Fundamental Characteristics of Neuron Adhesion Revealed by Forced Peeling and Time-Dependent Healing

Abstract

A current bottleneck in the advance of neurophysics is the lack of reliable methods to quantitatively measure the interactions between neural cells and their microenvironment. Here, we present an experimental technique to probe the fundamental characteristics of neuron adhesion through repeated peeling of well-developed neurite branches on a substrate with an atomic force microscopy cantilever. At the same time, a total internal reflection fluorescence microscope is also used to monitor the activities of neural cell adhesion molecules (NCAMs) during detaching. It was found that NCAMs aggregate into clusters at the neurite-substrate interface, resulting in strong local attachment with an adhesion energy of ∼0.1 mJ/m² and sudden force jumps in the recorded force-displacement curve. Furthermore, by introducing a healing period between two forced peelings, we showed that stable neurite-substrate attachment can be re-established in 2–5 min. These findings are rationalized by a stochastic model, accounting for the breakage and rebinding of NCAM-based molecular bonds along the interface, and provide new insights into the mechanics of neuron adhesion as well as many related biological processes including axon outgrowth and nerve regeneration.

Statement

Although adhesion between neural cells and their microenvironment is known to play key roles in processes like axon outgrowth and nerve regeneration, a quantitative method to characterize such interactions is still lacking. In this work, by combining atomic force microscopy peeling, total internal reflection fluorescence microscope imaging, and stochastic modeling, we developed a novel approach to characterize neuron adhesion. Specifically, through repeated peeling and self-healing of neurite branches adhered on a substrate, two fundamental characteristics of neuron adhesion, the characteristic time for the formation of adhesion (between 2 and 5 min) and the adhesion energy density (∼0.01–0.1 mJ/m²), were revealed. These findings provide new insights into the mechanics of neuron adhesion and related biological processes such as axon outgrowth and nerve regeneration.

Introduction

There has been mounting evidence that neuron-extracellular matrix (ECM) and neuron-neuron adhesion play key roles in important biological processes, such as nervous system development and memory consolidation (1,2). For example, axon growth has been shown to be guided by cell-ECM interactions (3). In addition, it is commonly believed that the formation of synapses, where information is exchanged between neurons, is possible only when stable cell-cell attachment has been established (4). For these reasons, extensive effort has been spent over the past few decades to understand the formation of neuron adhesion as well as identify key physical mechanisms involved. In particular, it was found that binding of transmembrane proteins like neural cell adhesion molecule (NCAM), L1, and N-cadherin to their counterparts from outside (i.e., the ECM or another cell) is largely responsible for bringing two surfaces together (5,6). Interestingly, besides chemical factors, various studies have also shown that the physical properties of the environment, such as the rigidity (7) and surface topology (8), can significantly affect the adhesion of neural cells as well.

Despite the aforementioned efforts and progresses, several important issues remain unsettled. First of all, many existing experimental investigations on neuron adhesion are qualitative in nature; that is, the focus so far has been to observe whether different chemical or mechanical cues will change the adhesion characteristics and affect processes such as neurite outgrowth (5, 6, 7, 8, 9). However, a method allowing us to precisely measure the interactions between neural cells and their microenvironment is still lacking, and fundamental questions like how strong neuron adhesion is and how fast such an attachment can be established remain largely unanswered. Furthermore, although it is well documented that various adhesion proteins might be involved in neuron-neuron or neuron-ECM interactions (1,2,4, 5, 6), it is unclear whether and how these molecules will work independently or collectively during attaching/detaching. Evidently, finding answers to these questions will be crucial for us to understand how neuronal motility (10) and axon formation (11,12) take place from a physics point of view as well as to properly model these adhesion-mediated processes in the future.

Here, we developed a novel method to peel neurite branches from a substrate by an atomic force microscopy (AFM) tipless cantilever, whereas a laser total internal reflection fluorescence microscope (TIRFM) was used to monitor the role of NCAMs. The penetration of cantilever between neurite-substrate interface causes no disruption of neurite, thus repeated peeling of the same neurite is allowed after healing/re-establishment of focal adhesion. Taking advantage of this novel method, we found the characteristic establishment time of NCAM-mediated focal adhesion ranges 2–5 min. Meanwhile, by combining stochastic bonds model, the adhesion energy density is estimated as ∼0.1 mJ/m².

Materials and Methods

Cell culture and substrate preparation

Cortical neuron cells were microdissected from 17-day-old Sprague Dawley Rats (The Laboratory Animal Unit of The University of Hong Kong, Pok Fu Lam, Hong Kong) in phosphate-buffered saline (PBS) medium containing 18 mM glucose. Cells were then subjected to mechanical trituration and resuspended in neurobasal medium containing 2% B-27 supplement, L-glutamine (2 mM), penicillin (50 U/mL), and streptomycin (50 μg/mL). After that, cells were seeded onto glass-bottom dishes precoated with poly-L-lysine (PLL) (25 μg/mL) at a density of 3.5 × 10⁵/dish. The culture environment was maintained at 37°C in a humidified atmosphere with 5% CO₂ supply.

Indirect immunofluorescence of NCAM

Neural cells were first rinsed with balanced salt solution and incubated at room temperature and pH 7.4 for 7 min with 4% paraformaldehyde in balanced salt solution (BSS). After that, cells were loaded with monoclonal anti-NCAM antibody (Sigma, St. Louis, MO) (for 1 h at room temperature) and then incubated for another 1 h at room temperature with secondary anti-mouse IgG Alexa Fluor 488 (Invitrogen, Carlsbad, CA).

Adhesion test between NCAM and PLL-coated substrate

Carboxylated polystyrene microspheres (Bangs Laboratories, Fishers, IN) with a diameter of 10 μm were activated by 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDAC) in 2-(N-morpholino)ethanesulfonic acid (MES) buffer (50 mM, pH 6). Specifically, the suspension of microspheres was stirred at 30 rpm for 30 min at room temperature, incubated in sterile PBS containing NCAMs (R&D Systems, Minneapolis, MN), and then diluted to a concentration of 20 μg/mL overnight at 4°C with constant mixing. After that, the precoated microsphere was attached to a tipless AFM cantilever (Arrow TL1-50; NanoWorld, Neuchâtel, Switzerland) with epoxy glue and incubated in sterile PBS overnight at 4°C before actual tests. To measure adhesion between the NCAM and PLL-coated surfaces, the microsphere was moved into the substrate until a set point of 0.5 nN is reached and then held there for a period time ranging from 30 to 300 s before being retracted from the surface. By calculating the area under the force-displacement curve in the retraction stage, the adhesion energy (i.e., work of separation) between the microsphere and the PLL-coated substrate after different contact time was estimated.

Forced peeling and healing of adherent neurite

Cortical neuron cells were tested in the apparatus shown in Fig. 1 a in which a tipless AFM (NanoWizard II; JPK Instruments, Berlin, Germany) cantilever (Arrow TL1-50; NanoWorld) was used to penetrate between a well-developed neurite and the cover glass. Gradual detachment between the cell and substrate was induced by moving the tip away from the surface with a retraction speed of 0.5 μm/s. Simultaneously, a laser TIRFM (Zeiss, Oberkochen, Germany) system was placed on the other side of the coverslip to record the activities of fluorescently labeled NCAMs during detaching. After the initial peeling, the neurite was lowered back to its original position, and a healing period from 120 to 300 s was allowed for re-establishment of adhesion before another peeling test was performed.

Figure 1.

(a) Schematic diagram of the combined AFM-laser TIRFM system. (b) A typical fluorescent image taken by the TIRFM shows that NCAMs tend to aggregate into small clusters (manifested as bright spots) at the neurite-substrate interface. (c) Areal densities of NCAM clusters in the neurite (calculated by dividing the total number of NCAM clusters observed in the TIRFM image by the apparent cell-substrate contact area) and in the cell main body are shown. (d) Shown is the adhesion energy between a 10-μm polystyrene microsphere, deposited with or without (CTL) NCAMs, and a PLL-coated substrate after different contact time. (e) Typical force-displacement curve obtained from the peel test illustrates that such a curve is usually decorated with sudden force jumps. A negative value here represents the fact that the force is “tensile” (i.e., pointing away from the substrate). Three snapshots showing the peeling of neurite from the substrate by an AFM probe are also presented. To see this figure in color, go online.

Data processing

All the measured force and piezo movement data were imported into JPK Data Processing software, in which the recorded tip movement z was corrected to tip-sample separation Δ by subtracting the cantilever deflection x (=F/K, with F and K being the force and cantilever spring constant, respectively) from z, i.e.,

$$\Delta =z-x=z-\frac{F}{K}.$$ (1)

For simplicity, the resulting force versus tip-sample separation curve is referred to as force-displacement curve in this work.

Results

Repeated peeling and healing reveals characteristic time of adhesion establishment

A typical TIRFM image of the stained NCAMs at the cell-substrate interface is given in Fig. 1 b, which clearly indicates that these molecules tend to aggregate into small clusters. Interestingly, compared to the main cell body, significantly more clusters were observed in neurite branches (Fig. 1 b). Specifically, based on images of 15 cells, we found that the areal density of NCAM clusters in neurites is almost 10 times higher than that in the cell body (Fig. 1 c). Given that NCAM is a unique carrier of the polyanionic carbohydrate, polysialic acid (13,14), it is conceivable that interactions between the positively charged PLL and the polysialic acid chain will physically bind NCAM to the coverslip. To further confirm this, forced separation between a 10-μm polystyrene microsphere (Bangs Laboratories), deposited with (or without) NCAMs, and a PLL-coated substrate was also conducted. As shown in Fig. 1 d, it was indeed found that adhesion is significantly enhanced by the appearance of NCAM as well as the time of contact (15). A representative force-displacement curve obtained from the peeling of a well-developed neurite is shown in Fig. 1 e (with actual images given in the insets). Several observations can immediately be made. First of all, during detaching, the peeling force will first climb to a maximum, of the order of several nanonewtons, before decaying gradually with a further increase in the tip-substrate separation. More interestingly, the curve itself is not smooth but decorated with sudden force jumps, with magnitudes typically around 0.1–1 nN (Fig. 1 e), presumably corresponding to the disruption of individual NCAM clusters mentioned earlier.

After the initial peeling, all the bright spots in the fluorescent image disappeared (Fig. 2, a and b), demonstrating that stable adhesion is necessary for the clustering of NCAM at the cell-substrate interface. An immediate question is whether the neurite-substrate attachment can be re-established, partially or fully, when the AFM tip is lowered back to its original position and held for a period of time. Indeed, as shown in Fig. 2, c–e, the force-displacement curves obtained after 5 min of healing exhibit more or less the same peak force (in terms of counts and magnitude of force jumps) as that of the original peeling. On the other hand, the largest force that the interface can sustain, as well as the size of force jumps, after 2 min of healing is significantly lower, suggesting that only weak attachment has been formed (Fig. 2, d and e). These evidences demonstrate that the characteristic time needed for the formation of neurite adhesion is between 2 and 5 min. The re-establishment of neurite-substrate attachment was also found to be coupled with the re-emergence of NCAM clusters. In particular, aggregates of NCAMs reappear after 5 min of healing, whereas, in comparison, very little bright spots (with much weaker intensities) are observed from the fluorescent image taken after 2 min of waiting (Fig. 2 b). Note that the results shown in Figs. 2, d and e, 3 b, and 4, b and d are based on at least 15 independent tests, all conducted on well-developed neurite branches that have a relatively uniform width of ∼2 μm. In addition, it was found that the testing result depends on the retraction speed of the AFM tip to a certain extent (Supporting Materials and Methods, Section A).

Figure 2.

(a) Fluorescent image of a well-developed neurite subjected to forced peeling. Outlines of the AFM cantilever and neurite are indicated by the dash lines. ROI here stands for region of interest. (b) Shown is a series of TIRFM images on the region of interest during the test. Image I was taken before peeling. Images II, III, and IV were obtained after 0, 2, and 5 min healing, respectively. Clusters of NCAM are indicated by arrows. (c) Shown are representative force-displacement curves corresponding to the first peeling and the second peelings after a healing period of 2 and 5 min, respectively. (d) Shown is the average peak force achieved during the peeling test; n = 15. (e) Shown are the accumulated counts of force jumps during the peeling test and the corresponding probability density function (p.d.f); n = 15. To see this figure in color, go online.

Figure 3.

(a) Schematics of the structure and cohesive law used in both cohesive zone and stochastic bonds models. The inset shows the distributions of NCAM clusters captured by TIRFM after 2 and 5 min of healing. (b) Shown are comparisons between the force-displacement curves from experimental measurements and cohesive zone/stochastic bonds model simulation. To see this figure in color, go online.

Figure 4.

(a) Comparison between the force-displacement curves obtained from stochastic bonds model with various adhesion energy density and measurement from the second peeling after 2 min healing. (b) Shown is a comparison between the p.d.f of force jumps obtained from stochastic bonds model and that of second peeling after 2 min healing, γ_s = 0.1 mJ/m²; n = 15. (c) Shown is a comparison between the force-displacement curves obtained from stochastic bonds model with various adhesion energy density and measurement from the second peeling after 5 min healing. (d) Shown is a comparison between the p.d.f of force jumps obtained from stochastic bonds model and that of second peeling after 5 min healing, γ_s = 0.1 mJ/m²; n = 15. (e) Peeling rate effect arising from the stochastic breakage of bonds is shown. Simulation results were collected from eight different random cluster distributions, with the shaded area corresponding to the 95% confidence region. To see this figure in color, go online.

Cohesive zone model and stochastic bonds model

To better understand the observed peeling response of neurite as well as extract key information from it, finite element method (FEM) simulations with cohesive zone/stochastic bonds were carried out using the commercial package ABAQUS. For simplicity, the neurite was treated as a three-dimensional viscoelastic layer represented by a classical generalized Maxwell model with a uniform cross section (with a width of 2 μm and a height of 2 μm), whereas the substrate was taken to be rigid. From microneedle tests, a generic homogenous neurite branch was found to be viscoelastic with an instantaneous Young’s modulus E₀ of ∼12 kPa and a relaxation time τ around 10 s (16,17). These values were adopted in this study (refer to Table S1). In our simulations, a force F was applied at one end of the layer, causing its detachment from the substrate (Fig. 3 a). Note that, because of symmetry, only half of the neurite was considered here.

We took neurite-substrate interaction into account by introducing cohesive zone or stochastic bonds between two surfaces (Fig. 3 a), two widely used approaches in studying problems like progressive delamination (18, 19, 20) and cell adhesion (21, 22, 23, 24, 25), in which the spatial distribution and sizes of adhesion clusters formed by ligand-receptor bonds aggregation were taken from the TIRFM image (inset of Fig. 3 a). Specifically, in the cohesive zone approach, the attraction between two surfaces was assumed to be given by a modified Xu-Needleman cohesive law (26):

$$T_n\left({\Delta }_n,{\Delta }_t\right)={\sigma }_{max}\cdot \exp \left(1-\frac{{\Delta }_n}{{\delta }_n}\right)\cdot \frac{{\Delta }_n}{{\delta }_n}\cdot \exp \left(-\frac{{\Delta }_t^2}{{\delta }_t^2}\right)+\zeta \frac{\text{d}}{\text{d}t}\left(\frac{{\Delta }_n}{{\delta }_n}\right),$$ (2)

$$T_{t\alpha }\left({\Delta }_n,{\Delta }_t\right)=2{\sigma }_{max}\cdot \frac{{\delta }_n}{{\delta }_t}\cdot \frac{{\Delta }_{t\alpha }}{{\delta }_t}\cdot \left(1+\frac{{\Delta }_n}{{\delta }_n}\right)\cdot \exp \left(1-\frac{{\Delta }_n}{{\delta }_n}\right)\cdot \exp \left(-\frac{{\Delta }_{t\alpha }^2}{{\delta }_t^2}\right)+\zeta \frac{\text{d}}{\text{d}t}\left(\frac{{\Delta }_{t\alpha }}{{\delta }_t}\right),$$ (3)

where Δ_n and ${\Delta }_t=\sqrt{{\Delta }_{t2}^2+{\Delta }_{t2}^2}$ represent the normal and tangential separations, with T_n and T_tα (α = 1 or 2 along two tangential directions) being the corresponding tractions. σ_max represents the maximal normal traction that can be achieved when the surface separation reaches δ_n (Fig. 3 a). Similarly, δ_t is a characteristic distance associated with relative sliding between two surfaces. ζ is a small viscosity parameter (refer to Supporting Materials and Methods, Section B for details) introduced here to regularize numerical instabilities that often occur when a weak interface starts to debond (21,26). A user-defined subroutine based on this traction-separation law was applied to model the detachment. Specifically, a three-dimensional cohesive element with eight nodes was constructed in the user-defined subroutine to implement the aforementioned cohesive law in FEM calculations (Supporting Materials and Methods, Section B).

On the other hand, each molecular bond (with density ρ in the adhesion cluster) formed between two surfaces was treated as a linear spring with the internal force given by the following:

$$f_n=k{\Delta }_n,$$ (4)

$$f_{t\alpha }=k{\Delta }_{t\alpha },\alpha =\mathrm{1,2},$$ (5)

where k represents the bond stiffness. The presence of this internal force is expected to alter the energy landscape of the bond and consequently make it more likely to rupture. Following Bell (27), the dissociation rate of the i-th bond, k_off(i) is assumed to increase exponentially with the total force $\left(F_i=\sqrt{f_n^2+f_{t1}^2+f_{t2}^2}\right)$ acting on it, that is

$$k_{off}\left(i\right)=k_0{e}^{F_i/F_b},$$ (6)

where k₀ represents the dissociation rate in the absence of loading, and F_b is a characteristic force of the order of a few piconewtons. At the same time, we assumed that any broken bond can reform with a constant association rate k_on. A kinetic Monte Carlo algorithm (25,28) was then used to implement such a stochastic description of bond breakage/formation in our FEM simulations.

Interestingly, by choosing the same in-cluster adhesion energy density between two surfaces (see Supporting Materials and Methods, Section B), both models produced similar simulation results (in terms of the maximal peeling force as well as the overall trend of the force-displacement curve), (Figs. 3 b and S3). Nevertheless, because the stochastic bonds formulation allows us to capture more features like small force jumps and rate dependency of the peeling curve, all the results presented hereafter were based on this model. Specifically, the peeling response of neurites under different in-cluster adhesion energy density γ_s (i.e., 0.1, 0.05, and 0.025 mJ/m², respectively, achieved by varying ρ) are shown in Fig. 4, a and c, in which the observed distribution of adhesion clusters (from TIRFM imaging) was adopted as the initial configuration in the simulation. Evidently, our results suggested that the second peeling response of neurites after 2 and 5 min of healing can both be well explained by the model if the in-cluster adhesion energy density is taken to be 0.1 mJ/m² (however, much more and larger adhesion clusters were formed after 5 min of healing, refer to the inset of Fig. 3 a). In particular, both the predicted peak force (Fig. 4, a and c) and probability density function of force jumps recorded in the force-displacement curve (Fig. 4, b and d) match very well with our experimental data. Note that surface attachment was assumed to be established only within discrete adhesion clusters. Therefore, γ_s = 0.1 mJ/m² here corresponds to an apparent neurite-substrate adhesion energy (i.e., if the adhesion is treated as continuous along the interface) of ∼ 0.014 mJ/m² after 5 min of healing. Finally, given that the association/dissociation kinetics of bonds was explicitly taken into account in the formulation, the influence of the peeling rate on the response of the neurite can also be examined. For example, based on eight different adhesion patterns (generated by randomly placing the seven adhesion clusters formed after 5 min of healing, as shown in the inset of Fig. 3 a, along the neurite-substrate interface), the simulated peak force of neurite as a function of the peeling velocity (varying from 0.2 to 1 μm/s) is shown in Fig. 4 e. In comparison, the recorded peak peeling forces in our experiment (under a peeling rate of 0.3, 0.5, and 1 μm/s, respectively) are also given in Fig. 4 e, which are all within the 95% confidence range (represented by the shaded region) of the simulation results. Clearly, our results showed that a higher separation rate will lead to a larger peeling force of neurite, a phenomenon that has been widely reported for cell adhesions (29,30).

Discussion

It is well known that the contact between neural cells is driven by the homophilic bonding of NCAMs (4,13,14). This study showed that the NCAMs are also involved in neuron-ECM adhesion by aggregating into small clusters at the interface to form strong local attachments. Although the exact mechanism remains unclear, it is conceivable that physical association between the NCAMs on the cell and PLL on the substrate will bring two surfaces into close proximity and hence make it energetically favorable for other NCAM molecules, initially outside the cluster, to join the aggregate, a picture that has been adopted in describing the growth of adhesion complexes mediated by ligand-receptor binding (31,32). On the other hand, it is also possible that the assembly of NCAMs is assisted by their cis interactions (13,14). On the intracellular side, there is emerging evidence that the NCAM clusters can be connected to the cell cortex through binding with spectrin (33,34) and ultimately activate intracellular signaling cascades that are essential for neurite formation (13,14,33,34), which is consistent with our finding that almost all NCAM aggregates are localized in such a finger-like structure extending from the main cell body. It must be pointed out that, besides PLL, peeling tests of neurites grown on substrates coated with fibronectin and collagen I, two other types of cell adhesion proteins, have also been conducted (Supporting Materials and Methods, Section C). Interestingly, the peak peeling force of neurite from PLL-coated surfaces was found to be much higher than that from fibronectin- or collagen I-coated substrates (Fig. S6). This observation is consistent with previous reports that compared to PLL coating, neurons attach relatively poorly to fibronectin- and collagen I-coated surfaces.

The adhesion energy density between neurite branches and PLL-coated surfaces, when fully developed, is estimated to be of the order of 0.01–0.1 mJ/m² in this study. In comparison, this energy density has been reported to be within 0.01–1 mJ/m² (depending on the types of ligands deposited on the substrate) for several adherent cells, including wild-type/mutant Dictyostelium discoideum (35), T lymphocytes (36), and murine sarcoma S180 cells (37). We have also (for the first time to our knowledge) demonstrated that the characteristic time needed for the re-establishment of neurite-substrate adhesion is between 2 and 5 min, which is consistent with the observation that the adhesion energy between a NCAM-coated microsphere and PLL-coated substrate more or less reaches a constant level after ∼2 min of contact (Fig. 1 d). These quantitative findings are expected to be critical for our understanding of how adhesion-mediated processes such as neuron migration (10) and axon outgrowth/retraction (8,11,12,38,39) take place.

A number of techniques, including laser shock (40), shear flow (41), and direct pulling by AFM (42, 43, 44), have been previously developed to induce cell-substrate detachment, from which the adhesion characteristics can be inferred. However, given that the entire cell is forced to separate from the surface in these approaches, relatively little control can be exerted. In addition, nontrivial issues like the complex geometry of the cell body often make it difficult to accurately analyze the data. In this regard, our method may serve as an alternative for overcoming these limitations. First of all, the simple geometry of well-developed neurites (with a width around 2 μm and a length of the order of tens of micrometers) allows us to interpret measurement results in a rather unambiguous manner. In addition, this setup also enables us to conduct repeated peeling-healing-repeeling tests on the same neurite, in which precise control of factors like the rate of separation, healing duration, and number of peeling-healing cycles can be exerted. As such, it might be possible to address important questions such as how the adhesion capability of neural cells is affected by their pathological state (dictated by, for example, the progression of disorders like autism (45) and Alzheimer’s disease (46)) as well as the topological (like curvature (47)) or physical (such as compliance (24) and predeformation (48)) features of the ECM on this platform.

It must be pointed out that several important factors were neglected in our theoretical analysis here. For example, studies have shown that tension can be built inside the neurite/axon because of actomyosin contraction (38,49). However, the role of such active forces in the peeling response of neurites has not been taken into account in our model. In addition, for simplicity, we did not consider thermal fluctuations of the membrane and deformability of the substrate in the current analysis, although these factors are known to significantly influence the formation and strength of cell adhesion (50, 51, 52). Carefully designed future studies (both theoretically and experimentally) are needed to unambiguously address these issues. Finally, the fact that the activity of different proteins during peeling/healing can be closely monitored in our setup suggests that it may also serve as a powerful tool in interrogating the rich dynamics involved in neuronal adhesion. For instance, the transport and assembly (31,32,53) of NCAMs and other adhesion molecules like L1 and integrin during the formation of stable neuron-ECM contact can be examined via this approach. The collective response (23,54,55) of these proteins/protein bonds under loading, their interplay with other dynamic cytoskeletal proteins such as F-actin (56,57), and the influence of their spatial distribution against peeling (58,59) may also be quantitatively studied. Indeed, further investigations along these directions are currently under way.

Author Contributions

Y.L. and H.G. conceived and designed the work. H.L. and Z.G. performed the experiments. C.F. implemented the simulations. H.L., C.F., Z.G., Y.L., R.C.-C.C., and J.Q. analyzed data. All authors wrote and edited the manuscript.

Editor: Cynthia Reinhart-King.