Alex Levine - Academia.edu (original) (raw)
Papers by Alex Levine
The spontaneously oscillating hair bundle of sensory cells in the inner ear is an example of a st... more The spontaneously oscillating hair bundle of sensory cells in the inner ear is an example of a stochastic, nonlinear oscillator driven by internal active processes. Moreover, this internal activity is adaptive -- its power input depends on the current state of the system. We study fluctuation dissipation relations in such adaptively-driven, nonequilibrium limit-cycle oscillators. We observe the expected violation of the well-known, equilibrium fluctuation-dissipation theorem (FDT), and verify the existence of a generalized fluctuation-dissipation theorem (GFDT) in the non-adaptively driven model of the hair cell oscillator. This generalized fluctuation theorem requires the system to be analyzed in the co-moving frame associated with the mean limit cycle of the stochastic oscillator. We then demonstrate, via numerical simulations and analytic calculations, that the adaptively-driven dynamical hair cell model violates both the FDT and the GFDT. We go on to show, using stochastic, fini...
Soft Matter
We consider the propagation of tension along specific filaments of a semiflexible filament networ... more We consider the propagation of tension along specific filaments of a semiflexible filament network in response to the application of a point force using a combination of numerical simulations and analytic theory.
We develop a framework for the general interpretation of the stochastic dynamical system near a l... more We develop a framework for the general interpretation of the stochastic dynamical system near a limit cycle. Such quasi-periodic dynamics are commonly found in a variety of nonequilibrium systems, including the spontaneous oscillations of hair cells in the inner ear. We demonstrate quite generally that in the presence of noise, the phase of the limit cycle oscillator will diffuse while deviations in the directions locally orthogonal to that limit cycle will display the Lorentzian power spectrum of a damped oscillator. We identify two mechanisms by which these stochastic dynamics can acquire a complex frequency dependence, and discuss the deformation of the mean limit cycle as a function of temperature. The theoretical ideas are applied to data obtained from spontaneously oscillating hair cells of the amphibian sacculus.
Proceedings of the National Academy of Sciences of the United States of America, Mar 27, 2017
The thermal fluctuations of membranes and nanoscale shells affect their mechanical characteristic... more The thermal fluctuations of membranes and nanoscale shells affect their mechanical characteristics. Whereas these fluctuations are well understood for flat membranes, curved shells show anomalous behavior due to the geometric coupling between in-plane elasticity and out-of-plane bending. Using conventional shallow shell theory in combination with equilibrium statistical physics we theoretically demonstrate that thermalized shells containing regions of negative Gaussian curvature naturally develop anomalously large fluctuations. Moreover, the existence of special curves, "singular lines," leads to a breakdown of linear membrane theory. As a result, these geometric curves effectively partition the cell into regions whose fluctuations are only weakly coupled. We validate these predictions using high-resolution microscopy of human red blood cells (RBCs) as a case study. Our observations show geometry-dependent localization of thermal fluctuations consistent with our theoretica...
Data in brief, 2016
We present here the calculation of the mean time to capture of a tethered ligand to the receptor.... more We present here the calculation of the mean time to capture of a tethered ligand to the receptor. This calculation is then used to determine the shift in the partitioning between (1) free, (2) singly bound, and (3) doubly bound ligands in chemical equilibrium as a function of the length of the tether. These calculations are used in the research article Fibroblast Growth Factor 2 Dimer with Superagonist in vitro Activity Improves Granulation Tissue Formation During Wound Healing (Decker et al., in press [1]) to explain quantitatively how changes in polymeric linker length in the ligand dimers modifies the efficacy of these molecules relative to that of free ligands.
Physical review. E, 2016
We report on the collapse of bubble rafts under compression in a closed rectangular geometry. A b... more We report on the collapse of bubble rafts under compression in a closed rectangular geometry. A bubble raft is a single layer of bubbles at the air-water interface. A collapse event occurs when bubbles submerge beneath the neighboring bubbles under compression, causing the structure of the bubble raft to go from single-layer to multilayer. We studied the collapse dynamics as a function of compression velocity. At higher compression velocity we observe a more uniform distribution of collapse events, whereas at lower compression velocities the collapse events accumulate at the system boundaries. We propose that this system can be understood in terms of a linear elastic sheet coupled to a local internal (Ising) degree of freedom. The two internal states, which represent one bubble layer versus two, couple to the elasticity of the sheet by locally changing the reference state of the material. By exploring the collapse dynamics of the bubble raft, one may address the basic nonlinear mech...
Physical Review Letters, 2000
Boundary effects in liquid-crystalline phases can be large due to long-ranged orientational corre... more Boundary effects in liquid-crystalline phases can be large due to long-ranged orientational correlations. We show that the chiral hexatic phase can be locked into an apparent three-dimensional N+6 phase via such effects. Simple numerical estimates suggest that the recently discovered "polymer hexatic" may actually be this locked phase.
Physical Review E, 2007
We study the capillary wave dynamics of a single viscoelastic supported film and of a double laye... more We study the capillary wave dynamics of a single viscoelastic supported film and of a double layer of immiscible viscoelastic supported films. Using both simple scaling arguments and a continuum hydrodynamic theory, we investigate the effects of viscoelasticity and interfacial slip on the relaxation dynamics of these capillary waves. Our results account for the recent observation of a wavelength-independent decay rate for capillary waves in a supported polystyrene/brominated polystyrene double layer [X. Hu et al., Phys. Rev. E 74, 010602 (R) (2006)].
We study the mobilities of point-like and extended objects (rods) on a spherical membrane to show... more We study the mobilities of point-like and extended objects (rods) on a spherical membrane to show how these quantities are modified in a striking manner by the curvature and topology of the membrane. We also present theoretical calculations and experimental measurements of the membrane fluid velocity field around a moving rod bound to the crowded interface of a water-in-oil droplet. By using different droplet sizes, membrane viscosities, and rod lengths, we show that the viscosity mismatch between the interior and exterior fluids leads to a suppression of the fluid flow on small droplets that cannot be captured by the flat-membrane predictions.
Semiflexible polymers such as filamentous actin play a vital role in the mechanical behavior of c... more Semiflexible polymers such as filamentous actin play a vital role in the mechanical behavior of cells, yet the basic properties of cross-linked F-actin networks remain poorly understood. To address this issue, we have performed numerical studies of the linear response of homogeneous and isotropic two-dimensional networks subject to an applied strain at zero temperature. The elastic moduli are found to vanish for network densities at a rigidity percolation threshold. For higher densities, two regimes are observed: one in which the deformation is predominately affine and the filaments stretch and compress; and a second in which bending modes dominate. We identify a dimensionless scalar quantity, being a combination of the material length scales, that specifies to which regime a given network belongs. A scaling argument is presented that approximately agrees with this crossover variable. By a direct geometric measure, we also confirm that the degree of affinity under strain correlates with the distinct elastic regimes. We discuss the implications of our findings and suggest possible directions for future investigations.
Proceedings of the …, 2010
The human red blood cell (RBC) membrane, a fluid lipid bilayer tethered to an elastic 2D spectrin... more The human red blood cell (RBC) membrane, a fluid lipid bilayer tethered to an elastic 2D spectrin network, provides the principal control of the cell's morphology and mechanics. These properties, in turn, influence the ability of RBCs to transport oxygen in circulation. Current ...
We determine the time-and force-dependent viscoelastic responses of reconstituted networks of mic... more We determine the time-and force-dependent viscoelastic responses of reconstituted networks of microtubules that have been strongly crosslinked by biotin-streptavidin bonds. To measure the microscale viscoelasticity of such networks, we use a magnetic tweezers device to apply localized forces. At short time scales, the networks respond nonlinearly to applied force, with stiffening at small forces, followed by a reduction in the stiffening response at high forces, which we attribute to the forceinduced unbinding of crosslinks. At long time scales, force-induced bond unbinding leads to local network rearrangement and significant bead creep. Interestingly, the network retains its elastic modulus even under conditions of significant plastic flow, suggesting that crosslinker breakage is balanced by the formation of new bonds. To better understand this effect, we developed a finite element model of such a stiff filament network with labile crosslinkers obeying force-dependent Bell model unbinding dynamics. The coexistence of dissipation, due to bond breakage, and the elastic recovery of the network is possible because each filament has many crosslinkers. Recovery can occur as long as a sufficient number of the original crosslinkers are preserved under the loading period. When these remaining original crosslinkers are broken, plastic flow results.
The spontaneously oscillating hair bundle of sensory cells in the inner ear is an example of a st... more The spontaneously oscillating hair bundle of sensory cells in the inner ear is an example of a stochastic, nonlinear oscillator driven by internal active processes. Moreover, this internal activity is adaptive -- its power input depends on the current state of the system. We study fluctuation dissipation relations in such adaptively-driven, nonequilibrium limit-cycle oscillators. We observe the expected violation of the well-known, equilibrium fluctuation-dissipation theorem (FDT), and verify the existence of a generalized fluctuation-dissipation theorem (GFDT) in the non-adaptively driven model of the hair cell oscillator. This generalized fluctuation theorem requires the system to be analyzed in the co-moving frame associated with the mean limit cycle of the stochastic oscillator. We then demonstrate, via numerical simulations and analytic calculations, that the adaptively-driven dynamical hair cell model violates both the FDT and the GFDT. We go on to show, using stochastic, fini...
Soft Matter
We consider the propagation of tension along specific filaments of a semiflexible filament networ... more We consider the propagation of tension along specific filaments of a semiflexible filament network in response to the application of a point force using a combination of numerical simulations and analytic theory.
We develop a framework for the general interpretation of the stochastic dynamical system near a l... more We develop a framework for the general interpretation of the stochastic dynamical system near a limit cycle. Such quasi-periodic dynamics are commonly found in a variety of nonequilibrium systems, including the spontaneous oscillations of hair cells in the inner ear. We demonstrate quite generally that in the presence of noise, the phase of the limit cycle oscillator will diffuse while deviations in the directions locally orthogonal to that limit cycle will display the Lorentzian power spectrum of a damped oscillator. We identify two mechanisms by which these stochastic dynamics can acquire a complex frequency dependence, and discuss the deformation of the mean limit cycle as a function of temperature. The theoretical ideas are applied to data obtained from spontaneously oscillating hair cells of the amphibian sacculus.
Proceedings of the National Academy of Sciences of the United States of America, Mar 27, 2017
The thermal fluctuations of membranes and nanoscale shells affect their mechanical characteristic... more The thermal fluctuations of membranes and nanoscale shells affect their mechanical characteristics. Whereas these fluctuations are well understood for flat membranes, curved shells show anomalous behavior due to the geometric coupling between in-plane elasticity and out-of-plane bending. Using conventional shallow shell theory in combination with equilibrium statistical physics we theoretically demonstrate that thermalized shells containing regions of negative Gaussian curvature naturally develop anomalously large fluctuations. Moreover, the existence of special curves, "singular lines," leads to a breakdown of linear membrane theory. As a result, these geometric curves effectively partition the cell into regions whose fluctuations are only weakly coupled. We validate these predictions using high-resolution microscopy of human red blood cells (RBCs) as a case study. Our observations show geometry-dependent localization of thermal fluctuations consistent with our theoretica...
Data in brief, 2016
We present here the calculation of the mean time to capture of a tethered ligand to the receptor.... more We present here the calculation of the mean time to capture of a tethered ligand to the receptor. This calculation is then used to determine the shift in the partitioning between (1) free, (2) singly bound, and (3) doubly bound ligands in chemical equilibrium as a function of the length of the tether. These calculations are used in the research article Fibroblast Growth Factor 2 Dimer with Superagonist in vitro Activity Improves Granulation Tissue Formation During Wound Healing (Decker et al., in press [1]) to explain quantitatively how changes in polymeric linker length in the ligand dimers modifies the efficacy of these molecules relative to that of free ligands.
Physical review. E, 2016
We report on the collapse of bubble rafts under compression in a closed rectangular geometry. A b... more We report on the collapse of bubble rafts under compression in a closed rectangular geometry. A bubble raft is a single layer of bubbles at the air-water interface. A collapse event occurs when bubbles submerge beneath the neighboring bubbles under compression, causing the structure of the bubble raft to go from single-layer to multilayer. We studied the collapse dynamics as a function of compression velocity. At higher compression velocity we observe a more uniform distribution of collapse events, whereas at lower compression velocities the collapse events accumulate at the system boundaries. We propose that this system can be understood in terms of a linear elastic sheet coupled to a local internal (Ising) degree of freedom. The two internal states, which represent one bubble layer versus two, couple to the elasticity of the sheet by locally changing the reference state of the material. By exploring the collapse dynamics of the bubble raft, one may address the basic nonlinear mech...
Physical Review Letters, 2000
Boundary effects in liquid-crystalline phases can be large due to long-ranged orientational corre... more Boundary effects in liquid-crystalline phases can be large due to long-ranged orientational correlations. We show that the chiral hexatic phase can be locked into an apparent three-dimensional N+6 phase via such effects. Simple numerical estimates suggest that the recently discovered "polymer hexatic" may actually be this locked phase.
Physical Review E, 2007
We study the capillary wave dynamics of a single viscoelastic supported film and of a double laye... more We study the capillary wave dynamics of a single viscoelastic supported film and of a double layer of immiscible viscoelastic supported films. Using both simple scaling arguments and a continuum hydrodynamic theory, we investigate the effects of viscoelasticity and interfacial slip on the relaxation dynamics of these capillary waves. Our results account for the recent observation of a wavelength-independent decay rate for capillary waves in a supported polystyrene/brominated polystyrene double layer [X. Hu et al., Phys. Rev. E 74, 010602 (R) (2006)].
We study the mobilities of point-like and extended objects (rods) on a spherical membrane to show... more We study the mobilities of point-like and extended objects (rods) on a spherical membrane to show how these quantities are modified in a striking manner by the curvature and topology of the membrane. We also present theoretical calculations and experimental measurements of the membrane fluid velocity field around a moving rod bound to the crowded interface of a water-in-oil droplet. By using different droplet sizes, membrane viscosities, and rod lengths, we show that the viscosity mismatch between the interior and exterior fluids leads to a suppression of the fluid flow on small droplets that cannot be captured by the flat-membrane predictions.
Semiflexible polymers such as filamentous actin play a vital role in the mechanical behavior of c... more Semiflexible polymers such as filamentous actin play a vital role in the mechanical behavior of cells, yet the basic properties of cross-linked F-actin networks remain poorly understood. To address this issue, we have performed numerical studies of the linear response of homogeneous and isotropic two-dimensional networks subject to an applied strain at zero temperature. The elastic moduli are found to vanish for network densities at a rigidity percolation threshold. For higher densities, two regimes are observed: one in which the deformation is predominately affine and the filaments stretch and compress; and a second in which bending modes dominate. We identify a dimensionless scalar quantity, being a combination of the material length scales, that specifies to which regime a given network belongs. A scaling argument is presented that approximately agrees with this crossover variable. By a direct geometric measure, we also confirm that the degree of affinity under strain correlates with the distinct elastic regimes. We discuss the implications of our findings and suggest possible directions for future investigations.
Proceedings of the …, 2010
The human red blood cell (RBC) membrane, a fluid lipid bilayer tethered to an elastic 2D spectrin... more The human red blood cell (RBC) membrane, a fluid lipid bilayer tethered to an elastic 2D spectrin network, provides the principal control of the cell's morphology and mechanics. These properties, in turn, influence the ability of RBCs to transport oxygen in circulation. Current ...
We determine the time-and force-dependent viscoelastic responses of reconstituted networks of mic... more We determine the time-and force-dependent viscoelastic responses of reconstituted networks of microtubules that have been strongly crosslinked by biotin-streptavidin bonds. To measure the microscale viscoelasticity of such networks, we use a magnetic tweezers device to apply localized forces. At short time scales, the networks respond nonlinearly to applied force, with stiffening at small forces, followed by a reduction in the stiffening response at high forces, which we attribute to the forceinduced unbinding of crosslinks. At long time scales, force-induced bond unbinding leads to local network rearrangement and significant bead creep. Interestingly, the network retains its elastic modulus even under conditions of significant plastic flow, suggesting that crosslinker breakage is balanced by the formation of new bonds. To better understand this effect, we developed a finite element model of such a stiff filament network with labile crosslinkers obeying force-dependent Bell model unbinding dynamics. The coexistence of dissipation, due to bond breakage, and the elastic recovery of the network is possible because each filament has many crosslinkers. Recovery can occur as long as a sufficient number of the original crosslinkers are preserved under the loading period. When these remaining original crosslinkers are broken, plastic flow results.