Bioelectrochemistry and Bioenergetics 41, 81-91, 1996.
Mae-Wan Ho, Julian Haffegee,Richard Newton, Yu-ming Zhou, John S. Bolton and Stephen Ross
Bioelectrodynamics Laboratory, and Physics Department Open University, U.K.
We review evidence supporting the idea that organisms are polyphasic liquid crystals and that liquid crystalline structure is fundamentally involved in biological organization and function, including pattern determination during development. A novel interference colour imaging technique is described, which enables us to detect, noninvasively, liquid crystalline domains in living organisms. Colour intensity is shown to be linearly related to molecular birefringence and degree of coherent alignment. We demonstrate the use of the quantitative imaging technique to reveal a phase-transition like increase in colour intensity of the body-wall musculature in the maturing Drosophila larva; and birefringent patterns in the early embryo when pattern determination processes are known to be occuring. The possible role of electrodynamical activities in pattern determiniation via phase ordering effects on liquid crystals is discussed.
Liquid crystals are phases of matter exhibited by certain anisotropic organic materials as they undergo a cascade of transitions between the solid and the liquid states (1-3). These mesophases possess symmetry and mechanical properties intermediate between those of liquids and of solid crystals: long range orientational order, and often also varying degrees of translational order. In contrast to solid crystals, liquid crystals are mobile and flexible, and highly responsive. They undergo rapid changes in orientation or phase transitions when exposed to electric (and magnetic) fields (2), or to changes in temperature, pressure, pH, hydration, and concentrations of inorganic ions. These properties are ideal for organisms (3 -5). Liquid crystals in organisms include the amphiphilic lipids of cellular membranes, the DNA in chromosomes, all proteins, especially cytoskeletal proteins, muscle proteins, collagens and proteoglycans of connective tissues. These adopt a multiplicity of mesophases that may be crucial for biological structure and function at all levels of organization from processing metabolites in the cell to pattern determination in development, and the coordinated locomotion of whole organisms (see below).
The importance of liquid crystals for living organization was recognized by Joseph Needham (6). He referred to some of the pioneers of biochemistry and biophysics such as F.G. Hopkins and R.A. Peters, who were very interested in the colloid theory of protoplasm developed especially by W.B. Hardy, following the work of I. Langmuir in the early part of this century. As Needham made clear, he and his contemporaries, including J.B. S. Haldane, D.M. Needham and J.D. Bernal, already entertained the idea that the protoplasm effectively channels metabolism at the molecular level, a topic which is much alive today (7). More specifically, Needham suggested that living systems actually are liquid crystals, and that many liquid crystalline mesophases may exist in the cell although the expected birefringence could not then be detected. He further suggested that liquid crystals are involved in determining body axes and polarities in development.
One of the first generalizations to emerge from developmental biology is that early embryos and isolated parts of early embryos show a strong tendency to form whole organisms. This gave rise to the notion of a morphogenetic field - a spatiotemporal domain of activities organized globally to form the whole organism.
At the start of embryogenesis, the morphogenetic field exhibits 'pleuripotency' or 'totipotency', where all parts has the potential to develop into any structure. In the course of early embryogenesis, however, determination occurs in which the different parts of the embryo become more and more restricted in their developmental potential. The determined state can be demonstrated by transplantation and grafting experiments. If a piece is removed from an embryo before determination and transplanted to a different location, or grafted to another embryo, then the piece will develop in harmony with its surroundings. If the same experiment is carried out after determination, the graft will develop into the structure it was determined to be, irrespective of its surroundings. Thus, the graft may develop into a limb on the back of the host, for example. The process of determination was discovered a century ago, but its basis remains largely unknown despite impressive advances in the molecular genetics of morphogenesis in recent years.
The significant feature of pattern determination is that the determinative influences not only possess dynamic field-like characterstics, but are material and transplantable. This has spurred generations of developmental biologists to hunt, in vain, for specific chemical 'morphogens', beginning with the nature of the organizing substance that was supposed to exist in a part of the gastrulating amphibian embryo called the "organizer", which when grafted onto the belly of a second embryo induced the formation of yet another whole embryo (reviewed by Needham (6).
A vital clue to the basis of determination may have been provided by Totafurno and Trainor (8) who successfully interpreted classical experiments on transplanting and grafting limb-buds in salamander, in which supernumery limbs were often induced, in terms of a non-linear vector field. This vector-field is precisely the sort that is embodied in liquid crystal phase alignments. In proposing that liquid crystals could be the basis for determining polarities and body axes, Needham (6) drew attention to the similarity between the 'successive stages of dimensional rigidity' that liquid crystals go through in transitions from the liquid to the solid state, which are comparable to the successive stages of determination of the limb-buds in amphibians: the anteroposterior axis is determined before the dorso-ventral or the proximal-distal. There is indeed a wide range of liquid crystalline mesophases from the most dynamic and liquid - possessing orientation order in one dimension without any translational order - to the most solid - with orientation order in 3-dimensions and also a large measure of translational order. It is conceivable that in the course of development, the relevant liquid crystalline mesophases do undergo transitions from the dynamic and fluid to the relatively more (meta)stable, patterned regimes (which may be further stabilized by cross-linking) (6).
Liquid crystals are constituents of the cell membrane and the cortical cytoskeleton. The egg cortex of many species has been known to have major determinative influences on morphogenesis since the beginning of the science of embryology, although the precise mechanisms have remained obscure (9). In Drosophila, the cortical cytoskeleton undergoes a dynamic sequence of changes in oogenesis which are implicated in the specification of the major body axes (10).These changes continue in embryogenesis after fertilization. Filamentous actin, and actin particles (11), as well as other components of the cytoskeleton - nonmuscle myosin, spectrin and tubulin (12) are concentrated in the yolk-free cortical cytoplasm just beneath the plasma membrane during the preblastoderm stages. Additional myosin particles form watermelon stripes converging towards the embryonic poles. Between the 9th and 10th nuclear division cycles, the nuclei, which have been migrating towards the cortex in synchronous steps, finally approach the embryonic surface. At the same time, the melon stripes of myosin particles disappear and the myosin, together with actin and spectrin, becomes concentrated into flat discs near the plasma membrane, centered with respect to each nucleus, where they may well continue to play a major role in subsequent determination of the segmental body pattern. But how might polarities and patterns be generated in liquid crystalline regimes?
The most obvious candidates for generating polarities and patterns in liquid crystals are electrodynamical forces. A large literature already exists on the ability of electric and magnetic fields to orientate liquid crystals and to form orientational and flow domains (1,2). Electric fields have been known to be involved in morphogenesis since the beginning of the present century (reviewed by Bischof, (13)). Electrical polarity was detected in hydra, with the oral end positive and the opposite end negative, and during its regeneration, the polarity could be controlled, and even reversed by small direct currents being passed through the animal's body. Similar potential differences were subsequently found in developing eggs. Burr and Northrup (14) detected electric fields around both developing embryos and adult organisms and postulated the 'electrodynamical field' as the basis of biological organization. These early findings have been confirmed as measurement techniques improved (15). Jaffe and coworkers invented the vibrating probe, which enabled them to detect transembryonic ionic currents in many developing systems (16,17).
Thus, electrodynamical activities may be instrumental in phase-ordering and patterning domains of liquid crystals in the cortex of the early embryo. These domains may undergo further stabilizing transitions corresponding to the progressive determination of polarities and patterns. In effect, they constitute a primary memory system (vector field) which in turn influences the expression of different genes, cell differentiation, and growth. That such domains can influence cellular activities is demonstrated by recent observations that the cholesteric mesophases of the primary cell wall in plant seedlings are sites of highly oriented surface growth, which ceases when the helicoidal pattern is completely randomized (18).
Circumstantial evidence that liquid crystalline mesophases are involved in pattern determination comes from our finding that brief exposures of early Drosophila embryos to weak, static magnetic fields result in a characteristic abnormality in the first instar larvae that hatch twenty-four hours later. The segmental pattern becomes transformed into continuous helices varying in extent from 2 or more adjacent segments up to the entire body. In some cases, two helices of opposite handedness are superimposed (19). As mentioned, the ability of magnetic and electric fields to orientate and re-orientate liquid crystals is well-known, nematic liquid crystals tending to align parallel to the magnetic field, and in the direction of the electric field (1,2). Our observations suggest that the external field may be acting on endogenous non-equilibrium electrodynamical processes involved in pattern determination which phase-order liquid crystals in the embryonic cortex (20). In this connection, it is significant that spiral waves and turbulent states have been generated experimentally in nematic liquid crystal slabs in electric fields when a weak magnetic component is introduced perpendicular to the electric field (21).
Until quite recently, there has been no direct evidence that liquid crystalline mesophases exist in living organisms. Apart from obviously birefringent fibres, bones, teeth, exoskeleton and muscle, it has not been possible to detect smaller birefringences in biological materials, and especially not liquid crystalline mesophases that Needham and others thought to exist in the cytoplasm and in entire living organisms. This hypothesis has now been confirmed as the result of a novel noninvasive imaging technique discovered in our laboratory, that optimizes the detection of small birefringences, and hence enables us to obtain high resolution and high contrast coloured images of live organisms based on visualizing coherent liquid crystalline mesophases (22-24). In the rest of this paper we shall briefly describe how the technique is used for quantitative imaging in developing organisms, enabling us to observe phase-transition like organization of the body-wall musculature of the maturing Drosophila larva, and dynamic birefringent patterns in the early embryo during the period when pattern determining processes are known to be taking place. These observations accord with the hypothesis that organisms are polyphasic liquid crystals. Successful applications of the quantitative imaging technique on well-fixed histological sections and preparations are described elsewhere (25-27).
The technique involves viewing the organism in series with a compensating full wave-plate (relative retardance 560nm) between crossed polarizers. This is as in conventional crystallographic work, except that the wave-plate is not aligned with its slow (or fast) vibrational direction at 45o to the crossed polarizers, but at a small angle between 2 - 15o, with the optimum about 4 - 7.5o depending on the species of organism. As a result, brilliant interference colours are generated in the tissues of all live organisms, fresh frozen sections, and well-preserved histological sections, for which the conventional wave-plate angle at 45o gives little or no colour response.
Like ordinary interference colours, they change according to the orientation of the optical axis of the sample with respect to the polarizers. It is of interest that the anteroposterior axis is also the major optical axes in all organisms, from protozoa to vertebrates without exception. In other words, organisms are predominantly uniaxial with regard to polarization. For maximum colour, the anteroposterior axis must be aligned at 45o to the crossed polarizers. Rotating the organism horizontally 45o from that alignment will extinguish all the colours (though the extinction is much less than for uniaxial mineral crystals, see below), while rotating it 90o will result in all of the colour to take on the maximum complementary hues (addition or subtraction of colours according as to whether the slow and fast waves of the birefringent tissues and those of the waveplate are aligned or 90o out of phase).
As distinct from colours due to static mineral crystals or liquid crystals at equilibrium, those in the tissues of living organisms are generated by coherent phase ordering due directly, or indirectly, to energy input, or, in the case of muscle, due to the molecules themselves transforming energy. As visible light is about 1014hz and coherent motions generally less than 1010hz, the molecular arrays will appear as though static to the light passing through so long as their motions are sufficiently ordered. For the same reason, incoherent (thermal) motions will render the anisotropic, birefringent array more isotropic, and hence reduce the brightness of the colour. The colours, therefore, carry structural information concerning birefringence (the anisotropy of the molecules), orientation, as well as degree of dynamic order of the molecules, all of which can, in principle, be distinguished.
The optical basis of our technique has been described in detail in other publications (23,24), where we showed how it maximizes colour contrasts and optimizes overall colour detection by considering the intensity of light emerging from two superposed crystal plates at different orientations between crossed polarizers (28):
I = - sin2(y2- y1) sin 2y1 cos 2y2 sin2 d1/2
+ sin2(y2 - y1) cos 2y1 sin 2y2 sin2 d2/2
+ cos2(y2 - y1) sin 2y1 sin 2y2 sin2(d1 + d2)/2 (1) - sin2(y2 - y1) sin 2y1 sin 2y2 sin2(d1 + d2)/2
where d1 and d2 are the phase differences respectively of the wave-plate and the biological 'crystal', and y1, y2 , the angles that their slow (or fast) wave makes with the polarizer.
Simple solutions are obtained when constant angles are maintained:
For y1 = 7.5° and y2 = 45°, when we measure the difference, DI, between the peak intensity (+45o) and the minimum intensity (-45o), and using the approximation for small retardances, sinx ~x, we obtain.
DIb = Io,b[ 3.6 x 10-3 Rb]
DIr = Io,r [ 2.2 x 10-3 Rr] (2)
Ignoring absorption, depolarizing scattering and dispersion effects, these relationships are exact for mineral crystals or crystals with perfect molecular alignment. For liquid crystals, however, only an effective relative retardance is being measured, for the light intensity depends, not just on intrinsic birefrin-gence, but also on the degree of coherent alignment.
For uniaxial nematic liquid crystals, which include nearly all biological liquid crystals to first approximation, the order parameter, S, measuring the state of alignment of the molecules along the direction of the nematic axis, is given by,
S = <(3 cos2q - 1)>/2 (3)
where <> denotes the average and q is the polar angle between the direction of the nematic axis (the average direction of alignment of the molecules) and the long axis of the individual molecule. S varies from 0 in isotropic material to 1 when full alignment is attained. Isotropic material is dark at all angles of rotation whereas fully aligned material is maximally bright at 45o between crossed polarizers. In Appendix 1, an expression is dertived to show that, for small birefringences, the intensity of light transmitted does indeed vary linearly with the degree of molecular alignment.
We have developed an image analysis package which enables us to quantify colour intensities, standardize the measurements and to determine the orientation of the sample. Colour intensities are measured with a ccd colour camera which outputs in red, green and blue. The output of the camera is registered directly via image acquisition in the computer. In order to standardize the measurements and to correct for variations associated with different objectives and levels of lighting necessary to produce good images, a set of mica plates of known retardances are used. These were independently checked in our Laboratory by measurements using a Sénarmont compensator on a Zeiss Universal microscope fitted with a mercury vapour light source and interference filter to isolate the green line at 546nm. For each mica standard, we determined the +45o blue and red colour intensities by automated stepwise rotation at 5o intervals for 180o and registering the r, g, b values at each step. The results for DI are plotted against the corresponding retardances, from which it was ascertained that the response is linear for both blue and red for retardances between 1 and 100nm. The linear graphs serve as calibration curves for the retardance values. The calibration is repeated for each set of recording conditions so that different recordings can be compared where required. In order to work out the orientation of the sample, some reference axis is chosen, such as the anteroposterior axis in the case of an organism, or a fibre axis, in the case of a section or isolated fibre. The sample is then rotated in the same way and the colour intensities recorded.
As a rule, samples to be compared are recorded under the same conditions, as are the calibration curves whenever required. For time-lapse studies carried out over long periods, the stability of the colour response is monitored by the background values, which, in our case are found to remain constant to within +5%. The main causes of fluctuation are the light level and the focus (especially where long time-lapse sequences are involved). These are minimized by good voltage control to the microscope lamp, and autofocus interfacing between the computer and the microscope.
Phase-transition like increase in colour intensity in the body-wall musculature of the maturing larva
In one application, we quantify the changes in colour intensities in the course of embryogenesis. Preliminary investigations have shown that chromaticity varies according to the developmental and energetic status of the organism (22,23). The intensity of colours waxes and wanes in the course of development, and in different locations in the embryo. In Drosophila for example, there are chromatic stages between 1.5 to 3h of development, which are associated with cryptic pattern determining processes (29). The major chromatic period begins at stage 16 when the embryo starts to move (about 17-18h after oviposition at 25oC in our stock). The blue colour of the musculature appears to undergo a sudden increase in intensity, thereafter growing in extent as well as intensity as the maturing larva increases its activity up to the time of hatching (Fig. 1).
In order to quantify this colour change, we have obtained time-lapse images of the entire developmental sequence. Dechorionated embryos were placed in a specially constructed observation chamber perfused with distilled water maintained at 24.5+1o. An embryo selected for observation was aligned in its maximum colour position, with the anteroposterior axis at 45o to the crossed polarizers so that the body musculature which eventually develops appears blue. Successive images were recorded every 15 minutes starting from 1h 15m after oviposition to just before hatching. A colour threshold based on a range of r,g,b values characteristic of the body-wall musculature was applied to the sequence to aggregate the typical blue colour. The results are plotted in term of the total area in the embryo showing blue, positive birefringence, as well as the average colour intensity. A typical sequence appears in Figure 2.
As can be seen, the total area shows a steep ascent starting from about 18h a.o., reaching a maximum at hatching. The average colour intensity increases abruptly from zero to 150 approximately 2 hours before the upturn in area. The abruptness of the increase in average intensity is in part due to the thresholding, but it also reflects the first appearance of the typical blue colour in very small areas long before it spreads in extent. What are the corresponding events in the muscle that give rise to these increases? It is reported that the molecular constituents of muscle, when first formed, are randomly arranged, and that between 16 and 18 h, they become organized into regular myofilament bundles typical of muscle, but no quantitative time course of the process has been presented (30,31). Our data suggests that there are at least two phase-transition like events: the first associated with the increase in colour intensity of the muscle in limited areas; the second of the rapid spread of blue areas accompanied by a further increase in intensity of the blue colour. Both may involve transitions from random to oriented alignment.
Early Drosophila embryos (between 1.5 to 3 h a.o.) are birefringent. The birefringence is concentrated in the cortex and periplasm of the pole-cell stage and syncytial blastoderm embryo, coinciding with the periplasmic concentration of the cytoskeletal proteins. In the preblastoderm embryo, the most conspicuous feature is a patch of blue birefringence in the dorsal cortex just behind the anterior pole. As development proceeds, this patch subdivides and faint blue periodic bands also appear in the rest of the periplasm which is otherwise predominantly orange, except near the poles. These birefringent patterns and their evolution are most prominant during the period when body pattern is progressively determined (between 1.5 and 3.0h a.o.). They effectively provide a liquid-crystal display of the otherwise cryptic electrodynamical activities taking place concurrently in the embryo, that may be involved in pattern determination. The birefringent patterns are complex, and consist of superposed oriented domains of both membrane and cytoskeletal components. Nevertheless, they are all subject to the same global electrodynamical orienting processes.
We have carried out preliminary quantitative measurements of the birefringent patterns. Freshly laid eggs were dechorionated at about 1h a.o. and mounted on its side on a microscope slide in distilled water, under a cover-slip supported by a 200m thick ring of plastic. The slide was rotated to position the embryo with its anteroposterior axis at 45o with respect to the crossed polarizers, so that positively birefringent molecules with their long axis aligned along the anteroposterior axis are maximally blue in colour. A shutter was placed over the microscope light which was opened briefly only during image capture so as to minimize exposing the developing embryo to light. Between 1h 30m and 3h a.o., five images were captured in rapid succession every 15 minutes. After the measurements, the cover-slip was removed and the embryo allowed to continue development in a moist chamber. The 24h survival and hatching rates under those conditions were at least as high as unmeasured controls on the same slide.
For each image, a profile was taken from the anterior to the posterior pole through the dorsal and the ventral periplasm respectively and the blue and red colour values measured at evenly spaced points. Care was taken to avoid the vitelline membrane, and the nuclei just beneath, which appear as a bright rim around the embryo. The same coordinates of measured points were automatically reproduced on every image of the same embryo. The five successive measurements of each image capture period were joined end to end and treated as a single sequence on Fast Fourier Analysis. The results are presented below.
In our measurements, the embryo is so placed that blue colour is generated by positively birefringent molecules with their long axis parallel to the anteroposterior axis, or alternatively, by negatively birefringent molecules with the long axis perpendicular to the anteroposterior axis. Similarly, red colour is generated by negatively birefringent molecules aligned parallel to the anteroposterior axis, or positively birefringent molecules aligned perpendicular to the anteroposterior axis. To first approximation, red and blue colours can be regarded as representing different superposed components of the plasma membrane and the cortical/periplasmic layers. A total of 7 embryos were measured lying on one side of the body so that the mid-dorsal and mid-ventral profiles are directly trans-illuminated. Of these, 5 developed normally to hatching. Blue and red colour intensity values vary in characteristic fashion from anterior to posterior, and the dorsal profiles are distinct from the ventral ones, especially in the preblastoderm stages (Fig. 3a,b). The signatures of the anteroposterior and dorsoventral polarities, which have already been determined during the maturation of the egg, are thus evident in most of the preblastoderm embryos.
Superimposed on the major patterns associated with the anteroposterior and dorsoventral polarities are spatial periodicities that fluctuate and evolve in the course of early development. The period 1 (corresponding to the full body length) dominates all the periodograms, reflecting the anteroposterior polarities, and interferes with the detection of the shorter periods. Nevertheless, the following features may be noted.
(a) Red and blue colour intensities vary independently, but the same set of periodicities are present in both periodograms.
(b) In the course development, the shorter periods tend to show maximum amplitude at later times. A series of dorsal profiles is shown in Figure 4 (from an embryo in which the anterior-dorsal signature is less evident) and the corresponding periodograms in Figure 5.
(c) The amplitudes of different periods tend to fluctuate, with some of the periods disappearing and reappearing.
The birefringent patterns in early Drosophila embryos are by no means exceptional. Similar patterns have been observed in the undifferentiated head region of the zebra-fish embryo (32) and in the sea-urchin egg after fertilization (33). Our preliminary measurements and analyses show that the birefringent patterns fluctuate and evolve in the course of development, as consistent with the existence of concurrent electrodynamical activities that phase order cortical and membrane liquid crystals.
Let us review what is known of concurrent electrodynamical activities in Drosophila in order to see how they could give rise to orientational effects in membrane/periplasmic liquid crystals. In Drosophila, as in other insects, transembryonic ionic currents have been detected in the maturing oocyte (16). Large electric currents flow through the cytoplasmic connections between the nurse cells and the oocyte, transporting material into the oocyte and orienting the cytoskeletal elements for body axes determination (34). Thereafter, transembryonic currents of decreased magnitude and of a different pattern persist in the mature oocyte. Fertilization initiates Ca2+ waves in many animal species which can be observed with flourescent probes (17), and Drosophila will probably not prove exceptional. Simultaneously, a number of other electrical events are triggered, including electric currents or polarization waves flowing along the membrane and periplasm, which may be most important for orienting liquid crystalline mesophases. These membrane currents have not yet been directly observed, though transembryonic ionic currents have been detected in the preblastoderm Drosophila embryo (34), which probably accompany the membrane currents. The membrane current is expected to be triggered by the sperm as it enters the egg at its anterior pole, causing the membrane to depolarize, with the influx of Na+ and other ions such as Ca2+. Membrane depolarization is expected to give rise to action potentials in a ring-shaped region around the point of sperm entry, which propagate down the egg, converging at the posterior pole. (These action potentials have been measured, see below.) The resultant, massive depolarization concentrated at the posterior pole is expected to rebound, or back propagate to interact with the incoming waves. It is these current fluxes that are most likely to be responsible for creating dynamic, orientational or flow domains that appear as birefringent patterns.
As mentioned earlier, orientational and flow domains of liquid crystals subjected to sustained electric and magnetic fields are well-characterized both experimentally and theoretically (1,2,21). Do sustained electrodyanmical activities exist in the Drosophila embryo during the period of early embryogenesis in question? Although membrane currents have not been directly observed, electrical activities in the form of action potentials have been recorded with microelectodes placed inside the anterior or posterior polar pocket of the preblastoderm embryo (29). The electrical activities are intermittent, with amplitudes varying at different times, but increasing in frequency as development proceeds from about 1hz soon after oviposition to about 15-30hz in late syncytial blastoderm. It appears that fertilization triggers sustained electrodynamical activities.
Do the putative liquid crystalline domains determine segmental pattern? Unfortunately, we have not found periodicities that exactly parallel the evolution of the gene expression patterns, or the patterns of abnormalities induced by exposure to ether vapour suggesting a successive bifurcation sequence with periods approximately 1/2, 1/4, 1/8 and 1/16 of the embryo body length (35,36). The present picture suggests that all normal modes are excited at the earliest time of measurement, but that the higher frequency (shorter period) modes increase in amplitude and reach their maximum at later times. Furthermore, some modes disappear by the time of cellularization.
Part of the difficulty is that, as mentioned above, the birefringent patterns are composite of many different layers in the periplasm, not all of which may be involved in pattern determination. Thus, a more detailed structural analysis of the periplasmic layers would be appropriate. This could be achieved by using our technique in conjunction with confocal facilities for optical sections.
We have described a noninvasive technique that enables us to follow the evolution of liquid crystalline mesophases in the developing organism. This led to two main discoveries. The first consists of phase-transition like increases in birefringence of the bodywall musculature in the maturing first instar Drosophila larva, implying rapid changes from random to coherent alignment of the molecular constituents of the muscle. The second involves dynamic birefringent patterns in the early Drosophila embryo - created by concurrent electrodynamical activities - which may, in turn, determine body pattern. These findings support the idea that organisms are polyphasic liquid crystals and that the different mesophases may have important implications for biological organization and function.
We plan to carry out histochemical and electronmicroscopic studies on the relevant stages. In the case of the bodywall musculature, we wish to correlate the degree of order in the muscle fibres with the changes of colour intensity. In the case of birefringent patterns in early embryogenesis, we wish to identify the precise molecular components involved and to refine our measurements and analyses to provide better data for modelling the evolution of birefringent liquid crystalline domains under the influence of propagating and interacting membrane currents.
This research was supported by a project grant from the Open University Research Committee and an EPSRC-LINK grant to M.W.H. We thank Lyndon Davies for his interest and support in coordinating the LINK grant, Prior Scientific for supplying the Prior polarizing microscope and accessories and Data Cell for the Optimas imaging package for which Interference Colour Imaging software is an extension. We are grateful to D.J. Goldstein for his generous loan of microscope and accessories as well as advice on polarized light microscopy; and to David Knight for introducing us to the liquid crystal literature and for stimulating discussions. Thanks are also due to Michael Lawrence for assistance with microscopy and video recording and Mike Dodd, Steve Swithenby and Oliver Josephs for advice on statistical analyses.
Article first published 1999
The relationship between the light intensity and the order parameter Equation (2) can be simplified for fixed alignment angles, y1 = 7.5° and y2 = 45°,
Ib = I0,b (0.032+0.129 sin d2+0.968sin2d2/2) Ir =I0,r (0.023+0.123 sin d2+0.912sin2d2/2) (A.1) Ig = I0,g sin2d2/2
where d2=2pd (ve1 - ve2 )/l =2pR/l, R is the retardance of the sample, e1 and e2 are small dielectric constants parallel and perpendicular to the optical axis of the biological sample. d is the thickness of the sample and l is the wavelength. In the mean field approximation,37
e1 =1+ 4 p NrhF/M ( a + 2/3 ø S + (Fmm/ 3KBT) (1-(1-3 cos2q) S) (A.2)
e2 =1+ 4 p NrhF/M ( a + 2/3 ø S + (Fmm/ 3KBT) (1+1/2(1-3 cos2q) S)
where r is density, h =3 e/(2e+1), e is the mean dielectric constant, F =1/(1- af), f = 4p Nr( 2e -2)/3M(2e+1), a is the mean polarization, m, is the dipole moment, M is the molecular weight,S is the order parameter, ø is the polarizability anisotropy. Equation (A.2) can be simplified as follows:
e1 =1+ A (a + b +B S) (A.3) e2 =1+ A (a + b + CS)
where A, B, C and b are constants unrelated to S.
Equation (A.1) can be simplified in the case of small retardances, when sin x ~ x, and the sin2 term, being much smaller, can be ignored. Substituting the expressions for dielectric constants (A.3) into (A.1) gives light intensity as a function of relative retardance, R
Ib = I0,b (0.032+0.129 (2pR/l) (A.4)
Ir =I0,r (0.023+0.123 (2pR/l)
where, R = A(B-C) d ( S - A(B+C)S2 ) 2C + A(a +b) 2C + A(a +b)
Hence intensity is approximately linearly related to S.
Legends
Figure 1. Interference Colour image of first instar Drosophila larva about to hatch, captured during active contractions of its body wall musculature which appears as a brilliant blue colour just inside the body. The image was captured by computer and transferred to photographic film via a slide maker.
Figure 2. Evolution of positive birefringence in the maturing Drosophila larva.
The images are analyzed for the area (in pixels) showing the range of blue colour characteristic of the musculature, plotted in a. and for the average intensity of the colour, plotted in b.
Figure 3. Profiles of birefringent patterns in the preblastoderm embryo. (a) Dorsal, (b) Ventral. Thick trace represent blue values, thin trace, red values.
Figure 4. Evolution of birefringent patterns. (a) - (e) Dorsal profiles at 15 mins intervals beginning at 1h 30min a.o. Blue and red traces as in Figure 2.
Figure 5. Periodograms of red and blue dorsal profiles. (a) red (b) blue.
Article first published 1999
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