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Bioenergetics and mechanical actuation analysis withmembrane transport experiments for use in biomimeticnastic structures

Luke Matthewsa)

Department of Mechanical Engineering, Laboratory for Active Materials and Smart Structures,University of South Carolina, Columbia, South Carolina 29208

Vishnu Baba SundaresanDepartment of Mechanical Engineering, Center for Intelligent Materials and Smart Systems, VirginiaTech, Blacksburg, Virginia 24061

Victor GiurgiutiuDepartment of Mechanical Engineering, Laboratory for Active Materials and Smart Structures,University of South Carolina, Columbia, South Carolina 29208

Donald J. LeoDepartment of Mechanical Engineering, Center for Intelligent Materials and Smart Systems, VirginiaTech, Blacksburg, Virginia 24061

(Received 31 January 2006; accepted 18 April 2006)

Nastic structures are synthetic constructs capable of controllable deformation and shapechange similar to plant motility, designed to imitate the biological process of nasticmovement found in plants. This paper considers the mechanics and bioenergetics of aprototype nastic structure system consisting of an array of cylindrical microhydraulicactuators embedded in a polymeric plate. Non-uniform expansion/contraction of theactuators in the array may yield an overall shape change resulting in structuralmorphing. Actuator expansion/contraction is achieved through pressure changesproduced by active transport across a bilayer membrane. The active transport processrelies on ion-channel proteins that pump sucrose and water molecules across a plasmamembrane against the pressure gradient. The energy required by this process issupplied by the hydrolysis of adenosine triphosphate. After reviewing the biochemistryand bioenergetics of the active transport process, the paper presents an analysis of themicrohydraulic actuator mechanics predicting the resulting displacement and outputenergy. Experimental demonstration of fluid transport through a protein transporterfollows this discussion. The bilayer membrane is formed from1-Palmitoyl-2-Oleoyl-sn-Glycero-3-[Phospho-L-Serine] (Sodium Salt),1-Palmitoyl-2-Oleoyl-sn-Glycero- 3-Phosphoethanolamine lipids to support the AtSUT4H+-sucrose cotransporter.

I. INTRODUCTION

In the plant kingdom, plants are capable of localizedmovement due to a biological process called nastic mo-tion generated with the help of specialized motor cells.The motor cells cause a change in confirmation of theleaves or stem from external stimulus like sunlight or aprey as in the case of insectivorous plants.1,3 Nasticmotion in plants results from osmotic pressure regulationin cellular compartments causing bulk expansion in thetissue. A nonuniform volume change throughout the

tissue results in different configurations of the tissue.1

Motor cells respond to the stimulus by converting bio-chemical energy in sugars into mechanical. This responseto an external stimulus in plants qualifies it as a biologi-cal actuator. To determine the feasibility of constructingsynthetic nastic structures, the natural bioenergetic sys-tem needs to be studied to develop analytical models fordetermining the possible range of energy release andfluid transport as function of various physical and chemi-cal conditions. This will help determine the optimalchemical conditions for nastic actuation as well as otherfactors that favor the energy exchange.

In this work, the mechanical response of nastic actua-tors that imitate plant motor cells were examined to de-termine how the system will respond to increasing

a)Address all correspondence to this author.e-mail: [email protected]

DOI: 10.1557/JMR.2006.0250

J. Mater. Res., Vol. 21, No. 8, Aug 2006 © 2006 Materials Research Society2058

osmotic pressure and to determine what physical dimen-sions and properties will produce the desired volumeexpansion for nastic actuation. Analytical models weredeveloped for application in synthetic nastic structuresdesign. Furthermore, the biochemical and bioenergeticprocesses that power biological nastic motion were ex-amined. The mechanical response of the actuator to thepressure was modeled, predicting the range of volumeexpansion possible during actuation. The experimentsdemonstrated fluid transport against a small potentialhead through a protein transporter extracted from plantsand reconstituted on a bilayer lipid membrane (BLM)formed from purified lipids. The transport experimentswere used to characterize the protein transporters andidentify a control stimulus for actuation.

II. BIOCHEMISTRY AND BIOENERGETICS OFNASTIC MOTION IN PLANTS

The biochemical energy source is adenosine triphos-phate (ATP) in living cells. Each ATP molecule releasesenergy during hydrolysis catalyzed by the hydroxylaseenzyme (ATP-ase) to result in Adenosine di-phosphate(ADP) and a phosphate ion.22 Hydrolysis of ATP is re-versible, and ATP can be regenerated by plant cells usingspecific pathways.9,10 The chemical reaction can be writ-ten as

ATP + H2O →ATPase

ADP + PO42− + �GATPH .

(1)

The exergonic reaction occurs at biological pH (usu-ally pH 7–7.25). The energy released per mole of ATP atstandard conditions of temperature and pressure is rep-resented by �G0 � 30.5 kJ/mol.12 Altering the pH levelby introducing hydrogen ions or amino acid buffers andmodifying the concentration of ATP, ADP, or PO4

2− willaffect the energy released by hydrolysis.12 When the re-actant concentration is not equal to the product concen-tration, the energy release can be approximated by thefollowing equation:

�GATPH = �G0 + R�T ln�ADP��PO4

2−�

�ATP�. (2)

The chemical symbol for the molecule enclosed inbrackets indicates the molar concentration in moles perliter, and �G is in units of kJ/mol. The ratio of ADP andPO4

2− to ATP is referred to hereafter as the mass-actionbalance ratio and is denoted as

KMA =�ADP��PO4

2−�

�ATP�. (3)

When the pH level deviates from the standard value of7 or a H+ concentration of 106 mol/l, the free energy ofhydrolysis is given by the expression:

�GATPH = �G0 + R�T ln pH . (4)

Because the pH value is dependent on the hydrogenion concentration and expressed as −log[H+], the ratioKMA can be similarly simplified:

pK = −log�KMA� . (5)

The total effect of modified pH and KMA yield thefollowing change in energy release:

�GATPH = �G0 − R�T�ln KMA + 2 pH� . (6)

ATP hydrolysis is also a reversible process when theenzyme ATPase is present, which rejoins ADP and PO4

2−

without requiring an equivalent �G energy input.Once ATP hydrolysis releases energy, it is used by the

plant cell to transport fluid across its membrane. Plantmembranes are composed of a bilayer of phospholipidsmade of a hydrophobic lipid tail and a hydrophilic phos-phate head. Because of the hydrophilic/hydrophobic na-ture of the two parts of the membrane molecule, watercan pass slowly through the membrane by diffusion.However, it requires a pumping action to move wateracross the membrane at a high rate and against a con-centration gradient. Embedded in the membrane are pro-teins that move water as well as other specific moleculesinto or out of the cell through a process called activetransport.2,13,14 Figure 1 illustrates the process of activetransport proteins using energy released from ATP hy-drolysis to move fluid across the membrane from a lowto high concentration area.

The energy required for proteins to move water from alow concentration area C1 to a higher concentration C2 isexpressed in kJ/mol as:

�EAT = R�T lnC2

C1. (7)

FIG. 1. Active transport process moves sucrose and water moleculesacross the phospholipid membrane into a higher concentration area.

L. Matthews et al.: Bioenergetics and mechanical actuation analysis with membrane transport experiments for biomimetic nastic structures

J. Mater. Res., Vol. 21, No. 8, Aug 2006 2059

If C1 is larger than C2, �EAT will be negative, indi-cating that the hydrostatic fluid force within the cell willcause water to naturally diffuse from the cell. For activetransport and nastic movement to be possible in plants,�GATPH � �EAT, or else there will not be sufficient en-ergy to pump the fluid molecules through the proteingates against the concentration gradient and into the cell.To apply the bioenergetics of nastic motion to the syn-thetic nastic actuator, the biomimetic design must first beaddressed.

III. MORPHING NASTIC STRUCTURESMIMICKING BIOLOGICAL MOTOR CELLS

Nastic structures are desirable for use in mechanicalsystems that use morphing parts that must sustain highlevels of stress (Fig. 2). An example of nastic structuresapplication is in the field of inflating and morphingwings for aerial vehicles. For nastic structures to be ef-ficient and safely used in mechanical applications, anumber of qualities are required that are considered intheir research and design. Some requirements of nasticactuator systems include a low power consumption, rapidreaction speed, low weight, high blocked stress, ability tobe actuated repeatedly with little residual stress and fa-tigue, and the capability to sustain a deflected positionover time and under stress.18,19

Nastic structures are composed of an array of actuatorsthat can be individually controlled, allowing for a rangeof actuation across the structure surface. Each actuatorhas several layers that are needed for it to be able toactuate and expand in such a way that would cause over-all bulk deformation across the array. Figure 3 details theactuator schematic, and Table I gives a range of physicaldimensions and material properties considered duringanalytical modeling of the system during actuation.

The simplified actuator considered in our analysis con-sists of actuation cylinder manufactured in the polymer

FIG. 2. (a) Nastic actuator arrays, before and after local actuation causes expansion and twisting shape change; (b) micro-hydraulic actuation platefor nastic structures experiments.

FIG. 3. Actuator schematic with biochemical reactions and factorsindicated.


J. Mater. Res., Vol. 21, No. 8, Aug 20062060

matrix, a membrane transfer membrane at the bottom,and a deformable cover plate at the top (Fig. 3). Theactuation cylinder is also referred to as the barrel. Thebottom membrane is made of reinforced phospholipidbilayer, which is created using a process detailed later inthis article. It is assumed that the membrane is polymer-ized and reinforced to make it rigid. A fluid reservoircontains a mix of ATP, ADP, PO4

2−, sucrose, and water.It is in this reservoir that hydrolysis occurs, and the ad-jacent membrane is host to the active transport proteinsthat will pump sucrose and water into the barrel, causingactuation when the fluid pressure has increased enoughto force the actuator walls outward.

Table I describes the range of dimensions and materialproperties chosen for our analytical modeling. The de-sired range of osmotic pressure inside the actuator barrelis from an initial 1 MPa to a maximum 5 MPa. The me-chanical reaction to the pressure increase will be exam-ined shortly, but first, the energy implications are con-sidered.

Prior to actuation, there is fluid present in both reser-voir and barrel, and both areas have an equal osmoticpressure of 1 MPa. It is assumed that the fluid reservoiris replenished during actuation, keeping the osmoticpressure in the reservoir constant as water moves into thebarrel. At maximum actuation, the barrel pressure is5 MPa.

The energy required for active transport is dependenton molar concentration, so the osmotic pressure can beconverted to molar concentration using the formula:

C =P

R�T, (8)

where C is the molar concentration in mol/l, P is thepressure in MPa, T is the temperature in degrees K, andR is a universal constant. Temperature is a factor in allenergy equations, but for this article it is assumed con-stant at 300 K. As molar concentration and pressure arelinearly related, the ratios of barrel/reservoir concentra-tion and pressure, denoted by the subscripts A and R,respectively, are equal:

PA

PR=

CA

CR. (9)

Recalling Eq. (7), theCA

CRratio increases from 1 to 5

during actuation. Therefore, the energy required for ac-tive transport at the peak of actuation when the differencebetween concentration areas is greatest is 4.055 kJ/molof fluid transported. Figure 3 shows the relationship be-tween increasing actuator pressure and the consequentenergy requirements.

Equation (6) can be examined to determine chemicalconditions that would release enough energy for activetransport to be possible, knowing how much energy isrequired. Substituting the known, desired value of �EAT

for �GATPH and rearranging Eq. (6) yields:

KMA = exp��EAT − �G0

−R�T− 2�pH� . (10)

TABLE I. Actuator dimensions and physical properties.

Symbol Property Default Minimum Maximum

r, micron Barrel radius 250 25 500%d Relative pitch, %r 150% 400% 130%rp, micron Pitch 750 200 1300rs, micron External radius, 1⁄2 pitch 375 100 650h, micron Barrel height 200 100 400E, GPa Elastic modulus 3.79 30 2� Poisson’s ratio 0.34 0.45 0.3PA, MPa Applied pressure 5 1 5

FIG. 4. Energy required to transport fluid from fluid reservoir to thehigh pressure actuator barrel.

FIG. 5. Possible actuator pressure increase given chemical conditions.



This allows for the selection of molar concentrations ofATP, ADP, and PO4

2− that will enable enough energy tobe released so that the active transport proteins will becapable of pumping fluid against an increasing concen-tration gradient.

To find the possible osmotic pressure increase given bio-chemical concentration conditions, Eqs. (5), (6), and (7) arecombined by setting �GATPH � �EAT � 4.055 kJ/mol,C2 � PA, pressure inside the actuator, and C1 � Pf, thepressure of the fluid reservoir. Rearranging and solvingfor PA yields the following equation:

�PA = Pf exp��G0

R�T− 2.3 pK + 2 pH� . (11)

When pH � 4 and pK � 0.01, the greatest possiblepressure increase is 6.486 MPa. This is greater than themaximum desired value of 5 MPa, so it is possible tocreate enough pressure to cause nastic actuation usingenergy from ATP hydrolysis and active transport as amicro-hydraulic actuator pump.

IV. MECHANICAL ACTUATION

During the actuation process, the nastic actuator barrelincreases in volume due to fluid pressure forcing thecylinder walls and cover plate to bulge outward. The totalvolume change, �VISA can be expressed by

�VISA = �Vcomp + �Vbarrel + �Vcap − �Vload , (12)

where �Vcomp is fluid compressibility, �Vbarrel is the ra-dial and longitudinal barrel wall expansion, �Vcap is theoutward bulging of the cover plate, and �Vload is anyoutside blocking force that acts against the cover platedisplacement.3 In this article, the volume increment fromactuation is considered without any outside forces, so�Vload can be evaluated as zero.

The fluid compressibility under high fluid pressureforces is dependent on the volume of the cylinder, bulkmodulus of the fluid, and the applied pressure. The vol-ume change due to fluid compressibility is expressed as

�Vcomp =PA��h�d2

4B. (13)

The volume change due to actuator barrel expansion isa product of longitudinal and radial expansion, uL and uR,respectively, and dependent on the barrel radius and theouter radius rs, which is half the pitch rp, the distancebetween barrels.15 Material properties that affect the bar-rel expansion are the elastic modulus of the housing plateand Poisson’s ratio.

�Vbarrel = 2��uR�uL , (14)

uR =r�PA

E�rs2 − r2�

��1 + ��rs2 + �1 − ��r2� , (15)

uL =rs

2

rs2 − r2

PA�h

E. (16)

The total barrel expansion volume increase can besimplified to

�Vbarrel. = 2��r2h�PA

E ��1 + ��rs4 + �1 − ��rs

2�r2

�rs2 − r2�2

� .

(17)

The cover plate displacement and volume change fromthe outward bulging are found using the analytical solu-tion to the bending of a clamped circulate thin plate.16 Aspressure is applied to the plate, it bulges outward, creat-ing a blister profile, where maximum displacement is atthe center. The plate displacement is

ucap =PA�r4

64�D. (18)

The variable D represents the plate bending stiffness,

D =E�t3

12�1 − �2�. (19)

The volume under the cover plate blister is found byintegrating the displacement in Eq. (18):

�Vcap = 2� �0

rr�ucapdr =

PA��r6�1 − �2�

16E�t3. (20)

Table II lists the properties and dimensions analyzedduring actuation modeling to determine optimal param-eters, as well as possible volume increments from each ofthe three factors that contribute to the total overall ac-tuator volume expansion. Values were chosen fromTable I to produce a minimum and maximum volumechange, and optimal values, listed as default values, werefound that would provide for a design that would producedesirable volume change during actuation. The volumeincrement described in the table occurs under an appliedpressure of 5 MPa. The volume increase due to fluid

TABLE II. Volume increments during actuation.

Volume (pl) Minimum values Maximum values Default values

Preactuation 0.196 314.15 39.27�Vcomp 4.4 × 10−4 0.71 0.089�Vbarrel 1.842 × 10−8 0.04 7.234 × 10−4

�Vcap 7.171 × 10−5 0.967 36.775�V total 5.117 × 10−4 1.717 36.86Final 0.197 315.231 76.13% increase 0.5% 0.3% 93.8%



compressibility and barrel expansion is very small com-pared to the volume under the cover plate bulging. Theresponse of the cover plate during actuation has beenfurther studied to understand its nonlinear deformationbehavior.

To study the range where linear and nonlinear defor-mation is observed, the system is analyzed nondimen-sionally.17,18 The applied pressure is converted using

� =6�1 − �2�PAr4

E�t4. (21)

The central deflection becomes

W0 =PA

2 �2�1 − I0��

�3I1��+

1

�2� , (22)

where the subscript 0 denotes deflection at the center ofthe circular plate, so the displacement is not dependenton radial position. The symbol � represents initial mem-brane stress, which signifies bending behavior while at alow value, and stretching as � increases. In the case ofthe nastic actuator, � is taken as a low value because theplate edges are evaluated as clamped and there is nostress in the plate prior to actuation.

Table III describes the property values used for linearanalysis and the nondimensional values they become, aswell as the resultant nondimensional displacement. Equa-tion (22) is plotted to show the nonlinear transition as theapplied actuation pressure increases.

At low applied pressure, the plate’s displacement islinear but undergoes a transition period when W0 � 0.3to 3. After this transition, the displacement is nonlinearand approaches a cubic asymptote. Knowing the nondi-mensional range of pressure that causes linear and non-linear cover plate deformation allows for understandingthe effect of dimensional pressure on the actual deflec-tion. The ranges for pressure are summarized inTable IV.

V. EXPERIMENTAL DEMONSTRATION OFION TRANSPORT

The actuation scheme in Ref. 2 above requires forminga membrane similar to biological membranes that can

serve as a framework to hold the biological ion trans-porters. The membrane assembly that pumps species intothe barrel for any applied stimulus forms the active partof the micro-hydraulic actuator. The experiment focuseson forming the membrane interface that has the ability totransport fluid across the lipid membrane using biologi-cal ion transporters for a known applied stimulus. Iontransporters are protein molecules that can self-assembleacross the planar BLM without losing its functionality.Our experiment focuses on reconstituting the ion trans-porters on an artificial BLM and quantifying the ob-served flux for different stimulus in a transport assay cup.The experiment can be divided into the following threesteps: (i) forming the BLM, (ii) reconstituting ion trans-porters in the BLM to render it functional, and (iii) dem-onstration of controlled transport through the functionalBLM.

A. Materials and methods

The necessary materials and equipment used in ourexperiment are described here. The first item was aCaCo2 transport assay multi-well plate. The ion trans-porter was AtSUT4 H+-Suc co-transporter extracted fromArabidopsis thaliana expressed in yeast, extracted, and

TABLE III. Dimensional and nondimensional values for linearityanalysis.

Symbol Property Default

Pa, MPa Applied pressure 5r, micron Barrel radius 250t, micron Cover plate thickness 23E, GPa Elastic modulus 3.79� Poisson’s ratio 0.34� Dimensionless pressure 97.719W Dimensionless displacement 3.063

TABLE IV. Pressure ranges that yield linear and non-lineardeflection.

Deflection Non-D pressure range Pressure range, MPa

Linear 0 → 9.57 0 → 0.48Transition 19.544 → 95.711 0.48 → 4.897Cubic 95.711 → 97.719 4.897 → 5

FIG. 6. Nonlinear nondimensional cover plate deflection with linearasymptotes.



purified. Lipids were 1-Palmitoyl-2-Oleoyl- sn- Glycero-3- [Phospho-L-Serine] (Sodium Salt) (POPS) mixed with1-Palmitoyl-2-Oleoyl- sn- Glycero-3- Phosphoethanol-amine (POPE) in the weight ratio 5:4 and dissolved inn-decane (40 mg/ml for transport assay cups). The elec-trodes were silver-silver chloride half-cell reference elec-trode and 0.8-mm-diameter platinum electrode wire. Ex-perimental equipment included HP 4192 A impedanceanalyzer, HP 34401 A digital multimeter, and AgilentE3648A digital power supply.

B. Forming a planar BLM

Forming a planar BLM on a transport assay cup wasaccomplished by introducing the POPS:POPE lipid mix

dissolved in n-decane at the bottom of the cup and bring-ing it in contact with an aqueous medium on either side.Individual wells chipped away from the multi-well platewere used for each trial. A fixture shown in Fig. 7 wasused for holding the cups. Impedance measurement asdiscussed in Ref. 21 is one of the many methods ofqualitatively confirming the presence of BLM. Imped-ance measured over a frequency range from 5 Hz to 1MHz at 50 mV oscillator level using the HP 4192A Im-pedance analyzer was used to calculate the capacitance ofthe self-assembled BLM. The stability of the impedancevalue measured over time was used as a qualitative meas-ure to detect the ability of the BLM to hold on to thesubstrate.

C. Reconstituting ion transporters on BLM andtransport experiment

Reconstituting SUT4 transporters on the membranebottom of the transport assay cup with BLM was similarto forming a bilayer membrane. The experimental setupfor transport experiment is shown in Fig. 8. Ten micro-liters lipid mixture were added, followed by 20 �l pro-teins suspended in pH 7 medium to the bottom of thecup. The cup was kept undisturbed for 15 min and thenplaced in the fixture supported by the cup holder. Thisbrought the membrane in contact with the pH 4.0 bufferfrom the bottom in the reservoir. One hundred microliterspH 7.0 buffer were added into the cup from the top.

Approximate volume of the fluid in the bottom cham-ber was 30 ml. On coming into contact with an aqueousmedium, it was observed from impedance measurementsthat the phospholipid mix self-assembled into a BLM and

FIG. 7. Fixture for resistance measurement experiments.

FIG. 8. Transport experiments in the transport assay cups.



accommodated the SUT4 transporter across its thickness.Amount of sucrose present in pH 4.0 buffer in the reser-voir was varied for each trial to understand the effect ofsucrose concentration on transport properties.

D. Flux through ion transporter

The change in fluid level was calculated by measuringthe change in ionic conductance between the platinumelectrodes kept immersed in the fluid within the topchamber. The depth of immersion of the electrodes wasalways kept a constant at 5 mm. We used the HP 4192Aimpedance analyzer for measuring the capacitance acrossthe Pt electrodes by applying a 50 mV signal at 100 kHz.Prior to the experiment, change in conductance for dif-ferent levels of fluid was calibrated. The change in elec-trical conductance for 1 mm change in depth of immer-sion of electrodes in plain pH 7.0 buffer and in 1–5 mMsucrose mixed with pH 7.0 buffer was within 1% toler-ance limit. This allowed monitoring the fluid level andquantifying the change in volume in real time. A dataacquisition interface to record the data was built withLabView 7.1 that interfaces via IEEE488.2(GPIB) pro-tocol. VISA communication driver software forHP4192A analyzer was available from National Instru-ments Developers Zone.

VI. RESULTS AND DISCUSSIONFROM EXPERIMENTS

A. Reconstitution of functional BLM

Artificial bilayer membrane behaves very much like aconventional lipid bilayer membrane present in livingcells except that it lacks the cytoskeleton. It can serve asa substrate to carry ion transporters. The BLM formedacross the porous substrate should mimic the cellularmembranes. After placing the porous substrate on thefixture with lipids in water, we need to confirm the pres-ence of the bilayer membrane. One of the popular meth-ods for confirming BLM formation across the pores is bymeasuring the impedance measured across the poroussubstrate before and after introducing the phospholipidmix. Forming a stable BLM was essential for proceedingfurther and to introduce SUT4 transporter proteins. Theobserved impedance increases on introduction of thephospholipids to the membrane bottom over the entirefrequency range, as shown in Fig. 9.

The impedance data in Fig. 9 show the observed im-pedance and phase for different conditions in the trans-port assay cups. It is observed that the impedance de-creases after the introduction of SUT4 ion transporter tothe bilayer membrane. Selective transport of ions/electrical charges through SUT4 is not well understood,and hence electrical modeling is not attempted here. Todetect the presence of SUT4 reconstituted across the bi-layer membrane the key role played by SUT4 in plants

for sucrose transport demonstrated by Frommer et al.20

was used.

B. Transport of fluid through functional BLMreconstituted with SUT4 ion transporter

The ion transporters were reconstituted on thePOPS:POPE BLM on the membrane bottom of the trans-port assay cups. The transporter protein when placed in apH gradient in the presence of sucrose translocates pro-tons down the pH gradient. Sucrose is carried with each

FIG. 9. Impedance data for transport assay cups.

FIG. 10. Fluid flux in transport assay cups for different input condi-tions.



proton and water molecules travel with sucrose, as shownin Ref. 20. This selectivity of SUT4 transporters to trans-port sucrose and water for a known pH gradient was usedto detect the functionality and presence of SUT4 iontransporter on the BLM. The fixtures shown in Fig. 8provided the tooling to form bilayer membranes, recon-stitute the SUT4 ion transporter and to check the amountof species transported. SUT4 ion transporters are proteinsthat retain their functionality in their folded forms withthe cell membranes on which they were formed. SUT4ion transporter available with backing native membraneis considered to position itself across the artificial BLM.Adding purified SUT4 transporters to the phospholipidmixture on porous substrate under the assumption thatthey are available with cell membranes holding proteinsin the right configuration (folded form), should causeself-assembly across the thickness of BLM.

The BLM was formed with pH 4.0 buffer supporting itat the bottom and pH 7.0 buffer at the top and dispersedwith SUT4 transporters as in the experimental descrip-tion. Due to the selective nature of the transporter, itspresence was detected by varying the concentration ofsucrose. The pH 4.0 buffer carried 1, 5, and 10 mM su-crose in different trials. It is observed from this plot offlux of species against gravity into the top chamber is dueto the presence of SUT4 proton transporter when sucroseis available in the pH 4.0 buffer medium. Dependence offlux on the sucrose concentration and the saturation ki-netics of fluid transport indicates that a specific saturablenumber of sites on the membrane were involved in trans-port, as shown in Ref. 22.

The observed flux rate for fluid transport was calcu-lated to be approximately 1.5 �l/min for 5 and 10 mMsucrose concentration in pH 4.0 buffer and 0.5 �l/min for1 mM sucrose concentration. The BLM was found to beimpermeable to the fluid in the top chamber in the ab-sence of transporter proteins. When transporter proteinswere added without lipids, a small head of fluid wasobserved in the top chamber, similar to the one shownthat resulted in leakage flux.

The transport assay cups were small and gave us littlefreedom to increase the flux. The fluid flux observed intransport assay cups had to be scaled up to demonstratethe use of biological ion transporters for actuation. Thiswork demonstrates the method and experimental setuprequired to form a bilayer lipid membrane (BLM) on aporous substrate. The POPS:POPE BLM formed on theCaCo2 membrane had a capacitance of 0.45 nF and anadmittance of 12.3 �S. The resistance of the access me-dium was found to vary with electrode distances to theBLM. The sucrose transporter AtSUT4 extracted fromplants and grown in yeast by our collaborator Dr. Cup-poletti at the Medical School, University of Cincinnati,Cincinnati, OH, was made available to us. The SUT4transporter was reconstituted on the POPS:POPE bilayer

membrane. This was verified by checking the reconsti-tuted BLM for SUT4 functionality to selectively movesucrose and water along an established proton gradient.This was additionally confirmed by the dependence andsaturation of flux on the concentration of sucrose inpH 4.0 buffer. Our current and future efforts are directedtoward harnessing the ability of ion transporters to movefluid in a controlled manner using bio-fuels like ATP andto demonstrate mechanical actuation.

VII. CONCLUSION

In this article, the bioenergetics behind plant nasticmotion is examined to illustrate the efficiency and me-chanics of motor cells that function as biological actua-tors. Biological processes are usually more efficient inenergy production and consumption than mechanicalprocesses. Biomimetic nastic structures aim to imitateplant tissue shape change in process as well as in effi-ciency. After the energy release and usage in plants weremodeled, chemical conditions that affect the energy sup-plying ATP hydrolysis reaction were analyzed to under-stand what can be modified to moderate energy release tocontrol actuation in synthetic nastic structures. From ourstudies, it was shown that the pH level of the nasticstructures fluid reservoir can be modified to raise orlower the energy released by ATP hydrolysis. With thepresence of the enzyme ATPase, hydrolysis becomes areversible process with low reassociation energy, so ATPhydrolysis becomes a renewable energy source.

The mechanical response of the nastic actuator wasmodeled to predict a possible range of volumetric expan-sion. It was found that using optimal, default parameterswith an applied osmotic pressure increase to 5 MPa, theactuator size will increase by 93%. The main contributorto actuation volume change is the outward bulging of thecover plate, and non-dimensional analysis shows that theblister created by the plate displacement deforms non-linearly. This produces a greater blister volume increasethan a linear response would.

Further studies will examine structural integrity duringactuation and predict a lifespan in terms of cyclic actua-tion before residual stress and ultimate failure.3 Researchis also currently underway to examine the introduction ofthe enzyme ATPase to reverse ATP hydrolysis, makingthe reaction renewable. Future research will also involve,among other things, taking into consideration the effectof atmospheric temperature change and blocking forceson the nastic energy system.

ACKNOWLEDGMENTS

This research was carried out under a Defense Ad-vanced Research Projects Agency (DARPA) contract asa part of the Nastic Structures project (ARO Grant No.W911-NF-04-1-0421). The authors greatly acknowledge



the support. We also acknowledge the support providedby our collaborators from Dr. Subash Narang, ShaktiTechnologies, CA and Dr. John Cuppoletti, Professor inMolecular and Cellular Biology, University of Cincin-nati, Cincinnati, OH, by providing us with the requiredmaterials for experiments.

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