Functional significance of morphological variation in the mechanosensory lateral line system of fishes and its biomimetic potential

Significance

Neuromast sensory organs of the lateral line system allow all fishes (and aquatic amphibians) to detect water flows enabling formulation of behaviors critical for survival. A computational model was designed to ask how known variation in neuromast morphology can predict variation in sensitivity to flows. It revealed unappreciated structure–function relationships at the level of individual hair cell–based sensory organs that change in size and shape through developmental and evolutionary time. It can now be used to ask questions placing structure–function relationships in behavioral and ecological contexts. This work has demonstrated how a synergistic relationship between engineers and biologists can advance the identification of structural parameters in a biological system for optimization of bioinspired sensor designs in different flow sensing applications.

Abstract

The mechanosensory lateral line system, found in all fishes, detects water movement and pressure fields and mediates crucial behaviors in aquatic environments. Neuromast sensory organs, the functional units of the system, exhibit diversity in shape and size among species, but structure–function relationships that could explain this impressive diversity have not been explored. Here, we employ a fluid–structure interaction–based computational model that uses the shape and size of the base of the cupula (the gelatinous cap covering the neuromast) as a proxy for neuromast shape and size. Simulations showed that sensitivity of the cupula (bending response to defined water flows) varies with its shape and size, direction of water flow relative to the major axis of the cupula, as well as with cupula height and material properties (elastic modulus). Sensitivity varied among cupulae with shapes known among superficial neuromasts and canal neuromasts within narrow and widened canals. In addition, predictions made by the model for the sorts of changes in neuromast morphology known to occur during ontogeny predict complex changes in neuromast sensitivity through developmental time. In using variation in cupula responses to flow as a proxy for neuromast responses, this work has revealed an unexplored aspect of adaptive functional evolution in the lateral line system with the potential to inspire the development of biomimetic sensors and robots with applications in industry, medicine, and environmental monitoring and exploration.

Nature provides fascinating examples of how mechanoreceptors interact with flows in remarkably specialized ways and highlights how they have evolved to sense environmental cues critical for survival. Insects, for example, possess filiform hair structures on their cerci mechanoreceptors, capable of detecting minute air currents that provide them with three-dimensional spatial awareness (1). Similarly, seals possess undulating whisker morphologies that minimize vortex-induced vibrations while amplifying wake-induced vibrations, enabling precise fish-wake tracking with a high signal-to-noise ratio (2). Soft corals, such as bipinnate sea plumes, feature flexible skeletons that exhibit vortex-induced vibrations to enhance food particle capture efficiency by 40% (3). All fishes (34,000+ species, representing ~50% of vertebrates) have a mechanosensory lateral line system that is used to detect water movements (0 to 200 Hz) and pressure fields in order to evade predators, detect prey, communicate, orient (e.g., in schooling), and navigate throughout their lives. The lateral line system enables fishes to thrive in marine and freshwater environments with diverse and often extreme hydrodynamic features, and in circumstances in which vision, in particular, is of limited utility, such as at night, in caves, in turbid waters, and in deep-sea habitats (4–11).

The neuromast receptor organs of the lateral line system (Fig. 1) are found on the head, trunk (including some fins), and tail (caudal fin) of fishes. Each neuromast is composed of a population of sensory hair cells (like those of the vertebrate inner ear) each of which possesses an apical ciliary bundle composed of a single kinocilium and a group of shorter stereocilia to one side of it. This “planar polarity” defines a hair cell’s axis of best physiological sensitivity (10). Dozens to hundreds of hair cells are found within a neuromast, which are always oriented 180° to one another, thus defining a single axis of best physiological sensitivity of the neuromast (10). The ciliary bundles of all the hair cells project into a dome-like or elongated gelatinous cupula (12) whose base covers the entire neuromast, thus ensuring that the shape of the base of the cupula is the same as the shape of the neuromast [Fig. 1e and (10)]. Unidirectional or low-frequency oscillatory flows (0 to 200 Hz) in the vicinity of a neuromast cause the cupula to bend, which deflects the ciliary bundles of the hair cells embedded within it. Mechanical displacement of the ciliary bundles in a direction with a vector component in the axis of best physiological sensitivity of the hair cells results in a response (proportional to the magnitude and direction of cupula deflection) by the neurons that innervate each of the hair cells, which is communicated via a lateral line nerve to the primary lateral line center of the hindbrain (13–17). Neuromasts are found on the skin (superficial neuromasts, SNs; Fig. 1 b–e) where they respond to the velocity component of flows (13, 15, 17–19) and in positions alternating with pores in the epithelial lining of fluid-filled bony canals [canal neuromasts, CNs; Fig. 1 c–e and (20)] where they respond to the acceleration component of flows [generated by pressure differences between canal pores (13, 14, 19)]. Both types of neuromasts demonstrate dramatic variation in shape and size among fish species and during ontogeny [Fig. 1 d and e, SI Appendix, Table S1 and (9, 10)] thus suggesting that neuromast morphology is of adaptive significance.

Fig. 1.

(a) Schematic representation of a lateral line canal, containing canal neuromast and superficial neuromast on skin of the trunk of a fish. (b) Superficial neuromast (SN) showing the relationship of the cupula to the apical hair cell bundles within it, and the magnitude of flow velocities and (c) canal neuromast (CN) indicating the location of canal pores and the free-stream velocity outside the canal and pressure differences at adjacent canal pores that causes fluid to move within the canal. (d) Schematics of neuromasts shapes found among fishes. Teal = SNs, maroon = CNs. (e) SEM images of some of the CN and SNs shapes (and sizes) found among fishes, showing the apical ciliary bundles of the sensory hair cells (white; cupula is lost during preparation for SEM). (A) Robust oval SN on trunk of juvenile windowpane flounder (Scophthalmus aquosus). (B) Bar-shaped CN in narrow cranial canal of juvenile zebrafish (Danio rerio). (Scale bar, 10 µm.) (C) Oval CN in narrow cranial canal of an adult mottled sculpin (Cottus bairdi). (Scale bar, 100 µm.) (D) CN in widened canal in an adult clown knifefish [Chitala (=Notopterus) chitala]. (E) Cross-shaped SN from the blind side of the head of an adult California tongue sole (Symphurus atricauda). (Scale bar, 10 µm.) (F) Diamond-shaped CN in widened canal on the blind side of the head in an adult rex sole (Glyptocephalus sp.). (G) Diamond-shaped SN on the head of a larval line snout goby (Elacatinus lori). (Scale bar, 2 µm.) (H) Enlargement of hair cells in another diamond-shaped SN in a larval E. lori showing hair cell orientation defining the axis of best physiological sensitivity (double-headed arrow). (Scale bar, 1 µm.) (I) Equilateral diamond-shaped CN in a cranial canal in a juvenile flavescent peacock cichlid (Aulonocara stuartgranti). (Scale bar, 10 µm.) (J) Robust oval SN on the head of a juvenile brook trout (Salvelinus fontinalis). (Scale bar, 5 µm.) (K and L) Diamond-shaped SNs on the scales of an adult tiger barb (Puntigrus tetrazona, a cypriniform) with (K) and without (L) the cupula showing that the shape of the base of the cupula is indeed the same as the shape of the neuromast. (Scale bar, 25 µm.) (M and N) Diamond-shaped SNs on the scales of an adult tiger barb (Puntigrus tetrazona, a cypriniform) showing (in M) that the cupula appears to be composed of two layers; one half is absent in N revealing the sensory hair cells. (Scale bar, 10 µm.) Double-headed arrows = axis of best physiological sensitivity (orientation) of the sensory hair cells (A–F) modified from (21), reprinted with permission from Elsevier. (G-H) modified from (22), reprinted with permission from the American Society of Ichthyologists and Herpetologists. (I) modified from (23) and (J) modified from (24), both reprinted with permission of Wiley and Sons.

The diversity of the lateral line system is further defined by variation in the morphology of the lateral line canals, especially those on the head (9, 10, 25). Narrow and widened canals act as high or low-pass frequency filters, respectively (26, 27) modifying the stimuli available to canal neuromasts. Narrow canals (defined by a small diameter and small canal pores) are typically found in swimming species or those species inhabiting high-flow or turbulent environments in which precise detection of transient high-frequency stimuli against background flows is crucial. In contrast, widened canals (defined by larger diameters and larger canal pores) are common in species that are not active swimmers or that live in hydrodynamically “quiet” habitats (10). Neuromasts within widened canals are considered to be more sensitive than those in narrow canals and enable fishes to be particularly sensitive to lower-frequency stimuli (26, 27). In addition, as a fish progresses through its life history, the lateral line system (composed of neuromasts on the skin) is transformed with changes in neuromast shape and size and the gradual enclosure of a subset of neuromasts (“presumptive” canal neuromasts) into pored canals, which leave “superficial neuromasts” on the skin that tend to stay small, but may increase in number quite dramatically as a fish grows (9, 28, 29).

Due to its remarkable sensitivity to flows and the similarities of the hair cells of neuromasts to those of the vertebrate inner ear, the lateral line system has garnered interest from a wide range of biomedical (sensory neurobiology) and engineering (mechanical, electromechanical) disciplines. Biologists have explored neuromast morphology, biomechanics, and physiology in a small number of intensely studied experimental systems, primarily the small, round superficial neuromasts of larval Zebrafish, the SNs of blind cave fish (Astyanax mexicanus), and the large diamond-shaped canal neuromasts in adults of the unrelated Eurasian Ruffe (5, 6, 15, 17, 19, 30–33). Modeling approaches have revealed mechanisms of selective frequency filtering and object localization responses at the level of an individual neuromast (17, 18, 32–35). Other studies have examined the functional significance of the placement of lateral line canals on the head [in a trout (36)] and high pass filtering capabilities by lateral line canals using artificial canal encapsulated piezoelectric sensors (37). The contribution of the morphology and material properties of the cupula has also been examined, but only to a limited extent (38).

Most recently, the lateral line system has been used to advance the field of biomimetics with respect to the development of underwater sensors with a range of applications (37–41). The design of artificial lateral line receptors has been inspired by the basic attributes of neuromast sense organs (e.g., directionally sensitive cilia embedded in a bendable cupula). Known variation in neuromast morphology (Fig. 1E and SI Appendix, Table S1) has not been considered for its applicability in the design of artificial flow sensors and neither has it been explored in studies of the functional morphology and biomechanics of the lateral line system in fishes. For biologists to address the functional impact of variation in neuromast morphology in comparative physiological or biophysical laboratory studies, one would need to identify species that exhibit differences in neuromast size and shape (likely distinct in ecology and behavior) that are closely related, readily accessible, and are amenable to laboratory study. These factors, in addition to the micron-scale size of neuromasts (Fig. 1) and location of some neuromasts in bony canals, present significant logistical and technological challenges for experimental work. Thus, we have taken an alternative approach, of value to both engineers and biologists, that uses a fluid–structure interaction (FSI) model of cupula shape and size as a proxy for neuromast shape and size. We explore how known variation in neuromast shape and size among species, as well as the angle of flow relative to the long axis of the cupula, and placement of a cupula (neuromast) on skin or in canals can be used to predict functional variation at the level of individual neuromasts, which can be used as a source of inspiration for engineering applications.

Results

Our simulations showed that cupula tip displacement (sensitivity) in response to steady unidirectional flows (0 Hz) is affected by the height, material properties (elastic modulus), flow velocity (Fig. 2), and morphology of the cupula (shape, size) and angle of flow relative to the major axis of the cupula (Fig. 3). In addition, the location of a cupula either on the skin (representing SNs) or in fluid-filled narrow and widened canals (representing CNs; Fig. 1) affects sensitivity to flow (Figs. 4 and 5). Furthermore, the increases in cupula (neuromast) size and changes in shape, and transformation of an SN to CN and gradual enclosure within a canal, processes known to occur during ontogeny (Fig. 6) predict temporal changes in sensitivity to flows.

Fig. 2.

Sensitivity of cupula as function of flow velocity and structural properties for cupulae of three shapes. (A) flow velocity (1 to 11 mm s⁻¹), (B) cupula height (250 to 600 µm), and (C) elastic modulus of cupula (100 Pa to 500 kPa). Three cupula shapes: round (representing SNs), elongated oval (representing CNs in narrow canals), and elongated diamond (representing CNs in widened canals). All have a major axis = 25 µm, flow velocity = 1 mm s⁻¹ (flow direction from Left to Right, perpendicular to its major axis). Cupula tip displacement increases linearly with flow velocity (δ ∝ u), follows a fourth-power relationship with cupula height (δ ∝ h⁴), and decreases inversely with increasing elastic modulus (δ ∝ E⁻¹).

Fig. 3.

Tip displacement of cupulae of superficial neuromasts as a function of shape, direction (angle) of flow, and size. (A) Response of cupulae with symmetrical and nonsymmetrical shapes (major axis = 25 µm) to water flow. When flow angle = 0°, flow is parallel to the major axis of diamond, oval, and cross-shaped cupulae. Inset = magnified view of cupula tip displacement in round and cross-shaped cupulae. Maximum tip displacement occurs at flow angles of 90° and 270° (perpendicular to major axis), is observed in elongated diamond-shaped cupula. The round cupula displays the minimum tip displacement and shows no directional bias in sensitivity. (B) Tip displacement as a function of cupula size (major axis = 25 µm, 50 µm, and 100 µm) for elongated diamond-shaped cupulae. Tip displacement decreases cubically with increasing cupula size at all flow angles. Black oval icons and arrows in (A and B) indicate orientation of the long axis of the cupula relative to angle of flow (Left to Right). Analogous plots describing the effect of cupula size for robust oval, cross-shaped, and round cupulae are provided in SI Appendix, Fig. S2.

Fig. 4.

Sensitivity of cupula in canals (narrow, widened), with different shapes, and size relative to cupula height, and variation in canal diameter. (A) Tip displacement for cupulae of different shapes known to occur in narrow and widened canals. In all cases, flow is from Left to Right, and orientation of the long axis of cupulae with distinct major and minor axes is either parallel to flow or perpendicular to flow (as noted). (B) Maximum sensitivity of cupula (as in Fig. 3B) expressed as cupula size-to-cupula height ratio (keeping cupula height constant). As this ratio increases (i.e., larger cupula diameter, as indicated by size of icons), tip displacement decreases for all cupula shapes. This trend is consistent with results with SNs (Fig. 3B). 3-D shape of the cupulae is indicated. (C) For a robust oval cupula of constant size (major axis = 25 µm, height = 250 µm, placed with its long axis perpendicular to the canal axis), as canal diameter increases (indicated by gray gradient), tip displacement decreases.

Fig. 5.

Comparison of maximum tip displacement of cupulae of different shapes in a canal (CNs) or located on skin (SNs). Data from the same simulations illustrated in Fig. 3 (SNs) and Fig. 4 (CNs). CNs are located in a canal with a diameter of 300 µm (SI Appendix, Fig. S7C), and SNs are on the skin, in open flow (SI Appendix, Fig. S7A). Flow direction is from Left to Right, at a flow velocity of 1 mm s⁻¹ for all cupula shapes, but a flow velocity 0.1 mm s⁻¹ was used for the bar-shaped neuromast. “Perp.” indicates that the long axis of the neuromast is rotated so that it is perpendicular to flow direction. Diameter (round cupula) or length of major axis (cupulae with distinct equal or unequal major and minor axes) = 25 µm.

Fig. 6.

Ontogenetic decrease in cupula sensitivity as a function of neuromast size, shape, and placement in Brook Trout. Tip displacement (black dot) for neuromasts at three different stages in trout development (See data in SI Appendix, Fig. S2A). The relative size and shape of the neuromasts and the sensory strips in which hair cells are located are from a published study (22). Round cupula of superficial neuromast (diameter = 25 µm) in young (larval) trout. Robust oval cupula (major axis = 50 µm, 2:1 length-to-width ratio) in juvenile trout located in groove representing partially formed canal segment (dashed line). Elongated oval cupula in adult trout (major axis = 100 µm, 3:1 length-to-width ratio), within fully developed canal (solid line). In all cases, simulations assumed a cupula height = 250 µm, flow velocity = 1 mm s⁻¹ (from Left to Right, parallel to major axis of neuromasts); diameter of groove/canal = 300 µm. This shows that a decrease in cupula tip displacement is correlated with a change in the hydrodynamic environment experienced by larvae, juveniles, and adults as they transition from no-flow/low-flow gravel nests (within stream Bottom) to the water column in high-flow streams in which these fish actively swim.

Effect of Flow Velocity and Fundamental Morphological Attributes of Cupulae.

Our simulations showed that with increasing flow velocity, tip displacement (sensitivity) increased linearly for both round and elongated oval cupulae (3:1 length-to-width ratio) but for an elongated diamond it plateaued at velocities >2 mm s⁻¹ (Fig. 2A). In addition, as cupula height was increased, sensitivity increased for all cupula shapes (following a power-four dependence, Fig. 2B). Furthermore, as the elastic modulus of the cupula was increased, tip displacement decreased for all cupula shapes but increased sharply at values lower than ~100 kPa (Fig. 2C and SI Appendix, Fig. S1). Thus, unless noted otherwise, all simulations, as reported below, modeled cupulae with a major axis of 25 µm, cupula height of 250 µm, and elastic modulus of 100 kPa with a flow velocity of 1 mm s⁻¹.

Superficial Neuromasts.

Simulations showed that for cupulae in free flow (SNs), tip displacement (sensitivity) varied with cupula shape (round, cross, robust oval, and elongated diamond; Fig. 1D), flow angle relative to the major axis of the cupula (Fig. 3A), and cupula size (Fig. 3B).

Variation in shape.

Cupulae with pronounced major and minor axes (oval, diamond) showed higher tip displacements than those with equal major and minor axes (round, cross-shaped cupulae; Fig. 3A). For instance, elongated diamond-shaped cupulae exhibited high tip displacement when compared to most other shapes, and a robust oval cupula (2:1 length-to-width ratio) displayed lower sensitivity (Fig. 3A). A bar-shaped cupula was expected to show the highest tip displacement among all shapes when its long axis was perpendicular to the angle of flow (SI Appendix, Physics of Bending, Fig. S3), however at a flow velocity of 0.1 mm s^-1 it showed displacements lower than those for an elongated diamond-shaped CN and SN, respectively.

Variation in orientation to flow.

Round cupulae did not show variation in sensitivity with angle of flow, and the cross-shaped cupula (with two equal axes) appeared to show a small increase in sensitivity at flow angles of 0°, 90°, and 180° (Fig. 3A Inset) compared to sensitivity at angles of 90° and 270°. In contrast, cupulae with pronounced major and minor axes (elongated diamond, robust oval) showed dramatic variation in sensitivity with the highest sensitivity at flow at angles of 90° and 270° (flow perpendicular to major axis) and lowest sensitivity at 0^º and 180° (flow parallel to major axis) (Fig. 3A).

Variation in cupula size.

Neuromast size (diameter of round neuromasts or length of major axis of those neuromasts with unequal major and minor axes) is known to vary by at least an order of magnitude [∼10 µm to 500 µm (9)] among fishes and also increases during ontogeny within a species [e.g., ∼10 µm to 500 µm (9, 22, 24, 28)]. An increase in the size of an elongated diamond-shaped cupula (25 µm to 50 µm to 100 µm) resulted in a decrease in tip displacement following a cubic relationship [tip displacement ∝ (cupula major axis size)³; Fig. 3B]. Similar patterns were found for cupulae with other shapes (robust oval, cross-shaped, round; SI Appendix, Fig. S2).

Canal Neuromasts.

The neuromast shapes found in the narrow canals of fishes [e.g., robust oval (~2:1 length-to-width ratio), elongated oval (~3:1 ratio), elongated diamond] have their major axis oriented parallel to the canal axis (Fig. 1E and SI Appendix, Table S1). Other neuromast shapes (e.g., robust oval, elongated oval, elongated diamond, bar-shaped) are known to occur in widened canals but have their major axis oriented perpendicular to the canal axis (SI Appendix, Table S1). Simulations showed variation among cupulae representing CNs when modeled at the same flow velocity (Fig. 4A). Further, simulations showed variation in sensitivity as a function of the ratio of cupula diameter-to-cupula height (keeping cupula height constant; Fig. 4B) and the effect of canal diameter on sensitivity of cupula of a constant size (Fig. 4C).

Variation in cupula shape and size.

Cupula shapes representing CNs found in widened canals (with major axis perpendicular to flow) have higher sensitivity than the cupula shapes representing those CNs shapes found in narrow canals (with major axis parallel to flow; Fig. 4A). The bar-shaped cupula (tested at 0.1× of the flow velocity used for other cupula shapes due to very large deformation, i.e., potential structural failure at 1 mm s⁻¹) and the elongated diamond-shaped cupula, both found in widened canals (with major axis perpendicular to flow), showed the two highest sensitivities. When cupula diameter-to-height ratio (with constant cupula height) was modeled, sensitivity was shown to decrease for all cupula shapes (Fig. 4B). The highest sensitivities were found in instances when cupula height was 10× that of cupula length (lowest diameter:height ratio), especially for elongated oval, elongated diamond, and bar-shaped cupulae.

Variation in canal diameter.

Canal diameters of 100 µm to 1000 µm (in a minnow, the Ide, Leuciscus idus, and in a perch, the Eurasian Ruffe, Gymnocephalus cernua, respectively) have been reported among adult fishes (29, 42). Simulations for a robust oval cupula with a major axis of 25 µm (fixed at 25 µm above the canal base), height of 250 µm, located in a canal with diameters of 300 µm to 1200 µm and flow parallel to the major axis of the cupula showed that as canal diameter increased, while keeping cupula size constant, sensitivity decreased (Fig. 4C).

Comparison of cupulae representing superficial vs. canal neuromasts.

The maximum sensitivity of cupulae of the same shape and size representing SNs and CNs was compared to understand the effect of hydrodynamic environment on neuromast sensitivity (Fig. 5). Round cupulae and robust oval cupulae showed similar maximum sensitivities when representing SNs (on skin) and CNs (300 µm canal diameter). In contrast, cupulae of the same size and shape (length = 25 µm; height = 250 µm; at flow velocity of 1 mm s⁻¹, except for the bar-shaped cupula that was modeled at 0.1 mm s⁻¹) demonstrated tip displacements that were up to 2 to 3× higher when located within a canal (CN) than when located on the skin (SNs). The difference in sensitivity was greater for elongated oval, elongated diamond, and bar-shaped cupulae when the major axis was oriented perpendicular to the axis of the canal and thus to the direction of water flow within the canal.

Neuromast Sensitivity During Ontogeny.

Ontogenetic trends in neuromast size and shape have only been studied in detail in a few species (22–24, 28). The Brook Trout (Salvelinus fontinalis) provides a good example of how changes in neuromast sensitivity, predicted by known ontogenetic changes in neuromast size and shape [Fig. 6 and (24)], are correlated with ontogenetic transitions in their behavior and ecology. Brook trout larvae reside within gravel nests in streams and have small neuromasts in the skin (round, ∼25 µm diameter) that represent presumptive CNs (that will become enclosed in canals) and SNs (that will remain on the skin throughout life). CNs and SNs will both increase in size to become robust ovals with a major axis of ~50 µm. As “fry” emerge from the gravel and begin to swim in the water column, canal formation begins around the presumptive CNs, which gradually become elongate ovals sitting in open grooves representing partially formed canals. With transformation to the juvenile stage, young trout swimming in the water column experience higher flows. In adult trout swimming in higher-flow streams, smaller robust oval SNs remain on the skin while CNs enclosed in narrow canals are in the form of larger elongated ovals [(24); major axis of ~100 µm]. Our simulations predicted a reduction in sensitivity as presumptive CNs transition from neuromasts on the skin, in grooves, and in canals (Fig. 6).

Discussion

The FSI model used in this study has shown that cupula tip displacement (interpreted as neuromast sensitivity) is defined by the contributions of several morphological and physical factors—cupula shape and size, direction of flow relative to the major axis of the cupula (and thus of the neuromast), and material properties of the cupula. In addition, the relationship of these parameters to hair cell orientation (axis of best physiological sensitivity) and distribution within neuromasts, as known among fishes (but not considered in the model), reveals aspects of unappreciated complexity of structure–function relationships in the neuromasts. Thus, this work predicts functional consequences of important yet unexplored aspects of the evolutionary diversification of the lateral line system of fishes.

Functional Correlates of Neuromast Shape.

Our simulations showed that cupula shape (=neuromast shape) is an important determinant of sensitivity to flows. This can be explained by considering the combined effects of the second moment of area and fluid drag forces on the cupula (Figs. 3A, 4, 5 and SI Appendix, Fig. S3). For instance, the higher sensitivity of cupulae with unequal major and minor axes (oval, elongated diamond, bar-shaped; Figs. 3 and 5) can be attributed to their smaller second moment of area (SI Appendix, Physics of Bending and Fig. S3). The bar-shaped cupula (with the smallest second moment of area among the cupula shapes tested) was the most sensitive of all the shapes tested at a velocity 0.1× that used to model the response of other cupula shapes. The robust oval, elongated oval, and diamond-shaped cupulae (with major axis parallel to flow) and both equilateral diamond and round cupulae, were less sensitive, which can be explained as a result of their higher second moment of area despite higher drag force (SI Appendix, Fig. S3 and S4). The interplay between second moment of area and drag force might seem counterintuitive. However, cupula shapes experiencing higher drag force (round, robust oval, and cross-shaped; SI Appendix, Fig. S4) do not necessarily have higher tip displacements (Figs. 3A, 4A, and 5). In contrast, the high sensitivity exhibited by elongated diamond-shaped cupulae (Fig. 3A) is primarily due to its smaller second moment of area despite lower drag force (SI Appendix, Fig. S4). The ontogenetic transformation of round neuromasts into neuromasts of diverse shapes over developmental time (23, 28), the precocious development of diamond-shaped neuromasts in some larvae [Line Snout Goby (22)], and convergent evolution of neuromast shape (e.g., elongate diamond-shaped neuromasts) among diverse taxa [Fig. 1E, SI Appendix, Table S1 and (22)] all suggest that diversity in neuromast shape is key aspect of the functional evolution of the lateral line system.

Functional Correlates of Neuromast Size.

Our simulations showed that as cupula (neuromast) size increased tip displacement and thus sensitivity decreased (Figs. 3B and 4B). This can be explained as a result of two opposing effects: drag force, which increases linearly with cupula diameter (or length of the major axis) and increases tip displacement and the second moment of area, which scales with the fourth power of cupula diameter and reduces tip displacement (Fig. 2A and SI Appendix, Fig. S3 and Eq. 2). However, other morphological features of neuromasts correlated with their size, which are not considered in our model, likely also contribute to variation in sensitivity to flows. For instance, differences in neuromast size found among species and ontogenetic increases in neuromast size are accompanied by variation in hair cell number (28). A larger number of ciliary bundles projecting into a larger cupula will increase resistance to bending due to its effect on the overall mechanical properties of the cupula and will thus decrease neuromast sensitivity (43). If the number of hair cells within a neuromast were to continue to increase as neuromast size increases, the predicted decrease in sensitivity might impose an upper limit on neuromast size. This may explain why SNs remain quite small in adult fishes [Fig. 1E and (9, 10, 22)]. Furthermore, the model assumed a uniform distribution of hair cells (and thus hair cell bundles) throughout the cupula, which is the condition in the small round neuromasts on the skin of larval fishes (23, 28, 43). However, ontogenetic increases in neuromast size are known to be accompanied by the gradual restriction of hair cells to a central “sensory strip” surrounded by a peripheral population of nonsensory cells that defines overall shape and size of the neuromast and that of the base of the cupula [Fig. 1E and (9, 22, 24, 29)]. If the central and peripheral areas of the cupula differ in stiffness due to the presence and absence of hair cells, respectively, then neuromasts could increase in size without a proportional increase in hair cell number, which might offset the predicted decrease in sensitivity (Figs. 3B and 4B). Thus, we conclude that the occurrence of small SNs, as well as many small SNs in “arrays” (distinct lines, clusters, fields, or grids; e.g., refs. 44 and 21), as opposed to having fewer, larger SNs, is an adaptation for maintaining high sensitivity to environmental flows as well as for the ability to precisely localize the source of spatially restricted and transient flows generated by, for instance, predators, prey, and conspecifics.

Finally, our simulations showed that an increase in cupula height results in higher sensitivity to flows (Fig. 2B and SI Appendix, Eq. 4). This is consistent with the idea that SNs will be more sensitive to flows if their cupulae extend beyond the boundary layer associated with body surface allowing them experience higher drag forces and higher velocities (closer to free flow conditions). Our simulations support the hypothesis that the cupulae in the Mexican blind cavefish (A. mexicanus), which are 10× longer (10× the height) than those in the eyed surface form of this species (31), is an adaptation for increased neuromast sensitivity (for prey detection and navigation) to compensate for the absence of light in their cave habitats (45). The importance of cupula height is also illustrated in the diverse small, bottom-dwelling gobies that are primarily found on coral reefs. These fishes are well known for their proliferations of hundreds to thousands of small, diamond-shaped SNs (22), with long cupulae, and typically arranged in lines, which sit atop finger-like papillae [“sensory papillae,” reviewed in (22)] on the head, trunk, and tail. Our simulations predict that this combination of features would make gobies particularly sensitive to water flows in what are likely structurally complex and hydrodynamically diverse microenvironments, and in addition, that this may have contributed to their evolutionary success.

In addition to the morphological parameters defining variation in the functional attributes of neuromasts, material properties of the cupulae influence sensitivity by determining resistance to bending (SI Appendix, Eq. 4). Our simulations showed that sensitivity of the cupula increased as elastic modulus of the cupula decreases (Fig. 2C and SI Appendix, Fig. S1). Reported variation in the elastic modulus of the cupula of SNs among fishes [e.g., ~21 Pa in the small SNs of larval zebrafish (43), ~8 kPa in the SNs of adult blind cavefish (46)] suggests that variation in this parameter, and perhaps other material properties of the cupula, affect neuromast sensitivity. Finally, our simulations assumed that the cupula was of uniform composition, but evidence of nonuniform composition of cupulae (47), which may affect its overall material properties, may represent yet another mechanism for modulating neuromast sensitivity.

Determinants of Directional Sensitivity of Neuromasts.

Our simulations showed that, in addition to cupula shape and size, the angle of water flows relative to the major axis of a cupula determines the magnitude of cupula displacement, thus predicting variation in neuromast response to flows (Figs. 3 and 4A). This can be explained by a consideration of a cupula’s second moment of area and its projected area (SI Appendix, Fig. S3). For instance, a round cupula has the same second moment of area and projected area in all directions, which explains why it is equally responsive to flows regardless of the angle at which a flow approaches (lack of directional bias; Fig. 3A). Similarly, cross-shaped and equilateral diamond-shaped cupulae, which have two axes of equal length and thus with the same second moment of area and projected area, explains why sensitivity varies relative to those two axes (Fig. 3A). Further, cupulae with distinct major and minor axes (oval, diamond, bar) have more distinct second moments of area and projected areas, which explains the more dramatic variation in sensitivity with angle of flow with respect to the major axis of the cupula (Figs. 3, 4A, and 5).

The planar polarity of the sensory hair cells of neuromasts defined by the placement of the single kinocilium to one side of a group of stereocilia on the apical surface of the cell defines the directional sensitivity of each hair cell. The fact that hair cells are oriented 180^∘ to one another defines the axis of best physiological sensitivity of a neuromast [Fig. 1E and (9, 10)]. This fundamental feature of neuromasts was not considered in our model, but it is clear that a combination of hair cell orientation and neuromast shape ultimately determines the response of neuromasts to flow stimuli approaching at different angles. Our simulations showed that the cupula representing round neuromasts (like those in larval fishes, including zebrafish) shows similar responses (no directional bias) in their response to flows approaching from different angles (Fig. 3A). Thus, in these neuromasts, only hair cell orientation will determine directional sensitivity. In contrast, in cross-shaped or equilateral diamond neuromasts, hair cell orientation is parallel to one of the two equal axes of the neuromast (Fig. 1E). Our simulations showed that sensitivity varies with angle of flow in these cupulae (Fig. 3A), thus demonstrating that directional sensitivity is determined by cupula shape in addition to hair cell orientation.

In neuromasts with distinct major and minor axes (robust and elongated oval, elongated diamond-shaped, and bar-shaped neuromasts; Fig. 1) hair cell orientation is known to be either parallel or perpendicular to the neuromast’s major axis (22–24, 28). Our simulations showed that when flow is parallel to both the major axis of the neuromast and hair cell orientation [e.g., in the oval SNs of Brook Trout (24)] sensitivity will be at a minimum (Figs. 3A, 4A and 5), and that when a flow is perpendicular to the major axis of the neuromast and parallel to the axis of best physiological sensitivity of the hair cells [e.g., elongate diamond-shaped SNs of gobies (22)] neuromast sensitivity is at a maximum (Figs. 3A, 4A and 5). This shows how a combination of hair cell orientation and neuromast morphology can illustrate adaptive evolution in the lateral line system—reducing sensitivity for avoiding overstimulation in fast-flowing rivers and streams in Brook Trout (and likely in other salmonid fishes) and enhancing sensitivity among a wide range of taxonomically diverse fishes living in ecological and hydrodynamically diverse marine and freshwater habitats [e.g., gobies, cardinalfishes, tetras, plainfin midshipman; SI Appendix, Table S1 (9, 22)].

Canal vs. Superficial Neuromasts.

The functional predictions derived from our simulations are consistent with well-established correlations between general features of lateral line morphology and fish behavior and ecology. For instance, relatively few, small SNs and narrow canals (with small CNs) tend to be found in fishes that are active swimmers and/or those that tend to occur in higher flow conditions [e.g., salmonid fishes including Brook Trout (22)]. In contrast, high numbers of SNs tend to occur in fishes that live in hydrodynamically quiet environments [e.g., deep sea stomatiiform fishes (44)] as do widened canals (with large CNs), representing two instances of convergent evolution for higher sensitivity to flows among fishes in a small number of fish families living in midwater (including in the deep sea) or in association with the benthos (9–11, 48). However, the dramatic proliferation of diamond-shaped SNs found in gobies, diminutive but diverse bottom-associated fishes found primarily on coral reefs (and thus likely in complex hydrodynamic microenvironments) cannot yet be explained (22).

Superficial and canal neuromasts (SNs, CNs) comprise two distinct submodalities within the lateral line system (13, 14, 16, 17) that are defined by the distinct hydrodynamic microenvironments in which they function (on skin, in canals) and the components of hydrodynamic stimuli to which they respond (velocity and acceleration, respectively). Thus, we would expect that evolutionary trends for SNs and CNs are guided by different selective pressures as they relate to detection of different types of hydrodynamic stimuli (re: velocity, frequency, prevailing versus transient and spatially restricted stimuli) arising from different sources. Our simulations predict that sensitivity of SNs is highest when they are small (Fig. 3B and SI Appendix, Fig. S2), but that the relatively lower flow velocity within the boundary layer at the surface of the fish’s skin [(19, 49–52); Fig. 2A and SI Appendix, Fig. S5A] will reduce their ability to respond to flows (Fig. 2A). While SNs tend to be round (e.g., in fish larvae), those that are oval or diamond-shaped (22, 24) would be more sensitive to flows, particularly flows that are perpendicular to the long axis of the neuromast, thus defining higher capacity for directional sensitivity (Fig. 3A).

The sensitivity of CNs, like that of SNs, is a product of neuromast size and shape, as well as the alignment of the long axis of the neuromast relative to the canal axis, and their placement within narrow or widened canals. However, unlike SNs whose hair cell orientation may vary depending on its location on the body, in CNs hair cell orientation is always parallel to the canal axis regardless of location and CN shape (Fig. 1E) thus ensuring maximum sensitivity to the movement of water along the canal axis (generated by pressure gradients between pores parallel to the canal axis). In contrast to SNs, which may have long cupulae, the height of the cupulae of CNs is limited by canal diameter (Fig. 1 and SI Appendix, Fig. S5B). These factors would predict that CN sensitivity is lower than that of SNs of the same shape and orientation to flow (Figs. 2B and 3A). In addition, CNs are typically larger than SNs within a species (12, 24, 29, 53, 54), which would also predict lower sensitivity (Figs. 3B and 4B). However, our simulations reveal that CN sensitivity is higher than for SNs of the same size and shape (Fig. 5). This can be explained by the flow conditions within the canal where the boundary layer is associated with the internal surface of the canal (SI Appendix, Fig. S5B) and flow velocity is closest to free-stream velocity near the center of the canal (SI Appendix, Fig. S5B and S6 A and D). Thus, the maximum velocity encountered by CNs may be higher than that experienced by SNs whose cupulae may be entirely within the boundary layer on the skin (SI Appendix, Fig. S5A). However, the relationship between cupula height and canal diameter (and thus the position of the cupula tip relative to the region of highest velocity within the canal) in fishes is not understood. In addition, our simulations showed that the sensitivity of CNs is higher for those shapes found in widened canals compared to those in narrow canals (Fig. 4A). This can be explained by the orientation of the major axis of the CN parallel to the canal axis in narrow canals [Figs. 1E and 4A; e.g., Brook Trout (24); Mottled Sculpin (16, 17); and a cichlid, Tramitichromis sp. (23)], whereas the orientation of the major axis of the CN is perpendicular to the canal axis in widened canals [e.g., in a species shown to feed on benthic invertebrates using its lateral line system, Flavescent Peacock Cichlid (23, 48)]. The sensitivity of CNs found in narrow canals is a result of the higher resistance to bending (stiffness) of the cupula along the axis of the canal. This would result in the ability to detect higher-velocity and higher-frequency flow stimuli and an increase in the resonance frequency of CNs (correlated with the square root of the second moment of area of the neuromast). In contrast, widened canals have a lower internal flow velocity than narrow canals (SI Appendix, Fig. S6A), suggesting that modifications in the structure and function of CNs in widened canals to enhance sensitivity would be required if CNs are to be responsive to these low velocity flows.

However, our simulations showed that CNs become less sensitive as canal diameter increases (Fig. 4C) corroborating a prior computational study (24). CNs in widened canals tend to be larger than those in narrow canals [Fig. 1E and (55)], which would predict lower sensitivity (Fig. 4B), but the orientation of their major axis perpendicular to the canal axis [Figs. 1E and 4A and (23, 32, 33)], and the restriction of hair cells to a central “sensory strip” (Fig. 1E) are factors that are predicted to enhance their sensitivity to flows. Furthermore, the long axis of CNs in widened canals (perpendicular to the canal axis) is correlated with canal diameter among species and as canal diameter increases during development (9, 10, 29), which would increase the probability of cupula displacement. In combination, these factors would not only increase sensitivity (17, 32) but would lower the resonance frequency of stimuli to which they best respond.

Bar-shaped neuromasts (Fig. 1E) are rare, having only been described in the widened canals of two minnows [Zebrafish (28); Silverjaw Minnow (56)] and in a perch [the Rhone Streber, Aspro zingel (57)]. Their high sensitivity to flows predicted by our simulations (even at 0.1× the velocity used for other cupula shapes; Figs. 4A and 5 and SI Appendix, Fig. S1) can be explained as a product of two factors: long axis placed perpendicular to the canal axis, and their shape, with a very high aspect ratio (long axis: short axis), (Figs. 4A and 5 and SI Appendix, Fig. S3 and Eq. 4). In addition, hair cell orientation in these neuromasts is perpendicular to the long axis of the neuromast [Fig. 1E and (28, 56)], which would further enhance sensitivity. These neuromasts are known to occur only within canals on the head (as CNs), and not on the skin [as SNs; Fig. 1E and (28, 56)], likely because of the probability of overstimulation if exposed on the skin’s surface. However, sensitivity is likely reduced because hair cells are distributed throughout the neuromast [not limited to a central sensory strip as in other neuromasts; Fig. 1E and (28)], which would increase cupula stiffness (15). These unusual neuromasts had been hypothesized to be an adaptation for detection of benthic prey in the Silverjaw Minnow [(56); like the large diamond-shaped CNs in the widened canals in some cichlids (48)], but this was not borne out in behavioral experiments.

Structure–Function Relationships in Neuromasts During Fish Development.

A large number of studies have examined the role of the lateral line system (and the other senses) in the behavior of larval fishes (e.g., refs. 4, 9, 15, 18, 35, 43, and 56–61), but the morphological attributes of neuromasts had not been considered with respect to their contribution to the functional ontogeny of the lateral line system. Our simulations predict that the changes in neuromast size and shape that have been observed in developing fishes (e.g., refs. 9, 22, 23, 28, and 24) will result in dynamic changes in overall neuromast sensitivity and enhanced capacity for directional sensitivity. Larval neuromasts (in the skin) are small and typically round [Fig. 1 and (22, 24, 28)], two factors that predict higher and lower sensitivity, respectively (Fig. 3 A and B), but as they increase in size and add hair cells (28) it is predicted that they would experience a decrease in sensitivity (Figs. 3B and 6 and SI Appendix, Fig. S2). However, the reduction in sensitivity predicted to occur with an increase in neuromast size would likely be moderated by the gradual restriction of hair cells to a central sensory strip (22–24), which is predicted to alter the overall material properties of the cupula (15).

During the larval period, the two submodalities of the lateral line system also become distinct. Neuromasts that will remain on the skin throughout life (SNs) increase somewhat in size (22–24, 28), but ontogenetic changes in shape, for instance, round to robust oval to elongate oval [with hair cell orientation parallel to the long axis of the neuromast; brook trout (24); Fig. 6] or round to diamond-shaped [with hair cell orientation perpendicular to the long axis of the neuromast; line snout goby (22)], would affect sensitivity and enhance directional sensitivity to flows (Fig. 3A). At metamorphosis (the larval-to-juvenile transformation) a subset of neuromasts, presumptive CNs, are gradually enclosed in bony canals (9) thus changing the hydrodynamic microenvironments in which they function (62). However, CNs may continue to increase in size and change shape (9, 22–24, 28) altering their overall sensitivity beyond that defined by just hair cell orientation (Figs. 3, 4 A and B, 5, and 6 and SI Appendix, Fig. S2). As CNs are enclosed in canals, they become responsive to the acceleration component of flows (Fig. 7C and SI Appendix, Fig. S6 and S7C). In addition, canals may diverge in morphology, becoming either narrow or widened (Figs. 4 A and C and 5), a feature that will further affect CN sensitivity (see above). These morphological changes occur as transforming fishes move from a larval habitat (typically the water column) to a juvenile habitat (in the water column or in association with the benthos and/or complex 3-D features, such as a reef) with an increase in swimming capabilities [e.g., Brook Trout (24)] further challenging the neuromasts’ ability to interpret biologically significant hydrodynamic stimuli. Thus, a complex combination of temporal changes in multiple parameters defining neuromast morphology, the hydrodynamic environment in which fishes live, and behavior will influence the ability of neuromasts to respond to flows during the life history of fishes.

Fig. 7.

Flow parameters for all simulations. (A) Schematic of a cupula showing major axis (d), minor axis (b), and height (h). (B) Simulation of cupula representing a superficial neuromast: Cupula (major axis = 25 µm, height = 250 µm) is placed in the center of a large cubical channel (1500 ⨯ 1500 ⨯ 1500 µm) and fixed to the base of the channel to establish open flow boundary conditions. Inlet (Left face of channel) has fully developed flow (u_max = 1 mm s⁻¹) and outlet (Right face) has pressure = 0. The cupula surface has a no-slip boundary condition, and channel walls have zero-velocity boundary condition. The water domain is represented by Ω_water, and the cupula domain is represented by Ω_cupula. (C) Simulation of cupula representing a canal neuromast: Cupula is fixed at 25 µm above the base of the canal between two adjacent canal pores, in the roof of cylindrical canal. (D) Enlarged view of control volume [maroon section in (C)] between the two pores with cupula height approximating channel diameter. Flow inlet and outlet are defined as the Left and Right ends of the canal section. Flow boundary conditions are implemented as in (B) with flow along the canal axis. Details on flow, fluid, and cupula properties are the same for superficial (B) and canal (D) neuromasts.

Adaptive Evolution in the Lateral Line System and Inspirations for Biomechanics.

The computational approach used in this study reveals quantifiable structure–function relationships at the level of an individual neuromast that can explain an important, but heretofore unexplored, aspect of the functional evolution of the lateral line system in fishes. The results of this study will stimulate additional modeling efforts that broaden the range of morphological and physiological parameters examined and will suggest the species that should be used for future experimental work in both comparative and developmental contexts. Further, individual neuromasts do not function in isolation [Discussion in (22)], so future studies will need to consider how series of CNs (within canals) and lines and more complex arrays of SNs (on skin) function in concert in response to biologically relevant unidirectional and oscillatory flows, and how flow information is communicated and processed in the peripheral and central nervous systems resulting in the formulation of critical behaviors. Finally, the functional consequences of defined features of neuromast morphology revealed in this study will provide insights for the design of highly sensitive, durable, and efficient biomimetic sensors and robotic devices capable of precisely detecting the dynamics of minute fluid flows in underwater environments. The simulations presented here also reveal the importance of acknowledging the balance between sensitivity and structural resilience (material properties of sensors) necessary for detecting flows under varying hydrodynamic conditions (e.g., for underwater exploration and pipeline monitoring). The synergy between biological discovery and technological innovation illustrated in our study exemplifies the transformative potential of biomimetics, bridging the gap between sensory biology and engineering.

Materials and Methods

We developed FSI model based on finite element method using Computational Multiphysics Service/Solutions Organization for Linked/Laboratory Simulation. Multiphysics v6.1 to investigate the relationship between structure (shape, size) and function (cupula displacement in response to flow) in the neuromast receptor organs of the lateral line system of fishes (Fig. 7; See also SI Appendix, Details of Modeling Methods). The model simulates fully coupled FSI for micrometer-sized neuromasts resulting in flows within the laminar regime (Re < 1; SI Appendix, Reynolds Number). Unless noted otherwise, simulations modeled a cupula with a major axis of 25 µm and height of 250 µm. A cupula height of 250 µm, which is within the range of a small number of reported values [e.g., 150 µm in Zebrafish (43), 200 µm in Brook Trout (24), 300 µm in Blind Cavefish (31)]. Cupulae were modeled at a steady flow, initially in open flow (SNs) with velocities ranging from 1 to 11 mm s⁻¹ [(61) and Fig. 2A]. At velocities greater than 2 mm s⁻¹, simulations failed for the most sensitive shapes due to large cupula tip displacements (Fig. 2A), so a flow velocity of 1 mm s⁻¹ was used for simulations except for the bar-shaped cupula (modeled at 0.1 mm s⁻¹). An elastic modulus of 21 Pa to >100 kPa had been reported for cupulae (12, 31, 43, 46, 47, 63). Elastic modulus values up to 500 kPa were used to test the effect of elastic modulus on cupula bending (Fig. 2C and SI Appendix, Fig. S1). Values <100 Pa led to very large cupula tip displacement, indicating the possibility of structural failure, so an elastic modulus of 100 kPa was used for all simulations.

The bending response of cupulae of neuromasts of different shapes known to occur among fishes (round, oval, diamond, cross, and bar-shaped cupula (Fig. 1D) was modeled. It is known that the base of the cupula covers the entire surface of a neuromast so that cupula shape can serve as a proxy for neuromast shape in considerations of structure–function relationships. The cupula shapes modeled are based on neuromast shapes found among fishes (Fig. 1 D and E and SI Appendix, Table S1). Published data on neuromast shape and size are from some of the most species-rich fish taxa (minnows, tetras, cichlids, gobies), which collectively represent 29% of all species of bony fishes; SI Appendix, Table S1). Thus, the range of simple geometric shapes currently known among neuromasts (and used herein) is likely to represent the range of neuromast shapes found among bony fishes more generally. The magnitude of the bending of a cupula in flow reflects the bending of the sensory hair cell bundles within the neuromast (64–66); thus, cupula tip displacement was used as a measure of neuromast sensitivity. The model assumed uniformity in the composition and material properties of the cupula and uniform distribution of sensory hair cells in the neuromast (and thus the uniform distribution of ciliary bundles within the cupula), simple hydrodynamic conditions in which neuromast function (unidirectional flow) and the functioning of individual neuromasts in isolation. These assumptions simplified the model so that the sensory response of a neuromast (sensitivity) is predominantly governed by fluid drag force that leads to the mechanical bending of neuromast cupula, akin to a cantilever beam fixed at one end (43). Superficial and canal neuromasts were modeled with specific boundary conditions to closely replicate the natural conditions under which they function [Fig. 7 B–D and (9, 10, 26, 33, 43)]. Future extensions of this model can enhance its predictive power by identifying additional synergies among variables and by incorporating additional sources of variation of biological relevance, including viscoelastic and history-dependent cupula material behavior, frequency-dependent flow responses across the biologically relevant range (0 to 200 Hz), more realistic hydrodynamic environments (including turbulence), and the response properties of multiple neuromasts arranged in biologically relevant patterns.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

All parameters and variables used in simulations are defined in the text and/or in SI Appendix. Simulations were run using commercially available software – COMSOL (version 6.1; https://www.comsol.com/comsol-multiphysics) (67).