Single bacterial cell detection with nonlinear rotational frequency shifts of
Single bacterial cell detection with nonlinear rotational frequency shifts of driven magnetic microspheres
Brandon H.McNaughton a?
Department of Physics,University of Michigan,Ann Arbor,Michigan48109-1040,USA
Rodney R.Agayan
Department of Chemistry,University of Michigan,Ann Arbor,Michigan48109-1055,USA
Roy Clarke
Department of Physics,University of Michigan,Ann Arbor,Michigan48109-1040,USA
Ron G.Smith and Raoul Kopelman b?
Department of Chemistry,University of Michigan,Ann Arbor,Michigan48109-1055,USA
?Received27July2007;accepted30October2007;published online29November2007?
Shifts in the nonlinear rotational frequency of magnetic microspheres,driven by an external
magnetic?eld,offer a dynamic approach for the detection of single bacterial cells.We demonstrate
this capability by optically measuring such frequency shifts when an Escherichia coli attaches to the
surface of a2.0?m magnetic microsphere,thereby affecting the drag of the system.From this
change in drag,the nonlinear rotation rate was reduced,on average,by a factor of3.8.Sequential
bacterial cell attachments were also monitored.?2007American Institute of Physics.
?DOI:10.1063/1.2817593?
Magnetic microspheres and nanoparticles have been used for a variety of applications and have even been incor-porated into medical diagnostic techniques.1–4The transla-tional properties of magnetic particles have proven to be ex-tremely useful in biomedical procedures,such as magnetic separation.1–3Other applications include giant magnetoresis-tive sensors5and magnetic tunnel junction sensors.6It is pos-sible,however,through standard microscopy techniques,to monitor the rotational behavior of single magnetic particles or small chains of them.7–11These small dynamic magnetic systems have been utilized to improve immunoassays,12act as micromixers,8study microrheology,9,13and reduce inter-fering backgrounds in?uorescent spectroscopy meas-urements.7The sensitive rotational dynamics of these mag-netic systems offer potential uses in the detection of single microbiological agents.We report on such an application, demonstrating single and sequential cell detection of E.coli.
The method is based on the nonlinear rotational dynam-ics that a magnetic particle undergoes when driven by a ro-tating magnetic?eld and depends both on environmental conditions and on properties of the particle.11,14,15At low external driving frequencies,the magnetic particle rotates continuously and synchronously?linear response regime?with the external?eld.At suf?ciently high external driving frequencies,the particle becomes asynchronous?nonlinear?with the driving?eld.The rotational dynamics of an actively rotated magnetic particle give the following,
??˙?=??,???c
????2??c,???c,?1?where??˙?is the particle’s average rotation rate and?is the driving frequency of the external magnetic?eld.The critical transition frequency is given by?c=mB/??V,where m is the strength of the magnetic moment of the microsphere,B is the external magnetic?eld amplitude,?is the shape factor,?is the dynamic viscosity of the surrounding?uid,and V is the volume of the microsphere.Equation?1?holds for low Reynolds number environments?Re?1?and for our system Re?5?10?6.Rotation for???c is nonlinear.16,17We dem-onstrate that this regime can be used to detect single micro-biological agents.For example,when a bacterium attaches to a nonlinearly rotating magnetic microsphere,the volume and shape of the rotating system are drastically changed,increas-ing the drag and thus slowing the rotation rate?see Fig.1?.
The ability to develop sensitive diagnostic techniques has been a topic of high interest,18especially with dynamic systems.19One related technology that has demonstrated ex-treme sensitivity in air and vacuum environments is the na-noelectromechanical systems?NEMS?approach.20NEMS have been used to detect a single microbiological agent,such as a virus or a bacterium.21–24One NEMS detection scheme utilizes resonant frequency changes when a microbiological agent attaches to a cantilever.However,the sensitivity of such NEMS devices is drastically reduced when operated in ?uidic environments.25In contrast,the sensitivity of nonlin-ear rotating magnetic microspheres is based on changes in drag.14This allows for single biological agent detection in ?uidic environments.Thus,we demonstrate single and se-quential bacterial cell detection using frequency shifts in the nonlinear rotation of magnetic microspheres in a?uidic en-vironment.
Measurement of this rotational frequency is straightfor-ward when utilizing standard microscopy techniques.Mag-netic microspheres were prepared by spreading a20?l ali-quot of stock solution?1%w/v?of2.0?m ferromagnetic microspheres functionalized with goat antimouse IgG ?Spherotech,Lake Forest,IL?onto a precut microscope slide. The sample was allowed to dry and then coated with ?50nm of Al.The sample was placed in a uniform mag-
a?Electronic mail:bmcnaugh@https://www.wendangku.net/doc/a53292494.html,.
b?Electronic mail:kopelman@https://www.wendangku.net/doc/a53292494.html,.URL:https://www.wendangku.net/doc/a53292494.html,/
?koplab
APPLIED PHYSICS LETTERS91,224105?2007?
0003-6951/2007/91?22?/224105/3/$23.00?2007American Institute of Physics
91,224105-1
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netic ?eld of 1.4kOe to induce magnetization perpendicular to the microscope slide.The spheres were collected and sus-pended in phosphate buffer solution ?PBS ?at a p H of 7.2.They were then functionalized with anti-E.-coli antibodies ?Cortex Biochem,San Diego,CA ?,following the manufac-turer procedures.Streptavidin magnetic microspheres func-tionalized with biotin conjugated anti-E.-Coli antibodies were also used.E.coli BL21?DE3?were made ?uorescent by introducing a DsRed plasmid according to a previously de-scribed transformation technique.26The bacteria were al-lowed to grow until the sample reached an optical density of 0.67at ??600nm,where the magnetic microspheres and bacterial solution were then mixed 1:1?by volume ?.The re-sulting sample had many single microspheres with 1–5E.coli bound to their surface,con?rmed using visual analysis ??uorescence microscopy ?.Rotational frequencies were mea-sured using bright-?eld,re?ection,or ?uorescence micros-copy,and image analysis techniques reported elsewhere.11,14
Measurements were performed in two homemade ?100?m thick ?uidic cells,where experiments were carried out in a pure PBS ??=0.001Pa’s ?or in or in a glycerol-PBS mass fraction of 0.5??=0.006Pa’s ?,where B ?10Oe.Average nonlinear rotational frequencies were determined using dis-crete Fourier transform techniques ?higher harmonics have been ?ltered in the resulting power spectrum ?to analyze the microspheres’intensity ?uctuations.Sequential cell detection was performed by tracking the rotation rate of a magnetic microsphere dimer,where intensity modulations were mea-sured using bright-?eld microscopy.
Theory and experiments for single magnetic particles,rotating in response to an external driving ?eld,have been demonstrated,11,14,15but measurements have not previously been made for the case of a magnetic particle attached to a bacterium.Figure 2?a ?shows the average rotation frequency of such a system for increasing external driving frequencies.The data are in good agreement with the ?t determined from Eq.?1?,and the critical onset of asynchronous rotation ?c was found to be 1.27Hz.Since the rotational dynamics of the magnetic particle were in good agreement with Eq.?1?,we assume that any forces resulting from bacterial motility were negligible.This measurement also shows that when a bacterium is bound to the surface of a magnetic microsphere,the system can still be analyzed using previously developed theory.11,14Thus,a change in rotational frequency can be used to detect pathogens such as bacteria.
While the entire range of frequencies for magnetic par-ticles,with and without bacteria,could be scanned,as was done in Fig.2?a ?,it is much faster and more straightforward to only measure the value of the nonlinear rotation fre-quency,??
˙?,at a given external driving frequency of ?,where ???c .Figure 2?b ?shows the result of such measure-ments in a ?uidic cell for the rotation rates of 20particles with bacteria and for 20particles without bacteria.The pres-ence of a bacterium on the surface of the magnetic micro-spheres caused a measurable change in the average rotation frequency,namely,the average frequency of the particles at a
driving frequency of 4.0Hz changed from ??˙1
?=0.72Hz to ??˙2?=0.19Hz,by a factor of ?3.8.This change in rotation frequency is similar in value to our previous measurements on a 1.0?m particle that was attached to a single 1.9?m ferromagnetic microsphere.14Sequential attachment of
bac-
FIG.1.?a ?Schematic of the single cell detection and the nonlinear rotation rate changes,which a magnetic microsphere undergoes when bound to a bacterium.The magnetic microsphere is functionalized with a secondary antibody ?goat antimouse IgG Ab 2?and primary antibody ?mouse anti-E.-Coli IgG Ab 1?.?b ?Series of successive ?uorescence microscopy images of a rotating 2.0?m magnetic microsphere with an attached E.Coli bacterium.The dotted circles indicate the location of the magnetic microsphere,where the axis of rotation lies in the plane of the
sample.
FIG.2.?a ?The rotational response of a single magnetic microsphere with an attached bacterium at various external driving frequencies,where the squares are experimental data and the line is a theoretical ?t from Eq.?1??the dotted line is an approximated curve for a microsphere without a bacterium ?.?b ?The average nonlinear rotation frequency of 20particles in a ?uidic cell incubated with bacteria ?solid curve ?and a ?uidic cell without bacteria ?dashed curve ?.The magnetic microspheres with one bacterium attached rotated an average of 3.8times slower than those without.?c ?Average rotation rate of a magnetic microsphere dimer driven at 3.75Hz,where 1,2,3,4,and 8bacterial cells were sequentially attached.The ?t corresponds to an expected change in the nonlinear frequency,determined from Eq.?1?for incremental additions of volume.The inset shows the normalized power spectral density of the intensity ?uctuations of the dimer with 1,2,3,4,and 8cells attached sequentially.
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terial cells was also observed,on a dimer of magnetic micro-spheres?Figure2?c??,showing single and multiple cell de-tection capabilities.
Once a bacterium is attached to a magnetic microsphere, this technique could also be used to monitor single bacterial cell growth.Indeed,preliminary experiments?to be pub-lished?have shown that shifts in the nonlinear rotational fre-quency are very sensitive to the growth of bacteria over sev-eral minutes.Changes in the nonlinear rotation frequency could therefore have further applications for the study of single bacterium growth dynamics and for rapid antibiotic susceptibility measurements.
In summary,optically monitored shifts in the nonlinear rotational frequency of driven magnetic microspheres were used to detect single bacterial cells as well as their sequential attachment,demonstrating the versatility of this dynamic ap-proach.The nonlinear rotational frequencies of2.0?m mag-netic microspheres were reduced,on average,by a factor of 3.8?i.e.,the rotational period increased by280%?,demon-strating single cell sensitivity in a?uidic environment.An additional feature of this method is its ability to detect single label-free bacterial cells.
The authors would like to thank Carol A.Fierke,Marcy Hernick,and Tamiika K.Hurst for help with the bacteria. R.R.Agayan acknowledges support from the Applied Phys-ics Program.R.Clarke is supported in part by Department of Energy under Grant No.DE-FG02-06ER46273.Funding was provided by NSF-DMR?No.0455330?.For additional infor-mation:publications,videos,etc.,see https://www.wendangku.net/doc/a53292494.html,/?koplab.
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