Compressibility and specific volume of actin decrease upon G to F transformation

A model of muscle contraction based on the Langevin equation with actomyosin potentials

We propose a muscle contraction model that is essentially a model of the motion of myosin motors as described by a Langevin equation. This model involves one-dimensional numerical calculations wherein the total force is the sum of a viscous force proportional to the myosin head velocity, a white Gaussian noise produced by random forces and other potential forces originating from the actomyosin structure and intra-molecular charges. We calculate the velocity of a single myosin on an actin filament to be 4.9-49 μm/s, depending on the viscosity between the actomyosin molecules. A myosin filament with a hundred myosin heads is used to simulate the contractions of a half-sarcomere within the skeletal muscle. The force response due to a quick release in the isometric contraction is simulated using a process wherein crossbridges are changed forcibly from one state to another. In contrast, the force response to a quick stretch is simulated using purely mechanical characteristics. We simulate the force-velocity relation and energy efficiency in the isotonic contraction and adenosine triphosphate consumption. The simulation results are in good agreement with the experimental results. We show that the Langevin equation for the actomyosin potentials can be modified statistically to become an existing muscle model that uses Maxwell elements.

Exploring the stability limits of actin and its suprastructures

Actin is the main component of the microfilament system in eukaryotic cells and can be found in distinct morphological states. Global (G)-actin is able to assemble into highly organized, supramolecular cellular structures known as filamentous (F)-actin and bundled (B)-actin. To evaluate the structure and stability of G-, F-, and B-actin over a wide range of temperatures and pressures, we used Fourier transform infrared spectroscopy in combination with differential scanning and pressure perturbation calorimetry, small-angle x-ray scattering, laser confocal scanning microscopy, and transmission electron microscopy. Our analysis was designed to provide new (to our knowledge) insights into the stabilizing forces of actin self-assembly and to reveal the stability of the actin polymorphs, including in conditions encountered in extreme environments. In addition, we sought to explain the limited pressure stability of actin self-assembly observed in vivo. G-actin is not only the least temperature-stable but also the least pressure-stable actin species. Under abyssal conditions, where temperatures as low as 1-4°C and pressures up to 1 kbar are reached, G-actin is hardly stable. However, the supramolecular assemblies of actin are stable enough to withstand the extreme conditions usually encountered on Earth. Beyond ∼3-4 kbar, filamentous structures disassemble, and beyond ∼4 kbar, complete dissociation of F-actin structures is observed. Between ∼1 and 2 kbar, some disordering of actin assemblies commences, in agreement with in vivo observations. The limited pressure stability of the monomeric building block seems to be responsible for the suppression of actin assembly in the kbar pressure range.

Concentration measurement of yeast suspensions using high frequency ultrasound backscattering

This work proposes the use of an ultrasound based technique to measure the concentration of yeasts in liquid suspension. This measurement was achieved by the detection and quantification of ultrasonic echoes backscattered by the cells. More specifically, the technique was applied to the detection and quantification of Saccharomyces cerevisiae. A theoretical approach was proposed to get the average density and sound speed of the yeasts, which were found to be 1116 kg/m(3) and 1679 m/s, respectively. These parameters were needed to model the waves backscattered by each single cell. A pulse-echo arrangement working around 50 MHz, being able to detect echoes from single yeasts was used to characterize experimentally yeast solutions from 10(2) to 10(7)cells/ml. The Non-negative Matrix Factorization denoising technique was applied for data analysis. This technique required a previous learning of the spectral patterns of the echoes reflected from yeasts in solution and the base noise from the liquid medium. Comparison between pulse correlation (without denoising) and theoretical and experimental pattern learning was made to select the best signal processing. A linear relation between ultrasound output and concentration was obtained with correlation coefficient R(2)=0.996 for the experimental learning. Concentrations from 10(4) to 10(7)cells/ml were detected above the base noise. These results show the viability of using the ultrasound backscattering technique to detect yeasts and measure their concentration in liquid cultures, improving the sensitivity obtained using spectrophotometric methods by one order of magnitude.

Protein osmotic pressure modulates actin filament length distribution

On these bases, we propose that the length distribution of the actin filaments is regulated by (a) the free energy of hydrolysis of ATP and (b) the macromolecular osmotic pressure.

Intermolecular interaction of actin revealed by a dynamic light scattering technique

The intermolecular interaction force of actin was studied by a dynamic light scattering technique. The mutual diffusion coefficients (D) of monomeric actin were accurately determined in a G-buffer with a low concentration of KCl from 0 to 10 mM. The translational diffusion coefficient was obtained as D(0) = (87 +/- 3) x 10(-12) m(2).s(-1) at 25 degrees C and pH 7.4, which gives a hydrodynamic radius of monomeric actin of r(H) = 2.8 +/- 0.1 nm. The Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, assuming electrostatic and van der Waals potentials, failed to describe the change in interaction parameter (lambda) with KCl concentration, but the extended DLVO theory succeeded if an additional repulsive potential was assumed. The Hamaker constant of actin in the Ca(2+)-ATP bound state was determined for the first time as A(H) = 10.4 +/- 0.6 k(B)T.

The polymerization of actin: extent of polymerization under pressure, volume change of polymerization, and relaxation after temperature jumps

The protein actin can polymerize from monomeric globular G-actin to polymeric filamentary F-actin, under the regulation of thermodynamic variables such as temperature, pressure, and compositions of G-actin and salts. We present here new measurements of the extent of polymerization (phi) of actin under pressure (P), for rabbit skeletal muscle actin in H2O buffer in the presence of adenosine triposphate and calcium ions and at low (5-15 mM) KCl concentrations. We measured phi using pyrene-labeled actin, as a function of time (t) and temperature (T), for samples of fixed concentrations of initial G-actin and KCl and at fixed pressure. The phi(T,P) measurements at equilibrium have the same form as reported previously at 1 atm: low levels of polymerization at low temperatures, representing dimerization of the actin; an increase in phi at the polymerization temperature (Tp); a maximum in phi(T) above Tp) with a decrease in phi(T) beyond the maximum, indicating a depolymerization at higher T. From phi(T,P) at temperatures below Tp, we estimate the change in volume for the dimerization of actin, DeltaVdim, to be -307+/-10 ml/mol at 279 K. The change of Tp with pressure dTp/dP=(0.3015+/-0.0009) K/MPa=(30.15+/-0.09) mK/atm. The phi(T,P) data at higher T indicate the change in volume on propagation, DeltaVprop, to be +401+/-48 ml/mol at 301 K. The phi(t) measurements yield initial relaxation times rp(T) that reflect the behavior of phi(T) and support the presence of a depolymerization temperature. We also measured the density of polymerizing actin with a vibrating tube density meter, the results of which confirm that the data from this instrument are affected by viscosity changes and can be erroneous.

Actin polymerization under pressure: A theoretical study

An extended Flory-Huggins-type equilibrium polymerization theory for compressible systems is used to describe experimental data for the unusual pressure and temperature dependence of the equilibrium polymerization of G-actin to F-actin. The calculations provide rich insights into the reaction mechanism and the thermodynamics of actin polymerization at the molecular level. Volume changes associated with individual steps of the mechanism are calculated to be DeltaVactiv=(s1*-s1)upsilon0=+1553 mlmol for the activation reaction, DeltaVdim=(s2-s1*)upsilon0=-3810 mlmol for dimerization, and DeltaVprop=(sP-s1)upsilon0=+361 mlmol for the propagation reaction, where s1upsilon0, s1*upsilon0, s2upsilon0, and sPupsilon0 are the monomer volumes in the G-actin monomer, the activated G-action, the dimer, and higher polymers, respectively. Comparison with experimental measurements is made, and discrepancies are discussed.

Guiding neuronal growth with light

Control over neuronal growth is a fundamental objective in neuroscience, cell biology, developmental biology, biophysics, and biomedicine and is particularly important for the formation of neural circuits in vitro, as well as nerve regeneration in vivo [Zeck, G. & Fromherz, P. (2001) Proc. Natl. Acad. Sci. USA 98, 10457-10462]. We have shown experimentally that we can use weak optical forces to guide the direction taken by the leading edge, or growth cone, of a nerve cell. In actively extending growth cones, a laser spot is placed in front of a specific area of the nerve's leading edge, enhancing growth into the beam focus and resulting in guided neuronal turns as well as enhanced growth. The power of our laser is chosen so that the resulting gradient forces are sufficiently powerful to bias the actin polymerization-driven lamellipodia extension, but too weak to hold and move the growth cone. We are therefore using light to control a natural biological process, in sharp contrast to the established technique of optical tweezers [Ashkin, A. (1970) Phys. Rev. Lett. 24, 156-159; Ashkin, A. & Dziedzic, J. M. (1987) Science 235, 1517-1520], which uses large optical forces to manipulate entire structures. Our results therefore open an avenue to controlling neuronal growth in vitro and in vivo with a simple, noncontact technique.

Sound attenuation of polymerizing actin reflects supramolecular structures: viscoelastic properties of actin gels modified by cytochalasin D, profilin and alpha-actinin

Polymerization and depolymerization of cytoskeletal elements maintaining cytoplasmic stiffness are key factors in the control of cell crawling. Rheometry is a significant tool in determining the mechanical properties of the single elements in vitro. Viscoelasticity of gels formed by these polymers strongly depends on both the length and the associations of the filaments (e.g. entanglements, annealings and side-by-side associations). Ultrasound attenuation is related to viscosity, sound velocity and supramolecular structures in the sample. In combination with a small glass fibre (2 mm x 50 microm), serving as a viscosity sensor, an acoustic microscope was used to measure the elasticity and acoustic attenuation of actin solutions. Changes in acoustic attenuation of polymerizing actin by far exceed the values expected from calculations based on changes in viscosity and sound velocity. During the lag-phase of actin polymerization, attenuation slightly decreases, depending on actin concentration. After the half-maximum viscosity is accomplished and elasticity turns into steady state, attenuation distinctly rises. Changes in ultrasound attenuation depend on actin concentration, and they are modulated by the addition of alpha-actinin, cytochalasin D and profilin. Thus absorption and scattering of sound on the polymerization of actin is related to the packing density of the actin net, entanglements and the length of the actin filaments. Shortening of actin filaments by cytochalasin D was also confirmed by electron micrographs and falling-ball viscosimetry. In addition to viscosity and elasticity, the attenuation of sound proved to be a valuable parameter in characterizing actin polymerization and the supramolecular associations of F-actin.

Viscoelastic properties of f-actin, microtubules, f-actin/alpha-actinin, and f-actin/hexokinase determined in microliter volumes with a novel nondestructive method

A nondestructive method to determine viscoelastic properties of gels and fluids involves an oscillating glass fiber serving as a sensor for the viscosity of the surrounding fluid. Extremely small displacements (typically 1-100 nm) are caused by the glass rod oscillating at its resonance frequency. These displacements are analyzed using a phase-sensitive acoustic microscope. Alterations of the elastic modulus of a fluid or gel change the propagation speed of a longitudinal acoustic wave. The system allows to study quantities as small as 10 microliters with temporal resolution >1 Hz. For 2-100 microM f-actin gels a final viscosity of 1.3-9.4 mPa s and a final elastic modulus of 2.229-2.254 GPa (corresponding to 1493-1501 m/s sound velocity) have been determined. For 10- to 100-microM microtubule gels (native, without stabilization by taxol), a final viscosity of 1.5-124 mPa s and a final elastic modulus of 2.288-2. 547 GPa (approximately 1513-1596 m/s) have been determined. During polymerization the sound velocity in low-concentration actin solutions increased up to +1.3 m/s (approximately 1.69 kPa) and decreased up to -7 m/s (approximately 49 kPa) at high actin concentrations. On polymerization of tubulin a concentration-dependent decrease of sound velocity was observed, too (+48 to -12 m/s approximately 2.3-0.1 MPa, for 10- to 100-microM tubulin). This decrease was interpreted by a nematic phase transition of the actin filaments and microtubules with increasing concentration. 2 mM ATP (when compared to 0.2 mM ATP) increased polymerization rate, final viscosity and elastic modulus of f-actin (17 microM). The actin-binding glycolytic enzyme hexokinase also accelerated the polymerization rate and final viscosity but elastic modulus (2.26 GPa) was less than for f-actin polymerized in presence of 0.2 mM ATP (2.28 GPa).

Adiabatic compressibility of flagellin and flagellar filament of Salmonella typhimurium

The partial specific volume and adiabatic compressibility of flagellin, its F40 fragment deprived of the disordered terminal regions, from Ala-1 to Arg-65 and from Ser-451 to Arg-494, and the flagellar filament of Salmonella typhimurium were determined from the density and the sound velocity measurements at 15 degrees C. The partial specific volumes were 0.728 cm3/g, 0.745 cm3/g, and 0.734 cm3/g, and the partial specific adiabatic compressibilities were 4.0 x 10(-12) cm2/dyn, 6.7 x 10(-12) cm2/dyn, and 4.7 x 10(-12) cm2/dyn, for flagellin, F40, and the filament, respectively. The smaller values of flagellin than those of F40 are reasonably explained by the presence of disordered terminal regions, which are supposed to be highly hydrated by water molecules. The volume increase upon polymerization of flagellin into the filament is also confirmed by depolymerization under a high pressure. The smaller volume and compressibility of the filament compared with those of F40 suggest an extensive hydration of the filament on its complex surface structure, which surpasses the effect on the volume and compressibility by a possible increase in the cavity volume at intersubunit interfaces upon polymerization.