The influence of photometer design on optical-conformational changes

J. theor. Biol. (1975) 51, 1-12

The Influence of Photometer Design on Optical-Conformational Changes PAUL LATIMER Department of Physics, Auburn University, Auburn, Alabama 36830, U.S.A. (Received 15 August 1972, and in revisedform

11 November 1974)

When cells and large subcellular structures suffer a change in volume or internal structure, their light-scattering properties are normally altered. These optical-conformation changes are potential sources of information about conformation and processes which alter it. Classical light-scattering theory for spherical particles is used to determine how the transmittance or extinction of a cell suspension should respond when such a conformational change occurs and the measurements are made with a conventional photometer. This extends an earlier study of transmittances measured with an “ideal” photometer. The photocell of an ideal instrument collects only the directly transmitted light. In a conventional instrument it also collects the light scattered at small angles, which is usually most of the scattered light. Extinction (optical density, absorbance) of suspensions of spherical cells was computed for several photometer designs. It is found that y, the angle of acceptance of the photocell, has a significant influence on the extent and even the nature of the photometric response to a given conformational change. Earlier, it was shown that a decrease in cell volume or increase in internal structure will increase extinction for cells of many sizes. Now it is found that a large y-value increases these effects. An approach to the interpretation of transmitted light fluxes in terms of theoretical predictions is outlined.

1. Introduction When a change takes place in the rate of internal processes or in the medium of cells or large subcellular structures in suspension, the transmittance or optical density is usually altered (Latimer, Moore & Bryant, 1968; Cohen, Keynes & Hille, 1968; Kamino & Inouye, 1969; Born, 1970; Keen & White, 1970; Scheintaub & Fiel, 1973). Such optical changes reflect changes in the size, shape and/or structure of these “particles”. Many such opticalconformational changes are reversible and involve no change in dry weight; some are closely related to physiological processes. Optical transmittance has potential as a source of information in real time about dynamic aspects of morphological properties and about proT.B.

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cesses which influence them. Of course, photometric techniques do not have the spatial resolution of the electron microscope. However, they are non-destructive and require no “fixing” procedures. A basic problem of electron microscopy is that of determining whether observed structural details are real or are artifacts introduced in specimen preparation. Thus any technique that provides independent structural information of unfixed samples complements microscopy. In addition since optical techniques can be used to monitor on-going events and supply their information in real time, they offer a dimension of information not accessible by microscopy. These optical-conformational changes have also been of interest because they can introduce errors in measurements of absorption or fluorescence by the sample material or by an added indicator (Straub & Lynn, 1965; Jobsis, 1969). Koch (1961) and Latimer, Moore & Bryant (1968) developed theoretical explanations of optical-conformational transmittance changes, while Latimer & Pyle (1972) treated changes of scattering at specific angles. The transmittances studied were those governed by total scattering, light scattered at all angles. However, even for non-absorbing particles, a conventional transmission photometer does not measure the effects of total scattering. It measures scattering at angles larger than y, where y z 2-30”. This is the first study of the influence of y on optical-conformational changes. While it was thought to be small and uninteresting, we now find that y is important. Bryant, Seiber & Latimer (1969a) osmotically swelled and shrank yeast cells and chloroplasts, and measured the volume changes. They measured the resulting changes in transmittance with Seiber’s “ideal” photometer, and compared the results with theoretical predictions of our 1968 study. Excellent agreement was found. However, transmittances measured with a conventional spectrophotometer such as a B & L Model 505 by Bryant and by Packer, Siegenthaler & Nobel (1965) did not change with particle volume as predicted by our 1968 methods. These apparent theory/experiment conflicts suggest that theoretical treatments which ignore y are not applicable to such transmittances. A change in suspension transmittance or optical density would be independent of photometer design only if the conformational change did not alter the angular dependence of scattering. However, Latimer & Pyle (1972) found theoretically that this angular dependence usually does change. Hence there are both experimental and theoretical grounds for supposing the design of the optical system to be important. The overall problem of interpreting changes in the optical properties of biological cells is largely one of identifying the important factors. We now

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examine the influence of one potentially important parameter, the angle of the photocell. We carry out explanatory computations Lorenz-Mie relations, which are the exact solutions to Maxwell’s for scattering by the homogeneous sphere, and recently developed methods (Latimer, 1972~). 2. Theory-Key

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acceptance using the equations numerical

to the Relation Between Light Fluxes and Conformation

The ability of conventional light scattering theory to predict the scattering properties of biological cells and large subcellular structures has been widely tested. The “static” properties examined include selective scattering (Latimer & Rabinowitch, 1959; Latimer, 1959; Charney & Brackett, 1961); absolute scattering and absorption cross sections (MacRae, McClure & Latimer, 1961; Latimer & Eubanks, 1962; Bryant, Seiber & Latimer, 1969u); and the angular dependence of scattering (Latimer & Tully, 1968; Mullaney, van Dilla, Coulter & Dean, 1969; Cross & Latimer, 1972; Brunsting, 1972). The dynamic scattering properties studied are changes in transmittance caused by changes in particle volume with no change in dry weight. Changes in the volume of cells and chloroplasts were found to cause both scattering and absorption to change in agreement with the predictions of theory (Bateman, 1968; Bryant et al., 1969a). These and other studies indicate that measured transmitted and scattered fluxes can be reliably interpreted in terms of cell morphology using scattering theory. The problem of interpreting optical changes produced by conformational changes has several dimensions. Several types of changes may take place in article conformation, i.e. (a) a simple change in particle volume, (b) a change in overall particle shape, (c) a change in gross internal particle structure, or (d) a change in fine internal structure. Then such a change may take place in various types of sample particles. Finally, several different optical quantities may be measured: (a) light scattered at the various angles, (b) transmittance as measured with a highly collimated optical system, (c) transmittance as measured with an integrating sphere and (d) transmittance as measured with a conventional optical system. In view of the multiplicity of variables it is difficult to reliably account for a given effect or to extrapolate from one sample material, optical system, etc., to another on the basis of empirical evidence only. The problem of identifying the conformational origin of given optical change is reminiscent of problems encountered long ago of determining whether a disease was caused by a bacterium and then of identifying the bacterium. A key step towards solving the problem was the formulation of “Koch’s postulates” (see Henrici & Ordal, 1948). Koch called for com-

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plementary lines of evidence which together leave little uncertainty. We suggest that similar sets of complementary evidence are needed for the reliable interpretation of optical changes. To establish the identity of the conformational origin of a given change, it should be demonstrated: (a) through direct observation that particle conformation actually changes in the presumed way, (b) with scattering theory that a conformational change of the type presumed to cause the effect should indeed be expected on theoretical grounds to produce such an effect and (c) from both experimental and theoretical evidence that it is unlikely that the observed optical change in actuality has another origin such as a different conformational change. After the conformational origin of an optical change is determined, it may be interpreted quantitatively in terms of a theoretical calibration or an empirical one. Ideally the two types should agree or differ only for well understood reasons. 3. Theoretical Predictions In a transmittance photometer, the photocell collects the transmitted beam plus that scattered at angles up to y, the half-angle subtended at the sample by the edge of the axial photocell (see Fig. 1). Although some photometers have convergent beams, the performance of any such optical system Photocell

FIG. 1. Photometer optical system. The incident beam is highly collimated; photocell collects transmitted light plus all light scattered at angles up to y.

the axial

is similar to that of a system with a highly collimated incident beam and a suitable value of y (Latimer, 1972a). The present study is limited to this optical system. Suspension extinction, B(y) = log,, (l/transmittance), is related to sample parameters by E(y) = 0*434LNAK(y),

(1)

where L is the path of light in the sample vessel, N is the number of particles

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5

per unit volume of suspension, A is the projected area of a single particle and K(y) is its extinction efficiency. A particle removes light from the beam by scattering and/or absorption: K(y) = KS,(y)+Kabs. E(y) is also called “optical density” or “absorbance”. K(y)-values of spheres were calculated on an IBM 360 computer (Fortran IV) from the Lorentz-Mie equations (van de Hulst, 1957; Moore, Bryant & Latimer, 1968; Kerker, 1969) in terms of y, x and m, where x = 2na/5 a is the sphere radius, 2 is the wavelength of the incident light in the medium, m = n = in’, where n governs phase, n’ is proportional to the absorption coefficient and i = (- l)l”. We assume changes in the particle volume and internal structure and use theory to predict transmittance as a function of particle conformation. Then the reverse or inverse problem is considered, that of interpreting observed fluxes. to determine what conformational change caused them to change. A biological cell or structure is approximated as a homogeneous sphere. When volume changes, radius is given by a = ao(V/Vo)1’3 and projected area by A = A,(V/V,) ‘I3 . The cell is assumed to behave optically like a water solution of protein, etc. Its refractive index, relative to the medium, varies with volume according to : m = l+(mo-l)VJV,

(2)

where “0” denotes the initial or normal value, K(y) depends on m and a, both of which depend on volume. On the other hand, N remains constant unless particle aggregation or disintegration take place. Using equation (2) and the above relations, K(y) was computed from X(0’), y, and the angular scattering functions. The results for particles of several sizes and photometers of several y-values are shown in Figs 2 and 3. Normalized extinction, E(Y)/E(~)~, is plotted as a function of normalized volume, V/V,. It is seen that y has a very significant influence on the AE produced by a given AV. In most cases, an increase in y raises the left side of a curve and lowers its right side. Thus, an increase in y enhances the tendency of particle shrinkage to increase suspension extinction (reduce transmittance) and that of swelling to reduce extinction. For intermediate particle sizes, even the sign of the slope of the curve at V = V, can depend on y, see parts (e) through (i) of Fig. 2. For optical purposes, the internal structure of biological cells or large subcellular structures is divided into two size classes: gross features and fine ones. The dividing line is at about 1, which is the nominal boundary between the “large particle” and “small particle” domains in light scattering.

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----I (i!

.

v/ v, FIG. 2. Suspension extinction, E(y) = log,, (l/transmission (y), of non-absorbing particles as a function of volume. The sample particles are spherical and non-absorbing and the dry weight remains constant. Initial particle volume is V,, relative refractive index is m. = 1.05, and 1 = 374.2 nm (green light in water). (a) V0 = 0.002 u3 (small bacteria); (b) VO = 0.5 p3 (mitochondria); (c) V. = 2 p3 (bacteria); (d) V. = 8 l.P (chloroplast fragments); (e) V. = 40 n” (chloroplasts); (f) V. = 85 p3 (erythrocytes); (g) V. = 130 ~~ (large erythmcytes); (h) V. = 700p3 (cells); (i) V. = 4000 J.L~(leucocytes). -, E (0'); --, E(2"); ----, E(4'); -.-, E (10’); -..-, E(30°).

I is, of course, also the approximate limit of resolution of a light microscope. Structural features in the two different size domains require different theoretical approaches. We presently consider only fine structure. To account for the effects of internal structure of non-absorbing particles, we use a complex particle refractive index, m = n = in:,, where n:, is a measure of internal particle turbidity (Latimer, Moore & Bryant, 1968).

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0.5

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I.0

I.5

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v/ v, FIG. 3. Suspension extinction of absorbing particles (wr = 1.05 - 0405i initially) function of particle volume. All other parameters are those of Fig. 2.

as a

Greenberg, Wang & Bangs (1971) used a somewhat similar approach to account for the effects of surface structure. To calculate the effects of changes in internal fine structure on transmittances, n& was varied for each of several combinations of y and I’,. The resulting E(y)-values are shown in Fig. 4. Most of the increases in internal structure are seen to cause E(r) to increase. For this computation it was assumed that none of the light scattered out of the beam by the internal structure enters the photocell. However, this is strictly the case only for y = 0. The solid angle subtended by the photocell may be up to about O-25 steradians. However, this is small compared with the total of 47~ about the sample. Since the present purpose is merely to

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I.0

.--

I

‘.=O

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s=--.-- ----_

0

04

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FIG. 4. The dependence of E(y) of non-absorbing cells on internal particle structure (&) for indicated y-values. All other parameters are those of Fig. 2.

determine the nature and order of magnitude of effects of internal structure on transmittances, no correction was made for the effects of the collection by the photocell of the internally scattered light that is scattered within y. While Figs 2 and 3 reveal the effects on E(y) of changes in volume for particles of nine different sizes, an analytic relationship between E(y) and volume would be useful. For that purpose we consider only small volume changes, i.e. IAV/Vl < O-2. An index of the dependence of E(y) on Vis (3)

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In the limit, (41

$ is the slope of a curve in Figs 2 and 3 at V = V,. It is also proportional to the second coefficient in a Taylor’s series expansion of E(y) = f(y). Ic/ was calculated as a function of particle size for non-absorbing and absorbing particles. Size is measured in terms of van de Hulst’s particle size parameter pti = 47ca(n- 1)A. The results are shown in Fig. 5. This reveals that E(y) may either increase or decrease with an increase in Y depending on V, and y.

FIG. 5. The fractional change in extinction with particle volume, y(y), as a function of the particle size parameter p = 4na(n - 1)/A: (a) non-absorbing particles (m = l.OS), (b) absorbing particles (WI = 1~05-0~005~). -, 1, = 0”; --, y = 2”; ----, y = 4”; -.-,y=lo”; -*.-, y 130”.

4. Discussion The present models for volume and structural changes are idealizations; we do not know how closely they represent the actual conformational changes. It is known that volume changes are readily caused by the flow

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of water plus a few small ions into or out of a cell. However, some of these volume changes are apparently accompanied by simultaneous alterations of internal structure, as indicated by the results of Bryant et al. (19693). A systematic exploration of the effects of changes in gross internal structure is beyond the scope of this study. However, to characterize them one would represent the particle by an appropriate model such as a sphere or ellipsoid of revolution with a concentric coating or shell (Bryant et al., 1969a; Cross & Latimer, 1972; Wyatt, 1972; Brunsting & Mullaney, 1972). Then the effects of changes in these structures would be calculated while varying the relevant parameters in the equations. Some light is thrown on the problem of accounting for effects of changes in gross internal structure by unpublished photomicrographs of Hind from the study of Hind & Olson (1967). The pictures of cells which had undergone optical-conformational changes indicate that the interiors had suffered an internal “precipitation”; the cell contents, dry weight, had clumped into highly refractile centers, large and small. The resulting irregular internal structures would be expected to diminish the transmitted wave. This is indeed what & does. Thus some of the actual effects of gross structure on transmittance should be similar to those predicted with n& for fine structure. Changes in the angular dependence of scattering with apparent changes in internal structure were reported by Cram & Brunsting (1973). They found more scattering at small angles from virus-infected mammalian cells (PK- 15) than from their healthy counterparts. Their results can be accounted for in terms of internal particle turbidity. Scattering at all angles is influenced by the particle size parameter x and the relative refractive index m. Both factors change when particle volume changes. Our computations indicate that small angle scattering is governed primarily by x while large angle scattering is controlled mostly by m. The relative influence of m on observed transmittance is increased by increasing y. There is a curious fine structure in $-curves in Fig. 5. It originates with the well-known predicted fine structure of the Mie extinction curves. The fact that $ is essentially a derivative accentuates the effect. The influence of this structure is ordinarily not observable; it is obscured by the non-negligible values of AV and by heterogeneity of particle size in ordinary systems of sample particles. Information theory (Friedlander, 1970; Latimer, 19726) suggests that information from scattered light should take the form of the answers to simple “yes-no” questions. To interpret an optical change, the first problem is frequently to identify the responsible conformational change, i.e. “Which one?“. A comparison of Figs 2 and 4 reveals that the influence of y on transmittance changes may be useful in distinguishing optical changes

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caused by volume and structural changes. The latter would be more sensitive to y. They should also be more sensitive to d. Once the responsible conformational property is identified, the question becomes “In what way, or in which direction, did it change ?‘. The sign of $ supplies this information. The final question is, “How much?“. The magnitude of @ and the uncertainties therein provide the appropriate answer. The time dependence of biological structure under some circumstances may be of much greater practical interest than the details of the pattern itself at any moment. Actually it appears that many biological structures in areas where there is a high rate of physiological activity undergo continuous changes in conformation. Optical techniques, which are inherently non-destructive and are compatible with many other measurements, have promise as sources of information about dynamic aspects of cell structure. 5. Concluding Remarks From conventional light-scattering theory it is found that large acceptance angles of the photocell should substantially enhance the abilities of particle shrinkage and internal fine structure to decrease transmittance. The use of these predictions for quantitatively interpreting observed changes in transmittance is outlined. We cordially acknowledge P. Budenstein, D. Cross, W. Farthing and B. Pyle for helpful suggestions; P. Graham and T. Ray for assistance with the manuscript; and the Auburn University Computer Center for computer time. REFERENCES BATEMAN, J. B. (1968). J. Colloid ZnterJ Sci. 27, 458. BORN, G. V. R. (1970). J. Physiol., Land. 209, 487. BRKWTING, A. (1972).Doctoral Dissertation, University of New Mexico, Albuquerque. BRUNSTING, A. & MULLANEY, P. F. (1972).Appl. Opt. 11,675. BRYANT, F. D., SEIBER, B. A. & LATIMER, P. (1969u). Archs Biochem. Biophys. 135,97. BRYANT, F. D., LATIMER, P. & SEIBER, B. A. (1969b). Archs Biochem. Biophys. 135, 109. CHARNEY, E. & BRACKETT, F. T. (1961). Archs Biochem. Biophys. 92, 1. COHEN, L. B., KEYNES, R. S. & HILLE, B. (1968). Nature, Land. 218,438. CRAM, L. S. & BRTJNSTING, A. (1973). Expl Cell Res. 78,209. CROSS, D. A. & LATIMER, P. (1972). Appl. Opt. 11, 1225. FRIEDLANDER, S. K. (1970). Aerosol. Sci. 1,295. GREENBERG, J. M., WANG, R. T. & BANGS (1971). Nature Physical Science 230, 110. HENRICI, A. T. & Omm, E. J. (1948). The Biology of Bacteria, 3rd edn, p. 17. Boston: D. C. Heath. . HIND, G. & OLSON, J. M. (1967). In Energy Conversion by the Photosynthetic Apparatus, Brookhaven Symposia in Biology, No. 19, Brookhaven National Laboratory. JOBSIS, F. F. (1969). Curr. Top. Bioenerg. 3, 351.

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