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BioSystems 109 (2012) 367– 380

Contents lists available at SciVerse ScienceDirect

BioSystems

journa l h o me pa g e: www.elsev ier .com/ locate /b iosystems

tructural evidence for electromagnetic resonance in plant morphogenesis

lexis Mari Pietak ∗

ept. of Anatomy, University of Otago, Dunedin, New Zealand

r t i c l e i n f o

rticle history:eceived 16 November 2011eceived in revised form 13 January 2012ccepted 13 January 2012

eywords:ioelectromagnetismiological pattern formationlant morphogenesis

a b s t r a c t

How a homogeneous collective of cells consistently and precisely establishes long-range tissue patternsremains a question of active research. This work explores the hypothesis of plant organs as resonatorsfor electromagnetic radiation. Long-range structural patterns in the developing ovaries and male flowerbuds of cucurbit plants (zucchini, acorn, and butternut squash), in addition to mature cucurbit fruits(acorn, butternut, and zucchini squash; watermelon, and cucumber), were investigated. A finite elementanalysis (FEA) model was used to determine resonant EM modes for models with similar geometric andelectrical parameters to those of developing organs. Main features of the developing ovaries (i.e. shapeof placental lines, ovum location, definition of distinct tissue regions), male flower buds (i.e. early pollen

ielectric resonator tube features), and mature fruits (i.e. septa placement, seed location, endocarp and mesocarp) showeddistinct correlations with electric and magnetic field components of electromagnetic resonant modes.On account of shared pattern signatures in developing organs and the EM resonant modes supported bya modelled structure with similar geometric and electrical properties to those of cucurbit organs, exper-imental investigations are warranted. The concept of a developing organ as an EM dielectric resonatormay extend to a variety of morphogenetic phenomena in a number of living systems.

. Introduction

From the conventional view of modern biology, nearly everyingle aspect of development is seen as the consequence of molec-lar signals produced by, and often capable of further influencing,enetic expression. From this perspective, developmental phenom-na are assumed to ultimately be co-ordinated by molecular signalsmorphogens/hormones) produced by selective activation of cer-ain genes in certain cells at certain times in the developmentalrocess. For instance, in plant development various aspects ofelon fruit formation, from the sexual expression of flowers to

ruit ripening, are the consequence of tissue exposure to genet-cally regulated ethylene (Papadopoulou et al., 2005). Similarly,oloured stripes on the outside of some squash are the result of dif-erential expression of gene-regulated pigments in the rind (Paris,008). In plants, the five major hormone groups are the auxins,ytokinins, gibberellins, abscisic acid, and ethylene, all of whichre regulated by genes and evoke a variety of different physiolog-cal responses in target tissues from initiation of primordia, organevelopment, maturation, and senescence (Gaspar et al., 2003;

zga and Reinecke, 2003).

It is well established that molecular signals play essential rolesn development. However, in both plant and animal development

∗ Current address: 2345 Hughes Rd, Kingston, Ontario, Canada.E-mail address: alexis.pietak@gmail.com

303-2647/$ – see front matter © 2012 Elsevier Ireland Ltd. All rights reserved.oi:10.1016/j.biosystems.2012.01.009

© 2012 Elsevier Ireland Ltd. All rights reserved.

there remains little understanding of how these substances can besynthesized, transported, and act at the specific locations and timesnecessary to bring about intricate and even mathematically precisebiological patterns from a homogeneous primordium (Beloussov,2008; Ozga and Reinecke, 2003). In plant development, intricateand even mathematically precise structures are evident in leafvascular networks (Pietak, 2009), the arrangements of leaves orbranches on a stem (Jean, 1996), and as is explored here, in thearrangement of tissue in a developing ovary or flower bud. Whilethe form of these structures remains undoubtedly influenced bymolecular signals resulting from genetic expression, the mecha-nisms behind long-range pattern emergence from a homogeneousprimordium remain an unsolved problem (Lander, 2007).

Various systems-focused answers have been proposed toaccount for the manifestation of long-range spatial organizationin plant and animal development, and in reality a variety of dif-ferent mechanisms may be simultaneously involved. Mechanismsfor generating chemical patterns via differential diffusion of mor-phogenic chemicals, their inhibitors, and their interaction withgenetic expression have been put forth (Koch and Meinhardt, 1994;Meinhardt, 1996). Other studies suggest cellular collectives canrespond to mechanical stress fields generated in a growing embryo(Beloussov, 2008). A radically alternative perspective sees a devel-

oping organ as a dynamic system self-trapping electromagneticenergy in a stable spatial pattern capable of informing phenomenasuch as cell polarization, orientation, genetic expression, and dif-ferentiation state. In other words, a trapped electromagnetic field

3 tems 109 (2012) 367– 380

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Fig. 1. Developing ovaries of female flower buds begin as simple geometric shapes.

68 A.M. Pietak / BioSys

erves as a fundamental symmetry-breaking mechanism informingarly morphogenetic events and processes.

Electromagnetism (EM) refers to the phenomenon of oscillat-ng, coupled electric and magnetic fields which can propagate as a

ave with amplitude, frequency, and wavelength. The frequencyf the EM wave is related to its energy and instils it with differentroperties and interactions with materials. Lower frequency EMaves are used for radio broadcasts (∼106 Hz), intermediate-range

requencies heat food in the microwave (∼109 Hz), higher frequen-ies represent visual light (∼1015 Hz), and the highest correspondo ionizing radiation such as X- and gamma-rays (∼1019 Hz).

The prospect of endogenous EM production by biological sys-ems, in a range from 1011 to 1012 Hz, was first developed byhysicist Herbert Fröhlich in 1968 (Fröhlich, 1968a,b, 1975). Moreecently, quantum field theory (QFT) has been used to furtherlucidate the possibility of endogenous radiation in biological sys-ems (Del Giudice et al., 1985, 2010; Preparata, 1995). Recentxplorations using normal mode analysis of simulated microtubuletructures have determined microtubules to be a likely source ofndogenous EM up to several hundred gigahertz (Cifra et al., 2011b;eriu et al., 2010). Microtubule vibrations may be stimulated byydrolysis of GTP, motor protein–microtubule interactions, andnergy efflux from mitochondria (Cifra et al., 2011b).

In addition, a number of experiments have directly detectedon-thermal radiation in radio (Cifra et al., 2008; Pokorny et al.,001), microwave (Gebbie and Miller, 1997), and visible-UV (Poppnd Yan, 2002; Yan et al., 2005) frequencies from various organ-sms. Other experiments have shown cells and organisms respondn various distinct ways to externally applied non-ionizing radi-tion at powers low enough to avoid heating the tissue (Cifrat al., 2011a; Levin, 2003, 2009). In plants, applied low-power EMadiation in the range of 108–109 Hz results in changes to genexpression, aberrant meristem formation, altered patterns of cel-ular growth, and enhanced growth of the organism (Racuciu and

iclaus, 2007; Roux et al., 2008; Tafforeau et al., 2003; Tkalec et al.,009). In a variety of plants, static electric fields have also beenetected, and observed to be correlated to growth events and dailyhythms (Burr, 1942, 1945; Burr and Sinnott, 1944; Leach, 1987).o the author’s knowledge, plant emissions of, or responses to, EMadiation in the range of 200–1000 GHz have not yet been explored.

On account of their physical make-up, developing plant organsay act as dielectric resonators, trapping EM energy in a spatial

attern. A dielectric is a material with molecules that become polar-zed (assume an electric charge separation) when the material islaced in an applied electric (static) or EM (time varying) field. Thiseans the dielectric can support an internal electric field due to the

reation of electric dipoles, and can thereby store energy as a capac-tance. A dielectric resonator describes a dielectric that has trappedn EM wave in a characteristic spatial pattern (Staelin et al., 1994a;ang and Zaki, 2007). This happens as when an EM wave travel-

ing within a stronger dielectric medium hits an interface with aaterial of lower dielectric strength, some reflection of the inci-

ent EM wave occurs at the interface (Staelin et al., 1994b). Withinhe stronger dielectric’s interior, the incident and reflected wavesnterfere with one another. Depending on the geometry of theielectric material and wavelength of the EM wave in the dielectric,ertain patterns of radiation appear due to the superposition of inci-ent and reflected waves off of internal boundaries. These highlyharacteristic spatial patterns are called the resonant modes of theielectric structure, and occur only at specific frequencies of EMadiation. The resonant modes are quasi-standing wave patternslternating in time between purely electric and purely magnetic

eld components (Wang and Zaki, 2007). If exposed to an elec-romagnetic source comprised of many frequencies the dielectricesonator acts as a filter, selecting only resonant frequencies fromhe broadband signal (Wang and Zaki, 2007).

Panel A shows the cylindrical shape of the developing zucchini ovary. Panel B showsthe ellipsoidal shape of the developing acorn squash ovary. Black scale bar in imagesshows 1 cm.

Non-ideal dielectric resonators lose energy with time. Elec-tromagnetic energy may be lost due to leaking of fields fromincomplete reflection off of internal boundaries. The lower themismatch between the dielectric constant of the strong dielectricmaterial and the dielectric constant of its surroundings, the lowerthe internal reflection, and the more leakage occurs due to EM fieldtransmission across the boundary. Electromagnetic energy is alsodissipated in lossy dielectrics due to conversion of EM energy intoheat with delocalization and flow of charge carriers within the res-onator. The quality factor (Q-factor) is the ratio of energy stored tothe energy dissipated per oscillatory cycle. The Q-factor indicateshow well the material will resonate. In general, Q-factors less than0.5 will not support resonances and Q-factors greater than 0.5 will.The higher the Q-factor the longer a resonance will be supportedafter an initial energy input.

On account of its water content in the range of 85–96 wt%, adeveloping plant organ such as a zucchini ovary (Fig. 1A) is a rela-tively symmetric, cylindrically shaped organ expected to be a ratherstrong dielectric with an εr of approximately 40 at a frequencyof 20 GHz (Nelson and Trabelsi, 2005; Sipahioglu and Barringer,2003). Likewise, the acorn squash ovary and immature fruit havehigh water contents and an ellipsoidal geometry (Fig. 1B). Similarly,the developing early flower bud also has an ellipsoidal geometry(not shown). As a developing plant organ is surrounded by weaklydielectric air (εr = 1), any radiation produced within the organ, atfrequencies high enough to generate wavelengths smaller than theorgan diameter, would reflect from the internal air–tissue interface,leading to the formation of an EM resonant mode characteristic ofa similarly shaped (ellipsoidal or cylindrical) dielectric. Of course,a strong dielectric loss is also expected for EM radiation in waterytissue for the applicable frequency range of 109–1012 Hz (Gabrieland Lau, 1996; Liebe et al., 1991). These loss characteristics must beaccounted for in any model assessing the feasibility of the hypoth-esis of plants as EM resonators.

As a well-defined geometric structure existing distinguishedfrom the remaining flower anatomy from an early developmen-tal stage, the cucurbit ovary is a particularly straightforward casefor considering EM mode formation in plant development. Changes

in the ovary cross-section from the primordial (embryonic) stagethrough to maturity are outlined in Fig. 2. The cucurbit ovary pri-mordium appears as a distinguished structure from the flower (i.e.the petals, stigma, and style) early in development when flower

A.M. Pietak / BioSystems 109 (2012) 367– 380 369

Fig. 2. Stages of tissue pattern development in the cucurbit ovary. Panel A shows a cucurbit ovary primordium cross-section exhibiting a homogeneous cell collective with noovert signs of tissue pattern formation (ovary radius 0.6 mm). Panel B shows very early spiral pattern formation in a cucurbit ovary primordium consisting of early placentall s 0.70o et frui(

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ine formation with single cells composing main features of the pattern (ovary radiuf ovum formation and multicellular pattern (radius 1.2 mm). Panel D shows the sradius of fruit 20 mm). Scale-bar in images shows 250 �m.

rimordia measure approximately 0.3 mm in length (Pereira,968). The ovary continues to develop below the remaining flowertructures as an inferior ovary, and if pollinated, develops directlynto the mature fruit. When the ovary primordium first appears, andntil reaching a cross-sectional radius of approximately 0.6 mm,here is no discernable pattern within the cellular collectiveFig. 2A). However, shortly after this stage (i.e. cross-sectionaladius ∼ 0.7 mm) the symmetry of the collective is broken with theppearance of three axes with spiral-like structures of opposingurl existing at the periphery (Fig. 2B). As the ovary primordiumontinues to develop, these structures become more pronouncedhile conserving their initial form (Fig. 2C). The spiral-axes become

ines of placental tissue, while the geometric centre of the spiralsecomes the site of ova formation. The ova go on to become theeeds of the mature fruit. Remarkably, the essential nature of theriginal pattern found in the ovary primordium appears to remainonserved in the set fruit, which is approximately 200 times largerhan the primordium from which it arose (Fig. 2D).

While EM resonances may exist at any developmental stage, thisork focuses on the dimensions of the form at the time of the first

ymmetry-breaking (i.e. cucurbit ovary primordia dimensions onhe order of ∼0.5 mm radius). In development, cells proceed alongarious pathways of differentiation to become more and more spe-ialized. The main role of an EM resonance is thus hypothesized toreate positional information for undifferentiated cells to respondo, in order to create spatial patterns of different tissue types. Onceifferentiated, cells may no longer respond to EM fields in the sameay.

In this work the resonant frequencies and spatial patterns of EM-odes forming on dielectric structures with similar geometries,

imensions, dielectric permittivities, and dielectric loss tangentso developing plant ovaries and flower buds were estimated using

finite element analysis (FEA) model. Electromagnetic finite ele-ent analysis is a preeminent numerical method for finding

pproximate solutions to full-wave Maxwell’s equations on a three-imensional geometry and material of interest (Jin, 2002). Theesulting FEA-modelled EM resonant mode patterns were compre-ensively compared to tissue patterns in developing ovaries, maleower buds, and a variety of mature fruits. The Q-factors of EModes forming on models with similar permittivity and loss char-

cteristics to those of watery tissue were used as a gauge of thehysical feasibility of EM resonance in developing plant organs.

. Theory

In order to effectively model plant tissue in FEA, realistic val-es for the passive electrical properties (dielectric permittivitynd loss) were required over a large frequency range from 1 to000 GHz.

mm). Panel C shows intermediate ovary primordium development with initiationt which has largely conserved the pattern initiated in the early ovary primordium

In the time-dependent case of an applied EM field, the rela-tive electric permittivity becomes a complex number, ε∗

r , with realcomponent ε′

r reflecting the energy storage due to electrical polar-ization, and imaginary component ε′′

r reflecting the energy loss dueto movement of polarizable charges in phase with the electric field(i2 = −1):

ε∗r = ε′

r + iε′′r (1)

Under time-varying applied fields of frequency v, the sample’scapacitance (C) and conductivity (�) are measured to define theparameters ε′

r and ε′′r where (Pethig and Kell, 1987):

ε′r(v) ∝ C(v)

εo(2)

and

ε′′r (v) = �(v)

2�vεo(3)

The loss characteristics of a dielectric are typically expressed interms of the dielectric loss tangent, tan ı:

tan ı = ε′′r

ε′r

(4)

In the frequency range above 1 GHz, the passive electrical prop-erties of biological tissues are proportional to their water content.For instance, tissues such as the vitreous humour, which contain avery high water content of 95%, have dielectric permittivities andloss characteristics almost identical to those of water (Fig. 3A and B),whereas cartilage, with a lower water content of 75%, shows simi-lar, but non-identical dielectric permittivity and loss characteristics(Fig. 3A and B). The permittivity and loss values in Fig. 3A and Bwere obtained from parametric models of the frequency–responseof tissues (Gabriel and Lau, 1996). Similarly, plants with high watercontents (85–95%) have electrical properties converging towardsthose of water with increasing water content of the tissue (Nelsonand Trabelsi, 2005).

While the passive electrical properties of water have been wellcharacterized over a wide frequency range (Jiang and Wu, 2004;Liebe et al., 1991), those of plant and animal tissues have onlybeen characterized up to ∼100 GHz. As this present investigationrequired the electrical properties of plant tissue in a range from 1to 1000 GHz, it has been assumed that, on account of the high watercontent of plant materials considered in this work, their electricalproperties from 1 to 1000 GHz will be similar to those of water.

The dielectric permittivity and loss tangent of water over therange from 1 to 1000 GHz used in FEA modelling are shown in Fig. 3C

and D. The electrical properties of water from 1 to 350 GHz wereobtained from a parametric model (Meissner and Wentz, 2004),whereas values from 350 to 1000 GHz were obtained from actualmeasurements of water at 19 ◦C (Liebe et al., 1991).

370 A.M. Pietak / BioSystems 109 (2012) 367– 380

Fig. 3. Frequency-dependent passive electrical properties of water and biological tissues in the microwave-terahertz range. Panel A shows the permittivity, and Panel B theAC conductivity, of water, vitreous humour, and cartilage from 1 to 100 GHz. Panel C shows the permittivity and panel D the loss tangent of water over a range from 1 to1000 GHz, which was assumed to be representative of high-water content plant tissue in FEA analysis. Values for water were obtained from parametric models and actualmeasurements (Jiang and Wu, 2004; Liebe et al., 1991; Meissner and Wentz, 2004). Values for tissues were obtained from parametric models (Gabriel and Lau, 1996).

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. Materials and Methods

.1. Plant Samples and Microscopy

This study considered cross-sectional patterns in ovary primor-ia with cross-sectional radii ranging from ∼0.5 to 1 mm from acornquash (Cucurbita pepo), butternut squash (Cucurbita moschata),nd zucchini (C. pepo); the early development of acorn squash maleower primordia with cross-sectional radius from 0.5 to 0.7 mm;nd the set fruits of cucurbit-family plants acorn squash, butter-ut squash, zucchini, watermelon (Citrullus lanatus), and cucumberCucumis sativus).

Acorn, butternut, and zucchini squash plants were grown in anxperimental garden (Kingston, Ontario, Canada). A total of tenvary primordia from five different plants of each of the threequash types were selected at various stages of early development.n addition, a total of 10 male flower primordia were selected fromve acorn squash plants for microscopic inspection. Thin sectionsere carefully cut from fresh samples with a tissue blade. Sectionsere stained with methylene blue, and were investigated by lighticroscopy (Amscope T490-B, USA) at 80× and 200× magnifica-

ion.Tissue patterns in set fruits were also investigated. Sections

ere taken from the set fruit (cross-sectional radii ranging from

0 to 200 mm) from acorn squash, butternut squash, cucumber,atermelon, and zucchini fruits. Five samples of each fruit were

ut into cross and longitudinal sections and photographed using aigital camera.

3.2. Finite Element Analysis Modelling

A finite element analysis (FEA) model was used to identify theforms and resonant frequencies of EM resonant modes on dielectricstructures intended to simulate developing plant organs (ovariesand flower buds). The eigenmode solver of Ansoft HFSS 13.0 soft-ware (Ansys, USA) was utilized in all simulations.

As all organs considered in this study assumed either a cylin-drical or ellipsoidal geometry (Fig. 1), the FEA model considereddielectrics shaped as cylinders (r = 0.5 mm, h = 0.5 mm), and ellip-soids (r1 = 0.5 mm, r2 = 0.625 mm). The dimensions used in themodel approximated those of cucurbit ovaries when patterningwas first observed to arise (as shown in Fig. 2), and in corre-spondence with the observations of Pereira (1968). The number oftetrahedral mesh elements increased dramatically with increasingEM frequency, with a minimum of 9000 elements in the cylinderand a minimum of 10,000 elements in the ellipsoid. Typical modelsutilized 35,000 tetrahedral mesh elements. A maximum of 55,000mesh elements was used for highest frequencies.

The FEA model first considered dielectrics without loss (conduc-tivity of 0). Values of resonant frequencies change with dielectricpermittivity, and the dielectric permittivity of water varies withfrequency. To deal with this issue, modes were calculated for arange of dielectric permittivities from εr = 3.5–100. The frequencies

of the resulting modes were considered alongside the frequency-dependent permittivity of water (Fig. 3C). In the FEA model, thepermittivity of the modelled dielectric was incrementally adjusteduntil it was consistent with the permittivity of water in the range

A.M. Pietak / BioSystems 109 (2012) 367– 380 371

Fig. 4. Cross-sectional electric field patterns of three EM resonant mode series characteristic of dielectric cylinders and ellipsoids. Top row shows the electric field of thefirst four modes of the electric spiral (ES) series. Middle and bottom rows show the electric field of the first four modes of the contained electric spiral series (CES) and thedouble contained electric spiral series (DCES), respectively. Field strengths are represented in colour code with red (black) showing highest and dark blue (white) the lowestfi ld spiro sion o

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eld strength. Magnetic fields (not shown) are strongest at the centre of electric fief the references to color in this figure legend, the reader is referred to the web ver

f the resonant mode frequencies calculated. Using this manualterative procedure, a final value of εr = 5 was found to be approx-mately consistent with the permittivity of water in the rangef relevant mode frequencies produced for the model dimen-ions considered. Thus, εr = 5 was used in all reported modellingesults.

Dielectric loss was then introduced to the models in the form of conductivity � representative of a loss tangent via Eqs. (3) and (4).he Q-factors of modes as a function of loss tangent were evaluatedt the frequency of the mode for a range of loss values below andxceeding those of water (as shown in Fig. 3D).

.3. Definition of Mode Pattern Series on Dielectric Cylinders andllipsoids

Three different EM mode pattern series, all of them commono both cylindrical and ellipsoidal geometries, were found to be ofelevance to ovary, bud, and fruit structural patterns (Fig. 4).

In the most basic pattern series, the cross-sectional view ofhe electric field features pairs of electric field spirals appearingequentially as the mode frequency increases (Fig. 4 top row). Thisasic pattern series is referred to here as the electric spiral (ES)eries, with the mode number indicated as a number after the pat-ern series name. The electric field of the first four ES modes inross-section is shown in Fig. 4. The three-dimensional character-

stics of the electric field of the ES3 mode are shown in Fig. 5. The

agnetic field (not shown) is strongest at the centre of the electriceld spirals and is oriented in the longitudinal plane, perpendicularo electric field direction.

als and are oriented perpendicular to the cross-sectional plane. (For interpretationf the article.)

Other pattern series of significance were electric spiral modescontained within one or more radial wavelengths reducing theES pattern to a smaller zone closer to the centre. These patternseries are here referred to as the contained electric spiral (CES)series and the double contained electric spiral (DCES) series, withcross-sectional electric fields shown in Fig. 4 middle and bottomrows, respectively. In all modes, the magnetic field (not shown) isstrongest at the centre of the electric field spirals and is oriented inthe longitudinal plane.

All modes in the ES, CES, and DCES pattern series are three-dimensional constructs consisting of electric and magnetic fieldcomponents, and repeating the cross-sectional pattern continu-ously along the mid-section of the longitudinal direction. This canbe seen in the three-dimensional electric field patterns of the ES3mode forming on a dielectric ellipsoid (Fig. 5A) and a cylinder(Fig. 5C). The conserved cross-sectional patterns of the electric fieldof the ES3 mode on an ellipsoid and cylinder are shown in Fig. 5Band D, respectively.

3.4. Schematics

While different plant species may respond to the hypotheticalEM radiation in different ways, in all organs examined a consistentalgorithm involving key features of the mode pattern was apparent.A schematic representing this consistent algorithm was prepared

for each relevant mode by using computer drawing software (Pho-toshop CS4, Adobe, USA) to trace over the FEA-derived electric fieldpattern and superimposed magnetic flux pattern of the mode usingthe following rules.

372 A.M. Pietak / BioSystems 109 (2012) 367– 380

Fig. 5. Three-dimensional electric field patterns of the ES3 mode forming on a dielectric ellipsoid (panel A) and a cylinder (panel C). The cross-sectional views of the electricfield pattern of the ES3 mode on an ellipsoid and cylinder are shown in panels B and D, respectively. All patterns were obtained from FEA modelling. Field strengths arerepresented in colour code with red (black) showing highest and dark blue (white) the lowest field strength. Magnetic fields (not shown) are strongest in longitudinal columnsl ces to

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ocated at the centre of the six electric field spirals. (For interpretation of the referen

Firstly, in all organs evaluated, axes consisting of a significantissue structure (i.e. septa, placental lines) distinctly related to thelectric field component of the mode pattern were observed. Thesexes of the modelled electric fields are labelled axis ‘a’ in schematicsf Figs. 6–8. Alternate axes in relation to the electric field patternsre labelled axis ‘b’ in schematics of Figs. 6–8.

Secondly, the location of highest magnetic flux density wasabelled zone ‘c’ in the schematics of Figs. 6–8.

Thirdly, different circumferential zones of the EM mode patternere labelled zones ‘e’ and ‘f’ in the schematics of Figs. 6–8.

Finally, secondary magnetic flux density nodes were labelled ‘d’n the schematics of Figs. 6–8.

.5. Image Analysis

Images obtained from plant investigations and FEA models ofM resonant modes fields were quantified using a consistent set ofeometric measurements relating to the location of main patterneatures (outlined in Fig. 9). The main features in ovary/fruit/flowerross-sections were hypothesized to correspond to the main pat-

ern features of the electric and magnetic field cross sections of EMesonant modes.

Image measurements were performed in ImageJ 1.43u (NIST,SA), selecting features manually and using built-in commands to

color in this figure legend, the reader is referred to the web version of the article.)

fit circular zones and measure areas and angles. Measurements ofEM resonant mode features were made on an image with the elec-tric field represented by a vector field and the magnetic flux asa superimposed gradient (as shown in Fig. 9). Point markers wereused to identify the central location of ova/seeds or the central loca-tion of magnetic flux density maxima (red dots in Fig. 9A and B),and to define the circular boundaries and axes shown in Fig. 9. Notethat all area regions defined were normalized to the total area ofthe circular mesocarp region or the mode exterior (the perimetermarked as region 4 in Fig. 9).

The cross-sectional tissue patterns in ovaries/set fruit of acorn,butternut, and zucchini squash shared visible similarities, andtherefore these three varieties were all hypothesized to correspondto the CES3 mode pattern. For the CES3 mode, the q = 13 patternparameters were defined as:

1. Main axes angles: The five angles between the main axes ofthe spiral pattern, where main axes were defined as the pla-cental line or the midway-point between two ova in plants (seeFig. 9). Angles were measured progressively from a common start

position to retain their independence as variables.

2. Flux axes angles: The five angles between the flux axes, whichare defined as lines passing through the central region and theova of plants or flux maxima marker or modes. Angles were

A.M. Pietak / BioSystems 109 (2012) 367– 380 373

Fig. 6. Striking parallels exist between the tissue patterns of a developing cucurbit ovary (panel A) and the electric field (panel B) and magnetic flux (panel C) of the CES3electromagnetic resonant mode forming on an ellipsoidal or cylindrical dielectric. Note that all patterns shown are cross-sections of 3D geometries. Placental lines (p) formin response to highest electric field (panels A and B). Ovum development (O) begins at the six regions of highest magnetic flux (panels A and C). A circumferential regioncorresponding to the mesocarp (M) and separate from the endocarp (E) exists in the ovary and electric field pattern of the CES3 mode (panels A and B). The exocarp (X)appeared unrelated to mode features. A schematic illustrating the combined effects of the electric and magnetic fields as a systematic tissue response is shown in panel D.Black scale-bar in panel A shows 250 �m. Field strengths are represented in colour code with red (black) showing highest and dark blue (white) the lowest field strength.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Fig. 7. Additional patterns in cucurbit ovaries (top row) and male flower bud development (bottom row). First column shows plant cross-sections, second column showselectric field component of mode in cross-section, third column shows the magnetic flux of mode in cross section, and final column shows schematics based on hypotheticalsystematic tissue response to mode patterns. In one cucurbit ovary a pattern corresponding to the CES4 mode was discovered (top row). The male flower bud pollen tube (p)development is consistent with an ES15 mode (bottom row). Scale-bar in top row image shows 100 �m, while scale bar in bottom row image shows 250 �m. Field strengthsare represented in colour code with red (black) showing highest and dark blue (white) the lowest field strength. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of the article.)

374 A.M. Pietak / BioSystems 109 (2012) 367– 380

Fig. 8. Comparisons between cross-sectional tissue patterns in mature cucurbit-family fruits and cross-sectional EM mode structure. In order from top to bottom, the firstcolumn shows cross-sections of watermelon, zucchini squash, and cucumber. Second column shows electric field maps of the compared EM mode pattern in cross-section.Third column shows magnetic flux density in cross-section. Fourth column shows schematic representation of apparent fruit response to hypothetical EM radiation patternswith Pfit listed. The colour legend used for electric field and magnetic flux diagrams indicates highest fields in red (black) and lowest fields in dark blue (white). (Forinterpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Fig. 9. A definition of axes, regions, and angles used to parameterize and compare images from plant cross-sections and EM resonant modes from FEA. Panel A shows them radienf r intev

3

ain features for the superposition of electric (vector field) and magnetic (density gor the butternut squash ovary primordium in cross-section (radius ∼ 0.7 mm). (Foersion of the article.)

measured progressively from a common start position to retaintheir independence as variables.

. Inner region ratio: The normalized area of an inner circularregion defined by three dark-stained nodes in developing ovaries

t) fields of the CES3 mode shown in cross-section. Panel B shows the main featuresrpretation of the references to color in the text, the reader is referred to the web

or the central region of the EM mode. The perimeter of theboundary is marked as region 1 in Fig. 9. This parameter wasincluded for consistency with mode patterns with a large centralregion such as ES15.

A.M. Pietak / BioSystems 1

Table 1Summary of average parameter values (± standard error of the mean) obtained frommeasurements of cross-sectional images of acorn or butternut squash ovaries/fruitat early or late stages of development (N = 12) and zucchini squash ovaries/fruit atearly or late stages of development (N = 6). The corresponding parameters obtainedfor cross-section measurements of the combined electric and magnetic field infor-mation of the CES3 mode are shown for general comparison.

Parameter Acorn orbutternutsquash

Zucchinisquash

CES3 modeideal

Main axes angle 1 58 ± 2 57 ± 2 60Main axes angle 2 121 ± 2 119 ± 3 120Main axes angle 3 182 ± 2 180 ± 2 180Main axes angle 4 243 ± 3 237 ± 2 240Main axes angle 5 304 ± 1 298 ± 3 300Flux axes angle 1 63 ± 3 46 ± 2 60Flux axes angle 2 120 ± 3 122 ± 2 120Flux axes angle 3 184 ± 4 167 ± 2 180Flux axes angle 4 243 ± 4 246 ± 3 240Flux axes angle 5 303 ± 4 290 ± 3 300Inner region ratio 0.014 ± 0.002 0.012 ± 0.002 0.006Spiral region ratio 0.17 ± 0.01 0.16 ± 0.02 0.160

4

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shown in Fig. 6D. Cucurbit ovaries from acorn, butternut, and zuc-

Contained region ratio 0.51 ± 0.04 0.54 ± 0.05 0.522

. Flux region ratio: The normalized area of a circular region witha boundary passing through the centre of ova or flux maximawith perimeter marked as region 2 in Fig. 9.

. Contained region ratio: The normalized area of a circular regionwith a boundary corresponding to the division between theendocarp and mesocarp in plant ovaries or the exterior of thespiral pattern in the mode, marked as region 3 in Fig. 9.

Similar parameter sets were defined for other mode and tissueatterns studied (ES3, ES15, DCES3).

The parameter set obtained from image analysis allowed com-arisons to be made between patterns forming in cucurbit ovariesor different species/varieties (butternut squash, acorn squash,nd zucchini squash) and developmental stages (primordia andet fruit). Measurements were made for cross-sectional imagesf three replicates from each variety (butternut squash, acornquash, and zucchini squash) at two developmental stages (early:ross-sectional radius 0.6–1.2 mm; and late: cross-sectional radius0–40 mm). The resulting parameter sets were compared in SPSS7.0 software (IBM, USA). Independent samples t-tests were usedo assess differences between early and late stages of plant pat-ern for each parameter in the set within each variety group,ith p < 0.05 taken to be indicative of a significant difference in aarameter.

When no statistically significant differences were foundetween any parameter in early or late developmental stages of anyf the three varieties, one-way analysis of variance (ANOVA) testsith Bonferroni post hoc comparisons were used on each parame-

er to detect differences between species, with p < 0.05 taken to beignificant.

Image analysis also allowed for an assessment of the similarityetween patterns forming in plant samples and the electromag-etic fields of EM resonant modes. A probability of fit (Pfit)as obtained for a plant tissue image to a particular resonantode using the Chi2 test of independence. Here, the set of

EM mode parameters (indexed as j) were taken to be thexpected values (Ej), and the plant tissue features were taken toe the observed values (Oj) with the Chi2 statistic (�2) calculateds:

2 =q∑

j=1

(Oj − Ej)2

Ej(5)

09 (2012) 367– 380 375

A Pfit value was obtained by consulting the �2 distribution withq − 1 degrees of freedom. The �2 model was tested by introducingquantified variation to the ideal parameters, demonstrating that aPfit value of 83% represents a 20% variation between the observedand expected parameter set.

Comparisons were made between parameter sets representingthe averages of three biological samples (N = 3) in butternut acorn,acorn squash, and zucchini ovary primordia and mature fruitswith features of the CES3 mode. The Pfit was also used to assessimage similarities in cross-sections of mature cucurbit-family fruitswatermelon (N = 3) and cucumber (N = 3) with comparisons to ES3and DCES3 mode features, respectively. Cross-sections of maleacorn squash flower primordia (N = 3) were compared with the pat-tern of ES15. The similarities between an acorn squash bud withfour main axes and the CES4 mode were also assessed by calculatinga Pfit value (N = 1).

4. Results

4.1. Cucurbit Ovary Pattern Study

Patterns were found to be highly conserved amongst the threedifferent squash varieties and at different developmental stageswithin each variety. No statistically significant differences in anyof the 13 parameters (key image feature measurements) werefound between the primoridial patterns of a cucurbit variety andtheir respective patterns as set fruit (all p > 0.05 in independent t-tests). Comparing parameters for the three different varieties usingANOVA, only the flux angles 1 and 3 of zucchini showed signifi-cant differences with the acorn and butternut squash samples. Allsamples, with the effect becoming more pronounced in zucchiniplants, showed an alternating pattern indicating opposing ova wereattracted towards one another (this is evident in Fig. 9 where theflux angles can be seen to alternate between large and small val-ues). The main axes angles and relative proportions of the inner,middle, and outer circular regions were highly conserved (p > 0.05)in all three varieties.

These similarities between the patterns of different cucurbitvarieties indicate the existence of a similar shared physiologicalmechanism. The similarities between primordial and mature stagepatterns indicate that the tissue pattern remains invariant after theearly symmetry-breaking process in the ovary primordium. Theaverage parameter values and standard error of the mean of but-ternut or acorn squash and zucchini in comparison to the “ideal”values obtained from the CES3 mode are summarized in Table 1.

4.2. Parallels Between Developing Organs and EM Mode Patterns

Striking parallels (Pfit = 98.7–99.99%) were observed betweentissue patterns of a developing cucurbit ovary (Fig. 6A) and theelectric field (Fig. 6B) and magnetic flux (Fig. 6C) of a CES3 reso-nant mode forming on a dielectric cylinder or ellipsoid. Placentallines (p) appeared in regions coincident with the highest electricfield strength of the CES3 mode (compare Fig. 6A and B). Ovumdevelopment (O) was coincident with the six regions of highestmagnetic flux of the CES3 mode (compare Fig. 6A and C). A circum-ferential region corresponding to the primordial mesocarp (M) andseparate from the developing endocarp (E) was found to exist inboth the cucurbit ovary and electric field pattern of the CES3 mode(Fig. 6A and B). A schematic illustrating the proposed combinedeffects of the electric field and magnetic flux as a tissue response is

chini squash plants all showed a similar pattern to that shown inFig. 6A. The observed features of curcurbit ovaries were also consis-tent with the three-dimensional characteristics of the CES3 mode,

376 A.M. Pietak / BioSystems 109 (2012) 367– 380

Fig. 10. Details of pattern formation in cucurbit ovary primordia and their correspondence to the CES3 mode electric field pattern. Panels A–C show the correspondencebetween the whole CES3 mode (panel C) and full view of cucurbit cross sections at early (panel A) and intermediate (panel B) stages of development. Panels D–F highlightthe highly symmetric triple axis forming at the centre of ovaries at early (panel D) and intermediate (panel E) stages of development in comparison to the central view of theCES3 mode (panel F). Panels G–I highlight the alignment of cells at early (panel G) and intermediate stages (panel H) in similar curl patterns to the back-to-back electric fields ly (pat cept

wt

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pirals of the CES3 mode (panel I). Panels J–L highlight the alignment of cells at earhe facing electric field spirals of the CES3 mode (panel L). Scale-bar in all images ex

ith consistent tissue patterning observed in the longitudinal sec-ions.

The details of pattern formation in cucurbit ovaries, and theirorrespondence to the CES3 mode electric field pattern, are shownn Fig. 10. There is a distinct correspondence between the wholeES3 mode (Fig. 10C) and the full view of cucurbit cross sections atoth early (Fig. 10A) and intermediate (Fig. 10B) stages of develop-ent. The patterns contain a highly symmetric triple axis consisting

f placental lines forming at the centre of ovaries at early (Fig. 10D)nd intermediate (Fig. 10E) stages of development, which corre-pond to the central view of the CES3 mode (Fig. 10F). Cells at earlyFig. 10G) and intermediate stages (Fig. 10H) are oriented in sim-lar curl patterns to the back-to-back electric field spirals of theES3 mode (Fig. 10I). Similarly, both early (Fig. 10J) and interme-iate (Fig. 10K) stage ovary primordia feature regions where cellsre oriented into curl patterns corresponding to the facing electriceld spirals of the CES3 mode (Fig. 10L). Early in development, pat-ern features were largely composed of individual cells (Fig. 10A,, G, J). As the ovary matured, the pattern remained conserved but

ssumed a multicellular character (Fig. 10B, E, H, K).

In one of the 10 acorn squash ovaries inspected, a pattern basedn a 4-fold symmetry was found with features in direct correspon-ence to a CES4 mode with Pfit = 99.99% (Fig. 7, top row). Tissue

nel J) and intermediate stages (panel K) of development to similar curl patterns topanel B show 100 �m. Scale-bar in panel B shows 250 �m.

was observed to be developing in a manner consistent with thatfound in the more common 3-fold symmetry ovaries parallelingthe ES3 mode. Cells in developing placental lines were clearlyaligned with the electric field direction to form 4 sets of back-to-back spirals intersecting at a cross at the centre (Fig. 7, top row).Similarly, ovum formation was beginning at the 8 sites of highestmagnetic flux at the centre of each electric field spiral (Fig. 7, toprow).

The earliest development observed in male flowers of acornsquash concerned the formation of pollen tubes ‘p’ at the periph-ery of the developing flower bud (Fig. 7, bottom row). Similar to thedeveloping ovary, patterns were observed in early stage buds withcross-sectional radii of approximately 0.5 mm. The pattern of pollentube development was consistent with the features of an ES15mode (Pfit = 99.2%). Fifteen sets of back-to-back spiral-like septaformed close to the perimeter of the ellipsoidal bud, and pollenformation was coincident with the 30 sites of maximum magneticflux density (Fig. 7, bottom row). The proportions of developingpollen tube length in relation to cross-sectional diameter are con-

sistent in the male bud and the electric field spirals of the ES15 mode(Fig. 7, bottom row). Notably, in all 10 male flower buds observed,15 sets of developing pollen tubes (30 in total) were consistentlyobserved.

A.M. Pietak / BioSystems 109 (2012) 367– 380 377

Fig. 11. Resonant mode frequencies and Q-factors for the ES, CES, DCES, and TCES pattern series characteristic of cylinders with a cross-sectional radius of 0.5 mm and εr = 5.Panel A shows variation in resonant frequency of the four pattern series as a function of mode number. Panel B shows increasing Q-factor with increasing mode frequency.P tion off r at frei

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anel C shows the quality factor of the ES3 mode on a dielectric cylinder as a funcorms at a resonant frequency of 280 GHz. The loss tangents expected for pure wates shown as a dotted line.

.3. Patterns in Mature Fruits

In the cucurbitacea plant family, fruits arise directly from thevary without merging with the remaining female flower anatomy,nd are therefore likely to show a correspondence between firstymmetry breaking in the ovary and the set fruit.

In the squashes (acorn, butternut, and zucchini), cucumber, andatermelon, tissue fibres corresponding to placental line remnantsere observed aligned with the ‘a’ axis of electric field, while seed

ormation was coincident with the site of highest magnetic flux athe centre of electric field spirals in zone ‘c’ (Fig. 8).

Watermelon showed minimal distance between the endocarpnd the rind, which is consistent with the geometry of an ES3 modeith Pfit = 81.4% (Fig. 8). The squashes acorn, butternut, and zucchini

ll shared a similar pattern featuring a distinct rim of mesocarpissue surrounding a section of endocarp, with dimensions coin-iding with those of a CES3 mode and Pfit of 96.7, 99.99, and 88.6%,espectively (Fig. 8). The cucumber showed the largest region of

dielectric loss tangent. With a cylinder radius of 0.5 mm and εr = 5, the ES3 modequencies of 200–500 GHz are indicated by grey arrows. The critical value of Q = 0.5

endocarp to mesocarp, as well as variable-density tissue surround-ing the endocarp, all of which correspond to features of a DCES3mode with Pfit = 99.8% (Fig. 8).

The features of all fruits examined were consistent with thethree-dimensional characteristics of the EM modes. In general,all EM modes consisted of a cross-sectional pattern featuring anarrangement of electric field spirals which were repeated consis-tently through the midsection of the longitudinal dimension.

4.4. Resonant Mode Frequency and Feasibility in Plant Primordia

The resonant frequency of modes in each of the four patternseries (i.e. the ES, CES, DCES, and TCES) were calculated for a modelwith a similar radius (r = 0.5 mm) to that observed at the onset of

patterning in squash ovaries (see Fig. 2A). A dielectric permittivityof ε′

r = 5 was used in all models as it is consistent with the actualpermittivity of water in the range of the calculated mode frequen-cies (Fig. 3C). Using these parameters, the frequency range for EM

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odes of relevance to developing ovaries (i.e. ES1, ES3, CES3, CES10,CES3, TCES5) was found to span from 150 to 1000 GHz (Fig. 11A).he Q-factor of these modes was found to increase consistently withhe mode’s resonant frequency (Fig. 11B) indicating higher-order

odes resonate more effectively than lower-order modes.Dielectric loss was introduced to the models and computations

ere repeated for the ES3 mode with progressively increasingielectric loss tangents. While the Q-factor of the ES3 mode droppedrecipitously with increasing loss, it remained well above thehysical cut-off limit for resonance (Q > 0.5) even for loss valuesxceeding those of water in the frequency range of the modeFig. 11C).

. Discussion

It is well established that molecular signals play essential rolesn development. However, there remains little understanding ofow these substances can be synthesized, transported, and act athe specific locations and times necessary to bring about intri-ate and even mathematically precise biological patterns emergingpontaneously from a homogeneous primordium. The radicallylternative perspective presented herein sees a developing organs a dynamic system self-trapping EM energy in a stable spatial pat-ern hypothesized to inform phenomena such as cell orientation,irections of preferred growth, genetic expression, and differentia-ion state. Notably, the hypothesis of tissue as a dielectric resonatoras previously developed for plant leaves (Pietak, 2011), and a sim-

lar concept applicable to single cells was introduced independentlyy Popp et al. (2005) and explored by Cifra (2010).

The results show the three-dimensional tissue structure ofucurbit ovaries, male flower buds, and cucurbit fruits showemarkable similarities with three-dimensional EM resonant modeatterns calculated using a FEA model of a dielectric with similarlectrical and geometric properties to the developing plant organs.ain organ features such as placental lines and septa follow elec-

ric field spirals and form in relation to high electric field strength.ther features, such as ova/seeds and pollen tubes appear in loca-

ions correlated with areas of high magnetic field. Ultimately, theoncept of EM resonant modes helps account for early spontaneousmergence of patterns from an initially homogeneous collective ofells. Electromagnetic resonance also helps to explain how highlyonserved patterns can be created in different organs on the samelant, different plants, and plants of different species.

The high water content of plant tissue yields a relatively highermittivity, but also a high loss characteristic. The feasibility ofhis hypothesis of plants as dielectric resonators rests in part onhe capacity for lossy tissue to support EM modes. Finite elementnalysis modelling demonstrated EM modes could be supportedn the lossy organ if the mode is generated within an early devel-pmental structure of comparable dimensions to the penetrationepth of the resonant EM radiation. Even with loss characteristicsxceeding those expected for water at 150–1000 GHz, the Q-factorf resonant modes remained above 0.5, demonstrating the physicalapacity for resonant modes in plant tissue.

Observations of cucurbit ovary primordia indicate that once theymmetry has been broken early in development, a relatively con-istent pattern remains through to organ maturation and even theet fruit, with no statistically significant changes detected in indi-idual pattern parameters between the primordia and set fruittages. Therefore, it is suggested that the EM resonant mode actsnly during a sensitive early stage of the organ where it instigates an

nitial symmetry-breaking. Subsequent changes in tissue character

ould be mediated purely by molecular-genetic mechanisms.In this study, cell orientation was observed aligned with

ypothetical electric field direction, and different kinds of tissue

09 (2012) 367– 380

differentiation were correlated to respective areas of high elec-tric or magnetic fields. There are several ways that the electric andmagnetic field components of an EM resonant mode may influencecellular behaviour in a developing primordium, including: (i) directeffects of electric and magnetic fields on cell behaviour, (ii) elec-trophoretic movement of charged ions, and (iii) dielectrophoreticmovement/aggregation of neutral molecular and macromolecularcomponents in response to electric field gradients.

The activity of electric fields in developing and regeneratingbiological systems has been particularly well documented (Levin,2003, 2009). The application of physiologically relevant electricfields (∼50 mV/mm) can change the orientation of cells to lay paral-lel or perpendicular to field lines, induce migration of cells towardsthe positive or negative poles of the field (galvanotaxis), and caninfluence the direction of preferred growth in relation to field polar-ity (Hinkle et al., 1981; Levin, 2009; Zhao et al., 1999). Weak electricfields and intercellular ion flow have also been observed to influ-ence embryonic and stem cell differentiation states (Grattarolaet al., 1985; Harrington and Becker, 1973; Levin, 2003, 2009). Bio-logical voltage gradients and ion flow have also been associatedwith control of cell proliferation and controlled apoptosis (Levin,2009). Weak magnetic fields have been observed to induce changesin ion flux through cell membranes and altered cell growth char-acteristics (Blackman et al., 1994; Lednev, 1991).

Electrical signals may be converted into second-messenger bio-chemical signal cascades through mechanisms such as (Levin,2009; McCaig et al., 2005): (i) electric field modulation of voltage-sensitive ion channels, (ii) modulation of voltage-sensitive smallmolecule transporters, (iii) the spatial redistribution of electri-cally charged receptors on the surface of the cell, (iv) directionalelectrophoresis of morphogenic substances through the biologicalsystem, (v) signalling through electrically induced changes in mem-brane protein shape, and (vi) effects of field on genetic expressionvia affects on ion transporters in the nuclear membrane.

Dielectrophoresis describes force exerted on a dielectric parti-cle when it is in the vicinity of a non-uniform static or time-varyingelectric field (Pohl, 1978). The force depends on the dielectric prop-erties of the particle relative to those of the background medium.For biological systems in the frequency range of 1–1000 GHz, thepermittivity of water exceeds that of proteins, lipids, and biopoly-mers. Thus, biomolecular and macromolecular substances wouldbe expected to migrate towards areas of lowest electric field. Dielec-trophoresis may therefore alter the three-dimensional distributionof morphogenetic substances in relation to a static or dynamic elec-tric field, leading to changes in cell differentiation state and otherfeatures such as proliferation rates.

The specific mode selected by a plant organ may result from aconvergence of multiple constraining factors. As mentioned above,it is hypothesized that the primordium is only sensitive to EMradiation for a window of time early in development. The dimen-sions and permittivity of the developing plant organ at the timeit is sensitive to EM radiation define the minimum frequency thatcan create a resonance in the system. Generally in resonant sys-tems, the primary excitation is the fundamental mode of lowestfrequency. However, higher frequency modes are more physicallyfeasible considering (i) that modelling indicated Q-factors of res-onant modes decreased with decreasing mode frequency, (ii) thatthe loss characteristics of water increase at frequencies decreas-ing from 1000 GHz leading to further decreases in lower modeQ-factors, and (iii) that the mode Q-factors are close to the thresholdphysical minimum of 0.5. Therefore, modes appearing in the plantorgan may be the lowest mode that can be physically supported

given these three existing constraints.

It is important to note that the EM source does not need to becoherent to excite a resonance in a dielectric. A dielectric resonatorcan be excited by an incoherent multi-frequency radiation signal.

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n this scenario, the resonator will select only its resonant frequen-ies from the broadband signal. For this reason, dielectric resonancerinciples are used to create frequency filters for EM signals (Wangnd Zaki, 2007). The EM resonant mode may be excited by inco-erent radiation produced endogenously. In addition, incoherentlack-body radiation of thermal origin may be capable of stim-lating resonance in small (a radius of 0.5 mm or less) biologicaltructures. In the frequency range above 100 GHz and at a temper-ture of 20 ◦C, the power of black-body radiation is significant andncreases dramatically with increasing frequency. Moreover, waters a high emissivity substance. The suitability of various poten-ial excitation sources for EM resonance in plant tissue will be theubject of future work.

To date and the best of the author’s knowledge, little to no exper-mental reports have measured the effects of EM radiation in theange of 200–1000 GHz on plant tissue, nor have any attempted toeasure endogenous EM radiation in this range from plant tissue.

his is likely the case as there have been no reasons to investigateM radiation in the context of plant tissue in this range. In light ofhe evidence presented herein, experiments to detect or influencehe proposed developmental EM mechanism are warranted.

. Conclusions

Tissue patterns in developing cucurbit ovaries, male floweruds, and mature fruits were found to show significant correla-ions with electromagnetic modes forming on similarly shapedielectrics.

On account of the unique properties and characteristics of elec-romagnetic phenomenon, it is not possible to obtain identicalatterns to those of an electromagnetic resonator from other wavehenomena such as reaction-diffusion of molecules or mechanicaltress distributions. Nor are the patterns formed by an electro-agnetic resonator of an arbitrary or ubiquitous nature. Therefore,

he very strong correspondence between electromagnetic resonantode patterns of dielectric structures and biological patterns in

ucurbit ovaries/fruits, including the positioning of main biologicaleatures such as septa, placental lines, and ovum/seeds, supportshe existence of endogenous EM radiation.

Ultimately, the concept of EM resonant modes explains howattern formation can emerge spontaneously from a previouslyomogeneous collective of cells, and how highly conserved pat-erns can be created in different organs on the same plant, differentlants, and plants of different species.

Experimental investigations to detect or disturb EM radiationn these plants are warranted. The proven existence of endogenousM radiation would revolutionize the biological sciences by intro-ucing a radically new mechanism underlying morphogenesis.

cknowledgements

The author expresses her thanks to two anonymous reviewersor their helpful comments and advice.

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