Membrane undulations driven by force fluctuations of active proteins

Electromagnetic cellular interactions

Chemical and electrical interaction within and between cells is well established. Just the opposite is true about cellular interactions via other physical fields. The most probable candidate for an other form of cellular interaction is the electromagnetic field. We review theories and experiments on how cells can generate and detect electromagnetic fields generally, and if the cell-generated electromagnetic field can mediate cellular interactions. We do not limit here ourselves to specialized electro-excitable cells. Rather we describe physical processes that are of a more general nature and probably present in almost every type of living cell. The spectral range included is broad; from kHz to the visible part of the electromagnetic spectrum. We show that there is a rather large number of theories on how cells can generate and detect electromagnetic fields and discuss experimental evidence on electromagnetic cellular interactions in the modern scientific literature. Although small, it is continuously accumulating.

Effective zero-thickness model for a conductive membrane driven by an electric field

The behavior of a conductive membrane in a static (dc) electric field is investigated theoretically. An effective zero-thickness model is constructed based on a Robin-type boundary condition for the electric potential at the membrane, originally developed for electrochemical systems. Within such a framework, corrections to the elastic moduli of the membrane are obtained, which arise from charge accumulation in the Debye layers due to capacitive effects and electric currents through the membrane and can lead to an undulation instability of the membrane. The fluid flow surrounding the membrane is also calculated, which clarifies issues regarding these flows sharing many similarities with flows produced by induced charge electro-osmosis (ICEO). Nonequilibrium steady states of the membrane and of the fluid can be effectively described by this method. It is both simpler, due to the zero thickness approximation which is widely used in the literature on fluid membranes, and more general than previous approaches. The predictions of this model are compared to recent experiments on supported membranes in an electric field.

Effect of energy metabolism on protein motility in the bacterial outer membrane

We demonstrate the energy dependence of the motion of a porin, the lambda-receptor, in the outer membrane of living Escherichia coli by single molecule investigations. By poisoning the bacteria with arsenate and azide, the bacterial energy metabolism was stopped. The motility of individual lambda-receptors significantly and rapidly decreased upon energy depletion. We suggest two different causes for the ceased motility upon comprised energy metabolism: One possible cause is that the cell uses energy to actively wiggle its proteins, this energy being one order-of-magnitude larger than thermal energy. Another possible cause is an induced change in the connection between the lambda-receptor and the membrane structure, for instance by a stiffening of part of the membrane structure. Treatment of the cells with ampicillin, which directly targets the bacterial cell wall by inhibiting cross-linking of the peptidoglycan layer, had an effect similar to energy depletion and the motility of the lambda-receptor significantly decreased. Since the lambda-receptor is closely linked to the peptidoglycan layer, we propose that lambda-receptor motility is directly coupled to the constant and dynamic energy-consuming reconstruction of the peptidoglycan layer. The result of this motion could be to facilitate transport of maltose-dextrins through the porin.

Nonlinear dynamics of cell orientation

The nonlinear dependence of cellular orientation on an external, time-varying stress field determines the distribution of orientations in the presence of noise and the characteristic time, tauc, for the cell to reach its steady-state orientation. The short, local cytoskeletal relaxation time distinguishes between high-frequency (nearly perpendicular) and low-frequency (random or parallel) orientations. However, tauc is determined by the much longer, orientational relaxation time. This behavior is related to experiments for which we predict the angle and characteristic time as a function of frequency.

Observation of local thickness fluctuations in surfactant membranes using neutron spin echo

Experimental evidence of local thickness fluctuations of a surfactant membrane, as observed by neutron scattering, is reported. A swollen lamellar structure consisting of nonionic surfactant, water, and oil was investigated by neutron spin echo spectroscopy. Different dynamical processes are recognized at three different length scales. At length scales larger than the membrane thickness, the bending motion is observed, which follows the Zilman and Granek theory [Phys. Rev. Lett. 77, 4788 (1996)]. At the length scale corresponding to the membrane thickness, a clear excess dynamics in addition to the bending motion is observed. This mode is interpreted as the local thickness fluctuations. At even shorter length scales, smaller than the membrane thickness, intramembrane dynamics such as protrusion motions may have been observed.

Stochastic actin polymerization and steady retrograde flow determine growth cone advancement

Neuronal growth is an extremely complex yet reliable process that is directed by a dynamic lamellipodial structure at the tip of every growing neurite, called the growth cone. Lamellipodial edge fluctuations are controlled by the interplay between actin polymerization pushing the edge forward and molecular motor driven retrograde actin flow retracting the actin network. The leading edge switches randomly between extension and retraction processes. We identify switching of "on/off" states in actin polymerization as the main determinant of lamellipodial advancement. Our analysis of motility statistics allows for a prediction of growth direction. This was used in simulations explaining the amazing signal detection capabilities of neuronal growth by the experimentally found biased stochastic processes. Our measurements show that the intensity of stochastic fluctuations depend on changes in the underlying active intracellular processes and we find a power law eta = a*x(alpha) with exponent alpha = 2.63 +/- 0.12 between noise intensity eta and growth cone activity x, defined as the sum of protrusion and retraction velocity. Differences in the lamellipodial dynamics between primary neurons and a neuronal cell line further suggests that active processes tune the observed stochastic fluctuations. This hints at a possible role of noise intensity in determining signal detection sensitivity.

Physical model for the width distribution of axons

The distribution of widths of axons was recently investigated, and was found to have a distinct peak at an optimized value. The optimized axon width at the peak may arise from the conflicting demands of minimizing energy consumption and assuring signal transmission reliability. The distribution around this optimized value is found to have a distinct non-Gaussian shape, with an exponential "tail". We propose here a mechanical model whereby this distribution arises from the interplay between the elastic energy of the membrane surrounding the axon core, the osmotic pressure induced by the neurofilaments inside the axon bulk, and active processes that remodel the microtubules and neurofilaments inside the axon. The axon's radius of curvature can be determined by the cell's control of the osmotic pressure difference across the membrane, the membrane tension or by changing the composition of the different components of the membrane. We find that the osmotic pressure, determined by the neurofilaments, seems to be the dominant control parameter.

Lipid flip-flop driven mechanical and morphological changes in model membranes

We study, using dissipative particle dynamics simulations, the effect of active lipid flip-flop on model fluid bilayer membranes. We consider both cases of symmetric as well as asymmetric flip-flops. Symmetric flip-flop leads to a steady state of the membrane with an effective temperature higher than that of the equilibrium membrane and an effective surface tension lower than that of the equilibrium membrane. Asymmetric flip-flop leads to transient conformational changes in the membrane in the form of bud or blister formation, depending on the flip rate.

Membrane tension lowering induced by protein activity

Using videomicroscopy we present measurements of the fluctuation spectrum of giant vesicles containing bacteriorhodopsin pumps. When the pumps are activated, we observe a significant increase of the fluctuations in the low wave vector region, which we interpret as due to a lowering of the effective tension of the membrane.

Landscape of finite-temperature equilibrium behaviour of curvature-inducing proteins on a bilayer membrane explored using a linearized elastic free energy model

Using a recently developed multiscale simulation methodology, we describe the equilibrium behaviour of bilayer membranes under the influence of curvature-inducing proteins using a linearized elastic free energy model. In particular, we describe how the cooperativity associated with a multitude of protein-membrane interactions and protein diffusion on a membrane-mediated energy landscape elicits emergent behaviour in the membrane phase. Based on our model simulations, we predict that, depending on the density of membrane-bound proteins and the degree to which a single protein molecule can induce intrinsic mean curvature in the membrane, a range of membrane phase behaviour can be observed including two different modes of vesicle-bud nucleation and repressed membrane undulations. A state diagram as a function of experimentally tunable parameters to classify the underlying states is proposed.

Gradient sensing in reactive, ternary membranes

Using computer simulations, we investigate the behavior of reactive ternary ABC membranes that are subjected to an external, spatially nonuniform stimulus, which controls the rate of interconversion between the A and B components. We assume that A and B have different spontaneous curvatures. Furthermore, the C component is taken to be nonreactive and incompatible with both A and B. We find that a gradient in the applied stimulus causes the dynamic reconstruction of the membrane, with a preferential reorientation of the reactive AB domains along the gradient. In addition, the external gradient effectively controls the transport of the nonreactive C component within the membrane. The latter effect could potentially be exploited for cleaning the membrane of the nonreactive C "impurities" or for the targeted delivery of the C component to specific locations.

Mechanokinetic model of cell membrane: theoretical analysis of plasmalemma homeostasis, growth and division

A theoretical model dealing with endocytosis, exocytosis and caveolae invagination, describing plasmalemma homeostasis during cell growth and division, is proposed. It considers transmembrane pressure, membrane tension and mechanosensitivity of membrane processes. Membrane hydraulic conductivity and the flux of transmembrane nonvesicular transport are taken into account. The developed mathematical analysis operates with a formulated set of constitutive equations describing the mechanical state and kinetics of changes in an open dynamic membrane system. The standard version of a model with adjusted parameters was implemented, and predictions including a discussion on the effect of possible parameter modifications were presented. Computer simulations indicate big changes in the magnitude of membrane tension and elasticity, and in the number of membrane buddings in young cells and during mitosis. They also show the extent of cell growth inhibition resulting from a decrease in transmembrane transport or an increase in the exerted difference in osmotic pressure. Moreover, the simulations reveal that exocytosis regulated during mitosis may not be as important for cell growth, as sometimes presumed. Finally, practical application and possible extension of the model are discussed.

Fluctuations of coupled fluid and solid membranes with application to red blood cells

The fluctuation spectra and the intermembrane interaction of two membranes at a fixed average distance are investigated. Each membrane can either be a fluid or a solid membrane, and in isolation, its fluctuations are described by a bare or a wave-vector-dependent bending modulus, respectively. The membranes interact via their excluded-volume interaction; the average distance is maintained by an external, homogeneous pressure. For strong coupling, the fluctuations can be described by a single, effective membrane that combines the elastic properties. For weak coupling, the fluctuations of the individual, noninteracting membranes are recovered. The case of a composite membrane consisting of one fluid and one solid membrane can serve as a microscopic model for the plasma membrane and cytoskeleton of the red blood cell. We find that, despite the complex microstructure of bilayers and cytoskeletons in a real cell, the fluctuations with wavelengths lambda greater, similar 400 nm are well described by the fluctuations of a single, polymerized membrane (provided that there are no inhomogeneities of the microstructure). The model is applied to the fluctuation data of discocytes ("normal" red blood cells), a stomatocyte, and an echinocyte. The elastic parameters of the membrane and an effective temperature that quantifies active, metabolically driven fluctuations are extracted from the experiments.

Coherence properties of red blood cell membrane motions

We use a highly sensitive, noncontact, optical interferometric technique to quantify the red blood cell membrane fluctuations at the nanometer and millisecond scales. The results reveal significant properties of both temporal and spatial coherence associated with the membrane dynamics. We show that these correlations can be accounted for by the viscoelastic properties of the cell membrane. From this measurement, we extract the loss and storage moduli associated with the membrane and find a crossover frequency at which the buffer viscosity seems to become dominant.

Active membranes studied by X-ray scattering

In view of recent theories of "active" membranes, we have studied multilamellar phospholipid membrane stacks with reconstituted transmembrane protein bacteriorhodopsin (BR) under different illumination conditions by X-ray scattering. The light-active protein is considered as an active constituent which drives the system out of equilibrium and is predicted to change the collective fluctuation properties of the membranes. Using X-ray reflectivity, X-ray non-specular (diffuse) scattering, and grazing incidence scattering, we find no detectable change in the scattering curves when changing the illumination condition. In particular the intermembrane spacing d remains constant, after eliminating hydration-related artifacts by design of a suitable sample environment. The absence of any observable non-equilibrium effects in the experimental window is discussed in view of the relevant parameters and recent theories.

Viscoelasticity of the human red blood cell

We report here the first measurements of the complex modulus of the isolated red blood cell (RBC). Because the RBC is often larger than capillary diameter, important determinants of microcirculatory function are RBC deformability and its changes with pathologies, such as sickle cell disease and malaria. A functionalized ferrimagnetic microbead was attached to the membrane of healthy RBC and then subjected to an oscillatory magnetic field. The resulting torque caused cell deformation. From the oscillatory forcing and resulting bead motions, which were tracked optically, we computed elastic and frictional moduli, g′ and g‴, respectively, from 0.1 to 100 Hz. The g′ was nearly frequency independent and dominated the response at all but the highest frequencies measured. Over three frequency decades, g‴ increased as a power law with an exponent of 0.64, a result not predicted by any simple model. These data suggest that RBC relaxation times that have been reported previously, and any models that rest upon them, are artifactual; the artifact, we suggest, arises from forcing to an exponential fit data of limited temporal duration. A linear range of response was observed, but, as forcing amplitude increased, nonlinearities became clearly apparent. A finite element model suggests that membrane bending was localized to the vicinity of the bead and dominated membrane shear. While the mechanisms accounting for these RBC dynamics remain unclear, methods described here establish new avenues for the exploration of connections among the mechanical, chemical, and biological characteristics of the RBC in health and disease.

Biomechanics and biophysics of cancer cells

The past decade has seen substantial growth in research into how changes in the biomechanical and biophysical properties of cells and subcellular structures influence, and are influenced by, the onset and progression of human diseases. This paper presents an overview of the rapidly expanding, nascent field of research that deals with the biomechanics and biophysics of cancer cells. The review begins with some key observations on the biology of cancer cells and on the role of actin microfilaments, intermediate filaments and microtubule biopolymer cytoskeletal components in influencing cell mechanics, locomotion, differentiation and neoplastic transformation. In order to set the scene for mechanistic discussions of the connections among alterations to subcellular structures, attendant changes in cell deformability, cytoadherence, migration, invasion and tumor metastasis, a survey is presented of the various quantitative mechanical and physical assays to extract the elastic and viscoelastic deformability of cancer cells. Results available in the literature on cell mechanics for different types of cancer are then reviewed. Representative case studies are presented next to illustrate how chemically induced cytoskeletal changes, biomechanical responses and signals from the intracellular regions act in concert with the chemomechanical environment of the extracellular matrix and the molecular tumorigenic signaling pathways to effect malignant transformations. Results are presented to illustrate how changes to cytoskeletal architecture induced by cancer drugs and chemotherapy regimens can significantly influence cell mechanics and disease state. It is reasoned through experimental evidence that greater understanding of the mechanics of cancer cell deformability and its interactions with the extracellular physical, chemical and biological environments offers enormous potential for significant new developments in disease diagnostics, prophylactics, therapeutics and drug efficacy assays.

Modeling multicomponent reactive membranes

Using analytical calculations and computer simulations, we study binary AB and ternary ABC membranes that respond to an external stimulus by interconverting A and B components. The C component is assumed to be nonreactive and is incompatible with both A and B . We also assume that A and B have different spontaneous curvatures. The dynamics of the ternary system is described in terms of three order parameters: two specify the local composition and a third characterizes the local height of the membrane. Our description of the two-component membrane is based on a recent model proposed by Reigada [Phys. Rev. E. 72, 051921 (2005)]; we extend the latter approach by explicitly including the effects of the membrane's surface tension on the phase behavior of the system. By performing a linear stability analysis, we determine the behavior of the reactive AB membrane for a given bending elasticity and surface tension at different values of the reaction rate coefficients. We also numerically integrate the governing dynamic equations, and the results of these simulations are in agreement with the analytical predictions. For the two-component membranes, we calculate two critical values of the reaction rate coefficients, which define the behavior of the system, and plot the phase diagrams in terms of different parameters. We illustrate that the surface tension of the membrane strongly affects these critical values of the reaction rate coefficients and therefore the location of the phase boundaries. We also pinpoint the regions on the phase diagram where the late-time behavior is affected by the initial fluctuations, i.e., where such a reactive system has some "memory" of its prior state. In the case of the three-component system, we show that the presence of the nonreactive C component strongly affects the composition and topology of the membrane, as well as critically altering the propagation of the traveling waves within the system.

Mapping correlated membrane pulsations and fluctuations in human cells

The cell membrane and cytoskeleton are dynamic structures that are strongly influenced by the thermo-mechanical background in addition to biologically driven mechanical processes. We used atomic force microscopy (AFM) to measure the local membrane motion of human foreskin fibroblasts (HFFs) which were found to be governed by random and non-random correlated mechanical processes. Interphase cells displayed distinct membrane pulsations in which the membrane was observed to slowly contract upwards followed by a recovery to its initial position. These pulsations occurred one to three times per minute with variable amplitudes (20-100 pN) separated by periods of random baseline fluctuations with amplitudes of <20 pN. Cells were exposed to actin and microtubule (MT) destabilizing drugs and induced into early apoptosis. Mechanical pulsations (20-80 pN) were not prevented by actin or MT depolymerization but were prevented in early apoptotic cells which only displayed small amplitude baseline fluctuations (<20 pN). Correlation analysis revealed that the cell membrane motion is largely random; however several non-random processes, with time constants varying between approximately 2 and 35 s are present. Results were compared to measured cardiomyocyte motion which was well defined and highly correlated. Employing automated positioning of the AFM tip, interphase HFF correlation time constants were also mapped over a 10 microm2 area above the nucleus providing some insights into the spatial variability of membrane correlations. Here, we are able to show that membrane pulsations and fluctuations can be linked to physiological state and cytoskeletal dynamics through distinct sets of correlation time constants in human cells.

Active elastic network: cytoskeleton of the red blood cell

In red blood cells there is a cortical cytoskeleton; a two-dimensional elastic network of membrane-attached proteins. We describe, using a simple model, how the metabolic activity of the cell, through the consumption of ATP, controls the stiffness of this elastic network. The unusual mechanical property of active strain softening is described and compared to experimental data. As a by-product of this activity there is also an active contribution to the amplitude of membrane fluctuations. We model this membrane as a field of independent "curvature motors," and calculate the spectrum of active fluctuations. We find that the active cytoskeleton contributes to the amplitude of the membrane height fluctuations at intermediate wavelengths, as observed experimentally.

Optical measurement of cell membrane tension

Using a novel noncontact technique based on optical interferometry, we quantify the nanoscale thermal fluctuations of red blood cells (RBCs) and giant unilamellar vesicles (GUVs). The measurements reveal a nonvanishing tension coefficient for RBCs, which increases as cells transition from a discocytic shape to a spherical shape. The tension coefficient measured for GUVs is, however, a factor of 4-24 smaller. By contrast, the bending moduli for cells and vesicles have similar values. This is consistent with the cytoskeleton confinement model, in which the cytoskeleton inhibits membrane fluctuations [Gov et al., Phys. Rev. Lett. 90, 228101, (2003).

Observation of dynamic subdomains in red blood cells

We quantify the nanoscale structure and low-frequency dynamics associated with live red blood cells. The membrane displacements are measured using quantitative phase images provided by Fourier phase microscopy, with an average path-length stability of 0.75 nm over 45 min. The results reveal the existence of dynamic, independent subdomains across the cells that fluctuate at various dominant frequencies.

Fluctuation spectrum of quasispherical membranes with force-dipole activity

The fluctuation spectrum of a quasispherical vesicle with active membrane proteins is calculated. The activity of the proteins is modeled as the proteins pushing on their surroundings giving rise to nonlocal force distributions. Both the contributions from the thermal fluctuations of the active protein densities and the temporal noise in the individual active force distributions of the proteins are taken into account. The noise in the individual force distributions is found to become significant at short wavelengths.

Mechanics of nonplanar membranes with force-dipole activity

A study is made of how active membrane proteins can modify the long wavelength mechanics of fluid membranes. The activity of the proteins is modelled as disturbing the protein surroundings through nonlocal force distributions of which a force-dipole distribution is the simplest example. An analytic expression describing how the activity modifies the force-balance equation for the membrane surface is obtained in the form of a moment expansion of the force distribution. This expression allows for further studies of the consequences of the activity for nonplanar membranes. In particular the active contributions to mechanical properties such as tension and bending moments become apparent. It is also explained how the activity can induce a hydrodynamic attraction between the active proteins in the membrane.

Diffusion in curved fluid membranes

We analyze theoretically the effects of curvature on the diffusion in a fluid membrane, within the Saffman-Delbrück hydrodynamic model. We calculate the effect of curvature on the intrinsic fluidity of a membrane through changes in its thickness, for both static or fluctuating curvature. We treat both thermal curvature fluctuations, and fluctuations due to active processes. Such curvature fluctuations increase the average membrane thickness and diminish the projected area, thereby decreasing the diffusion coefficient. This calculation allows us to predict the effect of shear flow on the membrane diffusion, and to compare to observations on living cells.

Nonequilibrium membrane fluctuations driven by active proteins

We extend a model for nonthermal membrane undulations driven by active (adenosine triphosphate-dependent or light-harvesting) membrane proteins [N. Gov, Phys. Rev. Lett. 93, 268104 (2004)]. The present model accounts for the fact that proteins can diffuse laterally across the membrane surface and that individual proteins are expected to exert forces preferentially in one normal direction over the other (due to their orientation within the bilayer). The addition of these effects alters the scaling of fluctuation amplitudes with system size. Additionally, theoretical arguments and dynamic simulations both suggest that, in certain regimes, the probability distribution of fluctuation amplitudes is expected to be non-Gaussian (in contrast to thermal systems).

Erythrocyte structure and dynamics quantified by Hilbert phase microscopy

We present a new quantitative method for investigating red blood cell morphology and dynamics. The instrument integrates quantitative phase microscopy with an inverted microscope, which makes it particularly suitable for the noninvasive assessment of live erythrocytes. In particular, we demonstrate the ability of this approach to quantify noninvasively cell volume and dynamic morphology. The subnanometer path-length sensitivity at the millisecond time scales is exemplified by measuring the hemoglobin flow out of the cell during hemolysis.

Generation of dynamic structures in nonequilibrium reactive bilayers

We present a nonequlibrium approach for the study of a flexible bilayer whose two components induce distinct curvatures. In turn, the two components are interconverted by an externally promoted reaction. Phase separation of the two species in the surface results in the growth of domains characterized by different local composition and curvature modulations. This domain growth is limited by the effective mixing due to the interconversion reaction, leading to a finite characteristic domain size. In addition to these effects, first introduced in our earlier work [Phys. Rev. E 71, 051906 (2005)], the important new feature is the assumption that the reactive process actively affects the local curvature of the bilayer. Specifically, we suggest that a force energetically activated by external sources causes a modification of the shape of the membrane at the reaction site. Our results show the appearance of a rich and robust dynamical phenomenology that includes the generation of traveling and/or oscillatory patterns. Linear stability analysis, amplitude equations, and numerical simulations of the model kinetic equations confirm the occurrence of these spatiotemporal behaviors in nonequilibrium reactive bilayers.

Dynamics of membranes driven by actin polymerization

A motile cell, when stimulated, shows a dramatic increase in the activity of its membrane, manifested by the appearance of dynamic membrane structures such as lamellipodia, filopodia, and membrane ruffles. The external stimulus turns on membrane bound activators, like Cdc42 and PIP2, which cause increased branching and polymerization of the actin cytoskeleton in their vicinity leading to a local protrusive force on the membrane. The emergence of the complex membrane structures is a result of the coupling between the dynamics of the membrane, the activators, and the protrusive forces. We present a simple model that treats the dynamics of a membrane under the action of actin polymerization forces that depend on the local density of freely diffusing activators on the membrane. We show that, depending on the spontaneous membrane curvature associated with the activators, the resulting membrane motion can be wavelike, corresponding to membrane ruffling and actin waves, or unstable, indicating the tendency of filopodia to form. Our model also quantitatively explains a variety of related experimental observations and makes several testable predictions.

Implicit solvent simulation models for biomembranes

Fully atomic simulation strategies are infeasible for the study of many processes of interest to membrane biology, biophysics and biochemistry. We review various coarse-grained simulation methodologies with special emphasis on methods and models that do not require the explicit simulation of water. Examples from our own research demonstrate that such models have potential for simulating a variety of biologically relevant phenomena at the membrane surface.

Contribution of the Nernst potential to stiffness constants: the asymmetrical case

Inside biological membranes, one of the fundamental functions of active proteins such as pumps is to generate some electrochemical gradient across the membrane and then, to establish a new stationary state. The membrane electric potential generated by activity modifies the stiffness constants of the membrane. A spontaneous curvature appears if the inner and outer Debye lengths are different. The corresponding characteristic radius falls in the range from 0.08 microm to 50 microm. The bending elastic modulus is always increased. This effect is only noticeable in the limit of large Debye length from 0.5 microm to 0.09 microm. For a Nernst potential of 100 mV and a Debye length of 0.2 microm, the bending modulus can reach 40k(B)T.

Passive or active fluctuations in membranes containing proteins

We have experimentally investigated the effect of a transmembrane protein, the Ca2+-ATPase, on shape fluctuations of giant vesicles. By using the micropipette method, we have measured a substantial renormalization of the bending modulus due to the presence of proteins in the membrane. Moreover, we have produced the first quantitative measurement of the active force dipole associated with the amplification of the fluctuations when the proteins are activated by adenosine 5'-triphosphate (ATP).