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Downloaded by guest on October 1, 2021 www.pnas.org/cgi/doi/10.1073/pnas.1815655116 system a nervous a Smith L. lacking Carolyn ciliated in a modeled , toward movement directed Coherent iea lsi cfodhligbligclstgte.Arecent A together. cells pro- bolding can they holding contractile, scaffold are elastic cells epithelia an fiber ventral cells vide not and or dorsal fiber Whether the elongated 1). between (Fig. to a attributed in residing have (16) some that movements in identified 14), been (15). have 13, its in or (1, found connexins no connexins been and have or microscopy junctions and innexins gap no of direction but composed by particular coupled junctions of electrically any cells are gap beat- epithelial in and ciliated of , The aligned direction Ctenophores, orientations. the variable not dictate have are could which cilia, (9–12), its ing of axonemes its the on cells epithelial the of 1). proportion (Fig. surface large ventral a for 8 account ref. that (see the of part are 1). which Fig. of and two but all another one by types, to joined relative cells cells the of of (7). comprised positions epithelium the fix an that by junctions bounded is it (6), multicellular primitive differ- in a behavior need introduces - any modeling and an without . to cells food that approach move- between of demonstrates ent signaling search actual model in chemical the coherently The for resemble move movements animal. that can coordinated the mal shape produces of body and ments in viscoelas- cells changes for each chemoattractant of and values cells, a realistic properties epithelial incorporates to tic to ciliated model responding of model The set mathematical and gradient. a a from sensing of arise present independently actions could We movements collective it agar. ran- directional the that of coherent, in here disk how show moves explain a We embed- animal in food. toward ded of The preferentially contact absence moving stroke. chemotaxis, cilia the transiently exhibits in The each and directions gliding. with dom asynchronously, propel surface but the lower regularly, epithelium. 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Thomas by Contributed City, Aut Nacional Universidad ilmtr ndaee u only but diameter Bilate- many in plus millimeters earlier that diverged (Cnidaria have thought the (1–5). are the Placozoa, to and Porifera sister ria). the be of to member consider a is It T migration directed ainlIsiueo erlgclDsresadSrk,Ntoa ntttso elh ehsa D20892; MD Bethesda, Health, of Institutes National Stroke, and Disorders Neurological of Institute National Trichoplax Since Trichoplax utfrfo ept akn uce ranrossystem. nervous a or muscles lacking despite food for hunt animal ciliated small, he Trichoplax Trichoplax | Trichoplax uaytcchemotaxis eukaryotic ldsoe ufcs rple ymnclae cells monociliated by propelled surfaces, over glides loudrosaobi-iecagsi shape, in changes amoeboid-like undergoes also a oai fsmer n nysxietfidcell identified six only and symmetry of axis no has sruhyds-hpdi uln,u oseveral to up outline, in disk-shaped roughly is a,1,2 a ld naydrcin eifrthat infer we direction, any in glide can hmsS Reese S. Thomas , nm eM de onoma ´ sasal iitdmrn nmlthat animal marine ciliated small, a is | rcolxadhaerens Trichoplax oeetmotion coherent xc,050Mxc iy eio and Mexico; City, Mexico 04510 exico, ´ ∼ 20 hc.Lk l all Like thick. µm a,1,2 Trichoplax zp Govezensky Tzipe , | multicellularity oooe to locomotes yelectron by | c nttt eF de Instituto b,1 oeetmvmn ftewoeaia n iet tt food? to it directs produces and directions animal whole random the in of beat movement to coherent able a are that cilia sessing despite pref- them them. algae upon near of feeding remain from clump and blocked small algae being that a the containing toward discovery agar move of our erentially bed by a on motivated placed was (21), work food find present to chemotaxis on rely and metazoa, to fungi and tists, behavior. ulse nieArl1,2019. 12, April online Published 1073/pnas.1815655116/-/DCSupplemental. y at online information supporting contains article 2 1 BY-NC-ND) (CC 4.0 NoDerivatives License distributed under is article access open This interest.y of conflict no declare authors The endocytosed is 20). algae (7, lysed cells and epithelial the 18 overlying from (ref. the lipophil released cells by the ciliated Material cell, the 1). secretory among Fig. of interspersed type is second which be digested (18), a are could from Algae on surface. that feeds lower it by the while (19) underneath minutes lying several algae for the place a initiated, in is pause remains 1) a animal Once (Fig. the algae. cell epithelium detect to the gland used and in chemosensory Each cell by of initiated 19). type is Pausing (18, which a (18). beating, from abundant ciliary secreted are of algae arrest they where by algae, accompanied containing is in dish feed a to in pause placed being Upon microalgae. eiwr:EM,TeUiest fCiao n ... eitWt University. Heriot-Watt K.J.P., and Chicago; of University R.A.B. paper. The y and the E.M., wrote T.G., Reviewers: R.A.B. T.S.R., and T.S.R., performed C.L.S., C.L.S., R.A.B. tools; and and reagents/analytic ; analyzed C.L.S. new research; contributed designed R.A.B. R.A.B. research; and C.L.S. contributions: Author sheet. are elastic epithelium dynamic dorsal a as the behave of and cells contractile that demonstrates (17) report n aalA Barrio A. Rafael and , owo orsodnemyb drse.Eal [email protected] rtreese@ or [email protected] Email: addressed. mbl.edu. be may correspondence work.y whom this To to equally contributed R.A.B and T.G., T.S.R., C.L.S., n oaceotrcatgain u osrie ytheir by animal. constrained the in but cells gradient other to chemoattractant attachments a of to respond- actions independently ing each collective cells, ciliated from oriented arise randomly could how movement explain to directional do model mathematical oriented, cilia a randomly present its that and be show chemotaxis that We may epithelia. assume most and in we polarity cilia unlike so uniform direction, a feed- any have not in substrates cilia. move on beating can glides asynchronously cell It by It six propelled only microalgae, system. the on has nervous ing It of no today. those and on to types animals similar many of be ancestor could lifestyle and Trichoplax Significance hsbhvo assteqeto fhwa ra fclspos- cells of array an how of question the raises behavior This pro- , from complexity in ranging organisms, Many Trichoplax Trichoplax y sc,UiesddNcoa Aut Nacional Universidad ´ ısica, sads-hpdmrn nmlwoebd plan body whose animal marine disk-shaped a is a emitie ntelbrtr nade of diet a on laboratory the in maintained be can PNAS a eotdt oetwr lcn 2) The (22). glycine toward move to reported was | pi 0 2019 30, April c,1 b nttt eIvsiainsBiom Investigaciones de Instituto . y raieCmosAttribution-NonCommercial- Commons Creative | nm eM de onoma ´ o.116 vol. www.pnas.org/lookup/suppl/doi:10. oi S1 Movie Trichoplax | xc,000Mexico 01000 exico, ´ o 18 no. lutae this illustrates edicas, | ´ Trichoplax exhibits 8901–8908 y

BIOPHYSICS AND COMPUTATIONAL mals that were placed or wandered closer to the algae moved preferentially toward it. Thirty-seven out of 40 animals that came within 5 mm of the algae centroid eventually migrated over the algae. Upon reaching the algae, the animals typically remained nearby for the duration of the experiment. Only 1 of the 37 animals that migrated over the algae later moved >5 mm away. Representative trajectories for six of nine animals that were tracked as they migrated onto the algae are illustrated in Fig. 2A. A change in the behavior of the animals as they came into the vicinity of the algae is apparent. The trajectories are mean- dering and frequently change directions while the animals are distant from the algae (pink, blue, red, and aqua tracks). When the centroids of the animals move within 5 mm of the algae, segments of the tracks that are directed toward the clump of algae are longer than segments directed elsewhere. Only one animal (green) that approached within 3 mm of the algae centroid subsequently moved >5 mm away. This animal later reversed direction to reach the algae. Plots of the distances between the centroids of animals and the algae over show that four of the six animals (pink, blue, read, and teal) move faster and more persistently toward the algae than in other directions Fig. 2B. The meandering trajectories of the ani- mals as they approach the algae are characteristic of a type of Fig. 1. cell types in Trichoplax. Facing the substrate (below) is a thick chemotaxis sometimes referred to as stochastic chemotaxis or ventral plate composed of epithelial cells (VEC) (light green), each - “chemokinesis,” to differentiate it from another type of chemo- ing a cilium and multiple microvilli; lipophil cells (brick) packed with large taxis in which the moves directly toward the attractant secretory granules containing digestive ; and gland cells (green), distinguished by their contents of small secretory granules and prevalence (21, 30, 31). near the rim. Dorsal epithelial cells (DEC) (tan) form a roof across the top of The preferential movement of the animals toward the algae the animal. Fiber cells lying between the dorsal and ventral epithelia have suggests that the algae emit a chemical that attracts the animals. long branching processes that contact the other cell types. A crystal cell (pale The algae were alive, so we can assume that they continuously blue) containing a birefringent crystal lies under the dorsal epithelium near emit the attractant. We expect that the drops off the rim. Reproduced from ref. 8. Copyright (2014), with permission from steeply with distance because in agar is rapid (D = Elsevier. (8.8 ± 1.2) × 10−6 cm2/s), as obtained by measuring diffusion of a fluorescent in 1.7% agar.

There has been an increased interest in studying collective Model of Coherent Motion Originated by Random Propulsions. Our motion arising from random self-driven since the sem- aim is to build a model that is able to explain the emer- inal work of Vicsek et al. (23), which modeled swarms of gence of coherent motion from random propulsions without living individuals and tissues. This model is appropriate for having a regulatory system that choreographs the motion of swimming particles that align their velocities by hydrodynamic thousands of individual cells. This coherent behavior should interactions (24). There are also models that do not impose emerge from simple physical and chemical interactions among alignment explicitly, collective motion arising from either inelas- cells. We assume that the physical interactions can be described tic collisions (25), short range radial forces (26), or active as forces acting on each individual cell. Therefore, the basic elastic membrane spring-like interactions (27). In these mod- Newtonian equations of motion that each ciliated cell i els, collective coherent motion appears as a first- phase obeys are transition with the amount of disorder, or a jamming phase transition with increased density (28). The numerous models of locomotion developed for swimming ciliated and metazoans (see ref. 29) proved to be inadequate to explain locomotion of Trichoplax, since this animal does not swim but crawls. These models evoke hydrodynamic interactions between cilia to explain the metachronous beating of the cilia. Trichoplax cilia beat asynchronously and generate propulsion by pulling on the substrate. Hydrodynamic interactions are unlikely to come into play. Here, we take appropriate ele- ments of these models to build a model that provides a simple physical explanation of directional chemotactic gliding in Tri- choplax, based only on the known properties of its cellular components.

Results Fig. 2. Movements of Trichoplax in the presence of a focal food source. (A) Trichoplax Chemotax Toward Algae. We looked for evidence of Snapshot from Movie S2 showing positions of the animals after 8 h, when most of them had congregated near the algae. Colored tracks represent chemotactic behavior by observing the movements of animals the trajectories of six animals. The segments of the trajectories represent placed on the surface of a bed of agar overlaying a small (3- distances moved by the centroid of the animal over 2-min intervals. (B) Dis- mm) clump of algae (Movie S2). Animals that were placed tances of centroids of animals to algae for the six tracks illustrated in A >5 mm from the center of the clump of algae moved in versus the time spent reacting to the chemoattractant. Data points were random directions with respect to the algae. However, ani- measured at 10-s intervals.

8902 | www.pnas.org/cgi/doi/10.1073/pnas.1815655116 Smith et al. Downloaded by guest on October 1, 2021 Downloaded by guest on October 1, 2021 ~ mt tal. et Smith te hntenihos eosreta h oslepithelium dorsal the that observe We neighbors. the than other random linearly increases a that of area trajectory an visits the time. in animal follow whole would the system so walker, the center the of However, mass together. of walkers random the holding sion, andnmclqatt,wihi h oa eoiyo h cell the of velocity the total of the value the is changes v which and not quantity, stroke, continuously, dynamical ciliary acting is a main field is this there that when clear only cells is ventral It the Appendix animal. among the (SI interactions of fluid circle circular the random a simulates a a in field with produce This inscribed starting to size, points able same of is the collection alone (33, of cells force dissipation isotropic this for of that system account seen to field, is elastic term It abovementioned 34). friction the additional impose an we with which in the A.2) defines tion that point the cell of the of position mass the cilium. of center with the coincide of assuming should position by the possible, as equilibrium, equilibrium 2D) in in an that circular to or (spherical cells isotropic the as of 2D) in one value (area first volume The terms. the two collec- restores is containing which the coordinates, potential, the during “elastic” in restored an quadratic define be we should Therefore, motion. that produce tive shape to and able size is given springs. which with 27, masses of ref. sheet in the of used translations model steady would the This cilia. to exactly the be defining be would points field of neigh- elastic pairs of this among motion describe springs the attach to to way due easiest cells The the cells. of bor restore shape to and tends size that in potential changes elastic an imposes together joined where aigfo h odsuc htbae t oeeti the in movement F its biases ema- chemoattractant that a food. source the of food two to direction the in able model from is a cell nating build ciliated to assume each we us Furthermore, that cells. allows which ciliated This ventral cells, their the plane. ciliated for through dimensions the a of forces in motions situated these the and are in of shapes cells the effects other on the influence to consider connections We indirect animal. and direct both from labeled is cell each A.1 of section dynamics ciliary the the to of contribution strokes the displace- The mean time. and with quadratic walk, linearly a increasing random with ment a diffuse, would be the cells neighbors, would of their cells collection to the connected of not were motion cells displacement individual the small If a cell. produces the beating, adher- of and comes when surface which, force the cilium, driving to its the ing of that movement the and cell from direction ciliated exclusively arbitrary each an that assumes substrate in model beats the Our reg- (18). contacting beat beat each transiently cilia during asynchronously, the but that indicate ularly observations Microscopic cilia. (m mass same the have cells consider all that assume we Since cell of velocity ~ (i t hr r diinleatcitrcin oigfo cells from coming interactions elastic additional are There sec- Appendix , (SI tessellation Voronoi a define we this, do To a have that cells with dealing are we case, our in However, nsm ae,tefrecudb eie rmasaa field scalar a from derived be could force the cases, some In arising forces to subject are also cells ciliated the However, the by originated propulsion the is force obvious most The (i , t = ) hsfil rvnsteices fvlm u odiffu- to due volume of increase the prevents field This ). A ~ r 0 −∇V (i h eodoersoe h hp fteclst be to cells the of shape the restores one second The . m , ). t 1 = ) (i and i ihu oso generality. of loss without o xml,tefc httevnrlclsare cells ventral the that fact the example, For ). and , ~ v (i m F ~ , i t d t d (i ~ r ) ~ v dt ) (i dt (i r h ntnaeu oiinand position instantaneous the are stettlfreatn nec cell. each on acting force total the is , , t t ) ) = = ~ v F ~ (i t , (i t , ), t ), ~ v 1 IAppendix, (SI i i.S2). Fig. , = m ,we ), [1b] [1a] r 0 hsdpnso he aaees aeytesrn constant spring the called namely is parameters, interaction k three this to on to contribution depends due The cell This the A.3). of animal of section mass the dynamics of of Appendix , the radius center the (SI to the equilibrium congruent value from in given cells a that to cells these animal peripheral of the the There- distance on epithelium. acting the ventral field restores elastic the an to define of connects we edge fore, it the the around where cells, force animal epithelial restoring to the a dorsal Due exert the can epithelium. of epithelium ventral dorsal dorsal contractility the the and in elasticity of movements fiber cells the cells contractile of some that their independently for (17) that occur but shown except contractile been animal con- are has no the epithelium has It in epithelium processes. dorsal cells cell the edge other of the with rest around the epithelium nections but ventral animal, the the to of connected plane a is sarsl,teei opnn ftevlct fec cell B call each section us sensitivity of Let chemotaxis velocity the chemoattractant. the to of of gradient the component component this of a direction is the there fixed. in considered result, be can a and that As sub- appreciably food this change the not of fact around does profile stance concentration moving the chemo- the is of model chemoattractant, animal advantage we the the emits taking this, time chemotaxis way, of the about possible view during that simplest In known the cells. is in attached little taxis of very group a bacteria, in and cells otic relative the called namely, is interaction model, this interaction the contribution of this to The strength of parameter size. another cells given adds the a This of of coher- region dynamics a a the produce in to to cells is is of This effect motion ). A.4 whose radius ent section model, certain Appendix , Vicsek (SI a cell so-called each within the of cells mass fiber of the aver- the center by of the of rule velocities this effect simu- extending the The by be aging only. modeled can being rule its fish is simple of connections or cell this velocity average imposing of the by swarms copy lated of to motion tries The cell neighbors. each cells. produce that dorsal) considered effect already (and have the ventral we that distant interactions connect elastic The which cells, fiber the coefficient yaia ucini Eq. in function dynamical Simulation. iceiigtetm,ta is, that time, the discretizing chemotaxis. Finally, of cells. effect fiber the to and due interactions animal, elastic the produce of and edge membrane the elastic on an as act cells epithelial where h nmlrahstefo n orsm etn fe h food the after beating resume to and when food beating the ciliary reaches stop animal to the mechanism a include must model our ti osbet eemn that determine so to of observations, possible speed experimental is the it the that matches so animal chosen is simulated time the of for unit 0.05 The and simulations. 0.01 puter between value a where p h qiiru aiso h animal the of radius equilibrium the , h qain fmto ol eitgae ueial by numerically integrated be could motion of equations The ommctelcmtradfeigbhvo fteanimal, the of behavior feeding and locomotor the mimic To lhuhceoai sawdsra hnmnni eukary- in phenomenon widespread a is chemotaxis Although to due present is interaction range medium another Finally, ealddsrpino h oe sgvnin given is model the of description detailed A ~ v 1 ~ v ). ersnsterno oino h iim h dorsal the cilium, the of motion random the represents (i κ h oa iedpnetvlct,wihi h main the is which velocity, time-dependent total The , p t . = ) ~ v ~ v ~ r 4 (i (i ~ v (i 1 , , PNAS , (i t t t + + , h tegho hstr sproportional is term this of strength The ). t δ δ + ) t t | = ) a hsb rte as written be thus can 1b, = ) k ~ pi 0 2019 30, April v s 2 n ti called is it and χ, . ~ v ~ r (i δ (i ~ v (i , t 3 t , = , rssfo h medium-range the from arises + ) t t + ) + ) 6s. 26 ~ v F 3 ~ ~ v (i | (i (i δ , , o.116 vol. t , t R t t + ) a sdi l com- all in used was )δ )δ n h damping the and , t t A ~ , v , ~ v 4 f IAppendix. SI 4 (i | IAppendix, (SI ersn the represent , o 18 no. t ), ~ v ~ v 2 ~ v d 2 3 acting | (i (i from 8903 , . [2] [3] [4] t t ). ).

BIOPHYSICS AND COMPUTATIONAL BIOLOGY is consumed. Arrest of ciliary beating is thought to be elicited of chemoattractant is small and the random motion dominates. by a secreted from gland cells upon detection of algae However, a nonzero v4 slowly directs the cells toward regions (19). For simplicity, our model excludes the gland cells and con- with increasing concentration until a point is reached at which siders only the ciliated cells, which we postulate cease beating the chemotaxis dominates over the random propulsion. The autonomously at a specific distance from food. behavior predicted by the model is complicated because the The gland cells of the animal are symmetrically situated model is nonlinear and the action of very different phenomena around the center of mass. Therefore, at each time step, we test that contribute to the final motion. the distance between the center of mass and any food source, and The sensitivity analysis performed in SI Appendix, section C if this distance is sufficiently small (we choose R/4), we stop the showed that the system is robust against changing parameter motion of the cilium and diminish gradually the amplitude of the values in a wide range (in the sense that the model produces food source until it is consumed. Then, we resume the normal qualitatively the same behavior). Once the elastic and geomet- motion. rical parameters have been adjusted to mimic the real animal, With these ingredients at , we integrate the equations of the behavior changes when varying the Vicsek radius and the motion and are able to mimic the chemotactic movements of ani- chemotactic sensitivity. mals toward algae. We show an example calculation in Movie S3. The parameters used for the simulation are depicted in Table 1. Experimental Validation of the Model Compare Movie S3 to Movie S1, which shows a single Trichoplax Our model predicts that the animal moves toward the food in gliding and feeding on algae. meandering trajectories that approach the source in a similar The values shown in Table 1 are in arbitrary computer units. way as the observed animals. To quantify this similitude, we have Several experimental movies (see, for example, Movies S1 and examined the data to produce scatter plots of the dependence S2) were used to investigate the correspondence of computer of the component of the velocity along the vector R~cf (t) that units of distance and velocity to the ones measured experimen- links the center of mass of the animal to the position of the food, tally. A computer unit distance corresponds to 25 µm, and a time as a function of the distance from the food source. Notice that unit is 26 s. The elastic module of the was esti- R~cf (t) changes with time; thus, the velocity component in the mated to be of the order of 10 MPa (32, 35), which corresponds ~ ~ Rcf (t)·S(t) direction of the food is vL = , where S~ (t) =~rcm (t + to 80 computer units for the elastic constants. |Rcf (t)| In Fig. 3A, we show the results from theoretical simulations ∆t) −~rcm (t). We examined eight different experimental - of the motion of the animal in the presence of a single food surements and eight randomly selected theoretical simulations. source. In Fig. 3B, we plot the distance from the centroid of the In both kinds of data, one notices that, on average, the velocity animal to the food source. Note that chemotaxis is not direct- component in the direction of the food is larger than in the oppo- ing the animal straight to the food source; there are hesitations site direction, and, in general, it increases when approaching the and turns, just as in real animals (compare with Fig. 2; also see food source. Movies S1 and S2). The continual changes in the relative posi- In Fig. 4 we compare the experimental measurements (red) tions of the cilia suggests the flow of a liquid material, similar to with the theoretical results (blue). The data have been smoothed the flowing motions of particles in the interior of the real ani- to produce clearer scatter plots. mal (Movie S1). The model also recapitulates to some extent In Fig. 4A, we show the results when the animals are around the deformations of the outline of the animal while moving, the food source (between 1 and ∼9 mm). Notice that the ani- although the magnitude of the deformations are larger in the mals show acceleration when approaching the food source and real animal, where contractile cells may participate in changing a sudden deceleration when they are very near. In Fig. 4B, we its shape. show the same scatter plot for animals far from the food source The very interesting sharp transition in Fig. 3B from random (between 6 and 18 mm). Notice that the behavior of both sets of motion to a direct approach to the food, as observed in real data is very similar, partially validating the model. animals, is a feature that arises from the competition between The calculations in SI Appendix, section C demonstrate the the strength of the chemotactic term and the random propul- importance of medium-range forces in the model. The elastic sion of the cilia. When far from the source, the concentration constants of the model should also be important. In SI Appendix, Fig. S4B, we show two ways of changing shape of the animal: (i) as the elastic constants (or the Viscek strength ks ) increase, Table 1. Values of the parameters the shape becomes less circular; and (ii) as the Viscek radius Variable name Value increases, the shape index becomes larger (more circular shape). The combined result of these dependencies is that when the ani- Animal parameters Radius R 10 mal is more circular, its velocity is smaller for the same value of Number of cells N 1,000 the chemotactic parameter (SI Appendix, Fig. S5). Cell area A 0.7528 0 An indirect way to test these predictions experimentally is Elastic constants to monitor the motion of the animal at different temperatures Dorsal membrane Bulk k 50 p of the . Thermorheological experiments (36) using laser Friction coefficient κ 10 p beams to heat a section of a microchannel, while measuring Cell relaxation Area restoring k 50 a the instantaneous deformations of a single living breast epithe- Centroid restoring k 50 c lial cell, demonstrate that heat softens the cellular instantaneous Friction coefficient κ 10 rearrangements of the cytoskeleton. The long-term response or Fiber cells Strength k 67.6 s adaptation, which has to do with the changes in viscosity of Viscek radius d 15 × d min the intracellular medium, was also investigated by performing experiments at various temperatures of the water. Both experi- L × L L 8R ments imply that the mechanical response of the cell stiffens in Food landscape Number of Gaussians n 1 cold water. Amplitude A 2+0.8(ζ –0.5) m We have performed experiments studying the shape index of Width σ 4R + Rζ(1, n) m animals moving in water at different temperatures. The shape Feeding parameter Food strength A 1.5 f index is the ratio between the area of the animal and the area of

All are kept fixed in the simulations, except d and Af . a circle with the same perimeter.

8904 | www.pnas.org/cgi/doi/10.1073/pnas.1815655116 Smith et al. 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N . β A α f x h ooso h uvsmatch curves the of colors The A. Γ(α) α orsodt oeskewed more to correspond −1 e −β rvre n1 s), 10 in traversed µm x Trichoplax , Trichoplax ntepres- the in ihthe with α α α 1 = ∼ 1 = 1 = 1.6, [5] . .8 92 .8 eia rjcoisitrutdb nemtettrs Directional along turns. forward intermittent swim by interrupted trajectories Ciliated helical swim. studies that from primarily cells comes of cells mechanisms ciliated cellular of chemotaxis the for about used Information 37–39). elementary 30, most (21, taxis the obey that food rules finding few and a for of physics. searching result being the in to intelligent are appear variations animal but an by model of and the animal those of move- local the movements be fluid-like allow of The outline. the interior but body the in group its in manifest cohesive cells are of a that ments they as constraints bearing move which These in to cells. with deviations intervening cells cells via the other and compel from directly arising linked forces are cells elastic of neighboring with movements by junctions The their and by chemoattractant. constrained are the to cells postulated the to the each respond from cells, and arises ciliated sense movement individual of directed directed motion this model, collective explains our that cells In its movement. of properties model known physical on a develop based and algae from emanating gradient tant that show We future in behavior Discussion of enough changes with predict model to the in able experiments. used be quantities to elastic precision of value the C etydrce oadtetre u nta sis as for meanders, mechanisms stochastic instead persis- use that but not chemotaxis. organisms is target and cells trajectory the of Its typical toward target. are directed its cells cells from tently other the animal with that interactions the fact their deviates the by and synchronized partially cells only ciliated move- random individual the of but food, ments to it directs mechanism chemotactic which in way the reproduces h vrg au o ohtebu n e ice szr,adteei no is there and zero, since is important, circles not red and is blue fact the trend. case This both particular each for difficult. in value is range average distance comparison the the and because wildly necessary is varies This interval. (0,1) the fo o1 m.Tedsac nti aewsnraie ntefol- the in normalized was case this in distance data The experimental mm). way: and 18 lowing negative to theoretical the as 6 the Same than (from of (B) abundant similar. averages very more the are much that Observe are mm. and 1 The velocities length values, velocities. positive of positive distance negative averaged the of averaged the intervals that the eight are in are taken lines lines were continuous averages dashed red the theoret- and and red the blue The velocities, ones data. blue The numerical the results. and and ical measurements, experimental experimental of the set are whole circles the of velocity value The source mum source. food the the from near distance chemotaxing the of function a 4. Fig. ayekroi el,icuigclae el,ehbtchemo- exhibit cells, ciliated including cells, eukaryotic Many utemr,tesniiiyaayi in analysis sensitivity the Furthermore, closely model the that conclude to us allow comparisons These ftese ieadtesaeidxalwdtriainof determination allow index shape the and size step the of cte lto h eoiycmoettwr h od(v food the toward component velocity the of plot Scatter (A) δ (n) = Trichoplax (max(δ PNAS ) − δ A oe rfrnilyu chemoattrac- a up preferentially moves | )/(max(δ hnteaiasaei h itn range distant the in are animals the when pi 0 2019 30, April Trichoplax ) − min(d v L a omlzdt h maxi- the to normalized was oe oadfo.The food. toward moves | ) oboth so )); δ o.116 vol. = section Appendix, SI |R cf | o ih animals eight for | |v o 18 no. L | and δ | r in are 8905 L as )

BIOPHYSICS AND COMPUTATIONAL BIOLOGY because they are the closest (45). Choanoflagellates have a single cilium surrounded by a collar of microvilli, some- what similar to the ciliated epithelial cells of Trichoplax. The choanoflagellate cilium beats in an undulatory waveform draw- ing water currents into the microvillar collar, to capture bacteria, and propelling swimming (46). The colonial forms consist of clus- ters of fewer than 50 cells, each with its cilium directed outward. The cilia of cells in colonies beat asynchronously and propel the animal along meandering trajectories typical of random walkers (47). Colonial organisms that use this form of locomotion have been referred to as aggregate random walkers, an apt descrip- tion of Trichoplax. Directed movement of both unicellular and colonial choanoflagellates in an gradient, aerotaxis, has been reported (31). Analysis of the navigation strategy showed that it is of the stochastic type and achieved by modulating the angle of turns with respect to the direction of the gradi- ent. The trajectories of the colonies are highly erratic and do not exhibit the striking persistence in the direction up the gra- dient that is evident in both Trichoplax and our model animal. This persistent movement is a property that emerges from the combined interactions between cells choreographed and medi- Fig. 5. The shape index of the animal as a function of the velocity at three ated by the cell junctions and the fiber cell connections. This different temperatures of the water (squares). Shape index as a function produces the effect that correlations are extended over larger of the velocity using the three values for the Vicsek radius indicated in the distances, so the correlation length due to elastic interactions legend in units of the minimum distance between cilia (stars). increases. The mechanism we propose for directed ciliary gliding in Tri- choplax probably could not work in animals much larger than a motion in a chemotactic gradient depends on mechanisms to few millimeters in diameter, because of the fact that the medium- modulate ciliary beating as a function of the strength of the range interactions needed to produce a swarm behavior have . Small ciliated cells typically use a stochastic navigation an upper limit imposed by the actual value of the elastic mod- strategy, such as modulating the frequency of turns. Some larger uli of the materials being bonded and by the mass that needs to cells, such as , are able to adjust their helical paths so as to be moved. As we enlarge the animal, the number of cilia scales steer more persistently up the gradient (37, 38, 40, 41). with the surface while the mass scales with the volume. There- Our model assumes that the ciliated cells sense and respond fore, there is a point at which there is not sufficient propulsion to to the chemoattractant gradient but does not depend on any move the mass. particular chemotactic mechanism. In fact our model, as it is, predicts that in the absence of any chemotactic signal, the animal acquires a coherent motion, but it is not directed to a particular target (Movie S7). As a result, the center of mass moves ran- domly in a diffusive way, just like the real animal when it is far from algae or in an isotropic environment (42). However, the real animals also engage in additional behaviors not manifested by our model animal. For example, they occasionally pause even when no food is present. These spontaneous pauses are similar in duration to pauses that occur during feeding or in response to exogenous peptide (19), so we suspect that they are elicited by peptide secreted from gland cells, but why might occur in the apparent absence of any sensory stimulus remains unknown. In addition, the animals sometimes stop migrating and rotate in place. Our model can be expanded to predict rotation under circumstances of enhanced traction of cilia around the rim and preferential beating in the tangential direction. We do not include these calculations in the present work because it remains to be seen what mechanisms exist in Trichoplax for regulating traction or beat direction of cilia. Multicellularity has evolved multiple times in . Well-known examples are the volvocine algae, organisms that exist in both solitary and colonial forms. Their cells are biflagel- late, and, in solitary cells, the flagella beat in a breast-stroke like motion to propel the cell forward. Colonies are spheroid with the cells arranged such that the effective strokes of the flagella push the in the same direction (43). Hydrodynamic cou- pling causes the flagella to beat in metachronous waves (44). The uniform beat direction and metachrony of the flagella of colonial volvocine algae contrasts with asynchronous and variable beat directions of cilia in Trichoplax. Fig. 6. Comparison of the probability distributions of steps for 10 exper- Choanoflagellates also exist in solitary and colonial forms and imental and 10 theoretical trajectories. (A) Probability histogram. (B) are particularly relevant with regard to the of Metazoa Cumulative probability comparison using the same parameters.

8906 | www.pnas.org/cgi/doi/10.1073/pnas.1815655116 Smith et al. Downloaded by guest on October 1, 2021 Downloaded by guest on October 1, 2021 3 re R(99 ndra a ucin:Srcue ucinadevolution. and function Structure, in junctions: gap structures Cnidarian axonemal (1989) CR of Green rotation without 13. reversal Ciliary (1981) S Tamm SL, Tamm 12. 5 rvsaaM ta.(08 The (2008) al. et M, alternative. Srivastava pannexin –The 15. junction gap of Evolution (2005) Y Panchin 14. flagella. and cilia of the movement and The proven (1962) The beating: MA ciliary Sleigh and 11. Flagellar (2010) KA Lesich CB, Lindemann 10. itfo e us aeUiest,NwHvn T were CT, Haven, New University, Yale Buss, with Leo dishes culture from in maintained gift a adhaerens, T. Methods and by Materials lifestyle this it acquired so had placozoans, already time. extant that they sustains that that plausible by food covered seems was the bottom mats, sea the microbial when survival to times, well-suited Precambrian appear plan. during feeding body that of mode present evidence and their lifestyle phylum acquired Their no long the placozoans is when of very there reveal but origin a could , the for the place survive in analyses Placozoa to clock Placozoa Molecular it the primitive, time. enabled appears and food has coupled toward evidently mech- movement are colonial this directed While they a for other. each because anism resemble to connections only closely their by together indepen- more constrained work behave could that and cells it dently self-propelled which of gut- composed in ancestor a attention way calls into work a present epithelium Our to ventral feeding. to of the dedicated cells and like of signaling, arrangement peptidergic enzymes, orderly digestive by secrete communication that cells intracellular and cells neurosecretory of similarities many the emphasized trajectory has between metazoans 51). 52–55) (50, evolutionary 19, complex systems (8, digestive work the internal Recent to and nervous in ancestor and muscles stage with choanoflagellate-like intermediate a an from at of mal origin the before ner- possible a muscles. not and and was large muscles of probably Evolution uses gliding. animals of animal gliding direction The the control axis. to direction system that uniform vous a well-defined to in a respect beat has cilia with organism the the and of, axis, aware anterior–posterior are such all we In bilaterians 49). that larger (48, examples molluscs some some as and (flatworms) well Platyhelminthes as as Cnidaria, some of larvae mt tal. et Smith agarose melting-point con- low were in algae Algae suspended assays, Micro chemotaxis and 1% in centrifugation use with by For ) centrated Farms). (Instant Aqua (ASW) (Florida of seawater Grow Cultures artificial (18)]. al. in et tained [Smith previously described as .GbosI 16)Terltosi ewe h n tutr n ieto fbeat of direction the and structure of fine plan the body between and relationship The cells, (1961) neurosecretory IR types, cell 9. Novel (2014) al. et CL, epithelial Smith between diffusion 8. modulate junctions Adherens (2016) TS the Reese metazoans. CL, of and Smith novelty evolutionary signal, 7. an Error, Epithelia, (2012) (2015) A Riesgo KM SP, Leys Halanych 6. LL, Moroz KM, Kocot sister the NV, as placement Whelan their and 5. relationships Ctenophore (2017) its al. and et NV, leidyi supports Whelan dataset phylogenomic 4. consistent ctenophore and large the A (2017) of al. et genome P, Simion The 3. (2013) al. et JF, neural Ryan of origins evolutionary 2. the and genome ctenophore The (2014) al. et LL, Moroz 1. Trichoplax the as such small many by used is gliding Ciliary Systems Nervous First the of plates. comb ckenophone Biology: Applied 127–169. and pp 12, Pure Vol on Oxford), Monographs (Pergamon, of Series International Flagella, Biol possible. mollusc. lamellibranch a of cilia gill in adhaerens. Trichoplax it metazoan early-diverging in cells Evol Dev animals. Mol B other all to sister 112:5773–5778. Ctenophora of placement animals. other all to group animals. other all to group sister the as evolution. type cell for implications systems. 208:1415–1419. rcolxadhaerens. Trichoplax 454:955–960. Nature Trichoplax elSci Cell J a encniee ersnaieo nani- an of representative a considered been has 318:438–447. 510:109–114. 123:519–528. n ope eaon,sc spossession as such metazoans, complex and elBiol Cell J a clEvol Ecol Nat Srne,Bso) p3–20. pp Boston), (Springer, ilBull Biol Trichoplax hdmnssalina Rhodomonas Science 89:495–509. ipy ice Cytol Biochem Biophys J 231:216–224. urBiol Curr 1:1737–1746. 342:1242592. eoeadtentr fplacozoans. of nature the and genome 27:958–967. urBiol Curr h ilg fClaand Cilia of Biology The rcNt cdSiUSA Sci Acad Natl Proc safo source food a as algae 24:1565–1572. . R. 11:179–205. eemain- were x Zool Exp J Evolution Exp J 9 awleY aawm ,RoM ih A(04 hooyo active- Tetrahymena. of of Rheology behaviour Chemosensory (2004) (1992) P RA Hellung-Larsen V, Simha Leick M, 30. S, Ramaswamy at Y, particles soft Hatwalne Self-propelled jamming: 29. Active (2011) MC Marchetti Y, Fily S, Henkes the 28. for mechanism Elasticity-based (2013) C Huepe M, Dorigo AE, Target E, Ferrante to 27. due and filaments migration swarm active agent Szab of of Emergence 26. (2008) EB Jacob IS, Autonomous Aranson D, (2012) Grossman al. 25. et G, Jayaraman 24. (2014) Czir R T, Wyeth Vicsek J, Kranyak 23. S, Goodall R, Croll of A, Heyland epithelium (1973) 22. ventral ed A, The Perez-Miravete (1986) 21. R Wahl G, in Behrendt behavior of A, integration Ruthmann Neuropeptidergic (2017) 20. CL Smith TS, Reese A, in Senatore behavior feeding 19. Coordinated (2015) TS Reese N, Pivovarova CL, Smith 18. contractions epithelial Ultrafast (2018) M Prakash AJ, Aranda-Diaz MS, Bull S, Armon 17. Placozoa. (1991) A Ruthmann KG, Grell 16. (∼ ih n hnteds a oddwt Lo gr(.%i S)a 37– at ASW) in Petri (1.7% glass agar 50-mm of mL a 4 of with center flooded the was 40 in dish placed the then was and disk dish, A diameter. in mm ∼3 a upre yteItaua eerhPormo h I,National NIH, the of Program Stroke. work and Research This Disorders Intramural Neurological 283279. of the Project Institute through by Conacyt, supported acknowl- del and from was Asuntos Mexico, Personal support de de del financial Autonoma R.A.B. Superacion General Nacional edges la manuscript. Universidad Direccion para la the from de Apoyos Academico on grant de Shahid Programa sabbatical comments Academico, Zimmerberg, a helpful Personal Joshua for for grateful and Maini is imaging Philip and time-lapse Khan, with assistance for request. ACKNOWLEDGMENTS. upon available is model the for code source with The simulations data, experimental the the sim- for for the 0.59) 0.54) (0.49, (0.50, for of interval 1.96) confidence (1.69, 99% the data, within experimental the with for ulations 1.99) (1.85, of parameter interval The SAS. ware Microscopy). Zeiss (Carl images 5× Fluorescence a agar. diffusion with in observing captured embedded were Biotium) by 633; estimated (CF was dye fluorescent agar of low-molecular- 1.7% sequences of the within diffusion image of substances of from rate The weight outline constructed minute. per the were frames with two movies to fused resampled and Tracks animal Figures animals. the pellet. other pro- of algae the contacting outline because animals the that analysis track when Animals for terminated accurately algae. selected not the were could from animals far gram other remained onto contact that migrated not nine that did and animals Analysis nine pellet Image track Volocity algae to (19). the used previously was described (PerkinElmer) behavior software of coordina- many in type which moving a in and two tion, pausing excluded intermittently ani- together, the and clustered of other them lasting most each of which ani- experiments from in of separate experiments seven remained five behavior from analysis mals The for movies selected images. We time-lapse Canon collect h. in 14–28 with and examined camera equipped was the Camera mals control Digital to MP 1–5× used f/2.8 22.3 was mm III 5 Mark 6 5D MP-E with Canon captured were low-intensity a minute) a per provide on frames (six to 18 placed recordings at Time-lapse set was controller. maintained dish Imaging) was temperature The mL Light The pellet. 10 (Northern illumination. algae with box 20 the filled light to from and precision distances Thirteen hours varying use. 1–2 at before for dish ASW temperature fresh room at of kept was dish ttsia nlsso rbblt itiuin a aeuigtesoft- the using made was distributions probability of analysis Statistical 14:61–66. suspensions. density. model high A interactions: springlike swarms. artificial with and natural particles for self-propelled system of motion collective model. and Experiment collisions. inelastic through formation vortex breaking. flow-symmetry spontaneous particles. self-driven of system a in transition potential. with metazoan enigmatic phology adhaerens synapses. without animal an adhaerens, Trichoplax synapses. without animal an integrity. tissue and limits USA speed contraction into insights provide 13–27. pp York), New (Wiley-Liss, Westfall FW, Harrison 10 ◦ .Atrteaa oldadsldfid 0m fAWwsadd The added. was ASW of mL 10 solidified, and cooled agar the After C. 5 ,e l 20)Paetasto ntecletv irto ftsu cells: tissue of migration collective the in transition Phase (2006) al. et B, o 115:E10333–E10341. ´ cells/10 106:115–122. Paoo) yokltlsrcue,cl otcsadendocytosis. and contacts cell structures, Cytoskeletal (Placozoa): hsRvLett Rev Phys N hsRvE Rev Phys kA e-ao ,ChnI hce 19)Nvltp fphase of type Novel (1995) O Shochet I, Cohen E, Ben-Jacob A, ok ´ ) oiie grcnann la a lcdit disks into sliced was algae containing agar Solidified µL). = 6,ad(.8 .)for 2.2) (1.88, and 560, PNAS hsRvE Rev Phys etakTtaaMyrv n onChludzinski John and Mayorova Tatiana thank We 84:040301. .5N betv naLM0cnoa microscope confocal LSM10 a on objective NA 0.25 92:118101. ar ht es O tlt .34. software 2.13.40.2 Utility EOS . Photo Macro eaiu fMicro-organisms of Behaviour LSOne PLoS α | efudwswti h 9 confidence 99% the within was found we pi 0 2019 30, April 74:061908. 10:e0136098. hsRvLett Rev Phys N hsRvLett Rev Phys eds Invertebrates, of Microscopic = ehd o Biol Mol Methods 6,ad(.5 .4 for 0.54) (0.45, and 560, hsRvLett Rev Phys e Phys J New N Trichoplax ,0.Teparameter The 5,000. = x Biol Exp J | 109:158302. o.116 vol. 111:268302. 10:023036. ◦ 75:1226–1229. Srne,Boston). (Springer, an adhaerens, Trichoplax ihatemperature a with C 1128:45–61. eepae nthe in placed were 220:3381–3390. | rcNt cdSci Acad Natl Proc o 18 no. N Trichoplax, Trichoplax 5,000. = Bioessays Zoomor- | β 8907 was

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