A Precision Method for Generation of Solvent Gradients Frederick R. Blattner and John
N. Abelson,l
HE EXTENSIVE application of density Tgradient centrifugation in recent years has led to the development of a number of systems for generating solvent gradients (1, 2). This communication describes a new type of gradient generating system based on a punched tape prepared by a digital computer. This system is capable of generating gradients of any desired shape with great precision and is generally applicable to a variety of problems requiring solvent gradients, including sucrose gradient zone sediment at ion. Operating Principle. -i block diagram of the system is illustrated in Figure 1. Two reservoirs containing, for example, 1% and 25% sucrose are connected to a common mixing chamber by way of two pulse-operated solution metering pumps. These pumps deliver a small precisely determined volume to the mixing chamber each time they receive an electrical impulse. The mixing chamber, which is fitted with a magnetic stirring bar, leads via a short delivery tube in which it is desired to build the gradient. Electric impulses which drive the pumps are generated from a punched paper tape by a photoelectric tape reader. -4s the tape is transported past the photoelectric cells, holes on one edge of the tape activate the 1% pump and holes on the other edge activate the 25% pump. The concentration being delivered to the mixing chamber is determined by the relative frequency of holes in the two channels. h third channel is provided to stop the tape transport. Tape Format. At the beginning of the tape is a section which flushes the mixing chamber with 20y0 sucrose. Xext the gradient is begun and after a volume of gradient equal to the volume of the delivery tube has been delivered, a stop appears. The operator now places the centrifuge tube into position and restarts the tape. In this way the beginning of the gradient is delivered to the bottom of the centrifuge tube. As the tape progresses, the relative frequency of holes in the two
Present address, MRC Laboratory of Molecular Biology, Hills Road, Cam-
bridge, England.
21 21 8
Department of Biophysics, Johns Hopkins University, Baltimore, Md.
channels gradually changes, giving the desired gradient. When the end of the gradient has been delivered to the end of the delivery tube, a final stop appears and the gradient is ready for use. Preparation of Tapes. The paper tape is punched in advance by a digital computer using a specially designed program which is detailed in Figure 2. Since the volume of the
mixing chamber is not negligibly small, the tape must be punched so that the chamber output (rather than its input) conforms to the concentration gradient desired. This requires that the volume of the mixer as well as the volume of the fluid pulses be taken explicitly into account. At any given point in the gradient the computer has three options: punch
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Figure 1.
Block diagram of gradient generating system VOL 38, NO, 9, AUGUST 1966
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Figure 2. Flow diagram of ccnnputer program which produces tapes for gradient generator The program has three main partSection 1 detarmlnsi the f o n d of the tape and placer step puncher in the proper ploesr. Section 2 determines the form of the gradient delivered. Each time rn punching cycle has been completed the program employs (I subroutine te compute the desired concentration for the next cycle. The operator eon specify the form of the grodiont b y oltering this subroutine. Section 3 contains the logic for deciding which type of punch to place on the tope for eosh cycle. G , i s the concentration in the mixer. cl, ch, and cb ore the concentrations that would result from o low, 0 high, or 0 both punch. el, eh, and eb are the corrssponding deviations from the desired grodient. Ct ond Cu are the desired concvltrationi one ond two DUIS. volumes hence.
a 1% hole, punch a 25% hole, or punch both simultaneously. Given e,, the concentration in the mixer, a t that point, simple formulas can be derived giving the new values of e, after each of the three options. By subtracting these from the desired concentration at that point an error can be determined for each option. The option giving the least error is then punched and e, replaced by its newly calculated value. As this cycle is repeated any errors tend to cancel and the desired gradient emerges from the mixmg chamber. Apparatus. Figure 3 shows a photograph of the apparatus we have built. The solution metering pumps (center) consist of 5-ml. multifit syringes driven by precision screws geared to solenoidtype stepping motors (iModel SM-300-1, Step er Motors Carp., Culver City, Cali?). In each of the two pumps, three syringes are driven in pnrallel so that three gradients can be generated simultaneously. A friction clutch is 1280
ANALYTICAL CHEMISTRY
included in the gear train to prevent damage to the apparatus if the syringes reach the end of their excursion or get
Figure 3.
jammed. This also permits the screws to be rewound at the end of a NIL A haircurler spring is placed around each of the syringe plungers to ensure positive feed and prevent bouncing of the plunger against the drive plate. The apparat,us is mounted with the syringe outlets on top so that bubbles can be expelled easily while tilling them. The mixing chambets (right) are constructed in triplicate from lucite. A a/,6 X ',flrinch stirring magnet coated with Teflon is placed in each chamber. The chamber cavities hnve pointed tops as detailed in Figure 1 from which the delivery tubes emerge, making it easy to expel bubbles. The mechaoical portion of the tape reader (left) was modified from a discarded microfilm reader. The electronic circuitry is conventional. Three photoconductive cells (Texm Instruments IN 2175) t.rigger mouostable multivibrators which deliver 10 millisecond square waves. The pulses are amplified by power transktors and delivered to the stepping motors, or in the case of the stop channel, a transport motor stopping relay. The gradient maker hm mixing chamber volumes of 0.09 ml. each and the volume per pulse employed is 0,00019 ml. It takes approximately 26,000 pulses to make a gradient. Three gradient,s cau be made in 20 minutes. Performance Tests. Theoretical analysis of the inherent accuracy of the system using the computer reveals that for a 5% to 20% sucrose gradient the average expected absolute error throughout the gradient is +0.008 wt. yo. The average error should he 100 times smaller, since errors tend to cancel. These errors are attributable solely to the granularity of the pulse system. Actual measurements of nine of is less than *O.l wt. % ' at every point in the gradient for three gradients made simultaneously, and less than +0.2 wt. yo for gradients made at different times. These variation.; are attributed t o mechanical variations and to errors
Photograph of gradient generating system
In other experiments we have determined the reproducibility of sedimentation distance in separate runs. When the utmost care is exercised to control temperature and speed, the reproducibility is on the order of *0.06 cm., which corresponds to a *2.5% variation in absolute sedimentation coefficient. Since the machine was built, 5 or 6 workers have been using it routinely and over 1000 gradients have been satisfactorily generated. We have found it a rapid, convenient, flexible, and accurate method. ACKNOWLEDGMENT
Figure 4.
Test sedimentation of T 7 DNA in gradients
in measuring the refractive index of the solutions. We have tested the gradients produced by the machine in centrifugation experiments using T7 bacteriophage deoxyribonucleic acid as a standard. Figure 4 shows the profiles obtained in two runs of different durations in which identical samples were sediniented in the three buckets of the Spinco SW39
rotor. Samples of P3*-labcled DNA were spun for 3 hours (peak 1) and 6 hours (peak 2) at 35,000 r.p.m. The positions of the centers of gravity of the three peaks varied by no more than 10.01 cm. in both experiments. This reproducibility makes it possible to determine the relative sedimentation coefficients of samples run in different buckets.
The authors thank C. A. Thomas, who gave this project impetus through his realization of the need for a precision gradient maker. We also thank T. C. Pinkerton and T. J. Kelly for help in performing some of the experiments reported, and W. E. Love for the use of his Ro17al McBee LGP-30 computer. This work was done while both of us were pre-doctoral fellows of the Public Health Service. LITERATURE CITED
(1) Britten, R. .J., Roberts, R. B., Science 131, 32-3 (1960). (2)(de Duve, C., Berthet, J., Beaufay, H., Progress in Bio hysics and Biophysical Chemistry,” Vof: 9, 326-69, Pergamon Press, New York, 1959. WORKsupported by Atomic Energy Commission Grant AT(30-1)-2119.
A Nomogram for Calculating the Results of an Automatic Amino Acid Analysis W. A. Schroeder, W. R. Holmquist, and J. Roger Shelton, Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, Calif. 91 109
the description by Spackman, S Stein, and Moore (6) of an automatic amino acid analyzer, continued INCE
improvement has increased the number of analysis from one to several per day. On the other hand, because the time required to calculate the results of the analysis by hand from the automatic record can not be appreciably shortened per analysis, commercial integrators have become available and computer systems have been devised to do all or part of the calculation (7). Manual calculation is normally done by the formula H x TV/C = pmoles, where H is the net absorbance of the peak, W the width at half net absorbance (in terms of the number of dots) , and C a constant from the standardization (6). For convenience, calculation done in this way will be referred to as “the usual method.” This formula is valid for Gaussian shaped curves, and, in practice, is sufficiently accurate even for curves which deviate slightly from
a true Gaussian form. However, experimentally W is constant to within a few per cent over a wide range of H ; theoretically, also W is independent of H for Gaussian-shaped curves if the concentration of solute is not so high as to alter the number of theoretical plates and the distribution coefficient of the system (6) Consequently, the quantity of an amino acid is directly proportional to H itself to the same degree that W remains constant. Because of this relationship all calculations may be made readily with a nomogram. We shall describe the construction and use of a nomogram which permits the calculation of the results of an amino acid analysis in 5 minutes. It should be emphasized that this nomogram is a graphical representation of the relationship between four variables that is expressed by I
p=-
(P - B) K
where p is an amount of material whose dimensions depend on the constant K , P is the peak height, and B is the base line. It should be useful wherever such a relationship exists as it does, for example, in gas chromatograms. USE OF THE NOMOGRAM
The five scales of this nomogram are designed to subtract the base line absorbance B from the maximum absorbance P of the peak and to convert this difference H , by appropriate intersection of a straight line with other scales, to read directly the pmoles of each amino acid. The manner in which this is accomplished is shown in Figure 1. On the left-hand scale P , the maximum absorbance of the peak is found (for example, at R ) whereas, on the righthand scale B , the absorbance of the base line is located (say at S ) . The net absorbance is at T where the line from R to S intersects scale H . Scale A A , which is on the left-hand side of scale VOL. 38, NO. 9, AUGUST 1966
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