# Difference between revisions of "Dynamic Viscoelasticity of Actin Cross-Linked with Wild-Type and Disease-Causing Mutant α-Actinin-4"

Original entry: Warren Lloyd Ung, APPHY 225, Fall 2009

"Dynamic Viscoelasticity of Actin Cross-Linked with Wild-Type and Disease-Causing Mutant α-Actinin-4"
S. M. Volkner Ward, A. Weins, M. R. Pollak, & D.A. Weitz, (2008).
Biophysical Journal.

UNDER CONSTRUCTION

## Soft Matter Keywords

biopolymer network, viscoelasticity, actin

## Summary

The authors used rheological methods to elucidate the effects of mutant α-actinin-4 on networks of actin biopolymers. Actin is a biopolymer commonly found in cells as double-stranded filaments. Actin filaments are part of the cellular cytoskeleton and allow the cell to exert mechanical force, maintain cellular shape, and promote intracellular transport [1]. Actin also forms an integral part of muscles cells.

Gels formed with pure actin behave like a viscoelastic solid with a small elastic modulus (0.1 to 1Pa). Adding cross-links strengthens the gel; it may also cause actin to aggregate into large bundles, which influences the bulk viscoelastic properties. Of particular interest is a cross-linker called α-actinin-4. This cross-linker is present naturally in podocytes, the kidney cells responsible for the filtration of wastes. Mutations in the cross-linking protein often results in kidney diseases related to aggregates of actin, which prevent normal function. A single point mutation in this protein may be significant enough to cause kidney failure in extreme cases. Figure 1 below shows actin networks with and without α-actinin-4 cross-linker.

Figure 1: Actin stained with phalloidin: (A) no cross-linker, (B) wild-type α-actinin-4, and (C) mutant α-actinin-4. Scale bar is $40\mu m$

By performing rheological experiments, which compare the response of both the wild-type and mutant α-actinin-4, the authors confirm results obtained to date, and propose two possible mechanisms, which explain the differences between mutant and wild-type α-actinin-4.

Figure 2: Frequency dependence of elastic modulus (solid) and viscous modulus (open) for wild-type (circles) and mutant (triangles) α-actinin-4.
Figure 3: Frequency dependence of elastic modulus (solid) and viscous modulus (open) for different concentrations of (A) wild-type and (B) mutant α-actinin-4 for different molar concentrations of cross-linker.
Figure 4: Temperature dependence of the network relaxation frequency for wild-type (circles) and mutant (triangles) cross-linker.

## Soft Matter Discussion

The rheological properties, which are examined in these experiments, are the elastic modulus (G') and the viscous modulus (G") with respect to frequency (see Figure 2). As a viscoelastic material, we expect the elastic modulus and viscous modulus to converge for long timescales, while the viscous modulus dominates for long timescales. For both mutant and wild-type cross-linker, there is a plateau in the elastic modulus; the plateau is more pronounced in networks with the mutant cross-linker. This plateau occurs at $f_{plateau}$, which corresponds to the minimum in the viscous modulus. The authors also define $f_{relax}$ to correspond to the local maximum of G" as a method of measuring the width of the plateau.

The ratio of the elastic modulus to the viscous modulus at the plateau ($(G'/G)_{f = f_{plateau}}$) is a measure of whether the actin network behaves more like a solid material or a fluid material. Higher values of this ratio lead to networks with a more solid-like nature. Generally, larger values of G'/G" are linked with a larger plateau region for the viscous modulus. Increasing concentrations of cross-linker and decreasing the temperature produce networks with higher values of G'/G" (refer to Figure 3). Mutant α-actinin-4 also tends to have a larger plateau and a corresponding solid-like character.

For a fixed temperature and concentration, the mutant cross-linker has a smaller dissociation constant from actin compared to the wild-type cross-linker. By examining the relaxation frequency of the wild-type and mutant α-actinin-4 networks at various temperatures, the authors demonstrate that the relaxation frequencies for both types of cross-linker obey the Arrhenius equation (see Figure 4). In essence, networks containing the mutant cross-linker behave the same way - in rheological terms - as networks containing the wild-type cross-linker at lower temperatures.

From previous studies, it is known that the mutant cross-linker has an additional exposed actin binding site. Using this knowledge, the authors present two possible models for binding of mutant actin, which are consistent with the data. The first model suggests that the additional binding site simply reduces the energy of the state in which actin is bound to the mutant α-actinin-4; this simply increases the energy barrier for dissociation of the cross-linker from actin. The second model suggests that there may be two possible energy states, a transition state in which the actin is bound to the mutant cross-linker just as it is to the wild-type cross-linker, and an additional lower energy state in which the actin is bound more tightly to the cross-linker. Unfortunately the authors were unable to demonstrate, which mechanism occurs in this biopolymer network.

## Applications

By determining the mechanism, which causes mutant α-actinin-4 to behave distinctly from wild-type cross-linker, it is possible to begin searching for ways to counteract the specific kidney diseasess. Although it may not directly lead to a cure, understanding the effects arising from these mutatiosn is necessary to construct treatments for the problems, which result. At the very least, treatment of the resulting symptoms could lead to a stopgap for those suffering from such debilitating diseases until a cure is found.

This serves as a good demonstration of the way in which rheological methods can reveal elements of the physics and chemistry of biopolymer networks. Since such networks of microtubules and intermediate filaments as well as actin are ubiquitous in cell biology, these rheological techniques can lead to a greater understanding of the mechanisms present in cells of all kinds.

## References

1. "Cytoskeleton." Wikipedia.