Imaging material properties of biological samples with a force feedback microscope

Mechanical properties of biological samples have been imaged with a force feedback microscope. Force, force gradient, and dissipation are measured simultaneously and quantitatively, merely knowing the atomic force microscopy cantilever spring constant. Our first results demonstrate that this robust method provides quantitative high resolution force measurements of the interaction. The small oscillation imposed on the cantilever and the small value of its stiffness result in vibrational energies much smaller than the thermal energy, reducing interaction with the sample to a minimum. We show that the observed mechanical properties of the sample depend on the force applied by the tip and consequently on the sample indentation. Copyright © 2013 John Wiley & Sons, Ltd.     

The motion of a single molecule,the lambda-receptor,in the bacterial outer membrane

Using optical tweezers and single particle tracking, we have revealed the motion of a single protein, the lambda-receptor, in the outer membrane of living Escherichia coli bacteria. We genetically modified the lambda-receptor placing a biotin on an extracellular site of the receptor in vivo. The efficiency of this in vivo biotinylation is very low, thus enabling the attachment of a streptavidin-coated bead binding specifically to a single biotinylated lambda-receptor. The bead was used as a handle for the optical tweezers and as a marker for the single particle tracking routine. We propose a model that allows extraction of the motion of the protein from measurements of the mobility of the bead-molecule complex; these results are equally applicable to analyze bead-protein complexes in other membrane systems. Within a domain of radius approximately 25 nm, the receptor diffuses with a diffusion constant of (1.5 +/- 1.0) x 10(-9) cm(2)/s and sits in a harmonic potential as if it were tethered by an elastic spring of spring constant of ~1.0 x 10(-2) pN/nm to the bacterial membrane. The purpose of the protein motion might be to facilitate transport of maltodextrins through the outer bacterial membrane.     

Cell protrusions and tethers: a unified approach

Low pulling forces applied locally to cell surface membranes produce viscoelastic cell surface protrusions. As the force increases, the membrane can locally separate from the cytoskeleton and a tether forms. Tethers can grow to great lengths exceeding the cell diameter. The protrusion-to-tether transition is known as the crossover. Here we propose a unified approach to protrusions and tethers providing, to our knowledge, new insights into their biomechanics. We derive a necessary and sufficient condition for a crossover to occur, a formula for predicting the crossover time, conditions for a tether to establish a dynamic equilibrium (characterized by constant nonzero pulling force and tether extension rate), a general formula for the tether material after crossover, and a general modeling method for tether pulling experiments. We introduce two general protrusion parameters, the spring constant and effective viscosity, valid before and after crossover. Their first estimates for neutrophils are 50 pN μm⁻¹ and 9 pN s μm⁻¹, respectively. The tether elongation after crossover is described as elongation of a viscoelastic-like material with a nonlinearly decaying spring (NLDs-viscoelastic material). Our model correctly describes the results of the published protrusion and tether pulling experiments, suggesting that it is universally applicable to such experiments.     

Elasticity and Rupture of a Multi-Domain Neural Cell Adhesion Molecule Complex

The neural cell adhesion molecule (NCAM) plays an important role in nervous system development. NCAM forms a complex between its terminal domains Ig1 and Ig2. When NCAM of cell A and of cell B connect to each other through complexes Ig12(A)/Ig12(B), the relative mobility of cells A and B and membrane tension exerts a force on the Ig12(A)/Ig12(B) complex. In this study, we investigated the response of the complex to force, using steered molecular dynamics. Starting from the structure of the complex from the Ig1-Ig2-Ig3 fragment, we first demonstrated that the complex, which differs in dimensions from a previous structure from the Ig1-Ig2 fragment in the crystal environment, assumes the same extension when equilibrated in solvent. We then showed that, when the Ig12(A)/Ig12(B) complex is pulled apart with forces 30-70 pN, it exhibits elastic behavior (with a spring constant of ∼0.03 N/m) because of the relative reorientation of domains Ig1 and Ig2. At higher forces, the complex ruptures; i.e., Ig12(A) and Ig12(B) separate. The interfacial interactions between Ig12(A) and Ig12(B), monitored throughout elastic extension and rupture, identify E16, F19, K98, and L175 as key side chains stabilizing the complex.     

Dynamic force spectroscopy on supported lipid bilayers: effect of temperature and sample preparation

Biological membranes are constantly exposed to forces. The stress-strain relation in membranes determines the behavior of many integral membrane proteins or other membrane related-proteins that show a mechanosensitive behavior. Here, we studied by force spectroscopy the behavior of supported lipid bilayers (SLBs) subjected to forces perpendicular to their plane. We measured the lipid bilayer mechanical properties and the force required for the punch-through event characteristic of atomic force spectroscopy on SLBs as a function of the interleaflet coupling. We found that for an uncoupled bilayer, the overall tip penetration occurs sequentially through the two leaflets, giving rise to two penetration events. In the case of a bilayer with coupled leaflets, penetration of the atomic force microscope tip always occurred in a single step. Considering the dependence of the jump-through force value on the tip speed, we also studied the process in the context of dynamic force spectroscopy (DFS). We performed DFS experiments by changing the temperature and cantilever spring constant, and analyzed the results in the context of the developed theories for DFS. We found that experiments performed at different temperatures and with different cantilever spring constants enabled a more effective comparison of experimental data with theory in comparison with previously published data.     

Extending a spectrin repeat unit. I: linear force-extension response

Nonequilibrium molecular dynamics simulations were used to calculate the elastic properties of a spectrin repeat unit. A contiguous alpha-helical linker was constructed by employing periodic boundary conditions, allowing a novel scheme for evaluating the thermodynamic force as a function of extension. By measuring the force-extension response under small extensions, spectrin was observed to behave primarily as an elastic material with a spring constant of 1700 +/- 100 pN/nm. The implications of this spring constant, in terms of the properties of the spectrin tetramer, are also discussed.     

Temperature softening of a protein in single-molecule experiments

Mechanical flexibility is crucial for the function of proteins. However, such material properties are not easily accessible experimentally. We used single-molecule force spectroscopy to study the stiffness of a single domain of Dictyostelium discoideum filamin (ddFLN4) in a temperature range from 5 degrees C to 37 degrees C. Analyzing the distributions of unfolding forces allowed us to extract transition barrier heights and positions of the underlying energy landscape. We found a marked narrowing of unfolding force distributions with increasing temperature. This narrowing reflects an increase in transition state position from 2.7 A to 7.8 A and thus a reduction of the molecular spring constant of the protein by a factor of 7. We suggest this temperature softening reflects a shift in the nature of the interactions responsible for mechanical stability from hydrogen bonds to hydrophobic interactions. This result has important consequences for all interpretations of protein mechanical studies if experimental results obtained at room temperature are to be transferred to physiological temperatures.     

Is the spring quality of muscle plastic?

During locomotion, major muscle groups are often activated cyclically. This alternate stretch-shorten pattern of activity could enable muscle to function as a spring, storing and recovering elastic recoil potential energy. Because the ability to store and recover elastic recoil energy could profoundly affect the energetics of locomotion, one might expect this to be an adaptable feature of skeletal muscle. This study tests the hypothesis that chronic eccentric (Ecc) training results in a change in the spring properties of skeletal muscle. Nine female Sprague-Dawley rats underwent chronic Ecc training for 8 wk on a motorized treadmill. The spring properties of muscle were characterized by both active and passive lengthening force productions. A single "spring constant (Deltaforce/Deltalength) from the passive length-tension curves was calculated for each muscle. Results from measurements on long heads of triceps brachii muscle indicate that the trained group produced significantly more passive lengthening force (P = 0.0001) as well as more active lengthening force (P = 0.0001) at all lengths of muscle stretch. In addition, the spring constants were significantly different between the Ecc (1.71 N/mm) and the control (1.31 N/mm) groups. A stiffer spring is capable of storing more energy per unit length stretched, which is of functional importance during locomotion.     

Thermo-mechanical responses of a surface-coupled AFM cantilever

Atomic force microscopy (AFM) has been widely used for measuring mechanical properties of biological specimens such as cells, DNA, and proteins. This is usually done by monitoring deformations in response to controlled applied forces, which have to be at ultralow levels due to the extreme softness of the specimens. Consequently, such experiments may be susceptible to thermal excitations, manifested as force and displacement fluctuations that could reduce the measurement accuracy. To take advantage of, rather than to be limited by, such fluctuations, we have characterized the thermomechanical responses of an arbitrarily shaped AFM cantilever with the tip coupled to an elastic spring. Our analysis shows that the cantilever and the specimen behave as springs in parallel. This provides a method for determining the elasticity of the specimen by measuring the change in the tip fluctuations in the presence and absence of coupling. For rectangular and V-shaped cantilevers, we have derived a relationship between the mean-square deflection and the mean-square inclination and an approximate expression for the specimen spring constant in terms of contributions to the mean-square inclination from the first few vibration modes.     

Study of the time effect on the strength of cell-cell adhesion force by a novel nano-picker

Cell’s adhesion is important to cell’s interaction and activates. In this paper, a novel method for cell–cell adhesion force measurement was proposed by using a nano-picker. The effect of the contact time on the cell–cell adhesion force was studied. The nano-picker was fabricated from an atomic force microscopy (AFM) cantilever by nano fabrication technique. The cell–cell adhesion force was measured based on the deflection of the nano-picker beam. The result suggests that the adhesion force between cells increased with the increasing of contact time at the first few minutes. After that, the force became constant. This measurement methodology was based on the nanorobotic manipulation system inside an environmental scanning electron microscope. It can realize both the observation and manipulation of a single cell at nanoscale. The quantitative and precise cell–cell adhesion force result can be obtained by this method. It would help us to understand the single cell interaction with time and would benefit the research in medical and biological fields potentially.     

Contraction dynamics and function of the muscle-tendon complex depend on the muscle fibre-tendon length ratio: a simulation study

Experimental studies show different muscle-tendon complex (MTC) functions (e.g. motor or spring) depending on the muscle fibre-tendon length ratio. Comparing different MTC of different animals examined experimentally, the extracted MTC functions are biased by, for example, MTC-specific pennation angle and fibre-type distribution or divergent experimental protocols (e.g. influence of temperature or stimulation on MTC force). Thus, a thorough understanding of variation of these inner muscle fibre-tendon length ratios on MTC function is difficult. In this study, we used a hill-type muscle model to simulate MTC. The model consists of a contractile element (CE) simulating muscle fibres, a serial element (SE) as a model for tendon, and a parallel elastic element (PEE) modelling tissue in parallel to the muscle fibres. The simulation examines the impact of length variations of these components on contraction dynamics and MTC function. Ensuring a constant overall length of the MTC by \(L_\mathrm{MTC} = L_\mathrm{SE} + L_\mathrm{CE}\), the SE rest length was varied over a broad physiological range from 0.1 to 0.9 MTC length. Five different MTC functions were investigated by simulating typical physiological experiments: the stabilising function with isometric contractions, the motor function with contractions against a weight, the capability of acceleration with contractions against a small inertial mass, the braking function by decelerating a mass, and the spring function with stretch-shortening cycles. The ratio of SE and CE mainly determines the MTC function. MTC with comparably short tendon generates high force and maximal shortening velocity and is able to produce maximal work and power. MTC with long tendon is suitable to store and release a maximum amount of energy. Variation of muscle fibre-tendon ratio yielded two peaks for MTC’s force response for short and long SE lengths. Further, maximum work storage capacity of the SE is at long \(\mathrm{rel}L_\mathrm{SE,0}\). Impact of fibre-tendon length ratio on MTC functions will be discussed. Considering a constant set of MTC parameters, quantitative changes in MTC performance (work, stiffness, force, energy storage, dissipation) depending on varying muscle fibre-tendon length ratio were provided, which enables classification and grading of different MTC designs.     

Application of atomic force microscopy for characteristics of single intermolecular interactions

Atomic force microscopy (AFM) can be used to make measurements in vacuum, air, and water. The method is able to gather information about intermolecular interaction forces at the level of single molecules. This review encompasses experimental and theoretical data on the characterization of ligand-receptor interactions by AFM. The advantage of AFM in comparison with other methods developed for the characterization of single molecular interactions is its ability to estimate not only rupture forces, but also thermodynamic and kinetic parameters of the rupture of a complex. The specific features of force spectroscopy applied to ligand-receptor interactions are examined in this review from the stage of the modification of the substrate and the cantilever up to the processing and interpretation of the data. We show the specificities of the statistical analysis of the array of data based on the results of AFM measurements, and we discuss transformation of data into thermodynamic and kinetic parameters (kinetic dissociation constant, Gibbs free energy, enthalpy, and entropy). Particular attention is paid to the study of polyvalent interactions, where the definition of the constants is hampered due to the complex stoichiometry of the reactions.     

Unfolding and extraction of a transmembrane alpha-helical peptide: dynamic force spectroscopy and molecular dynamics simulations

An atomic force microscope (AFM) was used to visualize CWALP(19)23 peptides ((+)H(3)N-ACAGAWWLALALALALALALWWA-COO(-)) inserted in gel-phase DPPC and DSPC bilayers. The peptides assemble in stable linear structures and domains. A model for the organization of the peptides is given from AFM images and a 20 ns molecular dynamics (MD) simulation. Gold-coated AFM cantilevers were used to extract single peptides from the bilayer through covalent bonding to the cystein residue. Experimental and simulated force curves show two distinct force maxima. In the simulations these two maxima correspond to the extraction of the two pairs of tryptophan residues from the membrane. Unfolding of the peptide precedes extraction of the second distal set of tryptophans. To probe the energies involved, AFM force curves were obtained from 10 to 10(4) nm/s and MD force curves were simulated with 10(8)-10(11) nm/s pulling velocities (V). The velocity relationship with the force, F, was fitted to two fluctuation adhesive potential models. The first assumes the pulling produces a constant bias in the potential and predicts an F approximately ln (V) relationship. The second takes into account the ramped bias that the linker feels as it is being driven out of the adhesion complex and scales as F approximately (ln V)2/3.     

Force versus axial deflection of pipette-aspirated closed membranes

The axial deformation of a pipette-pressurized fluid membrane bag produces minuscule yet well-defined, reproducible forces. The stiffness of this ultrasensitive force transducer is tunable and largely independent of the constitutive membrane behavior. Based on a rigorous variational treatment, we present both numerical as well as approximate analytical solutions for the force-deflection relation of this unique biophysical force probe. Our numerical results predict a measurably nonlinear force-deflection behavior at moderate-to-large deformations, which we confirm experimentally using red blood cells. Furthermore, considering nearly spherical membrane shapes and enforcing proper boundary conditions, we derive an analytical solution valid at small deformations. In this linear regime the pressurized membrane bag behaves like a Hookean spring, with a spring constant that is significantly larger than previously published for the biomembrane force probe.     

Dynamics of the Coiled-Coil Unfolding Transition of Myosin Rod Probed by Dissipation Force Spectrum

The motor protein myosin II plays a crucial role in muscle contraction. The mechanical properties of its coiled-coil region, the myosin rod, are important for effective force transduction during muscle function. Previous studies have investigated the static elastic response of the myosin rod. However, analogous to the study of macroscopic complex fluids, how myosin will respond to physiological time-dependent loads can only be understood from its viscoelastic response. Here, we apply atomic force microscopy using a magnetically driven oscillating cantilever to measure the dissipative properties of single myosin rods that provide unique dynamical information about the coiled-coil structure as a function of force. We find that the friction constant of the single myosin rod has a highly nontrivial variation with force; in particular, the single-molecule friction constant is reduced dramatically and increases again as it passes through the coiled-uncoiled transition. This is a direct indication of a large free-energy barrier to uncoiling, which may be related to a fine-tuned dynamic mechanosignaling response to large and unexpected physiological loads. Further, from the critical force at which the minimum in friction occurs we determine the asymmetry of the bistable landscape that controls uncoiling of the coiled coil. This work highlights the sensitivity of the dissipative signal in force unfolding to dynamic molecular structure that is hidden to the elastic signal.     

Performance analysis of a cardiac assist device in counterpulsation.

Performance of a cardiac assist device pumping chamber in counterpulsation was evaluated using numerical simulations of the unsteady, three-dimensional flow inside the chamber and an analytical model of the force required to eject and fill the chamber. The wall shear stress within the device was similarly computed and modeled. The analytical model was scaled to match the numerical results and then used to predict performance at physiological operating conditions. According to these models for a stroke volume of 70 ml, between 0.4 and 1.0 W is required for counterpulsation at a frequency of 1.33 Hz against a restorative spring, depending on the spring constant chosen. The power and the maximum force calculated are within the ranges a trained skeletal muscle is capable of providing. Shear stress predictions show that platelet activation in the absence of surface effects and hemolysis due to high shear are unlikely to occur with this design. Furthermore, vortices that develop in the chamber during filling are predicted to increase blood mixing and provide favorable washing of the chamber walls. A computational-analytical approach such as this may have potential to aid rapid performance evaluation of new devices and streamline the design optimization process.     

Simulation of a Single Red Blood Cell Flowing Through a Microvessel Stenosis Using Dissipative Particle Dynamics

The motion and deformation of a single red blood cell flowing through a microvessel stenosis was investigated employing dissipative particle dynamics (DPD) method. The numerical model considers plasma, cytoplasm, the RBC membrane and the microvessel walls, in which a three dimensional coarse-grained spring network model of RBC’s membrane was used to simulate the deformation of the RBC. The suspending plasma was modelled as an incompressible Newtonian fluid and the vessel walls were regarded as rigid body. The body force exerted on the free DPD particles was used to drive the flow. A modified bounce-back boundary condition was enforced on the membrane to guarantee the impenetrability. Adhesion of the cell to the stenosis vessel surface was mediated by the interactions between receptors and ligands. Firstly, the motion of a single RBC in a microfluidic channel was simulated and the results were found in agreement with the experimental data cited by [1]. Then the mechanical behavior of the RBC in the microvessel stenosis was studied. The effects of the bending rigidity of membrane, the size of the stenosis and the driven body force on the deformation and motion of red blood cell were discussed.     

Sensing specific molecular interactions with the atomic force microscope

One of the unique features of the atomic force microscope (AFM) is its capacity to measure interactions between tip and sample with high sensitivity and unparalleled spatial resolution. Since the development of methods for the functionalization of the tips, the versatility of the AFM has been expanded to experiments where specific molecular interactions are measured. For illustration, we present measurements of the interaction between complementary strands of DNA. A necessary prerequisite for the quantitative analysis of the interaction force is knowledge of the spring constant of the cantilevers. Here, we compare different techniques that allow for the in situ measurement of the absolute value of the spring constant of cantilevers.     

Complex myograph allows the examination of complex muscle contractions for the assessment of muscle force, shortening, velocity, and work in vivo

Background

The devices used for in vivo examination of muscle contractions assess only pure force contractions and the so-called isokinetic contractions. In isokinetic experiments, the extremity and its muscle are artificially moved with constant velocity by the measuring device, while a tetanic contraction is induced in the muscle, either by electrical stimulation or by maximal voluntary activation. With these systems, experiments cannot be performed at pre-defined, constant muscle length, single contractions cannot be evaluated individually and the separate examination of the isometric and the isotonic components of single contractions is not possible.

Methods

The myograph presented in our study has two newly developed technical units, i.e. a). a counterforce unit which can load the muscle with an adjustable, but constant force and b). a length-adjusting unit which allows for both the stretching and the contraction length to be infinitely adjustable independently of one another. The two units support the examination of complex types of contraction and store the counterforce and length-adjusting settings, so that these conditions may be accurately reapplied in later sessions.

Results

The measurement examples presented show that the muscle can be brought to every possible pre-stretching length and that single isotonic or complex isometric-isotonic contractions may be performed at every length. The applied forces act during different phases of contraction, resulting into different pre- and after-loads that can be kept constant - uninfluenced by the contraction. Maximal values for force, shortening, velocity and work may be obtained for individual muscles. This offers the possibility to obtain information on the muscle status and to monitor its changes under non-invasive measurement conditions.

Conclusion

With the Complex Myograph, the whole spectrum of a muscle's mechanical characteristics may be assessed.     

The gaussian network model: precise prediction of residue fluctuations and application to binding problems

The single-parameter Gamma matrix of force constants proposed by the Gaussian Network Model (GNM) is iteratively modified to yield native state fluctuations that agree exactly with experimentally observed values. The resulting optimized Gamma matrix contains residue-specific force constants that may be used for an accurate analysis of ligand binding to single or multiple sites on proteins. Bovine Pancreatic Trypsin Inhibitor (BPTI) is used as an example. The calculated off-diagonal elements of the Gamma matrix, i.e., the optimized spring constants, obey a Lorentzian distribution. The mean value of the spring constants is approximately -0.1, a value much weaker than -1 of the GNM. Few of the spring constants are positive, indicating repulsion between residues. Residue pairs with large number of neighbors have spring constants around the mean, -0.1. Large negative spring constants are between highly correlated pairs of residues. The fluctuations of the distance between anticorrelated pairs of residues are subject to smaller spring constants. The importance of the number of neighbors of residue pairs in determining the elements of the Gamma matrix is pointed out. Allosteric effects of binding on a single or multiple residues of BPTI are illustrated and discussed. Comparison of the predictions of the present model with those of the standard GNM shows that the two models agree at lower modes, i.e., those relating to global motions, but they disagree at higher modes. In the higher modes, the present model points to the important contributions from specific residues whereas the standard GNM fails to do so.