Quantitative investigation of negative membrane curvature sensing and generation by I-BARs in filopodia of living cells

Membrane curvature has recently been recognized as an active regulator of cellular function, with several protein families identified as sensors and generators of membrane curvature. Amongst them, the inverse Bin/Amphiphysin/Rvs (I-BAR) domain family has been implicated in the sensing and generation of membrane structures with negative membrane curvature e.g. filopodia or dendritic spines. However, to date, quantitative biophysical investigations of I-BAR domains have mostly taken place in reconstitution. Here, we use fluorescence microscopy to quantitatively investigate membrane curvature sensing and generation by I-BARs in filopodia of living cells. As a model system, we selected two prototypic members of the I-BAR family, the insulin receptor substrate p53 and missing-in-metastasis. Our data demonstrated how I-BARs sense negative membrane curvature in the complex environment of live cells by revealing a dependence on membrane curvature for both their binding affinity to membranes and their saturation density. The non-monotonic dependence of protein sorting with negative membrane curvature allowed us to apply previously developed thermodynamic models to provide estimates of the effective intrinsic curvature and bending rigidity of the two I-BARs bound at the plasma membrane. Our results agree with studies performed on the insulin receptor substrate p53 in reconstitution. To quantitate membrane curvature generation by I-BARs we measured how their overexpression reduces the peak and the width of the size distribution of filopodia, resulting in filopodia populations with smaller and more uniform diameters. Our findings provide a quantitative biophysical insight in the ability of I-BARs to sense and generate negative membrane curvature in the crowded environment of living cells.

Accounting for inertia effects to access the high-frequency microrheology of viscoelastic fluids

We study the Brownian motion of microbeads immersed in water and in a viscoelastic wormlike micelles solution by optical trapping interferometry and diffusing wave spectroscopy. Through the mean-square displacement obtained from both techniques, we deduce the mechanical properties of the fluids at high frequencies by explicitly accounting for inertia effects of the particle and the surrounding fluid at short time scales. For wormlike micelle solutions, we recover the 3/4 scaling exponent for the loss modulus over two decades in frequency as predicted by the theory for semiflexible polymers.

Contact angle at the leading edge controls cell protrusion rate

Plasma membrane tension and the pressure generated by actin polymerization are two antagonistic forces believed to define the protrusion rate at the leading edge of migrating cells [1-5]. Quantitatively, resistance to actin protrusion is a product of membrane tension and mean local curvature (Laplace's law); thus, it depends on the local geometry of the membrane interface. However, the role of the geometry of the leading edge in protrusion control has not been yet investigated. Here, we manipulate both the cell shape and substrate topography in the model system of persistently migrating fish epidermal keratocytes. We find that the protrusion rate does not correlate with membrane tension, but, instead, strongly correlates with cell roundness, and that the leading edge of the cell exhibits pinning on substrate ridges-a phenomenon characteristic of spreading of liquid drops. These results indicate that the leading edge could be considered a triple interface between the substrate, membrane, and extracellular medium and that the contact angle between the membrane and the substrate determines the load on actin polymerization and, therefore, the protrusion rate. Our findings thus illuminate a novel relationship between the 3D shape of the cell and its dynamics, which may have implications for cell migration in 3D environments.

Hydrodynamic and subdiffusive motion of tracers in a viscoelastic medium

We investigate the diffusive motion of micron-sized spherical tracers in a viscoelastic actin filament network over the time span of 8 orders of magnitude using optical-tweezers single-particle tracking. The hydrodynamic interactions of a tracer with the surrounding fluid are shown to dominate at microsecond time scales, while subdiffusive scaling due to viscoelastic properties of the medium emerges at millisecond time scales. The transition between these two regimes is analyzed in the frame of a minimal phenomenological model which combines the Basset force and the generalized Stokes force. The resulting Langevin equation accounts for various dynamical features of the thermal motion of endogenous or exogenous tracers in viscoelastic media such as inertial and hydrodynamic effects at short times, subdiffusive scaling at intermediate times, and eventual optical trapping at long times. Simple analytical formulas for the mean-square displacement and velocity autocorrelation function are derived.

Optical trapping microrheology in cultured human cells

We present the microrheological study of the two close human epithelial cell lines: non-cancerous HCV29 and cancerous T24. The optical tweezers tracking was applied to extract the several seconds long trajectories of endogenous lipid granules at time step of 1μs. They were analyzed using a recently proposed equation for mean square displacement (MSD) in the case of subdiffusion influenced by an optical trap. This equation leads to an explicit form for viscoelastic moduli. The moduli of the two cell lines were found to be the same within the experimental accuracy for frequencies 10(2) - 10(5) Hz. For both cell lines subdiffusion was observed with the exponent close to 3/4, the value predicted by the theory of semiflexible polymers. For times longer than 0.1s the MSD of cancerous cells exceeds the MSD of non-cancerous cells for all values of the trapping force. Such behavior can be interpreted as a signature of the active processes and prevents the extraction of the low-frequency viscoelastic moduli for the living cells by passive microrheology.

Model-based estimation of 3-D stiffness parameters in photonic-force microscopy

We propose a system to characterize the 3-D diffusion properties of the probing bead trapped by a photonic-force microscope. We follow a model-based approach, where the model of the dynamics of the bead is given by the Langevin equation. Our procedure combines software and analog hardware to measure the corresponding stiffness matrix. We are able to estimate all its elements in real time, including off-diagonal terms. To achieve our goal, we have built a simple analog computer that performs a continuous preprocessing of the data, which can be subsequently digitized at a much lower rate than is otherwise required. We also provide an effective numerical algorithm for compensating the correlation bias introduced by a quadrant photodiode detector in the microscope. We validate our approach using simulated data and show that our bias-compensation scheme effectively improves the accuracy of the system. Moreover, we perform experiments with the real system and demonstrate real-time capabilities. Finally, we suggest a simple adjunction that would allow one to determine the mass matrix as well.

Intracellular nanomanipulation by a photonic-force microscope with real-time acquisition of a 3D stiffness matrix

A traditional photonic-force microscope (PFM) results in huge sets of data, which requires tedious numerical analysis. In this paper, we propose instead an analog signal processor to attain real-time capabilities while retaining the richness of the traditional PFM data. Our system is devoted to intracellular measurements and is fully interactive through the use of a haptic joystick. Using our specialized analog hardware along with a dedicated algorithm, we can extract the full 3D stiffness matrix of the optical trap in real time, including the off-diagonal cross-terms. Our system is also capable of simultaneously recording data for subsequent offline analysis. This allows us to check that a good correlation exists between the classical analysis of stiffness and our real-time measurements. We monitor the PFM beads using an optical microscope. The force-feedback mechanism of the haptic joystick helps us in interactively guiding the bead inside living cells and collecting information from its (possibly anisotropic) environment. The instantaneous stiffness measurements are also displayed in real time on a graphical user interface. The whole system has been built and is operational; here we present early results that confirm the consistency of the real-time measurements with offline computations.

The Absorption Spectrum of HDO in the 16 300-16 670 and 18 000-18 350 cm(-1) Spectral Regions

The absorption spectrum of HDO has been recorded by Intracavity Laser Absorption Spectroscopy in the 16 300-16 670 and 18 000-18 350 cm(-1) spectral regions corresponding to the weak 2nu(2) + 4nu(3) and nu(2) + 5nu(3) bands, respectively. The nu(2) + 5nu(3) band centered at 18 208.434 cm(-1) was found almost isolated and has been satisfactorily reproduced in the frame of the effective Hamiltonian model. On the other hand, the 2nu(2) + 4nu(3) band at 16 456.201 cm(-1) is strongly perturbed as the (0 2 4) bright state is involved in a complex interaction scheme including the (1 0 4), (5 0 1), (1 5 2), and (1 11 0) states. The rovibrational assignment of these interacting states was greatly helped by the high-accuracy ab initio predictions performed by D. Schwenke and H. Partridge [J. Chem. Phys. 000-000 (2000)]. They could be partly modeled by an effective Hamiltonian which has allowed the assignment and reproduction of most of the observed transitions. Copyright 2000 Academic Press.

The 5V(OH) Overtone Transition of HDO

The absorption spectrum of HDO has been recorded by intracavity laser absorption spectroscopy in the 16 540-17 055 cm(-1) spectral region corresponding to the 5nu(3) band centered at 16 920 cm(-1). The (0 0 5) vibrational state is found to be mostly isolated from the nearby rovibrational states. The corresponding rovibrational transitions were analyzed and fitted in the frame of the effective rotational Hamiltonian model in Pade-Borel approximants form. The spectroscopic parameters retrieved from the fitting reproduce 100 of the 109 determined energy levels with the root-mean-square deviation of 0.0072 cm(-1), close to the experimental accuracy. From the integrated relative intensities of a- and b-type transitions, the angle between the transition moment and the OH bond is estimated to be 46.4 degrees. This value is consistent with an increasing tilt of the transition dipole moment, away from the OH bond, when the OH stretching is excited. The evolution of the orientation of the transition dipole moment versus the vibrational excitation is then compared for the OH and OD overtone bands. Copyright 2000 Academic Press.

Experimental and Ab Initio Studies of the HDO Absorption Spectrum in the 13 165-13 500 cm(-1) Spectral Region

The HDO absorption spectrum was recorded in the 13 165-13 500 cm(-1) spectral region by intracavity laser absorption spectroscopy. The spectrum (615 lines), dominated by the 2nu(2) + 3nu(3) and nu(1) + 3nu(3) bands, was assigned and modeled leading to the derivation of 196 accurate energy levels of the (103) and (023) vibrational states. Finally, 150 of these levels were reproduced by an effective Hamiltonian involving two vibrational dark states interacting with the (023) and (103) bright states. The rms deviation achieved by variation of 28 parameters is 0.05 cm(-1), compared to an averaged experimental uncertainty of 0.007 cm(-1), indicating the limit of validity of the effective Hamiltonian approach for HDO at high-vibrational excitation. The predictions of previous ab initio calculations of the HDO spectrum (H. Partridge and D. Schwenke, J. Chem. Phys. 106, 4618-4639 (1997)) were extensively used in the assignment process. The particular spectral region under consideration was used to test and discuss the improvements of new ab initio calculations recently performed on the basis of the same potential energy surface but with an improved dipole-moment surface. The improvements concern both the energy levels and the line intensities. In particular, the strong hybrid character of the nu(1) + 3nu(3) band is very well accounted for by the new ab initio calculations. Copyright 2000 Academic Press.

High-Resolution Absorption Spectroscopy of the 3nu(1) and 3nu(1) + nu(3) Bands of Propyne

The 3nu(1) and 3nu(1) + nu(3) bands of propyne have been recorded at Doppler-limited resolution by Fourier transform spectroscopy and intracavity laser absorption spectroscopy, respectively. The two bands show a mostly unperturbed J rotational structure for each individual K subband. However, as a rule the K structure ordering is perturbed in overtone transitions of propyne and different effective parameters associated with each K subband have been determined. From the vibrational energy levels, a value of -6.6 cm(-1) has been obtained for the x(13) cross anharmonicity in perfect agreement with the origins of the nu(1) + nu(3) and 2nu(1) + nu(3) combination bands estimated from the FTIR spectrum. Hot bands from the v(9) = 1 and v(10) = 1 levels associated with the 3nu(1) + nu(3) combination band have been partly rotationally analyzed and the retrieved values of x(39) and x(3,10) are in good agreement with literature values. Finally, the 4nu(1) + nu(9) - nu(9) band centered at 12 636.6 cm(-1) has been recorded by ICLAS. The red shift of this hot band relative to 4nu(1) and the DeltaB(v) value are discussed in relation to the anharmonic interaction between the 4nu(1) and 3nu(1) + nu(3) + nu(5) levels. Copyright 2000 Academic Press.

The 4V(OH) Absorption Spectrum of HDO

The absorption spectrum of HDO was recorded by intracavity laser absorption spectroscopy in the 13 560-14 050 cm(-1) spectral region. Among 437 lines attributed to HDO, 399 were assigned to the 4nu(3) highly excited overtone transition. One hundred twenty-nine experimental energy levels were derived from the spectrum identification with rotational quantum numbers J as high as 16 and K(a) as high as 7. The (004) vibrational state of HDO was found to be nearly isolated. Rotational and centrifugal distortion parameters of the effective rotational Hamiltonian in the Pade-Borel approximants form, retrieved from the fitting, allow the reproduction of the experimental energy levels with the root-mean-square deviation of 0.012 cm(-1), close to the experimental accuracy. Some rotational energy levels of the (004) state seem to be slightly perturbed by local resonances with the (052) highly excited bending state. The resonance mixing was found to be large enough to give rise to seven 5nu(2) + 2nu(3) transitions, but otherwise too weak to be observable. The maximum difference between the derived experimental energy levels and the recent high accuracy ab initio predictions (H. Partridge and D. W. Schwenke, J. Chem. Phys. 106, 4618-4639 (1997)) is -2.7 cm(-1). Copyright 1999 Academic Press.