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An AFM-based stiffness clamp for dynamic control of rigidity.

Webster KD, Crow A, Fletcher DA - PLoS ONE (2011)

Bottom Line: Constant force or constant height can be maintained in an AFM experiment through feedback control of cantilever deflection, known respectively as a 'force clamp' or 'position clamp'.We demonstrated the AFM stiffness clamp on two different samples: a contracting fibroblast cell and an expanding polyacrylamide hydrogel.We found that the fibroblast, a cell type that secretes and organizes the extracellular matrix, exhibited a rapid, sub-second change in traction rate (dF/dt) and contraction velocity (dx/dt) in response to step changes in stiffness between 1-100 nN/µm.

View Article: PubMed Central - PubMed

Affiliation: Biophysics Graduate Group, University of California, Berkeley, California, United States of America.

ABSTRACT
Atomic force microscopy (AFM) has become a powerful tool for measuring material properties in biology and imposing mechanical boundary conditions on samples from single molecules to cells and tissues. Constant force or constant height can be maintained in an AFM experiment through feedback control of cantilever deflection, known respectively as a 'force clamp' or 'position clamp'. However, stiffness, the third variable in the Hookean relation F = kx that describes AFM cantilever deflection, has not been dynamically controllable in the same way. Here we present and demonstrate a 'stiffness clamp' that can vary the apparent stiffness of an AFM cantilever. This method, employable on any AFM system by modifying feedback control of the cantilever, allows rapid and reversible tuning of the stiffness exposed to the sample in a way that can decouple the role of stiffness from force and deformation. We demonstrated the AFM stiffness clamp on two different samples: a contracting fibroblast cell and an expanding polyacrylamide hydrogel. We found that the fibroblast, a cell type that secretes and organizes the extracellular matrix, exhibited a rapid, sub-second change in traction rate (dF/dt) and contraction velocity (dx/dt) in response to step changes in stiffness between 1-100 nN/µm. This response was independent of the absolute contractile force and cell height, demonstrating that cells can react directly to changes in stiffness alone. In contrast, the hydrogel used in our experiment maintained a constant expansion velocity (dx/dt) over this range of stiffness, while the traction rate (dF/dt) changed with stiffness, showing that passive materials can also behave differently in different stiffness environments. The AFM stiffness clamp presented here, which is applicable to mechanical measurements on both biological and non-biological samples, may be used to investigate cellular mechanotransduction under a wide range of controlled mechanical boundary conditions.

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Response of expanding hydrogel to step changes in stiffness.(a) The AFM stiffness clamp was applied to a rehydrated hydrogel that deflected an AFM cantilever as it expanded. Cantilever position is precisely measured using an optical lever system. Feedback was implemented by moving a piezo-controlled substrate. (b) A typical trace of how force and gel height () changed over time as the cantilever deflected in response to the expansion of the hydrogel against apparent stiffnesses of 1, 10, and 100 nN/µm. Separate experiments conducted on 5 different gels all exhibited the same stiffness-dependent behavior shown above. Note that the slope of the force trace clearly changes when the apparent stiffness changes, while the slope of the height trace remains basically constant over this range of stiffness. (c) Categorical plot of the force rate and velocity of gel expansion under three different apparent stiffnesses from the trace depicted in (b). The rates are determined from a linear regression fit where the 95% confidence interval for each slope is within 0.25 nN/min and 5 nm/min for the force and height, respectively. Force rate changes with stiffness while expansion rate does not over this range of stiffness. (d) Plot of force  versus gel height  as the gel expanded under a wide range of apparent stiffnesses. Each trace represents a different apparent stiffness listed in the table and applied using the stiffness clamp algorithm. The traces were translated to begin at the origin for comparison. The horizontal and vertical traces represent desired stiffnesses approaching 0 and , corresponding to a force and position clamp with standard deviations of 15 pN and 0.34 nm. Inset depicts the discrete but highly linear nature of the data. The * marks the trace without any feedback loop and whose slope is the spring constant of the cantilever, 42 nN/µm.
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pone-0017807-g003: Response of expanding hydrogel to step changes in stiffness.(a) The AFM stiffness clamp was applied to a rehydrated hydrogel that deflected an AFM cantilever as it expanded. Cantilever position is precisely measured using an optical lever system. Feedback was implemented by moving a piezo-controlled substrate. (b) A typical trace of how force and gel height () changed over time as the cantilever deflected in response to the expansion of the hydrogel against apparent stiffnesses of 1, 10, and 100 nN/µm. Separate experiments conducted on 5 different gels all exhibited the same stiffness-dependent behavior shown above. Note that the slope of the force trace clearly changes when the apparent stiffness changes, while the slope of the height trace remains basically constant over this range of stiffness. (c) Categorical plot of the force rate and velocity of gel expansion under three different apparent stiffnesses from the trace depicted in (b). The rates are determined from a linear regression fit where the 95% confidence interval for each slope is within 0.25 nN/min and 5 nm/min for the force and height, respectively. Force rate changes with stiffness while expansion rate does not over this range of stiffness. (d) Plot of force versus gel height as the gel expanded under a wide range of apparent stiffnesses. Each trace represents a different apparent stiffness listed in the table and applied using the stiffness clamp algorithm. The traces were translated to begin at the origin for comparison. The horizontal and vertical traces represent desired stiffnesses approaching 0 and , corresponding to a force and position clamp with standard deviations of 15 pN and 0.34 nm. Inset depicts the discrete but highly linear nature of the data. The * marks the trace without any feedback loop and whose slope is the spring constant of the cantilever, 42 nN/µm.

Mentions: We tested the ability of the AFM stiffness clamp algorithm to produce a range of apparent stiffnesses with an expanding hydrogel, and we characterized the material's response to step changes in stiffness. Addition of phosphate buffered saline (PBS) to a dehydrated ∼1 kPa polyacrylamide hydrogel caused it to gradually expand. As the gel expanded and increased in height, it pushed against the cantilever applying an increasing force (FIG. 3A&B). Without the stiffness clamp feedback loop, the spring constant of the cantilever defined how much force the gel applied to increase its height. When we changed the apparent stiffness of the cantilever using the stiffness clamp between 1–100 nN/µm, there was an immediate change in the force rate due to the modified feedback control of the cantilever position, while the gel expansion rate remained essentially constant (FIG. 3C). This behavior was observed for N = 5 gels.


An AFM-based stiffness clamp for dynamic control of rigidity.

Webster KD, Crow A, Fletcher DA - PLoS ONE (2011)

Response of expanding hydrogel to step changes in stiffness.(a) The AFM stiffness clamp was applied to a rehydrated hydrogel that deflected an AFM cantilever as it expanded. Cantilever position is precisely measured using an optical lever system. Feedback was implemented by moving a piezo-controlled substrate. (b) A typical trace of how force and gel height () changed over time as the cantilever deflected in response to the expansion of the hydrogel against apparent stiffnesses of 1, 10, and 100 nN/µm. Separate experiments conducted on 5 different gels all exhibited the same stiffness-dependent behavior shown above. Note that the slope of the force trace clearly changes when the apparent stiffness changes, while the slope of the height trace remains basically constant over this range of stiffness. (c) Categorical plot of the force rate and velocity of gel expansion under three different apparent stiffnesses from the trace depicted in (b). The rates are determined from a linear regression fit where the 95% confidence interval for each slope is within 0.25 nN/min and 5 nm/min for the force and height, respectively. Force rate changes with stiffness while expansion rate does not over this range of stiffness. (d) Plot of force  versus gel height  as the gel expanded under a wide range of apparent stiffnesses. Each trace represents a different apparent stiffness listed in the table and applied using the stiffness clamp algorithm. The traces were translated to begin at the origin for comparison. The horizontal and vertical traces represent desired stiffnesses approaching 0 and , corresponding to a force and position clamp with standard deviations of 15 pN and 0.34 nm. Inset depicts the discrete but highly linear nature of the data. The * marks the trace without any feedback loop and whose slope is the spring constant of the cantilever, 42 nN/µm.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3050926&req=5

pone-0017807-g003: Response of expanding hydrogel to step changes in stiffness.(a) The AFM stiffness clamp was applied to a rehydrated hydrogel that deflected an AFM cantilever as it expanded. Cantilever position is precisely measured using an optical lever system. Feedback was implemented by moving a piezo-controlled substrate. (b) A typical trace of how force and gel height () changed over time as the cantilever deflected in response to the expansion of the hydrogel against apparent stiffnesses of 1, 10, and 100 nN/µm. Separate experiments conducted on 5 different gels all exhibited the same stiffness-dependent behavior shown above. Note that the slope of the force trace clearly changes when the apparent stiffness changes, while the slope of the height trace remains basically constant over this range of stiffness. (c) Categorical plot of the force rate and velocity of gel expansion under three different apparent stiffnesses from the trace depicted in (b). The rates are determined from a linear regression fit where the 95% confidence interval for each slope is within 0.25 nN/min and 5 nm/min for the force and height, respectively. Force rate changes with stiffness while expansion rate does not over this range of stiffness. (d) Plot of force versus gel height as the gel expanded under a wide range of apparent stiffnesses. Each trace represents a different apparent stiffness listed in the table and applied using the stiffness clamp algorithm. The traces were translated to begin at the origin for comparison. The horizontal and vertical traces represent desired stiffnesses approaching 0 and , corresponding to a force and position clamp with standard deviations of 15 pN and 0.34 nm. Inset depicts the discrete but highly linear nature of the data. The * marks the trace without any feedback loop and whose slope is the spring constant of the cantilever, 42 nN/µm.
Mentions: We tested the ability of the AFM stiffness clamp algorithm to produce a range of apparent stiffnesses with an expanding hydrogel, and we characterized the material's response to step changes in stiffness. Addition of phosphate buffered saline (PBS) to a dehydrated ∼1 kPa polyacrylamide hydrogel caused it to gradually expand. As the gel expanded and increased in height, it pushed against the cantilever applying an increasing force (FIG. 3A&B). Without the stiffness clamp feedback loop, the spring constant of the cantilever defined how much force the gel applied to increase its height. When we changed the apparent stiffness of the cantilever using the stiffness clamp between 1–100 nN/µm, there was an immediate change in the force rate due to the modified feedback control of the cantilever position, while the gel expansion rate remained essentially constant (FIG. 3C). This behavior was observed for N = 5 gels.

Bottom Line: Constant force or constant height can be maintained in an AFM experiment through feedback control of cantilever deflection, known respectively as a 'force clamp' or 'position clamp'.We demonstrated the AFM stiffness clamp on two different samples: a contracting fibroblast cell and an expanding polyacrylamide hydrogel.We found that the fibroblast, a cell type that secretes and organizes the extracellular matrix, exhibited a rapid, sub-second change in traction rate (dF/dt) and contraction velocity (dx/dt) in response to step changes in stiffness between 1-100 nN/µm.

View Article: PubMed Central - PubMed

Affiliation: Biophysics Graduate Group, University of California, Berkeley, California, United States of America.

ABSTRACT
Atomic force microscopy (AFM) has become a powerful tool for measuring material properties in biology and imposing mechanical boundary conditions on samples from single molecules to cells and tissues. Constant force or constant height can be maintained in an AFM experiment through feedback control of cantilever deflection, known respectively as a 'force clamp' or 'position clamp'. However, stiffness, the third variable in the Hookean relation F = kx that describes AFM cantilever deflection, has not been dynamically controllable in the same way. Here we present and demonstrate a 'stiffness clamp' that can vary the apparent stiffness of an AFM cantilever. This method, employable on any AFM system by modifying feedback control of the cantilever, allows rapid and reversible tuning of the stiffness exposed to the sample in a way that can decouple the role of stiffness from force and deformation. We demonstrated the AFM stiffness clamp on two different samples: a contracting fibroblast cell and an expanding polyacrylamide hydrogel. We found that the fibroblast, a cell type that secretes and organizes the extracellular matrix, exhibited a rapid, sub-second change in traction rate (dF/dt) and contraction velocity (dx/dt) in response to step changes in stiffness between 1-100 nN/µm. This response was independent of the absolute contractile force and cell height, demonstrating that cells can react directly to changes in stiffness alone. In contrast, the hydrogel used in our experiment maintained a constant expansion velocity (dx/dt) over this range of stiffness, while the traction rate (dF/dt) changed with stiffness, showing that passive materials can also behave differently in different stiffness environments. The AFM stiffness clamp presented here, which is applicable to mechanical measurements on both biological and non-biological samples, may be used to investigate cellular mechanotransduction under a wide range of controlled mechanical boundary conditions.

Show MeSH
Related in: MedlinePlus