarchy of space or energy scales hindering normal diffusion. The normal diffusion law MSD(t) = 4Dμt, where Dμ is the microscopic diffusion coefficient, becomes MSD(t) ≈ Ωtα, where Ω is some coefficient and α is the anomalous diffusion exponent. In the case of subdiffusive behavior, α < 1. However, in cellular processes the hierarchy is always finite since there is a short distance cutoff that is larger than the molecular scale, and a large distance one that is typically cell size. Therefore, one can expect an anomalous diffusion regime on a transient time interval only and crossovers to normal diffusion at short and long timescales. It is precisely what Platani et al. (2) and Murase et al. (3) observed. In Fig. 1, the experimental apparent subdiffusive regimes can cover up to three orders of magnitude. n n n n nAnomalous diffusion is frequently invoked to interpret complex experimental data. However, the elucidation of the physical mechanisms at its origin remains a difficult and still open issue (5). In this context, the systematic research of the simplest mechanisms accounting for experimental observations should be preferred to avoid an over-interpretation of data. Without questioning the existence of subdiffusive behaviors, which certainly play a key role in numbers of mechanisms in living systems, we would like to point out that the data used by J. M. Saxton can be fitted as well by a simple law, resulting from confined diffusion at short times, with a slower free diffusion superimposed at larger times: n n n n n(1) n n nwhere there is now only one length-scale, L, the typical size of the confining domains. The timescale τ = L2/(12 Dμ) is the equilibration time in the domains (8). DM is the long-term diffusion coefficient, ensuing, for example, from the fact that the confining domains are semi-permeable (6). This law is a very good approximation of a more complex form (7) because it takes into account only the slowest relaxation mode of confined diffusion at short times (8). By contrast, the contribution of the free long-term diffusion is mathematically exact. It can be proven (calculations not shown) that this contribution is equal to L2/3 + 4 DM t, consistent with Eq. 1. In addition, the short-term expansion of Eq. 1 gives MSD(t) = 4(Dμ + DM)t when t ≪ τ, where one would expect MSD(t) = 4Dμt. This is because the calculation we referred to above does not take into account the correct time distribution of domain-to-domain jumps when t ≤ τ. It overestimates the probability of jumps at very short times. This problem, that will be addressed elsewhere, is beyond the scope of this Comment. Indeed, we work in the regime Dμ ≫ DM, where this issue is negligible, as confirmed in the simulations below. Fig. 1 illustrates that this law accounts quite well for the observed transient regimes without appealing for anomalous diffusion. Within this approximation (Fig. 1 b), the fit of experimental data by Eq. 1 gives Dμ = 0.36 μm2/s = 10DM. The numerical values that we get are consistently close to those of Murase et al. (3). In Fig. 1 a, the MSD is calculated from three-dimensional positions (2), and Eq. 1 must be multiplied by 3/2 to be adapted to three dimensions. In both sets of data (Fig. 1, a and b), the apparent anomalous exponents measured by M. J. Saxton are the slopes of the MSD/t profiles at their inflection points, in log-log coordinates. n n nTo confirm further our statements, we have performed numerical experiments of Brownian particles diffusing in a mesh-grid of semipermeable linear obstacles. The complete simulation procedure was detailed in Meilhac et al. (6). Our results are summarized in Fig. 2 where numerical MSD(t)/t plots are fitted by Eq. 1. Two conclusions can be drawn: 1), as anticipated, Eq. 1 is a very good approximation of the real diffusive properties of the system considered; and 2), between the short- and long-term regions where MSD is proportional to t, there is an intermediate region, the duration of which is comparable to the ratio Dμ/DM (in logarithmic scale). In this region, the MSD/t plots resemble anomalous diffusion plots, with slope tending to −1 when the previous ratio is large. Indeed, when Dμ ≫ DM, the log-log plot of MSD(t) is as follows. When t ≪ τ, MSD(t) = 4 Dμt and MSD/t is constant. When t ≫ L2/(12DM) = τesc, MSD(t) = 4 DMt and MSD/t is also constant. The time τesc = τ Dμ/DM corresponds to the typical time needed to escape boxes (6). In the intermediate region, MSD(t) = L2/3 is constant. There are two crossovers near τ and τesc. For the MSD/t representation, the constant transient regime becomes affine with slope −1. When the ratio Dμ/DM is large but finite, the slope of this intermediate region is still negative, but it is larger than −1. The graph resembles an anomalous diffusion graph on the time interval [τ,τesc] (see also Fig. 1). Note that, up to translations, the shapes of the MSD and MSD/t curves in log-log coordinates only depend on the ratio τesc/τ = Dμ/DM. n n n nFIGURE 2 n nNumerically simulated (symbols; L = 400 nm, τ = 0.22 s, Dμ = 0.06 μm2/s) MSD(t) (lower plots on the left-hand-side) and MSD(t)/t (upper plots), for Dμ/DM = 102 (black) and 103 (blue), on ... n n n n n nWhen visualizing MSD plots, the transition from short-term diffusion that is confined in domains of size L to slower, longer-term free diffusion can be confused with anomalous diffusion over several orders of magnitude of time. With the goal of researching the simplest mechanisms accounting for experimental observations, it seems reasonable to explore first the former possibility. In principle, elucidating the nature of domains with a single typical size L is a much easier task than identifying a hierarchy of space (or energy) scales ranging over several orders of magnitude. In the work of Murase et al. (3), domains of size L ≈ 30 nm are attributed to the cortical cytoskeleton meshwork. In the case of Cajal bodies (2), the fitted values L ≈ 1 μm will have to be interpreted in future work: the confining roles of chromatin-associated states and of possible division of the nucleus in functionally distinct compartments (2) will have to be investigated.

Mesoscopic models for DNA stretching under force: New results and comparison with experiments

AbstractSingle-molecule experiments on double-stranded B-DNA stretching have revealed one or two structural transitions, when increasing the external force. They are characterized by a sudden increase of DNA contour length and a decrease of the bending rigidity. The nature and the critical forces of these transitions depend on DNA base sequence, loading rate, salt conditions and temperature. It has been proposed that the first transition, at forces of 60–80 pN, is a transition from B to S-DNA, viewed as a stretched duplex DNA, while the second one, at stronger forces, is a strand peeling resulting in single-stranded DNAs (ssDNA), similar to thermal denaturation. But due to experimental conditions these two transitions can overlap, for instance for poly(dA-dT). In an attempt to propose a coherent picture compatible with this variety of experimental observations, we derive an analytical formula using a coupled discrete worm-like chain-Ising model. Our model takes into account bending rigidity, discreteness of the chain, linear and non-linear (for ssDNA) bond stretching. In the limit of zero force, this model simplifies into a coupled model already developed by us for studying thermal DNA melting, establishing a connection with previous fitting parameter values for denaturation profiles. Our results are summarized as follows: i) ssDNA is fitted, using an analytical formula, over a nano-Newton range with only three free parameters, the contour length, the bending modulus and the monomer size; ii) a surprisingly good fit on this force range is possible only by choosing a monomer size of 0.2 nm, almost 4 times smaller than the ssDNA nucleobase length; iii) mesoscopic models are not able to fit B to ssDNA (or S to ss) transitions; iv) an analytical formula for fitting B to S transitions is derived in the strong force approximation and for long DNAs, which is in excellent agreement with exact transfer matrix calculations; v) this formula fits perfectly well poly(dG-dC) and λ-DNA force-extension curves with consistent parameter values; vi) a coherent picture, where S to ssDNA transitions are much more sensitive to base-pair sequence than the B to S one, emerges. This relatively simple model might allow one to further study quantitatively the influence of salt concentration and base-pairing interactions on DNA force-induced transitions.n

Statistical Mechanics and Dynamics of Two Supported Stacked Lipid Bilayers

The statistical physics and dynamics of double supported bilayers are studied theoretically. The main goal in designing double supported lipid bilayers is to obtain model systems of biomembranes: the upper bilayer is meant to be almost freely floating, the substrate being screened by the lower bilayer. The fluctuation-induced repulsion between membranes and between the lower membrane and the wall are explicitly taken into account using a Gaussian variational approach. It is shown that the variational parameters, the effective adsorption strength, and the average distance to the substrate, depend strongly on temperature and membrane elastic moduli, the bending rigidity, and the microscopic surface tension, which is a signature of the crucial role played by membrane fluctuations. The range of stability of these supported membranes is studied, showing a complex dependence on bare adsorption strengths. In particular, the experimental conditions of having an upper membrane slightly perturbed by the lower one and still bound to the surface are found. Included in the theoretical calculation of the damping rates associated with membrane normal modes are hydrodynamic friction by the wall and hydrodynamic interactions between both membranes.

A Rationale for Mesoscopic Domain Formation in Biomembranes

Cell plasma membranes display a dramatically rich structural complexity characterized by functional sub-wavelength domains with specific lipid and protein composition. Under favorable experimental conditions, patterned morphologies can also be observed in vitro on model systems such as supported membranes or lipid vesicles. Lipid mixtures separating in liquid-ordered and liquid-disordered phases below a demixing temperature play a pivotal role in this context. Protein-protein and protein-lipid interactions also contribute to membrane shaping by promoting small domains or clusters. Such phase separations displaying characteristic length-scales falling in-between the nanoscopic, molecular scale on the one hand and the macroscopic scale on the other hand, are named mesophases in soft condensed matter physics. In this review, we propose a classification of the diverse mechanisms leading to mesophase separation in biomembranes. We distinguish between mechanisms relying upon equilibrium thermodynamics and those involving out-of-equilibrium mechanisms, notably active membrane recycling. In equilibrium, we especially focus on the many mechanisms that dwell on an up-down symmetry breaking between the upper and lower bilayer leaflets. Symmetry breaking is an ubiquitous mechanism in condensed matter physics at the heart of several important phenomena. In the present case, it can be either spontaneous (domain buckling) or explicit, i.e., due to an external cause (global or local vesicle bending properties). Whenever possible, theoretical predictions and simulation results are confronted to experiments on model systems or living cells, which enables us to identify the most realistic mechanisms from a biological perspective.