This document contains the draft version of the following paper:

A. G. Banerjee, S. Chowdhury, and S. K. Gupta. Optical Tweezers: Autonomous Robots for the Manipulation of Biological Cells.IEEE Robotics & Automation

Magazine, 21(3): 81-88, 2014

Readers are encouraged to get the official version from the periodical’s web site or by contacting Dr. S.K. Gupta (skgupta@umd.edu).

1

Optical Tweezers: Autonomous Robots for theManipulation of Biological CellsAshis Gopal Banerjee1, Sagar Chowdhury2, and Satyandra K. Gupta3

1Complex Systems Engineering Laboratory, General Electric Global Research, Niskayuna, NY,banerjee@ge.com

2Department of Mechanical Engineering and The Institute for Systems Research, University ofMaryland, College Park, MD, sagar353@umd.edu

3Department of Mechanical Engineering and The Institute for Systems Research, University ofMaryland, College Park, MD, skgupta@umd.edu

I. INTRODUCTION

Optical tweezers (OT) is a popular tool for manipu-lating biological objects especially cells [1], [2]. Usinga tightly focussed laser beam, it exerts sufficient forcesto tweeze, i.e., hold (trap) and move, freely diffusingcells in the vicinity of the beam focus. The beam canbe focussed at any point in the workspace that typicallyconsists of a liquid-filled glass slide. The trapped cellcan, thus, be translated and rotated (transported) in threedimensions by changing the beam focus position. OTprovides certain advantages over other cell manipulationtechniques. It is able to manipulate cells with a greaterdegree of precision as compared to microfluidic flow.Significant contact forces are not exerted on the cellsunlike mechanical manipulation, thereby avoiding dam-ages due to contact friction or surface chemistry. Cellsare also easily released at the end of manipulation bysimply switching off the laser beam. Hence, OT hasbeen extensively used for mechanical characterizationof cells by measuring their viscoelastic properties todistinguish between normal and diseased cells [3]. Ithas also been used for separating cells of different types[4] and investigating the response of cells to externalstimuli [5]. However, manual or teleoperated control ofthe laser beam has limited its applicability for multi-cellular studies.

Over the past decade or so, researchers have startedusing OT as an autonomous microrobot [6], [7], [8], [9],[10], [11]. Like any conventional robot, an OT systemcomprises of an actuator, sensor, and controller. Whilesensing is done by a video camera and the controllerhardware that sets the laser beam intensity, focal positionand speed is standard, actuation is performed using opti-

cal forces. The laser beam acts as the manipulator hand;it is focused using a high numerical aperture objectivelens that functions as the end effector. A computer-generated hologram [12], which can be dynamicallyreconfigured in real time, is commonly used to split thebeam into multiple components with complete controlover the focal positions of the individual beams in threedimensions. Thus, each split beam functions as an opticalfinger to grip the manipulated cell with three independentdegrees of freedom for every finger. This mutiplexingcapability enables deformation and concurrent transportof several cells. The number of manipulated cells isonly restricted by the number of split beams that canbe generated and goes up to a hundred. A representativeholographic OT set-up is shown in Figure 1 that pointsout how it is used as a robotic system.

Autonomous cell manipulation required significantdevelopments in robotic perception, planning, control,and design. These developments were necessary to adaptthe methods that were successful in macro scale roboticsand address the challenges present in the current problemdomain. More specifically, the perception algorithmshad to process both translucent (cells) and opaque(microparticles pushing the cells) objects of arbitraryshapes in the same workspace. The planning and con-trol methods needed to incorporate trapping dynamics,viscous drag, and fluid motion, and explicitly modelthe uncertainties in control action executions and sen-sor measurements. The manipulator designs had to bereconfigured during ongoing operations to accommodatechanging cell shapes. And, optimal actions and designsneeded to be computed within a few milliseconds toprevent them from being rendered ineffective due tovarying workspace conditions resulting from the random

(a) (b)

Fig. 1. Holographic optical tweezers illustrating its use as a microrobot: (a) Hardware set-up and (b) Schematic diagram.

Fig. 2. Autonomous robotic system for cell manipulation. Arrowsdenote the direction of information flow between the system compo-nents.

Brownian motions of the objects. These challenges areshown in Figure 2 using a system component diagram.

New strategies for autonomous cell manipulation havebeen developed [13], [14] recently that limit the exposureof laser light to the cells. Thus, these new strategies en-able experiments with cells that are sensitive to laser ex-posure. Moreover, it has been shown that OT is amenableto integration with other types of micromanipulationmodes like microfluidic flow [15]. This integration isfurther expanding our capabilities to perform usefulbiological experiments including cell sorting and cancerstudies via regulated cellular signaling. The goal of thisarticle is to inform the robotics community about thelatest advances in automated optical biomanipulation andfoster new developments in the biomanipulation area bypromoting the integration of OT with other modalities.

II. OPTICAL TWEEZERS

The advent of high intensity laser with intensity mil-lion times that of sunlight on the Earth surface made itpossible to generate forces of the order of picoNewtonsto manipulate objects at the micron size scale. Ashkinand his colleagues at Bell Laboratories first demonstratedthis capability, leading to the development of the opticaltweezers in 1986 [16].

For both axial and transverse displacements of anobject from the trap center (laser beam focus), theoptical trapping forces can be well approximated aslinear restoring spring forces [17] given by

Ftrap(∆x) =

{K1∆x, 0 < ∆x < x0−K2∆x+ c, ∆x > x0.

(1)

Here, ∆x is the displacement of the object center, K1

and K2 are trapping stiffness constants that are differentfor axial above focal plane, axial below focal plane, andtransverse displacements, and x0 and c are parametersthat depend on the object properties and laser power.The overall equation of motion of a trapped object [18]in any dimension then becomes

mx = Ftrap(∆x)− γx+ ζΓ(t) + Fext (2)

where γ = 6πηRo is the Stokes coefficient for aspherical object of radius Ro in medium of viscosityη. ζ =

√2γkBT is the scaling factor that is obtained by

applying the fluctuation-dissipation theorem [19], wherekB is the Boltzmann constant and T is the absolutetemperature. Thus, γx represents the viscous drag force,ζΓ(t) models the thermal force arising from Brownianmotion, and Fext encodes the external forces due to

2

collisions, gravity, and buoyancy. The stochastic formof Γ(t) prevents a direct analytical solution of Equation

(2). However, ζΓ(t) can be replaced by√

2γkBTδt N(0, 1)

to solve Equation (2) numerically in discrete time. Forsmall object transport speeds (few µm/s), the Reynoldsnumber is small and the inertial term on the left hand sideof Equation (2) can be ignored. Consequently, opticaltweezers can robustly manipulate an object when thepicoNewton magnitude trapping forces overcome dragand thermal forces either supported or opposed by otherexternal forces.

III. MANIPULATION USING DIRECT TRAPPING

Direct trapping of cells is the simplest and mostcommon optical manipulation strategy. Researchers atthe City University of Hong Kong have successfully useda suite of autonomous planning and control methods inconjunction with cell-trap dynamics analysis to transportliving yeast cells with as little as 10 mW of laser power.In particular, they have adapted graph search-basedplanning algorithms such as rapidly-exploring randomtrees and A* or derived closed-loop controllers usingsynchronization and potential functions for concurrentmanipulation of multiple cells. Their experiments haveshown that (a) cells can be transported while avoidingcollisions with other cells in the workspace [20], (b) cellshave limited possibilities of escaping from the opticaltraps [17], (c) multiple cells can be transported whilemaintaining a fixed pattern [9], and (d) cells can bearranged in stable array configurations while preservinga minimum distance among any two pairs of cells [21].These are significant advances that offer a lot of promisefor conducting robust and efficient multi-cell studiesusing optical tweezers without manual intervention.

Researchers at the University of Maryland, in col-laboration with biophysicists at the Vanderbilt Univer-sity, have adopted a different experimental set-up todemonstrate the power of autonomy. They have uti-lized a hybrid system, where optical tweezers is usedinside a continuous-flow microfluidic chamber to takeadvantage of the complementary benefits provided by thetwo manipulation types. While microfluidics provides alow cost technique for simultaneously manipulating alarge number of cells with small power consumption,optical tweezers enables much finer position control ofindividual cells at the expense of low throughput andhigher power consumption. The microfluidic chambercontains about 10000 microNets [22] that are createdso as to direct the fluid flow in a certain way andcapture the cells injected to the chamber. However, thenumber of the cells captured in the microNets cannot

be controlled by solely regulating the fluid flow. Thefluid flow results in statistical variations in the numberof cells inside each microNet, which is not desirable forcertain biological experiments like cell-cell interactionstudies [23]. Optical tweezers is then used for cleaningthe microNets by moving the excess cells from the overpopulated microNets to those with insufficient numberof cells or by releasing the cells at locations wherethey can be pushed out of the chamber by the fluidflow [15]. The success of such operations depends onaccounting for and utilizing fluid flow during optical cellmanipulation. This utilization is done by developing aphysics-based planning approach that combines offlinesimulation models of fluid flow with online D* Litegraph search algorithm to compute collision-free trajec-tories. An example cleaning operation is illustrated inFigure 3.

IV. MANIPULATION USING TOOL ATTACHMENT

Direct trapping of cells expose them to high intensitylaser causing structural damages and adverse effects onphysiological properties and processes [24]. In order toavoid direct laser exposure, cells are attached to inertmicroparticles with adhesives (see [25] for a review).The optically trapped microparticles, thus, act as attachedend effector tools to manipulate the cells indirectly. Eventhough autonomy has not yet been used for this manip-ulation strategy, we discuss it to highlight the gradualdevelopment of more complex optical micromanipulatordesigns.

Researchers at the National Taiwan University havedemonstrated this manipulation strategy for rotation con-trol of cells using irregularly shaped diamond micropar-ticles of size 15-25 µm as the tool fingers [26]. Diamondis chosen as the finger material as it is stable under theinfluence of laser and inert even in cell culture solutions.The particles are mixed with 0.01% poly-L-lysine toprovide strong adhesion. Cells undergo structural po-larity due to the membrane protein distribution acrossthe cell membrane that determines their physiologicalfunctions. Therefore, rotating cells in a controlled man-ner is important to study their physiological behaviors.Moreover, controlled cell rotation allows easy access tocell organelles for microinjection and microdissection.Rotation control is achieved by changing the focalplane of the laser at the interface to generate angularmomentum for the laser. Figure 4 shows full (360o)counterclockwise rotation of a mesophyll protoplast cellusing 150 mW of laser power.

A gel-based microtool is developed by researchers atthe Nagoya University [7]. The tool fingers are made of

3

(a) (b)

(c) (d)

Fig. 3. Autonomous transport of three yeast cells to their desired goals using direct optical trapping (the target cells are labeled as Ti, theirinitial locations are marked using green “×” symbols, and their corresponding release locations are marked using red “×” symbols and labeledas Gi, where i represents the index of the target cell): (a) initial scene where three target cells are directly trapped by three laser beams, (b)target cells are transported towards their respective goal locations while avoiding obstacles in the workspace (trajectories of the laser beams aremarked with white dots) (c) target cells T2 and T3 reach their goal locations G2 and G3 respectively, and (d) target cell T1 reaches its desiredgoal location G1.

(a) (b)

(c) (d)

Fig. 4. Rotation of a mesophyll protoplast using a laser trappeddiamond particle as an optical microtool: (a) a diamond particledenoted by “D” is tagged with a mesophyll protoplast cell and trappedby laser beam “L”, (b) the tool is moved along the periphery of thecell to induce rotation, (c) the cell rotates about the optical axis as thetool moves along its periphery, and (d) the cell gets rotated by 360 o.(This figure is adapted from [26].)

hydrophilic photo-crosslinkable resin. Spiropyran chro-mospheres, a type of photochromic polymer, is used foradhesion of the tool with the manipulated yeast cells.By adjusting the electrolyte concentration of the fluidsolution after the tool is subjected to ultraviolet illumina-tion, the adhesion can be either temporary or permanent.This set-up is used to transport cells by pushing andpulling, and measure cell pH levels by immobilizingthe cells and coating the tool with bromythol blue pHindicator. An alternative parallelizable tool fabricationprocess is reported in [27]. Polystyrene beads are usedas the finger material. Dispersed bead solutions areinjected over silicon substrates that have been patternedinto desired tool shapes, resulting in aggregation of thefingers due to surface tension. The aggregated fingersare then fused together by subjecting them to tem-peratures above the glass transition temperature. Thefused fingers can be detached from the patterns byultrasound treatment, thereby providing the option ofreconfiguring the tool shapes arbitrarily. This fabricationtechnique enables faster transport speed as compared tothe previous photofabrication process.

4

V. MANIPULATION USING RECONFIGURABLEGRIPPING

Since the attached end effector tools provide one-to-one adhesion with cells, one tool finger is enough tomanipulate a cell indirectly. However, the cells often can-not be easily released from the tools after manipulation,which poses problems especially for experiments wherethe cells need be arranged in certain configurations andthen allowed to exhibit natural behaviors for a long time.In such cases, an alternative manipulation strategy is togrip the cells using optically-trapped inert microparticlesthat do not have any adhesive coatings. We refer tothis strategy as optical gripping and the formation oftrapped beads to grip a cell as end effector gripper or justgripper in short. The trapped beads themselves form thegripper fingers. This strategy can prevent about 90% ofthe laser power from being incident on the cells, therebyenhancing their viabilities significantly.

Researchers at the University of Maryland have beensuccessful in bringing about autonomy for indirect ma-nipulation of yeast cells using silica as the gripperfinger material [13]. The sequence of operations duringmanipulation are as follows: (1) target gripper fingers aretrapped and transported to the cell to form the gripper,(2) the cell is transported using the gripper to the desiredgoal location, (3) the gripper fingers are moved awayfrom the cell to release the cell at the goal location,and (4) the manipulation is completed by removingthe fingers by switching off the laser beams. Imageprocessing is done using the Hough transform and thespherical cells are easily differentiated from the beadssince their radii are different. Successful manipulationthen depends not only on finding collision-free paths(defined using waypoint sequences) for the cells using anA* planner but also on the coordinated transport of thegripper fingers to move the cells along the desired paths.Based on the the current locations of the gripper fingers,an additional planner selects a sequence of atomic ma-neuvers, involving rotations, translations and retainingtrap positions, at a rate of 10Hz to push the cells fromtheir current waypoints to the next waypoints. Figure 5shows a representative experiment to transport a cellusing a three-finger gripper in a challenging workspacecontaining several obstacles.

VI. MANIPULATION USING INDIRECT PUSHING

Dictyostelium discoideum is used as a model or-ganism to study collective cell migration [28] that isimportant in many biological processes from organ de-velopment to immune response to cancer metastasis.With the ability to move directionally in the presence

of gradients of chemoattractants and relay signals to theneighboring cells, the migration of a large number ofD. Discoideum cells is seen as an important model ofhow cells operate collectively. While the migration istriggered by the presence of chemoattractants, the cellsdo not move towards the chemoattractants individually.Instead, they first form chains with the surrounding cellsand then approach the chemoattractants collectively. Thisbehavior poses interesting questions: what is the under-lying mechanism of this unique pattern of migration andwhat is the influence of the surrounding cells in themigration of an individual cell? The traditional way ofstudying neighboring cells as a single group is not able toanswer the questions. Instead, individual cells have to beperturbed from the chain systematically to arrange themin different configurations and investigate the resultingvariations in the collective migration trajectories. Theperturbations also need to be properly synchronized forthe individual cells to exhibit the desired motility. Thesestudies, therefore, require a strategy for fast, reconfig-urable, and precise manipulation of cells in parallel withcomplete control over individual cell manipulation.

Researchers at the University of Maryland have madesome progress in this regard. They first polarize (createstates of extended protrusions) the Dictyostelium cellsusing a regular pulse of chemoattractant cAMP. Opticaltweezers are then used to arrange the cells in pre-definedconfigurations to observe the evolution of their migrationbehaviors. However, the cells are very sensitive to thelaser beam. Even 10 % of laser exposure that occurs dur-ing gripping affects their normal physiological activities.Hence, a different stategy has been developed, where thecells are pushed indirectly by optically trapped beads thatdirectly push a non-trapped intermediate bead positionedbetween the optically trapped beads and the target cell.The trapped beads, thus, function as actuator fingersand the intermediate bead acts as a pushing finger. Theoverall strategy is referred to as indirect optical pushingand the collection of actuator and pushing fingers iscalled a pushing formation. The researchers have de-vised an autonomous approach [29], [14] that takes intoaccount the inherent instabilities of the contact pointsbetween the pushing fingers and the cells. A series ofoperations are performed on the input images to identifythe irregular shaped cells and the spherical finger ob-jects. Spherical objects are extracted and separated fromthe images using the Hough transform. The resultingimages are then processed with Canny edge detection,dilation, and flood filling successively to identify the cellboundaries. As in the case of reconfigurable gripping, anA* planner with a modified cost function based on the

5

(a) (b) (c)

(d) (e) (f)

Fig. 5. Indirect transport of a yeast cell using a 3-finger optical gripper: (a) initial scene where the cell is indirectly trapped by the gripper(initial and goal locations are marked by green and yellow “×” signs respectively), (b) the gripper rotates to align itself towards the waypointW1, (c) the cell is transported to the waypoint W1, (d) the cell is transported to the waypoint W2 through a sequence of rotation and linearmotion, (e) the gripper reaches the final goal G with the use of rotation and linear motion respectively, and (f) the cell is released by movingthe gripper fingers away from each other.

(a) (b) (c)

(d) (e) (f)

Fig. 6. Pushing a dynamic Dictyostelium discoideum cell with a formation (two actuator fingers are directly trapped by laser beams whilethe pushing finger is not directly trapped by any laser beam and is used to keep the cell away from the laser beam): (a) initial scene where thepushing formation location is marked by green “×” sign and the desired goal location of the cell is marked by yellow “×” sign and denotedby “G” , (b) the actuator fingers rotate about the optical axis to align the formation with the desired contact point denoted by white “+” sign,(c) the pushing formation gets aligned with the desired contact point, (d) the pushing formation reaches the contact location, (e) the formationstarts pushing the cell towards the goal G, and (f) the cell reaches the goal G.

pushing formation-cell ensemble dynamics is first usedto compute the collision-free paths for the cells. AnotherA* planner is then applied to compute the sequenceof waypoints for transporting the pushing formations to

the desired contact points on the cell boundaries. Themovement from one waypoint to the next is performedusing the same set of manuevers discussed in Section V.Figure 6 shows the re-orientation of a Dictyostelium

6

cell by a pushing formation composed of two actuatorfingers using only 5.3 mW of laser power.

VII. CONCLUSIONS

This article describes how optical tweezers haveevolved from a tool for single cell studies in the handsof biophysicists to powerful, precise, and flexible robotsfor autonomous manipulation of multiple cells. Table Ipresents a comparison of the different manipulationstrategies. While the complexity of controlling the ma-nipulation operations increases from direct trapping totool attachment/gripping to indirect pushing, laser ex-posure to cells is reduced progressively. The damagedue to such exposure can be completely eliminated forsensitive cells as opposed to occurrence rates of 67% and33% for direct trapping and tool attachment or gripping,respectively [29]. Even though both tool attachment andgripping utilize fingers (optically trapped beads) to ma-nipulate the cells, the presence of adhesive coatings onthe tool fingers means that it is often not possible to re-lease the cells after manipulation is over. Furthermore, itrequires a longer preparation time of the order of severalminutes (instead of a few seconds for the other strategies)and sometimes additional equipments and processes tofabricate the tools. However, this strategy enables pullingor stretching of the cells from two ends unlike any ofthe other strategies. Direct trapping, being the simpleststrategy, provides the least transport time even though thecells may no longer be viable if the operations last formore than a few seconds. Indirect pushing requires themaximum transport time among the other three strategiesparticularly when rotation maneuvers are required. Theactual times depend on laser power and the number andsize of the fingers; they are of the orders of tens ofseconds for transport operations shown in the Figures.Importantly though, tool attachment works slowest forcells with changing shapes due to the adhesive bondingbetween the fingers and cells making it difficult toremove and re-position the fingers at suitable contactpoints. On the other hand, indirect pushing works wellfor cells with changing shapes particularly for those withrelatively large dimensions of more than ten microns.

We have not yet, however, fully harnessed the po-tential of autonomous cell manipulation using opticalrobots. There are several important research directions,which include manipulating a large number of cells inthree dimensions (3D) to investigate tissue-level behav-iors, further leveraging the benefits of hybrid manip-ulation set-ups such as optofluidic and optoelectronic,optimizing the overall manipulator designs, and au-tomating complete operations from selecting the target

cells and beads to preserving the configurations of cellpatterns for hours. Such long-term automation of cellularsystems would require further advances in various areasof microrobotics. Examples include the development ofmore scalable yet tightly coupled planning and controlalgorithms, synchronized control of optical traps and mo-torized workstage, integration of fluorescence or phasecontrast microscopy to better estimate the irregular cellboundaries, additional optical imaging instrumentationto view the entire 3D workspace, and novel perceptionalgorithms to reconstruct the 3D workspace in real time.

VIII. ACKNOWLEDGEMENTS

This work was supported in part by the NationalScience Foundation (NSF) under Grant CMMI-0835572and Grant CPS-0931508. The opinions expressed in thispaper are those of the authors and do not necessarilyreflect the opinions of the sponsors.

REFERENCES

[1] A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping andmanipulation of single cells using infrared-laser beams,” Nature,vol. 330, pp. 769–771, Dec. 1987.

[2] K. K. Ramser and D. Hanstorp, “Optical manipulation for singlecell studies,” J. Biophotonics, vol. 3, pp. 187–206, Apr. 2010.

[3] J. P. Mills, L. Qie, M. Dao, C. T. Lim, and S. Suresh, “NonlinearElastic and Viscoelastic Deformation of the Human Red BloodCell with Optical Tweezers,” Mech. Chem. Biosyst., vol. 1,pp. 169–180, Sep. 2004.

[4] K. Dholakia, W. M. Lee, L. Paterson, M. P. MacDonald, R. Mc-Donald, I. Andreev, P. Mthunzi, C. T. A. Brown, R. F. March-ington, and A. C. Riches, “Optical separation of cells on po-tential energy landscapes: Enhancement with dielectric tagging,”IEEE J. Sel. Topics Quantum Electron., vol. 13, pp. 1646–1654,Nov./Dec. 2007.

[5] L. Y. Pozzo, A. Fontes, A. A. de Thomaz, B. S. Santos, P. M. A.Farias, D. C. Ayres, S. Giorgio, and C. L. Cesar, “Studying taxisin real time using optical tweezers: Applications for Leishmaniaamazonensis parasites,” Micron, vol. 40, pp. 617–620, Jul./Aug.2009.

[6] F. Arai, C. Ng, H. Maruyama, A. Ichikawa, H. El-Shimy, andT. Fukuda, “On chip single-cell separation and immobilizationusing optical tweezers and thermosensitive hydrogel,” Lab Chip,vol. 5, pp. 1399–1403, Dec. 2005.

[7] H. Maruyama, T. Fukuda, and F. Arai, “Laser manipulation andoptical adhesion control of functional gel-microtool for on-chipcell manipulation,” in Proc. IEEE/RSJ Int. Conf. Intell. Robot.Sys., (St. Louis, MO), pp. 1413–1418, 2009.

[8] A. G. Banerjee, A. Pomerance, W. Losert, and S. K. Gupta,“Developing a Stochastic Dynamic Programming Frameworkfor Optical Tweezer-Based Automated Particle Transport Opera-tions,” IEEE Trans. Autom. Sci. Eng., vol. 7, pp. 218–227, Apr.2010.

[9] S. Hu and D. Sun, “Automated transportation of biological cellswith a robot-tweezer manipulation system,” Int. J. Robot. Res.,vol. 30, pp. 1681–1694, Dec. 2011.

[10] A. G. Banerjee, S. Chowdhury, W. Losert, and S. K. Gupta,“Real-time path planning for coordinated transport of multipleparticles using optical tweezers,” IEEE Trans. Autom. Sci. Eng.,vol. 9, pp. 669 –678, Oct. 2012.

7

TABLE ICOMPARISON OF THE DIFFERENT CELL MANIPULATION STRATEGIES

Characteristic StrategyDirect trapping Tool attachment Gripping Indirect pushing

Control Simple Moderate; depends on Moderate; depends on Complexcomplexity number of fingers number of fingers

Cell exposure to laser Significant Moderate Moderate MinimalCell release Easy Often not possible Easy Easy

Preparation time Negligible Long Small SmallManipulation Translation Translation, rotation, Translation, rotation, Translation, rotation,

type and rotation pulling, and pushing and pushing and pushingTransport time More than direct trapping; More than direct trapping; More than gripping;

(same laser power Least slower for cells varies with the number faster forand finger material) with changing shapes and size of fingers larger cells

[11] X. Li, C. C. Cheah, S. Hu, and D. Sun, “Dynamic trappingand manipulation of biological cells with optical tweezers,”Automatica, vol. 49, pp. 1614–1625, Jun. 2013.

[12] J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographicoptical tweezers,” Opt. Comm., vol. 207, pp. 169–175, Jun. 2002.

[13] S. Chowdhury, A. Thakur, C. Wang, P. Svec, W. Losert, and S. K.Gupta, “Automated manipulation of biological cells using gripperformations controlled by optical tweezers,” IEEE Trans. Autom.Sci. Eng., vol. 11, pp. 338–347, Apr. 2014.

[14] A. Thakur, S. Chowdhury, C. Wang, P. Svec, W. Losert, and S. K.Gupta, “Indirect pushing based automated micromanipulation ofbiological cells using optical tweezers,” Int. J. Rob. Res., 2014.in press.

[15] S. Chowdhury, P. Svec, C. Wang, K. Seale, J. P. Wikswo,W. Losert, and S. K. Gupta, “Automated cell transport in opticaltweezers assisted microfluidic chamber,” IEEE Trans. Autom. Sci.Eng., vol. 10, pp. 980–989, Oct. 2013.

[16] A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu,“Observation of a single-beam gradient force optical trap fordielectric particles,” Opt. Lett., vol. 11, pp. 288–290, May 1986.

[17] Y. Wu, D. Sun, W. Huang, and N. Xi, “Dynamics analysis andmotion planning for automated cell transportation with opticaltweezers,” IEEE/ASME Trans. Mechatronics, vol. 18, pp. 706–713, Apr. 2013.

[18] A. G. Banerjee, A. Balijepalli, S. K. Gupta, and T. W. LeBrun,“Generating Simplified Trapping Probability Models From Sim-ulation of Optical Tweezers System,” J. Comput. Inf. Sci. Eng.,vol. 9, p. 021003, Jun. 2009.

[19] P. Grassia, “Dissipation, fluctuations, and conservation laws,”American J. Phy., vol. 69, pp. 113–119, Feb. 2001.

[20] T. Ju, S. Liu, J. Yang, and D. Sun, “Rapidly exploring randomtree algorithm-based path planning for robot-aided optical manip-ulation of biological cells,” IEEE Trans. Autom. Sci. Eng., 2013.In press.

[21] C. Haoyao and D. Sun, “Moving groups of microparticles intoarray with a robot-tweezers manipulation system,” IEEE Trans.Robot., vol. 28, pp. 1069–1080, Oct. 2012.

[22] K. T. Seale, S. L. Faley, J. Chamberlain, and J. P. Wikswo, Jr.,“Macro to nano: a simple method for transporting cultured cellsfrom milliliter scale to nanoliter scale,” Exp. Biol. Med., vol. 235,pp. 777–783, Jun. 2010.

[23] M. K. Driscoll, C. McCann, R. Kopace, T. Homan, J. T. Fourkas,C. Parent, and W. Losert, “Cell shape dynamics: From waves tomigration,” PLoS Comput. Biol., vol. 8, p. e1002392, Mar. 2012.

[24] T. Aabo, I. R. Perch-Nielsen, J. S. Dam, D. Z. Palima, H. Siegum-feldt, J. Gluckstad, and N. Arneborg, “Effect of long- andshort-term exposure to laser light at 1070 nm on growth ofSaccharomyces cerevisiae,” J. Biomed. Opt., vol. 15, p. 041505,Jul./Aug. 2010.

[25] A. G. Banerjee, S. Chowdhury, W. Losert, and S. K. Gupta,“Survey on indirect optical manipulation of cells, nucleic acids,and motor proteins,” J. Biomed. Opt., vol. 16, p. 051302, May2011.

[26] C.-K. Sun, Y.-C. Huang, P. C. Cheng, H.-C. Liu, and B.-L. Lin,“Cell manipulation by use of diamond microparticles as handlesof optical tweezers,” J. Opt. Soc. Am. B, vol. 18, pp. 1483–1489,Oct. 2001.

[27] H. Maruyama, R. Iitsuk, K. Onda, and F. Arai, “Massive parallelassembly of microbeads for fabrication of microtools havingspherical structure and powerful laser manipulation,” in Proc.IEEE Int. Conf. Robot. Autom., (Anchorage, AL), pp. 482–487,2010.

[28] P. Friedl, Y. Hegerfeldt, and M. Tusch, “Collective cell migrationin morphogenesis and cancer,” Int. J. Dev. Biol., vol. 48, pp. 441–449, Jul. 2004.

[29] S. Chowdhury, A. Thakur, C. Wang, P. Svec, W. Losert, and S. K.Gupta, “Automated indirect manipulation of irregular shaped cellswith optical tweezers for studying collective cell migration,”in Proc. IEEE Int. Conf. Robot. Autom., (Karlsruhe, Germany),pp. 2789–2894, 2013.

8