**2. Background**

### **2.1. Cells are tensegral structures**

In eukaryotic cells, structural integrity is achieved and maintained through tensegrity [1], a term originally coined by the architect R. Buckminster Fuller as a portmanteau of "tensile integrity." Tensegrity describes stable structures achieved through prestress and the interaction of opposing stretch and compression elements [2]. In the cell, cytoskeletal actin filaments act as the main stretch-generating elements and microtubules are the main compression-bearing elements [3]. The role of intermediate filaments is not as well defined, as vimentin has been suggested to act principally as a major component that allows chondrocytes to withstand compressive loading, its contribution to the regulation of cytoskeletal tension and elastic modulus being relatively minor [4, 5]. While tensegrity is mainly achieved through these cytoskeletal elements, the plasma membrane has also been shown to play a key role in the cell's tensegrity [6]. Indeed, the composition and shape of the plasma membrane [7, 8], its intrinsic in-plane tension and membrane-to-cortex attachments (MCAs) [6] and the various external forces that may act on a cell's plasma membrane [9–11] have all been suggested to contribute to cellular tensegrity. The terminology surrounding these forces can be somewhat opaque and as such are defined in greater detail in **Figure 1**.

### **2.2. Plasma membrane disruptions, tensegrity and spontaneous repair**

Early observations of lipid bilayers [12], liposomes [13] and erythrocyte ghosts [14] have shown that resealing of small lesions (<1 nm) are thermodynamically favored events [14]. Disruption of lipid membranes leads to the loss of barrier function of the plasma membrane, which may lead to uncontrolled changes in osmolality and hydrostatic pressure. These changes may be sufficient to alter the wounded cell's apparent membrane tension and thus its tensegrity state [11].

created by osmotic shock or bacterial toxins to mechanical damages of various origins and intensity. Whatever the origin, the loss of barrier function provided by the plasmalemma leads to many potentially harmful effects including, but not limited to, the loss of intracellular content, the uncontrolled entry of Ca2+ and exposure of the intracellular milieu to reactive oxygen species (ROS), all of which may lead to a broad range of diminished cellular function, or even cell death. The negative effects of cellular injury are not limited to biochemical processes, they also directly affect the cell's structural integrity. As such, single-cell repair is

While they share common general steps of wound stabilization, resealing of plasmalemma damage and cytoskeletal remodeling, wound-healing mechanisms have been shown to vary widely according to the types of injury and cell-types. This chapter, using ubiquitous and injury- and cell-specific examples, aims to present an overview of the different mechanisms proposed for wound healing. Particular focus is put on how mechanotransduction, tension

In eukaryotic cells, structural integrity is achieved and maintained through tensegrity [1], a term originally coined by the architect R. Buckminster Fuller as a portmanteau of "tensile integrity." Tensegrity describes stable structures achieved through prestress and the interaction of opposing stretch and compression elements [2]. In the cell, cytoskeletal actin filaments act as the main stretch-generating elements and microtubules are the main compression-bearing elements [3]. The role of intermediate filaments is not as well defined, as vimentin has been suggested to act principally as a major component that allows chondrocytes to withstand compressive loading, its contribution to the regulation of cytoskeletal tension and elastic modulus being relatively minor [4, 5]. While tensegrity is mainly achieved through these cytoskeletal elements, the plasma membrane has also been shown to play a key role in the cell's tensegrity [6]. Indeed, the composition and shape of the plasma membrane [7, 8], its intrinsic in-plane tension and membrane-to-cortex attachments (MCAs) [6] and the various external forces that may act on a cell's plasma membrane [9–11] have all been suggested to contribute to cellular tensegrity. The terminology surrounding these forces can be somewhat opaque and

Early observations of lipid bilayers [12], liposomes [13] and erythrocyte ghosts [14] have shown that resealing of small lesions (<1 nm) are thermodynamically favored events [14]. Disruption of lipid membranes leads to the loss of barrier function of the plasma membrane, which may lead to uncontrolled changes in osmolality and hydrostatic pressure. These changes may be sufficient to alter the wounded cell's apparent membrane tension and thus its tensegrity state

as much a return to normal cell function as it is a return to structural integrity.

and tensegrity influences single-cell wound healing.

as such are defined in greater detail in **Figure 1**.

**2.2. Plasma membrane disruptions, tensegrity and spontaneous repair**

**2. Background**

[11].

**2.1. Cells are tensegral structures**

194 Wound Healing - New insights into Ancient Challenges

### **Figure 1.** Tensile forces in the unwounded cell.

Immediately following its disruption, the plasma membrane also loses its asymmetry [15] and individual membrane phospholipids become disordered around the wound edge, which creates edge tension [16]. Indeed, plasma membrane damage directly alters the membrane composition, shape, and its physical properties. Mechanical damage also exposes hydrophobic domains of phospholipid molecules to the comparatively aqueous environment of the newly formed wound edge, which in turn creates a difference in chemical potential between the phospholipids of the wound edge and those of the planar membrane [13]. It is this so-called edge tension [16] that along with the line tension [17] present on the wound edge, provides the driving force necessary for the lateral movement of phospholipids [18, 19] and spontaneous resealing of phospholipid membranes. Rates of spontaneous resealing of these relatively simple systems have been shown to depend on a variety of factors that also affect single-cell wound healing: bilayer composition [19], Ca2+ concentration [20] and disruption radius [13]. On the contrary, liposomes, erythrocytes and erythrocyte ghosts membranes are associated with a variety of proteins such as spectrin, which diminish overall phospholipid lateral movement and lead to high tension at the wound edge [21]. As such, neither large liposomes, nor erythrocyte ghosts possess the machinery necessary to actively respond to the dramatic loss of tensegrity and changes in localized tensions that are created by large membrane disruption. Consequently, large erythrocyte ghosts' wounds do not spontaneously reseal under physiological conditions [14]. This has been attributed to a number of factors, including the presence of strong MCAs [19] and the lack of endomembranes [22] (**Figure 1**).

Finally, plasma membrane disruption also exposes the cell to high levels of ROS and Ca2+ ions, either of which can be detrimental to normal cell function. Numerous pathways involving membrane dynamics such as the capacitation [23] and acrosomal reaction [24] steps of sperm maturation (reviewed in [25]) involve Ca2+-dependent signaling. Exocytosis events, such as surfactant secretion [26–28], as well as neuroendocrine [29], synapses [30–32] and auditory cells exocytosis [33, 34], are similarly Ca2+ dependent. These events are mediated by a variety of Ca2+-binding proteins such as calpains, annexins and synaptotagmins. Unsurprisingly, the uncontrolled Ca2+ entry that accompanies plasma membrane damage has been shown to activate the same families of Ca2+-binding proteins (reviewed in [35]). The downstream effects of Ca2+ entry will eventually lead to an overall diminution of apparent membrane tension.
