893
Bioehimica et Biophysica Aeta, 444 (1976) 893--898
© Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
BBA 28038
PHOTON CORRELATION ANALYSIS OF CYTOPLASMIC STREAMING K.H. LANGLEY a, R.W. PIDDINGTON b, D. ROSS c and D.B. SATTELLE d a Department of Physics and Astronomy, University of Massachusetts, Amherst, Mass. O1002 (U.S.A.), b Department of Physiology, King's College, The Strand, London, c Department of Engineering, Queen Mary College, Mile End Rd., London and d A.R.C. Unit of Invertebrate Chemistry and Physiology, Department of Zoology, Cambridge University, Downing St., Cambridge (U.K.)
(Received March 2rid, 1976) (Revised manuscript received June 15th, 1976)
Summary Laser light scattering has been used to investigate particle movements in a plant cell. Intensity autocorrelation functions are obtained by digital p h o t o n correlation of laser light scattered from cells of Nitella opaca both during cytoplasmic streaming and during the transitory cessation of streaming induced by electrical stimulation. The average velocity computed from the periodic oscillation in the intensity autocorrelation function during streaming corresponds to the velocity estimated using light microscopy. An estimate of the distribution of streaming velocities has been obtained from the decay in the amplitude of the envelope of the autocorrelation function derived from a streaming cell.
W e describe preliminary studies in which the intensity autocorrelation function is measured for laser light scattered from cells of the giant Characean alga Nitella opaca. The aims of this work have been, first, to distinguish between the various particle motions in the cell and, secondly, to assess the use of information contained in the scattered laser light for investigation of the molecular basis of cytoplasmic streaming. The cytoplasm of Nitella is divided into an outer non-streaming zone, the cortical cytoplasm, and an inner layer of streaming endoplasm. The endoplasm streams along the cell as a spiral belt with a low pitch angle (approx. 15 ° ). To date, most quantitative descriptions of streaming in algal cells have relied on light microscopical observations [ 1 , 2 ] . Two mechanisms have been proposed for the generation of the motive force of streaming. In the first of these, the "active~hear" mechanism, the microfilaments located in the cortical cytoplasm at the shear zone between the cortex and the endoplasm are considered to provide the driving force [3]. The identification of actin microfilaments in Characean cells [4--6] suggests the
894
possibility that an actin-myosin interaction generates the streaming motion. Also, in experiments using a cell model derived from cells ofChara corallina, streaming has been activated by A T P [7]. The above evidence is consistent with the view put forward by H.E. Huxley [8] that motility in a variety of cells could be achieved by an actin-myosin interaction similar to that described for striated muscle. Another mechanism has been proposed based on light microscopical observations in which Nomarski differential interference optics are employed in conjunction with laser ~umination [9,10]. In this case the generation of the motive force is attributed to the beating within the endoplasm of microfilament bundles anchored in the cortical layer of cytoplasm. W h e n a plant cell scatters laser light, fluctuations in the scattered intensity are produced by motion of the material within the scattering volume. These fluctuations can be described in terms of the autocorrelation function G(T) of the instantaneous intensity of the light scattered through a particular angle: G(r) = < It It+r >, where It and It+r are the light intensitiesat times t and t + r respectively, and the bracket denotes an average over the time of the experiment. The autocorrelation function thus measures the degree to which the intensity at a particular time t is related to its value at some later time t + r on the average. Complete accounts of the applications of photon correlation techniques to the study of diffusion and flow of particles are given elsewhere [11, 12]. Only a brief review of a few relevant results is presented here. If laser light is scattered by Stationary particles the intensity autocorrelation function G(T) is a constant, independent of r, the intensity being a quantity which is independent of time. Motion of the scattering material introduced curvature into G(r). If the scatterersare particles of uniform size, of the order of a wavelength or less in diameter, and are undergoing Brownian motion in a homogeneous fluid, G(v) is a single exponentially decaying function G(r) oc exp(--2Doq2r) + 1
(1)
where Do is the diffusion coefficient and q = (2~n/Xo)sin 0/2 is the scattering wave vector (see Fig. la). Here n is the index of refraction and )~o is the wavelength of the light in air. For scatterers of different sizes diffusing in a heterogeneous medium such as cytoplasm, a multi~xponential correlation function would be expected. Directed movement of the scattering material, such as that found in cytoplasmic streaming, is expected to produce periodic oscillationsin G(r), the period of oscillation being inversely proportional to the average velocity of the scatterers. The decay in the amplitude of these oscillations is related to the velocity distribution. A wider range of velocities leads to a more rapid damping o f the oscillations. Cleaned single internodal cells of NiteUa opaca (length ~ 7 cm) were m o u n t e d horizontally on platinum stimulating electrodes under pond water (filtered using a miUipore filter with 0.45 # m effective pore diameter) in the index matched specimen cell o f a Precision Devices p h o t o n correlation spectrometer (Malvern System 4300). Light from an attenuated 15 mW He-Ne laser (Scientifica and Cook, )% = 632.8 nm) illuminated an area a b o u t 0.2 cm from one electrode with a focussed spot o f 100 #m diameter. A low dark current photomultiplier ($20 cathode) detected the scattered light at a chosen angle.
895
(a) 1 ki
~
0
q v
(e)
T Fig. 1. (a) Geometry of laser light scattering e x p e r i m e n t . Directions of the i nc i de nt light (~i) scattered ]~ght (~s)' scatte~zmg wave v e c t o r (~), and streaming particles (~) are indicated. The s c a t t e r i n g angle (8) and the angle b e t w e e n the scattering wave vector and the dire c t i on of streaming (~) are shown. The scattezing wave vector bisecte the angle c o m p l e m e n t a r y to 0. (b--d) I n t e n s i t y a u t o c o r r e l a t i o n functions of light scattered at 8 ffi 9 0 ° from a Nitelis cell. Streaming gives characteristically periodic correlation func t i ons (b,d). The perio d is inversely p r o p o r t i o n a l to the average streaming ve l oc i t y (v 0) and t h e r a t e of decay of the oscillation a m p l i t u d e is inversely p r o p o r t i o n a l to the w i d t h of the d i s t r i b u t i o n of velocities (~ v). Periodicity is abolished when =trearnin_a is arrested b y electrical s t i m u l a t i o n (c). (e) Calculated d i s t r i b u t i o n of streaming velocities where v is the streaming velocity and Pv is the p r o b a b i l i t y t h a t t he ve l oc i t y of a given particle is v.
The o u t p u t pulses from the photomultiplier were amplified, discriminated, and shaped into 30-ns wide pulses which were applied to the input of the singieclipped digital autocorrelator (see refs. 13 and 14 for full experimental details). Cells in which streaming was observed using a × 50 binocular microscope gave autocorrelation functions showing a distinct periodicity (Figs. lb,d), indicating directional flow. The period for the streaming autocorrelation function agrees with that calculated from the streaming velocity measured using light microscopy. When a single depolarizing pulse (5 V, 2 ms) of above threshold amplitude was applied to the cell via the platinum electrodes which served as a support for the cell, a temporary cessation (2--3 rain) of streaming was observed microscopically. During the arrest of streaming, autocorrelation functions of the type shown in Fig. lc were recorded. As the streaming (observed microscopically) began to recover following a shock, so did the periodicity in the autocorrelation function; the periodicity increasing in frequency as the streaming velocity increased until the initial periodicity was restored. When shocks at 5-s intervals were applied to the cell for 6 min, both the streaming and the periodicity in the autocorrelation function were abolished throughout the stimulus regime. We conclude that the periodic oscillations in the autocorrelation function are produced by cytoplasmic streaming. The shape of the autocorrelation function for streaming approximates to an exponentially
896
damped cosine curve added to a B ~ o ~ . ~ t i a l - l i k e function which is clearly seen when streaming is ~ (~ ~). This nonstreaming function probably results from B r o w a i ~ m o t l o n o f cytoplasmic components. Autocorrelation functions obtained from streaming cells were analyzed by computer fitting G(r) to the equation G(r) = A + B exp(--r/C) + D exp(--r/Td) cos(21rr/Tp)
(2)
by adjusting the parameters A, B, C, D, Td and Tp to minimize the meansquared difference between the data and Eqn. 2 and obtain the best fit to the data. Although the number of parameters seems large, each relates directly to some specific characteristic o f G(~) and is therefore quite well determined. The light scattered from s t a t i o n a t T n m ~ in the Nitella cell such as the cortical layer, is intense enough that we can assume a heterodyne signal for G(r) (see e.g. ref. 11 p. 90). The average streaming velocity for a particular cell was estimated from the period of the autocorrelation function since; for a Doppler-shift produced by flowing particles, 1 2nvo 0 T p - k0 c o s ~ s i n ~
(3)
where Tp is the period of the oscillation in the autocorrelation function; v0 is the average streaming velocity, and ~ is the angle between the direction of flow and the scattering wave vector. For light scattered at various angles, a plot of 1/Tp versus cos ~ sin 0/2 should be a straight line with a slope equal to 2nuo/Xo from which u0 can he obtained for a given cell. Measured values of 1/Tp are shown as the open circles in Fig. 2. By this method average streaming velocities of approx. 60 #m • s -t were determined from the straight line fit to the data in Fig. 2 for NiteUa opaca at room tern )erature. i
!
i
i
i
i
I
'16(] 0
120 (s-l)
8O ( s4) 40
O~
I
0.1
I
0.2
I
I
I
0.3 eO.4 0.5 sin ~ cos~
I
0.6
f
0.7
Fig. 2. Angular sealing of the osc/nation frequency (o, l l T p ) and os c ma t i on decay rate (s , l l T d ) from intens/ty autocorrelatlon functions obtained during streaming. The angles (z and 8 are as s how n in Fig. l a ; v 0 is the averale streaming velocity, n is the index of refraction end ~0 is the wavelength of the laser light. Straight line plots are e x p e c t e d for light from scatterers flowing with a Lore nt z i a n velocity distribution.
897 An estimate of the distribution of streaming velocities in the cytoplasm was derived from Td, the decay time of the envelope of the oscillation in the autocorrelation function (Fig. le). Our preliminary analysis is based on the following ideas. (a) A typical streaming particle is observed to remain in the scattering region for a long time (1 s or more) compared to the range of correlation times examined, therefore the measured correlation function should not be appreciably influenced by the slow decay introduced by intensity fluctuations due to particles entering/leaving the scattering volume. (b) We assume the velocity distribution is Lorentzian (the envelope of the decay of the measured streaming autocorrelation function approximates a single exponential); the probability that the velocity of a given particle is v is given by
AvI~ Pcv) = (v -- 00)2 + (Av) 2
(4)
where Av is the half-width at half-height of the probability distribution curve and v0 is the mean velocity (see Fig. le). (c) Details of the particle size distribution and indices of refraction are unknown, but the scattered intensity is certain to be dominated by the larger particles since the scattered intensity is proportional to the square of the particle volume (for particles that are not too large). Our estimates of v0 and Av are primarily d e t e r m i n e d b y these more strongly scattering particles which we assume to be uniformly distributed throughout the streaming endoplasm. We note that our m e t h o d includes scattering from particles which are too small to be seen in the light microscope. (d) Diffusion of the streaming particles in the flowing endoplasm would also contribute to the decay rate of the oscillations in G(z), decreasing Td in the third term on the right hand side of Eqn. 2. We find that this is a negligible effect (the decay rate of the oscillations is not proportional to q2 as one would expect for simultaneous streaming and diffusion), probably because the large strongly scattering particles diffuse very slowly. Under the above conditions, the particles streaming at each velocity contribute an oscillating correlation function of period given by Eqn. 3 and amplitude proportional to the probability of that velocity as given by Eqn. 4. Adding together the contributions from all velocities, the oscillating part of the correlation function will be an exponentially damped cosine curve which is related to the probability distribution of particle velocities in the following way: Av Tp v0 - 27rTd
(5)
(recall that Tp is the oscillation period of the autocorrelation function and Td is the time for the amplitude of the envelope of the oscillating part of the autocorrelation function to fall to 1/e of its initial value). For the autocorrelation function shown in Fig. l b , AV/Vo is approximately 0.12%. Since the decay time of the oscillations Td is proportional to the period of oscillation Tp (Eqn. 5), we expect that 1/Td should be directly proportional to c o ~ sin 0/2. Another way of stating this is that the measured width of the velocity distribution, AV/Oo should be independent of the scattering angle we choose to use in measuring it. Measured values of 1/Td are plotted as solid squares in Fig. 2. The departure from a straight line is n o t readily explained offer than ~being due tobialogical variability. If diffusion of streaming particles were significant, the c u ~ e would depart upward, not downward, from a straight line.
898 18
~ 10
"•..•
'.
8 O
/
6 4 2
I I I 100 150 200 Frequency (Hz) Fig. 3. P o w e r s p e c t r u m o f the f l u c t u a t i o n s in laser light scattered f r o m a s t r e a m i n g NiteUa cell c o m p u t e d b y p e r f o r m i n g the F o u r i e r t r a n s f o r m o f the a u t o c o r r e l a t i o n f u n c t i o n in Fig. 1 (d), Sf is the p o w e r per u n i t • frequency. 0
I 50
Fourier transforms of the autocorrelation functions for streaming cells give spectra (Fig. 3) which resemble those described by Mustacich and Ware [15] in studies on Nitella flexilis and Sattelle and Buchan [16] in studies on Chara corallina. The results demonstrate that the bulk of the moving scatterers in the streaming cytoplasm travel at about the same velocity. The tight distribution of velocities and the average streaming velocities noted in the present study of Nitella opaca are in good agreement with the light-microscopical [3] and lightbeating [15] studies on Nitella flexilis and Chara corallina [16]. When streaming is temporarily halted by electrical stimulation a residual level of motion is detected which can probably be ascribed to the Brownian motion of cytoplasmic contents. Thus, using laser light scattering it is possible to distinguish between some of the various particle motions in a cell and in the case of cytoplasmic streaming the velocity distribution can readily be determined. Our present data do not enable us to confirm or refute the models proposed for the generation of the motive force of streaming. Nevertheless, used in conjunction with the application to motile systems of chemical agents known to specifically affect components of the motile machinery of the cell, laser light scattering could serve as a rapid quantitative assay of motility in the further dissection of its molecular basis. References 1 Allen. R.D. and K a m i y a , N. (1964) Primitive M o t i l e S y s t e m s in Cell B i o l o g y , A c a d e m i c Press, N e w Yo rk 2 Rebhun, L.I. (1972) Int. Key. Cytol. 32, 93--137 3 Kamiya, N. (1962) In H a n d b . Pflm~e~aphyitol (Rushland, W., ed.), XVII (2), pp. 9 7 ~ - S 6 6 , Springer, Berlin 4 Palevitz, B.A., Ash, J.F. a n d H e l p e r , P.K. (1974) Proe. Natl. Acad. SeA. U.S. 71, 368--666. 5 W i l l / a m s o n , R.E. ( 1 9 7 4 ) N a t u r e 2 4 1 , 8 0 1 - - 8 0 2 6 K e r s e y , Y.M. ( 1 9 7 4 ) J. Cell Biol. 63, 165a 7 Willlamson, R.E. (1975) J. Cen SeA. 17,655---668 6 Huxley, H.E. (1 973) Nature 243, 44~--449 9 Allen, N.S. and Allen, R.D. (1972) J. Cell Biol. 55, 2a 10 Allan, N.S. (1974) J. Cell Biol, 63, 270--287 11 Cummins, H.Z. and Pike, E.R. ( i 9 1 4 ) P h o t o n C o r r e l a t i o n and L i g h t Beating S P e c t r o s c o p y , P l e n u m Press, N e w Y o r k 12 Chu, B. (1974) Laser IAght Scattering, A c a d e m i c press, N e w Y o r k 13 Plddington, R.W. In PersPective in A n i m a l E x p e r i m e n t a l B i o l o g y ( S p e n c e r Davies, P., ed.,), P e r g a m o n Pre~, London 14 Sattelle, D.B. and P i d d i n g t o n , R.W. (1975) J. Exp. BioL 62, 7 5 3 - - 7 7 0 15 Mustacich, lt.V. and Ware, B.R. (1974) Phys. Rev. Lett. 33, 617---620 16 Satteile, D.B. and B u c h a n , P.B. (1976) J. Ceil Sci., in the press
Bioehimica et Biophysica Aeta, 444 (1976) 893--898
© Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
BBA 28038
PHOTON CORRELATION ANALYSIS OF CYTOPLASMIC STREAMING K.H. LANGLEY a, R.W. PIDDINGTON b, D. ROSS c and D.B. SATTELLE d a Department of Physics and Astronomy, University of Massachusetts, Amherst, Mass. O1002 (U.S.A.), b Department of Physiology, King's College, The Strand, London, c Department of Engineering, Queen Mary College, Mile End Rd., London and d A.R.C. Unit of Invertebrate Chemistry and Physiology, Department of Zoology, Cambridge University, Downing St., Cambridge (U.K.)
(Received March 2rid, 1976) (Revised manuscript received June 15th, 1976)
Summary Laser light scattering has been used to investigate particle movements in a plant cell. Intensity autocorrelation functions are obtained by digital p h o t o n correlation of laser light scattered from cells of Nitella opaca both during cytoplasmic streaming and during the transitory cessation of streaming induced by electrical stimulation. The average velocity computed from the periodic oscillation in the intensity autocorrelation function during streaming corresponds to the velocity estimated using light microscopy. An estimate of the distribution of streaming velocities has been obtained from the decay in the amplitude of the envelope of the autocorrelation function derived from a streaming cell.
W e describe preliminary studies in which the intensity autocorrelation function is measured for laser light scattered from cells of the giant Characean alga Nitella opaca. The aims of this work have been, first, to distinguish between the various particle motions in the cell and, secondly, to assess the use of information contained in the scattered laser light for investigation of the molecular basis of cytoplasmic streaming. The cytoplasm of Nitella is divided into an outer non-streaming zone, the cortical cytoplasm, and an inner layer of streaming endoplasm. The endoplasm streams along the cell as a spiral belt with a low pitch angle (approx. 15 ° ). To date, most quantitative descriptions of streaming in algal cells have relied on light microscopical observations [ 1 , 2 ] . Two mechanisms have been proposed for the generation of the motive force of streaming. In the first of these, the "active~hear" mechanism, the microfilaments located in the cortical cytoplasm at the shear zone between the cortex and the endoplasm are considered to provide the driving force [3]. The identification of actin microfilaments in Characean cells [4--6] suggests the
894
possibility that an actin-myosin interaction generates the streaming motion. Also, in experiments using a cell model derived from cells ofChara corallina, streaming has been activated by A T P [7]. The above evidence is consistent with the view put forward by H.E. Huxley [8] that motility in a variety of cells could be achieved by an actin-myosin interaction similar to that described for striated muscle. Another mechanism has been proposed based on light microscopical observations in which Nomarski differential interference optics are employed in conjunction with laser ~umination [9,10]. In this case the generation of the motive force is attributed to the beating within the endoplasm of microfilament bundles anchored in the cortical layer of cytoplasm. W h e n a plant cell scatters laser light, fluctuations in the scattered intensity are produced by motion of the material within the scattering volume. These fluctuations can be described in terms of the autocorrelation function G(T) of the instantaneous intensity of the light scattered through a particular angle: G(r) = < It It+r >, where It and It+r are the light intensitiesat times t and t + r respectively, and the bracket denotes an average over the time of the experiment. The autocorrelation function thus measures the degree to which the intensity at a particular time t is related to its value at some later time t + r on the average. Complete accounts of the applications of photon correlation techniques to the study of diffusion and flow of particles are given elsewhere [11, 12]. Only a brief review of a few relevant results is presented here. If laser light is scattered by Stationary particles the intensity autocorrelation function G(T) is a constant, independent of r, the intensity being a quantity which is independent of time. Motion of the scattering material introduced curvature into G(r). If the scatterersare particles of uniform size, of the order of a wavelength or less in diameter, and are undergoing Brownian motion in a homogeneous fluid, G(v) is a single exponentially decaying function G(r) oc exp(--2Doq2r) + 1
(1)
where Do is the diffusion coefficient and q = (2~n/Xo)sin 0/2 is the scattering wave vector (see Fig. la). Here n is the index of refraction and )~o is the wavelength of the light in air. For scatterers of different sizes diffusing in a heterogeneous medium such as cytoplasm, a multi~xponential correlation function would be expected. Directed movement of the scattering material, such as that found in cytoplasmic streaming, is expected to produce periodic oscillationsin G(r), the period of oscillation being inversely proportional to the average velocity of the scatterers. The decay in the amplitude of these oscillations is related to the velocity distribution. A wider range of velocities leads to a more rapid damping o f the oscillations. Cleaned single internodal cells of NiteUa opaca (length ~ 7 cm) were m o u n t e d horizontally on platinum stimulating electrodes under pond water (filtered using a miUipore filter with 0.45 # m effective pore diameter) in the index matched specimen cell o f a Precision Devices p h o t o n correlation spectrometer (Malvern System 4300). Light from an attenuated 15 mW He-Ne laser (Scientifica and Cook, )% = 632.8 nm) illuminated an area a b o u t 0.2 cm from one electrode with a focussed spot o f 100 #m diameter. A low dark current photomultiplier ($20 cathode) detected the scattered light at a chosen angle.
895
(a) 1 ki
~
0
q v
(e)
T Fig. 1. (a) Geometry of laser light scattering e x p e r i m e n t . Directions of the i nc i de nt light (~i) scattered ]~ght (~s)' scatte~zmg wave v e c t o r (~), and streaming particles (~) are indicated. The s c a t t e r i n g angle (8) and the angle b e t w e e n the scattering wave vector and the dire c t i on of streaming (~) are shown. The scattezing wave vector bisecte the angle c o m p l e m e n t a r y to 0. (b--d) I n t e n s i t y a u t o c o r r e l a t i o n functions of light scattered at 8 ffi 9 0 ° from a Nitelis cell. Streaming gives characteristically periodic correlation func t i ons (b,d). The perio d is inversely p r o p o r t i o n a l to the average streaming ve l oc i t y (v 0) and t h e r a t e of decay of the oscillation a m p l i t u d e is inversely p r o p o r t i o n a l to the w i d t h of the d i s t r i b u t i o n of velocities (~ v). Periodicity is abolished when =trearnin_a is arrested b y electrical s t i m u l a t i o n (c). (e) Calculated d i s t r i b u t i o n of streaming velocities where v is the streaming velocity and Pv is the p r o b a b i l i t y t h a t t he ve l oc i t y of a given particle is v.
The o u t p u t pulses from the photomultiplier were amplified, discriminated, and shaped into 30-ns wide pulses which were applied to the input of the singieclipped digital autocorrelator (see refs. 13 and 14 for full experimental details). Cells in which streaming was observed using a × 50 binocular microscope gave autocorrelation functions showing a distinct periodicity (Figs. lb,d), indicating directional flow. The period for the streaming autocorrelation function agrees with that calculated from the streaming velocity measured using light microscopy. When a single depolarizing pulse (5 V, 2 ms) of above threshold amplitude was applied to the cell via the platinum electrodes which served as a support for the cell, a temporary cessation (2--3 rain) of streaming was observed microscopically. During the arrest of streaming, autocorrelation functions of the type shown in Fig. lc were recorded. As the streaming (observed microscopically) began to recover following a shock, so did the periodicity in the autocorrelation function; the periodicity increasing in frequency as the streaming velocity increased until the initial periodicity was restored. When shocks at 5-s intervals were applied to the cell for 6 min, both the streaming and the periodicity in the autocorrelation function were abolished throughout the stimulus regime. We conclude that the periodic oscillations in the autocorrelation function are produced by cytoplasmic streaming. The shape of the autocorrelation function for streaming approximates to an exponentially
896
damped cosine curve added to a B ~ o ~ . ~ t i a l - l i k e function which is clearly seen when streaming is ~ (~ ~). This nonstreaming function probably results from B r o w a i ~ m o t l o n o f cytoplasmic components. Autocorrelation functions obtained from streaming cells were analyzed by computer fitting G(r) to the equation G(r) = A + B exp(--r/C) + D exp(--r/Td) cos(21rr/Tp)
(2)
by adjusting the parameters A, B, C, D, Td and Tp to minimize the meansquared difference between the data and Eqn. 2 and obtain the best fit to the data. Although the number of parameters seems large, each relates directly to some specific characteristic o f G(~) and is therefore quite well determined. The light scattered from s t a t i o n a t T n m ~ in the Nitella cell such as the cortical layer, is intense enough that we can assume a heterodyne signal for G(r) (see e.g. ref. 11 p. 90). The average streaming velocity for a particular cell was estimated from the period of the autocorrelation function since; for a Doppler-shift produced by flowing particles, 1 2nvo 0 T p - k0 c o s ~ s i n ~
(3)
where Tp is the period of the oscillation in the autocorrelation function; v0 is the average streaming velocity, and ~ is the angle between the direction of flow and the scattering wave vector. For light scattered at various angles, a plot of 1/Tp versus cos ~ sin 0/2 should be a straight line with a slope equal to 2nuo/Xo from which u0 can he obtained for a given cell. Measured values of 1/Tp are shown as the open circles in Fig. 2. By this method average streaming velocities of approx. 60 #m • s -t were determined from the straight line fit to the data in Fig. 2 for NiteUa opaca at room tern )erature. i
!
i
i
i
i
I
'16(] 0
120 (s-l)
8O ( s4) 40
O~
I
0.1
I
0.2
I
I
I
0.3 eO.4 0.5 sin ~ cos~
I
0.6
f
0.7
Fig. 2. Angular sealing of the osc/nation frequency (o, l l T p ) and os c ma t i on decay rate (s , l l T d ) from intens/ty autocorrelatlon functions obtained during streaming. The angles (z and 8 are as s how n in Fig. l a ; v 0 is the averale streaming velocity, n is the index of refraction end ~0 is the wavelength of the laser light. Straight line plots are e x p e c t e d for light from scatterers flowing with a Lore nt z i a n velocity distribution.
897 An estimate of the distribution of streaming velocities in the cytoplasm was derived from Td, the decay time of the envelope of the oscillation in the autocorrelation function (Fig. le). Our preliminary analysis is based on the following ideas. (a) A typical streaming particle is observed to remain in the scattering region for a long time (1 s or more) compared to the range of correlation times examined, therefore the measured correlation function should not be appreciably influenced by the slow decay introduced by intensity fluctuations due to particles entering/leaving the scattering volume. (b) We assume the velocity distribution is Lorentzian (the envelope of the decay of the measured streaming autocorrelation function approximates a single exponential); the probability that the velocity of a given particle is v is given by
AvI~ Pcv) = (v -- 00)2 + (Av) 2
(4)
where Av is the half-width at half-height of the probability distribution curve and v0 is the mean velocity (see Fig. le). (c) Details of the particle size distribution and indices of refraction are unknown, but the scattered intensity is certain to be dominated by the larger particles since the scattered intensity is proportional to the square of the particle volume (for particles that are not too large). Our estimates of v0 and Av are primarily d e t e r m i n e d b y these more strongly scattering particles which we assume to be uniformly distributed throughout the streaming endoplasm. We note that our m e t h o d includes scattering from particles which are too small to be seen in the light microscope. (d) Diffusion of the streaming particles in the flowing endoplasm would also contribute to the decay rate of the oscillations in G(z), decreasing Td in the third term on the right hand side of Eqn. 2. We find that this is a negligible effect (the decay rate of the oscillations is not proportional to q2 as one would expect for simultaneous streaming and diffusion), probably because the large strongly scattering particles diffuse very slowly. Under the above conditions, the particles streaming at each velocity contribute an oscillating correlation function of period given by Eqn. 3 and amplitude proportional to the probability of that velocity as given by Eqn. 4. Adding together the contributions from all velocities, the oscillating part of the correlation function will be an exponentially damped cosine curve which is related to the probability distribution of particle velocities in the following way: Av Tp v0 - 27rTd
(5)
(recall that Tp is the oscillation period of the autocorrelation function and Td is the time for the amplitude of the envelope of the oscillating part of the autocorrelation function to fall to 1/e of its initial value). For the autocorrelation function shown in Fig. l b , AV/Vo is approximately 0.12%. Since the decay time of the oscillations Td is proportional to the period of oscillation Tp (Eqn. 5), we expect that 1/Td should be directly proportional to c o ~ sin 0/2. Another way of stating this is that the measured width of the velocity distribution, AV/Oo should be independent of the scattering angle we choose to use in measuring it. Measured values of 1/Td are plotted as solid squares in Fig. 2. The departure from a straight line is n o t readily explained offer than ~being due tobialogical variability. If diffusion of streaming particles were significant, the c u ~ e would depart upward, not downward, from a straight line.
898 18
~ 10
"•..•
'.
8 O
/
6 4 2
I I I 100 150 200 Frequency (Hz) Fig. 3. P o w e r s p e c t r u m o f the f l u c t u a t i o n s in laser light scattered f r o m a s t r e a m i n g NiteUa cell c o m p u t e d b y p e r f o r m i n g the F o u r i e r t r a n s f o r m o f the a u t o c o r r e l a t i o n f u n c t i o n in Fig. 1 (d), Sf is the p o w e r per u n i t • frequency. 0
I 50
Fourier transforms of the autocorrelation functions for streaming cells give spectra (Fig. 3) which resemble those described by Mustacich and Ware [15] in studies on Nitella flexilis and Sattelle and Buchan [16] in studies on Chara corallina. The results demonstrate that the bulk of the moving scatterers in the streaming cytoplasm travel at about the same velocity. The tight distribution of velocities and the average streaming velocities noted in the present study of Nitella opaca are in good agreement with the light-microscopical [3] and lightbeating [15] studies on Nitella flexilis and Chara corallina [16]. When streaming is temporarily halted by electrical stimulation a residual level of motion is detected which can probably be ascribed to the Brownian motion of cytoplasmic contents. Thus, using laser light scattering it is possible to distinguish between some of the various particle motions in a cell and in the case of cytoplasmic streaming the velocity distribution can readily be determined. Our present data do not enable us to confirm or refute the models proposed for the generation of the motive force of streaming. Nevertheless, used in conjunction with the application to motile systems of chemical agents known to specifically affect components of the motile machinery of the cell, laser light scattering could serve as a rapid quantitative assay of motility in the further dissection of its molecular basis. References 1 Allen. R.D. and K a m i y a , N. (1964) Primitive M o t i l e S y s t e m s in Cell B i o l o g y , A c a d e m i c Press, N e w Yo rk 2 Rebhun, L.I. (1972) Int. Key. Cytol. 32, 93--137 3 Kamiya, N. (1962) In H a n d b . Pflm~e~aphyitol (Rushland, W., ed.), XVII (2), pp. 9 7 ~ - S 6 6 , Springer, Berlin 4 Palevitz, B.A., Ash, J.F. a n d H e l p e r , P.K. (1974) Proe. Natl. Acad. SeA. U.S. 71, 368--666. 5 W i l l / a m s o n , R.E. ( 1 9 7 4 ) N a t u r e 2 4 1 , 8 0 1 - - 8 0 2 6 K e r s e y , Y.M. ( 1 9 7 4 ) J. Cell Biol. 63, 165a 7 Willlamson, R.E. (1975) J. Cen SeA. 17,655---668 6 Huxley, H.E. (1 973) Nature 243, 44~--449 9 Allen, N.S. and Allen, R.D. (1972) J. Cell Biol. 55, 2a 10 Allan, N.S. (1974) J. Cell Biol, 63, 270--287 11 Cummins, H.Z. and Pike, E.R. ( i 9 1 4 ) P h o t o n C o r r e l a t i o n and L i g h t Beating S P e c t r o s c o p y , P l e n u m Press, N e w Y o r k 12 Chu, B. (1974) Laser IAght Scattering, A c a d e m i c press, N e w Y o r k 13 Plddington, R.W. In PersPective in A n i m a l E x p e r i m e n t a l B i o l o g y ( S p e n c e r Davies, P., ed.,), P e r g a m o n Pre~, London 14 Sattelle, D.B. and P i d d i n g t o n , R.W. (1975) J. Exp. BioL 62, 7 5 3 - - 7 7 0 15 Mustacich, lt.V. and Ware, B.R. (1974) Phys. Rev. Lett. 33, 617---620 16 Satteile, D.B. and B u c h a n , P.B. (1976) J. Ceil Sci., in the press
