**4.2 Cell response is nonlinear**

*Recent Advances in Biomechanics*

**4.1 Shear stress thresholds**

amplitude of short duration (11.5 dyn/cm2

Using the previously described high-speed servo to generate well-defined shear stresses in a microfluidic chamber, the threshold shear stress to cell response in cultured astrocytes was analyzed. Ca2+ rise being the earliest measurable signal in cells, the Ca2+ rise in the cells was measured in real time. The thresholds were defined with multiple input parameters including magnitude, duration, and load rise time.

an effective threshold [30]. However, the amplitude of the force stimuli is not the only parameter, and a variety of relaxation times has been observed. Changes in pulse duration and rise time also affect the subthreshold responses. For example, a low

elevation, whereas a pulse width of 1000 ms of the same amplitude did. Together, the two parameters establish a multidimensional threshold matrix for pulses with a square profile, as shown in **Figure 3**. The relative significance of each stimulus

*(a) Profile of shear stimulus thresholds. (b) The damage threshold is defined by a 5% maximum response.*

with a transient

, 10 ms) did not trigger a measurable Ca2+

, thereby setting

The cells responded reliably to a shear stimulus of 23 dyn/cm2

Ca2+ increase, but they did not respond up to a pulse of 11.5 dyn/cm2

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**Figure 3.**

The cell response to shear stimuli is nonlinear. The nonlinear characteristic of Ca2+ response is demonstrated in **Figure 4**. For example, an abrupt increase in shear stress caused the Ca2+ rise, but a slow increase to the same amplitude failed to activate the cells, as shown in **Figure 4(a)**. The cell sensitivity decays rapidly with an increase in force rise time. Moreover, a brief mechanical shock is more important than a sustained shear force. As shown in **Figure 4(b)**, at short intervals of 10 ms, the pulse train caused a response that was three times higher than a single pulse of the same amplitude and a total pulse duration of 100 ms [30]. Thus, the total energy input of the stimulus is not the only determinant in Ca2+ response; the kinetics of the stimulus (force loading rate) also plays an essential role. This emphasizes the viscoelastic/plastic nature of the force transduction processes in cells [64, 69]. By using sine wave stimuli of different frequencies, it has been shown that cells' response is also frequency dependent; the peaks in response occur at a higher frequency (>80 Hz) or a lower frequency (<20 Hz) [30].

The strain rate dependence of cell injury has been observed in 3D matrix cultured neurons and astrocytes, showing an increase in membrane permeability to small molecules and an increase in post-insult cell death [70, 71]. However, this effect was not observed in hippocampal tissues under biaxial stretch at strain rates ranging from 0.1 to 50 s−1 [72]; this rate of ramping is likely outside the sensitivity

#### **Figure 4.**

*Nonlinear Ca2+ response of cells. (a) Ca2+ response to shear pulses of different rise times. (b) Ca2+ response to a train of 10 narrow consecutive pulses (10 ms wide) is three times higher than a single broad pulse (100 ms wide) of the same amplitude. (c) and (d) Ca2+ response to repeated pulses (11.5 dyn/cm2 , 10 ms) with intervals of 1 s and 10s, respectively, showing that the response is nonlinear.*

range of the cells [73]. In addition, different cell types have been found to exhibit different properties, which is not surprising.

#### **4.3 Response to repeated challenges**

It has been known for a long time that repeated low-amplitude shocks that never had any clear damage to the cells could be lethal in animal models of TBI [74–76]. This suggests that low subthreshold mechanical forces can be registered and accumulated by the cells. In other words, cells have a long-term pernicious "memory" to repeated stimuli. To study this memory effect, cells were exposed to repetitive low-amplitude stimuli that alone are not able to produce a Ca2+ rise. The response to a pulse train with 1 s intervals of 10 ms duration revealed that individual cells were activated at different times. About 20% of the cells responded to the second pulse, while 60% of the cells responded to the sixth and subsequent pulses (**Figure 4(c)**). Reducing the frequency sufficiently can eliminate the response (**Figure 4(d)**). There are two possibilities for this behavior: the plastic mechanical deformation due to cytoskeletal bonds break and reform, or the accumulation of second messenger (Ca2+) pools. Recent studies on cytoskeletal protein forces show that rapid shear stress can generate prolonged cytoskeletal tension, implying that the cytoskeletal deformation plays a key role.

As discussed in detail in the following sections, cells withstand mechanical loading through support from the cytoskeleton consisting of dynamically crosslinked structural proteins [77–80]. The deformation of a cell depends on the intrinsic elastic deformation of fibrous cytoskeletal proteins and plastic deformation involving reversible cross-linking and cytoskeleton reorganization [81, 82]. Slow shear loading engages the plastic processes that significantly modify the local forces around the Ca2+ transducers.

The nonlinear response of cells to external forces provides evidence that cells use complex force transduction mechanisms to register the forces. Understanding the force transduction pathways is an important step toward understanding the effectors that lead to TBI pathology.

#### **5. Force transduction mechanisms**

While fluid shear stresses act on the apical surface of the cells, this force can be transmitted to force-sensitive molecules that trigger ionic trafficking such as Ca2+ influx and other biochemical reactions via a variety of mechanosensitive mechanisms, a process called mechanotransduction. Recent studies suggest that shear stress transduction is mediated by the cytoskeleton, a filamentous network that connects different regions of the cells and holds the mechanical structure of cells [83–85].

#### **5.1 Role of actin cytoskeleton in force transduction**

The cytoskeleton is the universal mechanical structure of animal cells and responsible for cell shape, topography, and facilitating cell locomotion [86]. Cells resist the external mechanical forces via the cytoskeleton. The cytoskeleton consists of filamentous proteins that are interlinked to form filaments. Actin filaments are the smallest type of filaments. Single filaments of actin bind together via cross-linking proteins, such as α-actinin, forming a network that connects different regions of the cells. Actin bundles are found across the cell body; actin mesh is also found beneath the cell membrane, supporting the plasma membrane.

Like many other subcellular organelles, the actin cytoskeleton can be affected during TBI. Cytoskeleton damage has been observed in various moderate to severe

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time [114].

*Early Cell Response to Mechanical Stimuli during TBI DOI: http://dx.doi.org/10.5772/intechopen.93295*

**5.2 Mechanosensitive channels and Ca2+ signaling**

activate NMDARs in the absence of agonists [57].

[107–109]. Most likely, both mechanisms are correlated.

**6. Heterogeneous force distribution in single cells subjected** 

channel configuration.

**to shear pulses**

of cells in response to shear stresses.

**6.1 Cytoskeletal force measurements**

TBI conditions [87, 88]. A number of studies now suggest that trauma-induced neuronal cell death may be preceded by the disruption of the neuronal cytoskeleton [89, 90]. Through its connections, the cytoskeleton can also transmit forces to different functional elements of the cell to alter their functions [86, 91–93]. Among them are the mechanosensitive channels (MSCs) that permeate cation ions such as Ca2+.

Mechanosensitive ionic channels are transmembrane proteins that form a pore structure across the cell membrane. These channels are linked to the cytoskeletal proteins; thus, changes in cytoskeletal stresses may open the mechanosensitive channels [94, 95]. Similarly, changes in membrane tension could also alter the

Several MSCs have been identified in astrocytes that are members of the transient receptor potential (TRP) family including TRPV4, TRPC1, TRPC5, and TRPA1 [96–98, 99]. Studies of sensory neurons have suggested that Piezo channels play an important role in brain cells [100, 101]. Piezo-type MSCs are also present in astrocytes that can be inhibited with specific Piezo channel inhibitor [102]. Using an astrocyte model, a recent study has shown that N-Methyl-D-aspartic acid receptors (NMDARs) are the primary Ca2+ source in astrocytes and fluid shear stimuli can

The fluid shear forces can alter the channel activities via several mechanisms. They can modify the cytoskeletal stresses, and the cytoskeleton under high tension can pull the channel proteins via their links. Many MSCs are known to link with the actin cytoskeleton with cross-linking proteins [103–105]. In astrocytes and neurons, α-actinin binds to NMDA receptors, providing a mechanical link between NMDA receptors with the underlying cytoskeleton [106]. Shear stress can also cause transient deformation and bending of the lipid bilayer, altering the MSCs directly

The shear-induced strains and stresses in the cytoskeleton could be the core of the mechanical response of a cell. Since the cytoskeleton is an anisotropic collection of dynamically cross-linked structural proteins, the cytoskeletal stresses are intrinsically nonuniform. This heterogeneity could be responsible for the nonlinear behavior

The recent development of force probes based on fluorescence resonance energy transfer (FRET) technique [110–113] provides a powerful tool to observe cytoskeletal protein forces in live cells. The probe consists of two mutant fluorophores, a donor and an acceptor, linked with an elastic structure. Mechanical forces change the distance and/or the angle between the donor and the acceptor, resulting in a change in the energy transfer efficiency from donor to the acceptor [112, 113]. These probes were genetically encoded in cross-linking proteins, such as α-actinin and actin, and they are being used to report the strains in cytoskeletal linking proteins when cells are subjected to shear pulses. Using FRET probes, the distribution of protein forces induced by fluid shear stress has been mapped in real *Recent Advances in Biomechanics*

different properties, which is not surprising.

**4.3 Response to repeated challenges**

forces around the Ca2+ transducers.

effectors that lead to TBI pathology.

**5. Force transduction mechanisms**

**5.1 Role of actin cytoskeleton in force transduction**

the cell membrane, supporting the plasma membrane.

range of the cells [73]. In addition, different cell types have been found to exhibit

It has been known for a long time that repeated low-amplitude shocks that never had any clear damage to the cells could be lethal in animal models of TBI [74–76]. This suggests that low subthreshold mechanical forces can be registered and accumulated by the cells. In other words, cells have a long-term pernicious "memory" to repeated stimuli. To study this memory effect, cells were exposed to repetitive low-amplitude stimuli that alone are not able to produce a Ca2+ rise. The response to a pulse train with 1 s intervals of 10 ms duration revealed that individual cells were activated at different times. About 20% of the cells responded to the second pulse, while 60% of the cells responded to the sixth and subsequent pulses (**Figure 4(c)**). Reducing the frequency sufficiently can eliminate the response (**Figure 4(d)**). There are two possibilities for this behavior: the plastic mechanical deformation due to cytoskeletal bonds break and reform, or the accumulation of second messenger (Ca2+) pools. Recent studies on cytoskeletal protein forces show that rapid shear stress can generate prolonged cytoskeletal tension, implying that the cytoskeletal deformation plays a key role. As discussed in detail in the following sections, cells withstand mechanical loading through support from the cytoskeleton consisting of dynamically crosslinked structural proteins [77–80]. The deformation of a cell depends on the intrinsic elastic deformation of fibrous cytoskeletal proteins and plastic deformation involving reversible cross-linking and cytoskeleton reorganization [81, 82]. Slow shear loading engages the plastic processes that significantly modify the local

The nonlinear response of cells to external forces provides evidence that cells use complex force transduction mechanisms to register the forces. Understanding the force transduction pathways is an important step toward understanding the

While fluid shear stresses act on the apical surface of the cells, this force can be transmitted to force-sensitive molecules that trigger ionic trafficking such as Ca2+ influx and other biochemical reactions via a variety of mechanosensitive mechanisms, a process called mechanotransduction. Recent studies suggest that shear stress transduction is mediated by the cytoskeleton, a filamentous network that connects different regions of the cells and holds the mechanical structure of cells [83–85].

The cytoskeleton is the universal mechanical structure of animal cells and responsible for cell shape, topography, and facilitating cell locomotion [86]. Cells resist the external mechanical forces via the cytoskeleton. The cytoskeleton consists of filamentous proteins that are interlinked to form filaments. Actin filaments are the smallest type of filaments. Single filaments of actin bind together via cross-linking proteins, such as α-actinin, forming a network that connects different regions of the cells. Actin bundles are found across the cell body; actin mesh is also found beneath

Like many other subcellular organelles, the actin cytoskeleton can be affected during TBI. Cytoskeleton damage has been observed in various moderate to severe

**154**

TBI conditions [87, 88]. A number of studies now suggest that trauma-induced neuronal cell death may be preceded by the disruption of the neuronal cytoskeleton [89, 90]. Through its connections, the cytoskeleton can also transmit forces to different functional elements of the cell to alter their functions [86, 91–93]. Among them are the mechanosensitive channels (MSCs) that permeate cation ions such as Ca2+.
