Name: single wavelength shadow imaging of caenorhabditis elegans locomotion including force estimates
Uploaded: 2014-04-18T19:00:00
Duration: 8 min 41 s
Description: Watch this Scientific Journal Video about Single Wavelength Shadow Imaging of Caenorhabditis elegans Locomotion Including Force Estimates at JoVE.com

We are grateful for the support of the Vassar College Undergraduate Research Summer Institute (URSI), the Lucy Maynard Salmon Research Fund, NASA award No. NX09AU90A, National Science Foundation Center for Research Excellence in Science and Technology (NSF-CREST) award No. 0630388 and the NSF award No. 1058385.

1. C. elegans Preparation
<ol>
	<li>Prepare petri plates of young adult C. elegans as described in previous experiments involving suspension of C. elegans in a fluid filled cuvette11.</li>
	<li>On the day of the video analysis, pick live young adult nematodes directly into a cuvette filled with deionized, distilled water using a platinum pick as described in step 2.</li>
	<li>Prepare dead C. elegans with chloroform exposure. Continue by following the procedure described for picking live nematodes described in step 2.</li>
</ol>
2. Optical Setup for the Video Analysis
<ol>
	<li>Assemble the experimental setup to create shadow images as shown in Figure&#160;1. The camera can be placed at any distance from the screen as long as it is able to capture a frontal view of the screen. A good place is next to the cuvette facing the screen.
	<ol>
		<li>Using at least two mirrors to steer the tunable Helium-Neon laser output into a Galilean beam expander so that the beam is expanded to a diameter of 12 mm.</li>
		<li>Place one or two pinholes in the beam path so that the beam passes through the pinholes without being obstructed. Use the pinholes to assure the alignment is maintained.</li>
		<li>Direct the expanded beam onto a mounted quartz cuvette that is 10 mm wide, 10 mm deep and 4 cm tall.</li>
		<li>Magnify the beam using a plano-convex lens with a positive focal length of 75 mm.</li>
		<li>Place a projection screen approximately 120 cm from the lens. Distances greater than this will yield a greater magnification of the shadow image. However, the quality of the image will decrease with a lower light intensity and an increased noticeability of diffraction interference.</li>
		<li>Place a high-speed camera, which is capable of at least 60 fps, right next to the cuvette facing the screen.</li>
	</ol>
	</li>
	<li>Place a dissecting microscope near the optical setup for rapid transfer of nematodes into the cuvette.</li>
	<li>Temporarily secure a transparent ruler with mm divisions to the center of the cuvette holder perpendicular to the expanded beam so that the beam projects a magnified image of the ruler onto the screen. Set the length scale for video analysis.
	<ol>
		<li>On the projection screen, mark the scale distance using a transparent ruler off center&#160;from the projected image to avoid interfering with the projection. <a href="Video_1_633nm.MOV" target="_blank">Click here for video.</a></li>
		<li>Record this image and measure the magnification. Remove the ruler from the setup. Repeat this step for other wavelengths as the angle of refraction of light for each wavelength through the lens will vary due to chromatic aberrations.</li>
	</ol>
	</li>
	<li>Replace the cuvette and fill it to within 1 mm of the rim with distilled water.</li>
	<li>Begin recording while the room light is on so that the scale distance is included in the same footage as the projected image. Turn the light off.</li>
	<li>Using a thin, flattened platinum wire pick, move individual young adult C. elegans one at a time from the agar plate into the cuvette by touching the pick to the surface of the water. The nematode will become visible in the water column when it enters the beam due to scattered light. <a href="Video_2_CB678_633nm.mov" target="_blank">Click here for video.</a></li>
	<li>Film the projected images of the worms as they pass through the expanded laser beam. It is important to note that the projected image is inverted and the worms will appear to move in the opposite direction of their actual motion. Worms that are descending with gravity will appear to move upward on the screen (Figure&#160;2).</li>
</ol>
3. Video Data Preparation
<ol>
	<li>Import the video into the video analysis program.</li>
	<li>Set the scale using the magnification factor previously determined.</li>
	<li>Track the linear displacement of the head of the shadowed nematode with at least 10 data points over the entire path taken.</li>
	<li>Find the velocity in the vertical direction by taking derivative (&#34;Y&#34;, &#34;Time&#34;) and divide this value by the magnification factor determined in step 2.2.</li>
</ol>
4. Data Analysis
<ol>
	<li>Analyze the linear descent of a C. elegans:
	<ol>
		<li>Check to ensure that the data points on the vertical position versus time graph generally form a straight line. Some deviations can be ignored due to the head movement of the nematode. If the data points generally form a straight line, continue to step 4.1.2, otherwise the descent is nonlinear and the analysis should be continued using step 5.1 in this protocol.</li>
		<li>Create a linear regression line by fitting a straight line12 to the data from the Analysis menu. The slope of this line is then the vertical speed of the C. elegans. The slope is the change in position divided by the change in time over a particular interval. Determine the descending speed of the live and dead worms in this manner (Figure&#160;3).</li>
		<li>Average the vertical swimming velocities from the nematodes. A sample size of about 50 worms is sufficient. Compare swim velocities in live worms with drift velocities in dead worms.</li>
	</ol>
	</li>
</ol>
5. Analyze Nonlinear Motion of C. elegans
<ol>
	<li>From Section 3, select an analyzed video file, which shows a nonlinear descent within the water column (Figure&#160;4). A nonlinear descent can be identified using step 4.1.1 in this protocol.</li>
	<li>Select &#39;Curve Fit&#39; from the &#39;Analysis&#39; menu in the video analysis software. Select a second order (quadratic) polynomial. Fit the curve.</li>
	<li>For a region of interest, adjust the fit on the graph by sliding the brackets on each side of the fit on the graph until the curve is very close to the data points within the fit and/or well within the error bars. The fitting program gives a mathematical expression for the fitted curve, which is vertical position versus time. Consider the fitted curve errors given by the program associated with the physical properties. A relative error of 15% or below is usually acceptable.</li>
	<li>Add more curve fits to cover additional sections of data. Spline13 the functions for optimal coverage: make sure that the curve fits overlap and try to align adjacent curves so that the slopes match in the overlapping regions.</li>
	<li>Obtain the velocity for a region of interest by taking the derivative of the fitted curve using the mathematical expression obtained in step 5.1.3. Velocities may vary in time. Note that the derivative is the slope of a function. The derivative can be obtained mathematically or graphically. In this case it is practical to use the given mathematical expression.</li>
	<li>Take the second derivative of the fitted curves to obtain the acceleration. The acceleration may vary in time.</li>
	<li>Multiply the acceleration by the worm mass to calculate the thrust, which the worm exerts. A reasonable estimated mass is 3 &#956;g assuming that the worm consists mostly of water.</li>
</ol>

<ol>
	<li>Ward, A., Lie, J., Feng, Z., Xu, Z. S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Light-sensitive+neurons+and+channels+mediate+phototaxis+in+C.+elegans.">Light-sensitive neurons and channels mediate phototaxis in C. elegans.</a> Nature Neurosci. 11, 916-922 (2008).</li><li>Pierce-Shimomura, J. T., Chen, B. L., Mun, J. J., Ho, R., Sarkis, R., McIntire, S. L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Genetic+analysis+of+crawling+and+swimming+locomotory+patterns+in+C.+elegans.">Genetic analysis of crawling and swimming locomotory patterns in C. elegans.</a> Proc. Natl. Acad. Sci. USA. , 105-20987 (2008).</li><li>Vidal-Gadea, A. G., Davis, S., Becker, L., Pierce-Shimomura, J. T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Coordination+of+behavioral+hierarchies+during+environmental+transitions+in+Caenorhabditis+elegans.">Coordination of behavioral hierarchies during environmental transitions in Caenorhabditis elegans.</a> Worm. 1, 5-11 (2012).</li><li>Berri, S., Boyle, J. H., Tassieri, M., Hope, I. A., Cohen, N. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Forward+locomotion+of+the+nematode+C.+elegans+is+achieved+through+modulation+of+a+single+gait.">Forward locomotion of the nematode C. elegans is achieved through modulation of a single gait.</a> HFSP Journal. 3, 186-193 (2009).</li><li>Keller, H. E., Pawley, J. B. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Objective Lenses for Confocal Microscopy. Handbook of Biological Confocal Microscopy. , (2006).</li><li>Conrad, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Depth+of+Field+in+Depth.">Depth of Field in Depth.</a> Large Format Page Retrieved. , (2011).</li><li>Demtr&#246;der, W. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Laser Spectroscopy Basic Concepts and Instrumentation. , (2003).</li><li>Magnes, J., Raley-Susman, K., Melikechi, N., Sampson, A., Eells, R., Bello, A., Lueckheide, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Analysis+of+Freely+Swimming+C.+elegans+Using+Laser+Diffraction.">Analysis of Freely Swimming C. elegans Using Laser Diffraction.</a> Open J. Biophys. 2 (3), 101-107 (2012).</li><li>Mood, A., Graybill, F., Boes, D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Introduction to the Theory of Statistics. , (1974).</li><li>Taylor, J. R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Classical Mechanics. , (2005).</li><li>Magnes, J., Susman, K., Eells, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Quantitative+Locomotion+Study+of+Freely+Swimming+Micro-organisms+Using+Laser+Diffraction.">Quantitative Locomotion Study of Freely Swimming Micro-organisms Using Laser Diffraction.</a> J. Vis. Exp. (68), (2012).</li><li>Bevington, P. R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Data Reduction and Error Analysis for the Physical Sciences. , (1969).</li><li>Lyche, T., Schumaker, L. L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Local+spline+approximation+methods.">Local spline approximation methods.</a> Journal of Approximation Theory. 15 (4), 294-325 (1975).</li><li>Kim, N., Dempsey, C. M., Kuan, C. -. J., Zoval, J. V., O'Rourke, E., Ruvkun, G., Madou, M. J., Sze, J. Y. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Gravity+Force+Transduced+by+the+MEC-4/MEC-10+DEG/ENaC+Channel+Modulates+DAF-16/FoxO+Activity+in+Caenorhabditis+elegans.">Gravity Force Transduced by the MEC-4/MEC-10 DEG/ENaC Channel Modulates DAF-16/FoxO Activity in Caenorhabditis elegans.</a> Genetics. 177, 835-845 (2007).</li></ol>

The authors have nothing to disclose.

The SWSI technique provides an additional way to understand the locomotory capabilities of microscopic organisms like free-living nematodes. With this technique we have distinguished between active locomotion (swimming) and passive drift due to gravity operating on dead nematodes. In addition, when free-swimming nematodes change direction during locomotion in water, we are able to measure the drag forces and angular forces, which are operating on the nematodes and exerted by the nematodes.
Nematodes encounter different environmental conditions within the soil. There are water pockets within soil, as well as solid particles and biological materials of different shapes and textures. In addition, nematodes exist within a gravitational environment that they respond to14.&#160;Further, nematodes near the surface of the soil are exposed to different wavelengths of light, changes in temperature and humidity, as well as biological variables like bacteria, predatory fungi and other soil organisms. Nematodes must respond to all these different variables, swimming and crawling in different media, turning and altering navigational strategies. All of these complex computations are carried out by only 302 neurons, a subset of which are involved in locomotion, and 95 body wall muscle cells. Measurements of the sort described by SWSI technique provide important insight into how nematodes accomplish this navigational complexity.
For the first part, we have measured the overall descending rate of wildtype C. elegans in 633 nm light. Using these measurements, we can estimate the drag force a worm encounters.
For the case study of an accelerating nematode, the forces involved change continuously since the drag force changes with speed. There are some statements that we are able to make about the forces acting on the worm. As the worm slows down and tries to swim upwards the vertical component of the drag force decreases until it reaches zero at the low point of the nematode&#39;s trajectory. At this point, the worm must have&#160;an upward force to swim up.
This method can be modified in several ways. Any microscopic species that navigates in a clear liquid can be tracked using SWSI. Studies can be conducted with any wavelengths that are accessible to digital cameras. Digital cameras will typically pick up wavelengths ranging from the UV to near IR. In addition, horizontal studies can be conducted by directing the laser vertically upward. The species can then be placed on a horizontal transparent surface, like a microscope slide. Adjusting the beam expander or the magnifying lens after the beam expander can sharpen blurry images. The user should be sure to fasten all components to the table to ensure consistent and easy beam alignment.
The method is limited by available laser wavelengths and resolution. In essence the advantages of this method over existing microscopes, which are the flexibility in directions and wavelengths, are also weaknesses since the setup is simple. The unsophisticated optics and speckles of the laser limit the resolution. Some of these drawbacks can certainly be improved in the future by including spatial filter and projecting the image directly onto a CCD camera.
The most critical steps in the protocol can easily be learned as the experiment is performed for the first time. Placing the nematode in the cuvette without creating turbulence is critical. Also, vibrations may disturb the setup and alter the behavior of the worms. Be sure to limit the power, which is used to shadow image. 2 mW for a laser beam that is 1 mm in diameter should be the maximum to avoid heating effects. The setup should be tested for scattering effects when using liquids other than distilled water.
Currently most microscopes operate on a horizontal plane using white light or color filters, which are still very broad in the wavelength range. Microscopes that truly use single wavelengths and have flexibility in the viewing scenario, i.e.&#160;horizontal placement, are usually limited to one advantage or the other. Also, these types of microscopes are usually very expensive and still limited to focal planes unlike our method. Our setup can easily be built with an extremely low budget. This method is ready to be used by schools, environmental companies as well as other entities that operate with little funding. In the future, this method can be used in a very sophisticated setup to study real time effects on locomotion and mechanosensation of microscopic species. This method makes single wavelength studies at a wide range of angles and viewing depths easily available.

Caenorhabditis elegans is a free-living beneficial soil nematode that is a powerful model organism for studying mechanisms of gene regulation, development and more recently for understanding sensory biology and behavior. Despite having only 302 neurons, C. elegans are capable of complex locomotory patterns, reproductive behaviors, navigation, chemotaxis and many other behaviors. C. elegans possess mechanoreceptors, chemoreceptors and even detect blue wavelengths of light (Ward et al., 2008)1. While much is known about the neural circuitry of sensorimotor function and general locomotory patterns in C. elegans, less is known about the responses to multiple, concurrent stimuli or more complex environmental conditions than can be modeled under a microscope. A few studies have revealed more complex locomotory patterns that are highly plastic2,3,4. Our methodological approach will enable studies of nematodes in solution in real time where we can readily provide multiple environmental conditions simultaneously. This question is difficult to address using conventional microscope-based imaging techniques. We have developed an imaging technique that allows us to place nematodes within a water column to examine locomotory behaviors, as well as determine the capabilities of nematodes to change locomotion in response to different environmental conditions.
Single Wavelength Shadow Imaging (SWSI) is presented in this paper for the first time to address the shortcomings of traditional microscopes. Traditional microscopes are limited to observe species in a horizontal focal plane a few microns in depth5,6. Regarding single wavelength studies, most traditional microscopes use color filters to filter white light very broadly,&#160;typically, 50-100&#160;nm. Using a laser for SWSI narrows the wavelength selection to less than 1&#160;nm while maintaining significant light intensity7. Similarly, single wavelengths have been used to measure swimming frequencies of C. elegans in real time8.
For the first demonstration of our method, we monitor the horizontal position, x, and the vertical position, y, of a freely swimming C. elegans in a water column, over a distance of about a centimeter. In particular, we are interested in the vertical movement since gravity also acts vertically. The slope of a linear fit to the vertical position gives the vertical speed, vy, of the nematode as it descends in the water column: 
<img alt="Formula" fo:content-width="0.5in" src="/files/ftp_upload/51424/51424eq1.jpg" width="50" />&#160; &#160; &#160;(1)
The root mean square of the error (RMSE)9&#160;indicates the quality of the fit and indicates whether the descending speed is generally constant. The vertical speeds are then averaged for each species and dead worms. Using these results, the drag, which the worms experience can be estimated.
For the second demonstration of our method, we selected C. elegans that did not descend at a constant rate unlike the majority of the worms observed. The selected worms either turned around and swam upwards or hovered for a while before continuing the descent. Physically, this case study shows that the thrust of a swimming microorganism can be calculated. Newton&#39;s laws dictate that a body that changes directions accelerates, which implies a net force, <img alt="Formula 1" fo:content-width="0.3in" src="/files/ftp_upload/51424/51424eq.jpg" width="25" />, is acting on that body10: 
<img alt="Formula 2" fo:content-width="0.7in" src="/files/ftp_upload/51424/51424eq2.jpg" width="70" />&#160; &#160; &#160;(2)
where <img alt="p" fo:content-width="0.1in" src="/files/ftp_upload/51424/51424p.jpg" width="10" /> is the linear momentum and t is time. The acceleration of the worm is directly proportional to the force acting on the worm since the mass of the worm remains constant. As a result, the vertical net force is: 
<img alt="Formula 3" fo:content-width=".8in" src="/files/ftp_upload/51424/51424eq3.jpg" width="70" /> (3)
where m is the mass of a worm and ay represents the vertical acceleration. The net force in the vertical direction represents then the worm thrust in the same direction. The total thrust can be calculated by taking the horizontal component into account.

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			<td height="42" style="height:42px;width:216px;">Name of Material/ Equipment</td>
			<td style="width:143px;">Company</td>
			<td style="width:119px;">Catalog Number</td>
			<td style="width:375px;">Comments/Description</td>
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			<td height="21" style="height:21px;width:216px;">Tunable Helium-Neon laser&#160;</td>
			<td>Research Electro-Optics</td>
			<td>30602</td>
			<td>Four wavelengths can be selected between 543 nm and 633 nm.</td>
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			<td height="42" style="height:42px;width:216px;">2 Front Surface Aluminum Mirrors</td>
			<td style="width:143px;">Thorlabs</td>
			<td>PF10-03-F01</td>
			<td></td>
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			<td height="21" style="height:21px;">High Speed Exilim Camera</td>
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			<td height="21" style="height:21px;width:216px;">Quartz Cuvette</td>
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			<td>http://www.vernier.com/products/software/lp/</td>
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			<td height="21" style="height:21px;width:216px;">Mathematica 8</td>
			<td style="width:143px;">Wolfram</td>
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			<td>http://www.wolfram.com/</td>
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			<td height="42" style="height:42px;width:216px;">&#160;5x &#8211; 10x variable zoom Galilean beam expander</td>
			<td style="width:143px;">Thorlabs</td>
			<td>BE05-10-A</td>
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			<td height="42" style="height:42px;width:216px;">Plano-convex lens with a positive focal length of 75 mm</td>
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			<td style="width:119px;">LA1257</td>
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single wavelength shadow imaging of caenorhabditis elegans locomotion including force estimates

This study demonstrates an inexpensive and straightforward technique that allows the measurement of physical properties such as position, velocity, acceleration and forces involved in the locomotory behavior of nematodes suspended in a column of water in response to single wavelengths of light. We demonstrate how to evaluate the locomotion of a microscopic organism using Single Wavelength Shadow Imaging (SWSI) using two different examples.
The first example is a systematic and statistically viable study of the average descent of C. elegans in a column of water. For this study, we used living and dead wildtype C. elegans. When we compared the velocity and direction of nematode active movement with the passive descent of dead worms within the gravitational field, this study showed no difference in descent-times. The average descent was 1.5 mm/sec &#177; 0.1 mm/sec for both the live and dead worms using 633 nm coherent light.
The second example is a case study of select individual C. elegans changing direction during the descent in a vertical water column. Acceleration and force are analyzed in this example. This case study demonstrates the scope of other physical properties that can be evaluated using SWSI while evaluating the behavior using single wavelengths in an environment that is not accessible with traditional microscopes. Using this analysis we estimated an individual nematode is capable of thrusting with a force in excess of 28 nN.
Our findings indicate that living nematodes exert 28 nN when turning, or moving against the gravitational field. The findings further suggest that nematodes passively descend in a column of water, but can actively resist the force of gravity primarily by turning direction.

Steady Descent
The first investigation shows no distinguishable difference in the descending rates of the C. elegans during SWSI using 633 nm. The descending rates were found to be constant at 1.5 mm/sec &#177; 0.1 mm/sec for both the live and the dead C. elegans. A sample size of 50 worms generated a reasonable variance of 7% for both living and dead worms. There is no acceleration acting on the worms since the descending speed is constant, so that the drag force equals the gravitational force minus the buoyancy force. This implies that the density of the worm is slightly larger than that of water; however, for the estimations below it is still practical to assume that the density of a nematode is roughly that of water.
Changing Direction
The second investigation, a case study, demonstrates that nematodes are capable of changing direction and can swim upwards against gravity. Two curves were fitted to the vertical displacement of the nematode so that the second derivatives of those curves could be splined to graph acceleration versus time (Figure&#160;5).&#160;It is advisable to keep the polynomial order as low as possible while maintaining a good fit. A lower polynomial order indicates less variation in the acceleration over time. The higher order polynomial terms will be negligible, and therefore unnecessary, if the order of the polynomial is too high. This worm decelerates at a constant rate of 0.110 mm/sec2 &#177; 0.002 mm/sec2, turns around and accelerates at the same rate 0.110 mm/sec2 &#177; 0.002 mm/sec2 until shortly after the turnaround point. The C. elegans continues to move upwards with a diminishing acceleration of 1.252 - 0.00708 t in mm/sec2 until the acceleration falls to zero. Keeping in mind Eq. 3, and an estimated worm mass of 3 &#956;g, the worm undergoes a vertical net force, FNy, of 0.33 pN until shortly after the turnaround point.
Descent:&#160;There are three types of forces acting on the worm until the worm reaches the turnaround point: gravity, drag, buoyancy and thrust (Figure&#160;6a). The net force equals the vector sum of all three forces. Here we consider the vertical components only: 
FNy = FDy+FTy-Fg+FB &#160; &#160;&#160;(4)
where FB is the buoyancy force. Fg is equal in magnitude but opposite in direction to the buoyancy force assuming that the density of the worm is that of water. Eq. 4 can then be written in the following way: 
FNy = FDy+FTy &#160; &#160;&#160;(5)
FNy remains constant during the descent. This implies that FDy+FTy remains constant until the nematode reaches the turnaround point. FDy is largest at the top, which is the beginning of the path, and gradually reduces to zero until the speed is zero at the turnaround point while FTy must increase to keep FNy constant.
Turnaround: There is no drag force in the vertical direction at the turnaround point since the vertical speed equals zero at that point. The only forces acting in the vertical direction are gravity, -Fg, buoyancy, FB and the vertical worm thrust, FTy, as depicted in Figure&#160;6b. At this point, the thrust of the C. elegans can be determined: 
FTy = FNy &#160;(6)
The thrust at the bottom of the trajectory is then roughly equal to 0.33 pN, which is about 0.001% of the worm&#39;s weight. Taking into account that the estimated weight, Fg of a C. elegans is 28 nN,
Ascent: Similarly, during the ascent, drag increases but is pointed down (Figure&#160;6c): 
FNy = -FDy+FTy(7)
The thrust implemented by the worm must now be even larger and equal the sum of the drag force and the weight. The worm is slowing down after beginning to swim up. To swim up at the same rate as the worm descended, the worm would have to exert an upward thrust of at least twice its weight.
Hovering
An example of a worm that slows its descent for about 3 sec&#160;is presented in Figure&#160;7.&#160;A 3rd degree polynomial is a reasonable fit for the overall path. The errors in acceleration and velocity from this fit are less than 15%. The worm starts with a significant upward thrust, slows down and starts to turn around at 68 sec; however, the upward acceleration decreases continuously (Figure&#160;8)&#160;until the net acceleration equals zero around 68.5 sec. This eventually leads to a net acceleration in the downward direction followed by another zero point in the velocity (Figure&#160;9)&#160;and the nematode starts to descend again at 69 sec.
It is interesting that the maximum observed vertical acceleration in this case is 2.7 mm/sec2. The acceleration at the turning points are 0.455 mm/sec2 and - 0.455 mm/sec2 respectively; about four times larger than in the case of the nematode that turns around and swims up. Using Eq. 6, it can be estimated that the upward thrust is about 1.32 pN at the first turning point. At the second turning point, the net acceleration is negative so that the upward thrust is 1.32 pN.
<img alt="Figure 1" fo:content-width="5in" fo:src="/files/ftp_upload/51424/51424fig1highres.jpg" src="/files/ftp_upload/51424/51424fig1.jpg" /> 
Figure 1.&#160;Experimental setup. The laser, beam expander, lens and screen are essential to the experimental setup. The steering mirrors and pinholes may be omitted, but will make the optical alignment less stable.
<img alt="Figure 2" fo:content-width="5in" fo:src="/files/ftp_upload/51424/51424fig2highres.jpg" src="/files/ftp_upload/51424/51424fig2.jpg" /> 
Figure 2.&#160;Single Wavelength Shadow Image (SWSI). Using 2 mW of 543&#160;nm laser light the shadow of a worm is projected onto a screen. The image is inverted so that the nematode appears to fall upwards.
<img alt="Figure 3" fo:content-width="5in" fo:src="/files/ftp_upload/51424/51424fig3highres.jpg" src="/files/ftp_upload/51424/51424fig3.jpg" /> 
Figure 3.&#160;Vertical descent of a single wildtype C. elegans in a water column. This nematode was shadowed by 633 nm coherent light. The slope of the linear fit indicates a downward speed of 1.09 mm/sec &#177; 0.01 mm/sec. <a href="https://www.jove.com/files/ftp_upload/51424/51424fig3highres.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 4" fo:content-width="5in" fo:src="/files/ftp_upload/51424/51424fig4highres.jpg" src="/files/ftp_upload/51424/51424fig4.jpg" /> 
Figure 4.&#160;Displacement graph of a single upward swimming wildtype C. elegans. Two splined fits trace the overall path of the nematode. The second derivative of the fit reveals the acceleration. The maximum acceleration is easily determined from the first fit: 0.110 mm/sec2 &#177; 0.002 mm/sec2. Only a few error bars are shown so that the data points and the fit remain visible. This nematode was shadowed by 633 nm coherent light. <a href="https://www.jove.com/files/ftp_upload/51424/51424fig4highres.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 5" fo:content-width="5in" fo:src="/files/ftp_upload/51424/51424fig5highres.jpg" src="/files/ftp_upload/51424/51424fig5.jpg" /> 
Figure 5.&#160;Acceleration graph of a single wildtype C. elegans. This nematode maintains a constant upward acceleration of 0.110 mm/sec2 &#177; 0.002 mm/sec2 causing it to slow down and then move upwards. Shortly after the turnaround point the acceleration decreases steadily and the net acceleration diminishes to zero. <a href="https://www.jove.com/files/ftp_upload/51424/51424fig5highres.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 6" fo:content-width="5in" fo:src="/files/ftp_upload/51424/51424fig6highres.jpg" src="/files/ftp_upload/51424/51424fig6.jpg" /> 
Figure 6.&#160;Force diagrams for descent, turning point and ascent. Buoyancy and gravity are equal in magnitude and opposite in direction so that the effect of these forces cancel each other out. They are therefore not shown in these diagrams. (a) The worm is descending with drag and thrust pointing up. (b) The worm is at the low point of the trajectory without drag. Thrust is pointing up. (c) The worm is ascending with drag pointing down while thrust is pointing up.
<img alt="Figure 7" fo:content-width="5in" fo:src="/files/ftp_upload/51424/51424fig7highres.jpg" src="/files/ftp_upload/51424/51424fig7.jpg" /> 
Figure 7.&#160;Displacement graph of single hovering nematode. The worm slows down and starts to turn around at about 68 sec&#160;but starts descending around 69 sec. <a href="https://www.jove.com/files/ftp_upload/51424/51424fig7highres.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 8" fo:content-width="5in" fo:src="/files/ftp_upload/51424/51424fig8highres.jpg" src="/files/ftp_upload/51424/51424fig8.jpg" /> 
Figure 8.&#160;Acceleration graph of a single hovering nematode. This worm starts with an upward acceleration of 2.7 mm/sec2, decreases to zero and eventually has a downward acceleration of -2.6 mm/sec2. <a href="https://www.jove.com/files/ftp_upload/51424/51424fig8highres.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 9" fo:content-width="5in" fo:src="/files/ftp_upload/51424/51424fig9highres.jpg" src="/files/ftp_upload/51424/51424fig9.jpg" /> 
Figure 9.&#160;Velocity graph of a single hovering nematode. This worm comes to a stop at 68 sec and starts to head upward, slows down and reaches zero velocity in the vertical direction at 69 sec followed by a descent. <a href="https://www.jove.com/files/ftp_upload/51424/51424fig9highres.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Table 1" fo:content-width="4in" fo:src="/files/ftp_upload/51424/51424table1highres.jpg" src="/files/ftp_upload/51424/51424table1.jpg" width="400" /> 
Table 1.&#160;Average descent velocities of N2 C. elegans. 50 live and 50 dead nematodes are tracked during their descent. The average velocity for the descents is the same for the live and the dead worms: 1.5 mm/sec &#177; 0.1 mm/sec.

Watch this Scientific Journal Video about Single Wavelength Shadow Imaging of Caenorhabditis elegans Locomotion Including Force Estimates at JoVE.com

Single Wavelength Shadow Imaging of Caenorhabditis elegans Locomotion Including Force Estimates

The technique presented here measures the path of freely swimming microscopic species using single wavelength exposure. C. elegans are used to demonstrate shadow imaging as an inexpensive alternative to costly microscopes. This technique can be adapted to accommodate various orientations, environments and species to measure direction, speed, acceleration and forces.

Single Wavelength Shadow Imaging of Caenorhabditis elegans Locomotion Including Force Estimates

This study demonstrates an inexpensive and straightforward technique that allows the measurement of physical properties such as position, velocity, ...

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Compact Quantum Dots for Single-molecule Imaging

Single-molecule imaging is an important tool for understanding the mechanisms of biomolecular function and for visualizing the spatial and temporal heterogeneity of molecular behaviors that underlie cellular biology 1-4. To image an individual molecule of interest, it is typically conjugated to a fluorescent tag (dye, protein, bead, or quantum dot) and observed with epifluorescence or total internal reflection fluorescence (TIRF) microscopy. While dyes and fluorescent proteins have been the mainstay of fluorescence imaging for decades, their fluorescence is unstable under high photon fluxes necessary to observe individual molecules, yielding only a few seconds of observation before complete loss of signal. Latex beads and dye-labeled beads provide improved signal stability but at the expense of drastically larger hydrodynamic size, which can deleteriously alter the diffusion and behavior of the molecule under study.
Quantum dots (QDs) offer a balance between these two problematic regimes. These nanoparticles are composed of semiconductor materials and can be engineered with a hydrodynamically compact size with exceptional resistance to photodegradation 5. Thus in recent years QDs have been instrumental in enabling long-term observation of complex macromolecular behavior on the single molecule level. However these particles have still been found to exhibit impaired diffusion in crowded molecular environments such as the cellular cytoplasm and the neuronal synaptic cleft, where their sizes are still too large 4,6,7.
Recently we have engineered the cores and surface coatings of QDs for minimized hydrodynamic size, while balancing offsets to colloidal stability, photostability, brightness, and nonspecific binding that have hindered the utility of compact QDs in the past 8,9. The goal of this article is to demonstrate the synthesis, modification, and characterization of these optimized nanocrystals, composed of an alloyed HgxCd1-xSe core coated with an insulating CdyZn1-yS shell, further coated with a multidentate polymer ligand modified with short polyethylene glycol (PEG) chains (Figure 1). Compared with conventional CdSe nanocrystals, HgxCd1-xSe alloys offer greater quantum yields of fluorescence, fluorescence at red and near-infrared wavelengths for enhanced signal-to-noise in cells, and excitation at non-cytotoxic visible wavelengths. Multidentate polymer coatings bind to the nanocrystal surface in a closed and flat conformation to minimize hydrodynamic size, and PEG neutralizes the surface charge to minimize nonspecific binding to cells and biomolecules. The end result is a brightly fluorescent nanocrystal with emission between 550-800 nm and a total hydrodynamic size near 12 nm. This is in the same size range as many soluble globular proteins in cells, and substantially smaller than conventional PEGylated QDs (25-35 nm).

We describe the preparation of colloidal quantum dots with minimized hydrodynamic size for single-molecule fluorescence imaging. Compared to conventional quantum dots, these nanoparticles are similar in size to globular proteins and are optimized for single-molecule brightness, stability against photodegradation, and resistance to nonspecific binding to proteins and cells.

Single-molecule imaging is an important tool for  understanding the mechanisms of biomolecular function and for visualizing the  spatial and temporal ...

Atomic Force Microscopy of Red-Light Photoreceptors Using PeakForce Quantitative Nanomechanical Property Mapping

Atomic force microscopy (AFM) uses a pyramidal tip attached to a cantilever to probe the force response of a surface. The deflections of the tip can be measured to ~10 pN by a laser and sectored detector, which can be converted to image topography. Amplitude modulation or &#8220;tapping mode&#8221; AFM involves the probe making intermittent contact with the surface while oscillating at its resonant frequency to produce an image. Used in conjunction with a fluid cell, tapping-mode AFM enables the imaging of biological macromolecules such as proteins in physiologically relevant conditions. Tapping-mode AFM requires manual tuning of the probe and frequent adjustments of a multitude of scanning parameters which can be challenging for inexperienced users. To obtain high-quality images, these adjustments are the most time consuming.
PeakForce Quantitative Nanomechanical Property Mapping (PF-QNM) produces an image by measuring a force response curve for every point of contact with the sample. With ScanAsyst software, PF-QNM can be automated. This software adjusts the set-point, drive frequency, scan rate, gains, and other important scanning parameters automatically for a given sample. Not only does this process protect both fragile probes and samples, it significantly reduces the time required to obtain high resolution images. PF-QNM is compatible for AFM imaging in fluid; therefore, it has extensive application for imaging biologically relevant materials.
The method presented in this paper describes the application of PF-QNM to obtain images of a bacterial red-light photoreceptor, RpBphP3 (P3), from photosynthetic R. palustris in its light-adapted state. Using this method, individual protein dimers of P3 and aggregates of dimers have been observed on a mica surface in the presence of an imaging buffer. With appropriate adjustments to surface and/or solution concentration, this method may be generally applied to other biologically relevant macromolecules and soft materials.

A method for investigating the structure of a protein photoreceptor using atomic force microscopy (AFM) is described in this paper. PeakForce Quantitative Nanomechanical Property Mapping (PF-QNM) reveals intact protein dimers on a mica surface.

Atomic force microscopy (AFM) uses a pyramidal tip attached to a cantilever to probe the force response of a surface. The deflections of the tip can be ...

Preparation and Friction Force Microscopy Measurements of Immiscible, Opposing Polymer Brushes

Solvated polymer brushes are well known to lubricate high-pressure contacts, because they can sustain a positive normal load while maintaining low friction at the interface. Nevertheless, these systems can be sensitive to wear due to interdigitation of the opposing brushes. In a recent publication, we have shown via molecular dynamics simulations and atomic force microscopy experiments, that using an immiscible polymer brush system terminating the substrate and the slider surfaces, respectively, can eliminate such interdigitation. As a consequence, wear in the contacts is reduced. Moreover, the friction force is two orders of magnitude lower compared to traditional miscible polymer brush systems. This newly proposed system therefore holds great potential for application in industry. Here, the methodology to construct an immiscible polymer brush system of two different brushes each solvated by their own preferred solvent is presented. The procedure how to graft poly(N-isopropylacrylamide) (PNIPAM) from a flat surface and poly(methyl methacrylate) (PMMA) from an atomic force microscopy (AFM) colloidal probe is described. PNIPAM is solvated in water and PMMA in acetophenone. Via friction force AFM measurements, it is shown that the friction for this system is indeed reduced by two orders of magnitude compared to the miscible system of PMMA on PMMA solvated in acetophenone.

The methodology to perform friction force microscopy experiments for contacting brushes is presented: Two polymer brushes that are grafted from (a) substrates and (b) colloidal probes are slid to show that, by using two contacting immiscible brush systems, friction in sliding contacts is reduced compared to miscible brush systems.

Solvated polymer brushes are well known to lubricate high-pressure contacts, because they can sustain a positive normal load while maintaining low ...

Investigating Single Molecule Adhesion by Atomic Force Spectroscopy

Atomic force spectroscopy is an ideal tool to study molecules at surfaces and interfaces. An experimental protocol to couple a large variety of single molecules covalently onto an AFM tip is presented. At the same time the AFM tip is passivated to prevent unspecific interactions between the tip and the substrate, which is a prerequisite to study single molecules attached to the AFM tip. Analyses to determine the adhesion force, the adhesion length, and the free energy of these molecules on solid surfaces and bio-interfaces are shortly presented and external references for further reading are provided. Example molecules are the poly(amino acid) polytyrosine, the graft polymer PI-g-PS and the phospholipid POPE (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine). These molecules are desorbed from different surfaces like CH3-SAMs, hydrogen terminated diamond and supported lipid bilayers under various solvent conditions. Finally, the advantages of force spectroscopic single molecule experiments are discussed including means to decide if truly a single molecule has been studied in the experiment.

A protocol to couple a large variety of single molecules covalently onto an AFM tip is presented. Procedures and examples to determine the adhesion force and free energy of these molecules on solid supports and bio-interfaces are provided.

Atomic force spectroscopy is an ideal tool to study molecules at surfaces and interfaces. An experimental protocol to couple a large variety of single ...

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle

Plasmonics, which are based on the collective oscillation of electrons due to light excitation, involve strongly enhanced local electric fields and thus have potential applications in nonlinear optics, which requires extraordinary optical intensity. One of the most studied nonlinearities in plasmonics is nonlinear absorption, including saturation and reverse saturation behaviors. Although scattering and absorption in nanoparticles are closely correlated by the Mie theory, there has been no report of nonlinearities in plasmonic scattering until very recently. 
Last year, not only saturation, but also reverse saturation of scattering in an isolated plasmonic particle was demonstrated for the first time. The results showed that saturable scattering exhibits clear wavelength dependence, which seems to be directly linked to the localized surface plasmon resonance (LSPR). Combined with the intensity-dependent measurements, the results suggest the possibility of a common mechanism underlying the nonlinear behaviors of scattering and absorption. These nonlinearities of scattering from a single gold nanosphere (GNS) are widely applicable, including in super-resolution microscopy and optical switches. 
In this paper, it is described in detail how to measure nonlinearity of scattering in a single GNP and how to employ the super-resolution technique to enhance the optical imaging resolution based on saturable scattering. This discovery features the first super-resolution microscopy based on nonlinear scattering, which is a novel non-bleaching contrast method that can achieve a resolution as low as l/8 and will potentially be useful in biomedicine and material studies.

Saturable and reverse saturable scattering were discovered in isolated plasmonic particles and adopted as a novel non-bleaching contrast method in super-resolution microscopy. Here the experimental procedures of detecting and extracting nonlinear scattering are explained in detail, as well as how to enhance resolution with the aid of saturated excitation microscopy.

Plasmonics, which are based on the collective oscillation of electrons due to light excitation, involve strongly enhanced local electric fields and thus ...

Use of a Multi-compartment Dynamic Single Enzyme Phantom for Studies of Hyperpolarized Magnetic Resonance Agents

Imaging of hyperpolarized substrates by magnetic resonance shows great clinical promise for assessment of critical biochemical processes in real time. Due to fundamental constraints imposed by the hyperpolarized state, exotic imaging and reconstruction techniques are commonly used. A practical system for characterization of dynamic, multi-spectral imaging methods is critically needed. Such a system must reproducibly recapitulate the relevant chemical dynamics of normal and pathological tissues. The most widely utilized substrate to date is hyperpolarized [1-13C]-pyruvate for assessment of cancer metabolism. We describe an enzyme-based phantom system that mediates the conversion of pyruvate to lactate. The reaction is initiated by injection of the hyperpolarized agent into multiple chambers within the phantom, each of which contains varying concentrations of reagents that control the reaction rate. Multiple compartments are necessary to ensure that imaging sequences faithfully capture the spatial and metabolic heterogeneity of tissue. This system will aid the development and validation of advanced imaging strategies by providing chemical dynamics that are not available from conventional phantoms, as well as control and reproducibility that is not possible in vivo.

A multi-compartment dynamic phantom is used to simulate some biology of interest for metabolic studies using hyperpolarized magnet resonance agents.

Imaging of hyperpolarized substrates by magnetic resonance shows great clinical promise for assessment of critical biochemical processes in real time. Due ...

Sub-nanometer Resolution Imaging with Amplitude-modulation Atomic Force Microscopy in Liquid

Atomic force microscopy (AFM) has become a well-established technique for nanoscale imaging of samples in air and in liquid. Recent studies have shown that when operated in amplitude-modulation (tapping) mode, atomic or molecular-level resolution images can be achieved over a wide range of soft and hard samples in liquid. In these situations, small oscillation amplitudes (SAM-AFM) enhance the resolution by exploiting the solvated liquid at the surface of the sample. Although the technique has been successfully applied across fields as diverse as materials science, biology and biophysics and surface chemistry, obtaining high-resolution images in liquid can still remain challenging for novice users. This is partly due to the large number of variables to control and optimize such as the choice of cantilever, the sample preparation, and the correct manipulation of the imaging parameters. Here, we present a protocol for achieving high-resolution images of hard and soft samples in fluid using SAM-AFM on a commercial instrument. Our goal is to provide a step-by-step practical guide to achieving high-resolution images, including the cleaning and preparation of the apparatus and the sample, the choice of cantilever and optimization of the imaging parameters. For each step, we explain the scientific rationale behind our choices to facilitate the adaptation of the methodology to every user's specific system.

We present a method for achieving sub-nanometer resolution images with amplitude-modulation (tapping mode) atomic force microscopy in liquid. The method is demonstrated on commercial atomic force microscopes. We explain the rationale behind our choices of parameters and suggest strategies for resolution optimization.

Atomic force microscopy (AFM) has become a well-established technique for nanoscale imaging of samples in air and in liquid. Recent studies have shown ...

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Silicon photonic chips have the potential to realize complex integrated quantum information processing circuits, including photon sources, qubit manipulation, and integrated single-photon detectors. Here, we present the key aspects of preparing and testing a silicon photonic quantum chip with an integrated photon source and two-photon interferometer. The most important aspect of an integrated quantum circuit is minimizing loss so that all of the generated photons are detected with the highest possible fidelity. Here, we describe how to perform low-loss edge coupling by using an ultra-high numerical aperture fiber to closely match the mode of the silicon waveguides. By using an optimized fusion splicing recipe, the UHNA fiber is seamlessly interfaced with a standard single-mode fiber. This low-loss coupling allows the measurement of high-fidelity photon production in an integrated silicon ring resonator and the subsequent two-photon interference of the produced photons in a closely integrated Mach-Zehnder interferometer. This paper describes the essential procedures for the preparation and characterization of high-performance and scalable silicon quantum photonic circuits.

Silicon photonic chips have the potential to realize complex integrated quantum systems. Presented here is a method for preparing and testing a silicon photonic chip for quantum measurements.

Silicon photonic chips have the potential to realize complex integrated quantum information processing circuits, including photon sources, qubit ...

Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans

This manuscript describes how to classify nematodes using temporal far-field diffraction signatures. A single C. elegans is suspended in a water column inside an optical cuvette. A 632 nm continuous wave HeNe laser is directed through the cuvette using front surface mirrors. A significant distance of at least 20-30 cm traveled after the light passes through the cuvette ensures a useful far-field (Fraunhofer) diffraction pattern. The diffraction pattern changes in real time as the nematode swims within the laser beam. The photodiode is placed off-center in the diffraction pattern. The voltage signal from the photodiode is observed in real time and recorded using a digital oscilloscope. This process is repeated for 139 wild type and 108 &#34;roller&#34; C. elegans. Wild type worms exhibit a rapid oscillation pattern in solution. The &#34;roller&#34; worms have a mutation in a key component of the cuticle that interferes with smooth locomotion. Time intervals that are not free of saturation and inactivity are discarded. It is practical to divide each average by its maximum to compare relative intensities. The signal for each worm is Fourier transformed so that the frequency pattern for each worm emerges. The signal for each type of worm is averaged. The averaged Fourier spectra for the wild type and the &#34;roller&#34; C. elegans are distinctly different and reveal that the dynamic worm shapes of the two different worm strains can be distinguished using Fourier analysis. The Fourier spectra of each worm strain match an approximate model using two different binary worm shapes that correspond to locomotory moments. The envelope of the averaged frequency distribution for actual and modeled worms confirms the model matches the data. This method can serve as a baseline for Fourier analysis for many microscopic species, as every microorganism will have its unique Fourier spectrum.

Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans

This manuscript describes how to distinguish different nematodes using far-field diffraction signatures. We compare the locomotion of 139 wild type and 108 &#34;Roller&#34; C. elegans by averaging frequencies associated with the temporal Fraunhofer diffraction signature at a single location using a continuous wave laser.

This manuscript describes how to classify nematodes using temporal far-field diffraction signatures. A single C. elegans is suspended in a water column ...

Force-Clamp Rheometry for Characterizing Protein-based Hydrogels

Here, we describe a force-clamp rheometry method to characterize the biomechanical properties of protein-based hydrogels. This method uses an analog proportional-integral-derivative (PID) system to apply controlled-force protocols on cylindrical protein-based hydrogel samples, which are tethered between a linear voice-coil motor and a force transducer. During operation, the PID system adjusts the extension of the hydrogel sample to follow a predefined force protocol by minimizing the difference between the measured and set-point forces. This unique approach to protein-based hydrogels&#160;enables the tethering of extremely low-volume hydrogel samples (&#60; 5 &#181;L) with different protein concentrations. Under force-ramp protocols, where the applied stress increases and decreases linearly with time, the system enables the study of the elasticity and hysteresis behaviors associated with the (un)folding of proteins and the measurement of standard elastic and viscoelastic parameters. Under constant-force, where the force pulse has a step-like shape, the elastic response, due to the change in force, is decoupled from the viscoelastic response, which comes from protein domain unfolding and refolding. Due to its low-volume sample and versatility in applying various mechanical perturbations, force-clamp rheometry is optimized to investigate the mechanical response of proteins under force using a bulk approach.

A new force-clamp rheometry technique is used to investigate the mechanical properties of low-volume protein-based hydrogel samples tethered between a voice-coil motor and a force sensor. An analog proportional-integral-derivative (PID) system allows for the &#39;clamping&#39; of the force experienced to the desired protocol.

Here, we describe a force-clamp rheometry method to characterize the biomechanical properties of protein-based hydrogels. This method uses an analog ...