Distribution of Rhesus Antigens on Red Cell Surfaces E. G. KNOX Health Services Research Centre, Department of Social Medicine, The Medical School, Birmingham (Received 14 April 1977; acceptedfor publication 17June 1977) SUMMARY. T w o pieces of evidence suggest different conclusions about the arrangement of the rhesus antigens on the surfaces of red cells. Indirect evidence suggests an ordered arrangement; electron-microscopic evidence has been interpreted visually as essentially random. Re-analysis of electron-microscopic material, using a form of computer spectral analysis, suggests that the visual interpretation was mistaken, and that the pattern is orderly. The material suggests that the maternally derived and paternally derived proteins are linked into couplets, and that the couplets may be regularly linked or packed, a t least at shorter ranges. The material does not at present illuminate the question of longer range periodicity.
T w o distinct approaches to the study of cell surfaces can be recognized. The first considers the cell surface in section, which is currently characterized as a bilipid layer with each leaf of the membrane consisting of tightly packed elongated molecules standing perpendicular to the surface. Between the layers is a series of larger molecules, mainly proteins, protruding through the lipid. The second approach views the surface in plan rather than in section and asks questions about the organization of the proteins. Are they free to move, or are they fixed? Are they packed or perhaps linked in a regular arrangement? Does the arrangement of one class of molecule constrain the arrangements of the others? Knox (1966)assembled evidence which indicated a regular pattern for the rhesus antigen sites on the red cell. The hypothesis arose out of the observed difference in antigenicity of the R l r and the RZrgenotypes in haemolytic disease of the newborn, a difference manifest both in the risk ofinitial maternal isoimmunization, and in the severity of the disease. It was postulated that the antigenic-complex C occupied more surface-space than the complex c, so that for R l r there was room for fewer D-sites on each cell. It follows that the molecules responsible for rhesus antigenicity were either packed together, or linked into a mesh. The known limitation of the anti-f (anti-ce) antibody/antigen reactions to genotypes where c and e are represented on the same chromosome, indicated that maternally and paternally determined antigenic complexes maintained their separate identities on the surface of the cell. One possibility, therefore, was a mesh built up of these complexes, either in a random order or in the form of alternating maternal and paternal complexes. There are several ways in which such a mesh could be assembled. Further evidence of structure was adduced from the observed genetic linkage between the Correspondence:Professor E. G. Knox, Health Services Research Centre, Department of Social Medicine, The Medical School, Edgbaston, Birmingham BI5 zTJ.
537
538
E. G. Knox
rhesus gene loci and the locus responsible for elliptocytosis. It was suggested that elliptocytc represented a structural aberration, just as the rhesus characteristics represented antige variation, of an otherwise common material. Another mechanical correlate of the rhesus blc groups has since been discovered by Sturgeon (1970),namely the occurrence of haemolj anaemia and of deformed cells (stomatocytes) in people without Rh antigens (Rh-null disea Recent work by Nicolson et a1 (1971)attempted to display the surface arrangements of rhesus antigens directly. Anti-D globulins were attached to the surfaces of red cells and the c subsequently exposed to antiglobulins prepared in the goat, and labelled with ferritin. T enabled goat antibody to be located by electron microscopy, and Nicolson et al concluded t the distribution was aperiodic. This conclusion differs from that suggested by circumstantial evidence reviewed by Knox. The question therefore arises how one may reliably recognize an aperiodic arrangement fundamentally regular arrangement of the rhesus gene sites might be obscured in several wa First, the antigenic locations might suffer elastic perturbation around a central positil secondly, the main part of the anti-D globulin might be offset from a point of attachment 2 random angle by some (unknown) fixed or variable distance; thirdly, the attachment of goat antibody to the human globulin and of the ferritin to the goat antibody might redistrib the visible sites through further circles of uncertainty. In these circumstances it might reqt considerable effort and analysis to detect an underlying pattern which was truly present anc separate it from the random overlay. The present paper reports an analysis of Nicolson et al’s published photographic plates i manner which, given sufficient material, should be capable of detecting the presence of underlying regular arrangement. MATERIALS, METHODS AND RESULTS The materials used are photographs of red cells surfaces taken from the publication of Nicol! et al (1971)and marked with clusters of ferritin grains in the manner described earl Duplicates were taken in the form of transparencies and the centres of the grain clust estimated by eye, and marked with a dot. The transparencies were laid upon graph papei that the marked points could be expressed in terms of coordinates, and they were recorded the nearest 0.5 mm. The corners of the photographs and the scale marks were also record Two photographs were used (Figs 2 and 5 of Nicolson et al). The first is a rectangle approximately 90 x I I 5 mm (representing 950 x 1200nm) from a cell of genotype R2r; 1 D-sites are marked. The second photograph measures approximately 90 x 105m m (950x I nm) from a red cell of genotype RIRl; 260 D-sites are marked. The coordinates were prepa on punch cards for computer input and analysis. The method of analysis consisted in examining every possible pair of points within boundary of the figure, measuring the distances between these pairs, and assembling distances into a frequency distribution. A search was then made for oscillations of frequenc! varying inter-point distances. To this end, the observed frequency distribution was compa with the frequency distribution which would have been expected if the points had bc scattered in a truly random fashion within the rectangles. Pairs exhibiting ‘preferred’ distan are the minimum structured element of all higher-order patterns, and a positive finding wo
R h Antigens on R e d Cell Surfaces
539
indicate the presence of short-range order, and the possible presence of longer-range order such as would occur if there were a regular network, o r a regular packing pattern. If more than one 'preferred' distance were found it might be possible to draw inferences o n the form of such a pattern although, with the limited data available, it might be over-optimistic to expect to demonstrate more than the existence of a 'primary' connectivity. The approach is, in effect, a spcctral (Fourrier) analysis, carried out in two dimensions, with the objective o f testing for the cxistcnce of a dominant 'frequency'. The main technical problem encountered related to the frequency distribution appropriate to a random distribution ofpoints. This is required for comparative purposes (see above), but is
+ '1
E Y
- - _heterozygous _
-hOmOzygOuS
- 7
10
i.5
'
35.5' 6i.s'
67.5 ' i27.5. 157.5'
ib7.5
217.5 247.5' 237.5' 307.5' 337.5' 387.5' 397.5 427.5' 467.5' 487.5
Interval
(nm)
FIG I . Frequency distribution of inter-pair distances.
difficult to calculate. For an inddinite (unbounded) plane each increment of distance from an index point is rcprcsented as a ring, or an expanding ripple, i.e. the difference between the areas of a larger and a smaller concentric circle. The area of the ring is proportional to the mean radius, so that frequencies a t increasing distances rise linearly with the distance itself, as a straight line. However, the boundaries of a finite plane modify this picture and the longer distances are progressively censored by the boundaries of the rectangle. For instance, the maximum distance for random points within the material studied corresponds with the diagonals of the rectangles. Unfortunately, the exact form of the randomly expected distribution proved to be elusive, and failing a mathematical solution it was necessary to assemble an empirical distribution using computational rather than purely mathematical methods. First, the total number of possible pairs is easily calculated as n ( n - 1)/2,for n observations. Next, for the shorter range of distances from index points, where interference from the
540
E.C.Knox
boundaries of the rectangle is minimal, it is possible to calculate approximate expectations on a mathematical basis, namely as the product of the overall density of D-sites per unit area, and the increment of area represented by each increment of distance (i.e. density x n(d22-d12). Finally, the overall distribution of the shorter (calculated) distances, and the actual numbers of longer distances, were ‘smoothed’ repeatedly, using a five-point moving mean applied on 10 occasions. This produced a curve of expectations which was smooth to the eye. The observations themselves could then be expressed in terms of their departure from this curve and Fig I expresses the results. The departures are expressed in numbers of Standard Errors, the Standard Error being taken as the square root of the expected value. Two curves are represented, one corresponding with the homozygote (DD) genotype, and the other with the heterozygote (Dd) genotype, as obtained from Nicolson et al’s figures. The numbers of pairs upon which the different points are based, are given in some cases. Both curves are clearly non-random. For each there is a short-distance ‘forbidden-zone’, where the density of observations falls far below the random expectation. The forbidden zone is more extensive in the heterozygote than in the homozygote. Second, both forbidden zones are followed by a zone of ‘preferred intervals’, the preference being shorter in the homozygote than in the heterozygote; in the homozygote the preferred interval follows immediately upon the forbidden zone while in the heterozygote it follows after a short gap. The evidence for the existence of ‘preferred intervals’ is less convincing than that for the ‘forbidden zones’ but the peaks correspond with 2.70 and 3.04 Standard Errors, respectively. The first is expected to occur by chance about once in 300 samples; the second about once in 800 samples. For the remaining zone covered by the Figure, the points do not deviate significantly from the expectations of a random distribution. DISCUSSION The analysis permits the conclusion that the distribution of the ferritin markers is not random, exhibiting both proximity constraints and preferred distances. The simplest interpretation of the proximity constraints is one due to the physical size of the molecules, but there are several reasons for supposing that this is not simply a function of their being packed together on the surface. First, the forbidden intervals vary between homozygote and heterozygote cells, the distance for the former being about 65 nm, while that for the latter is about 85 nm. Both values are substantially more than the diameter of an immune globulin complex, about 9 nm. Even if we allow that the ferritin clusters are attached to the D-site through at least two immunoglobulin molecules, it is unlikely that their mutual repulsion from each other, at ranges of 65-86 nm, can be accounted for entirely in this way. The evidence for ‘preferred intervals’ is based upon 122measured pairs at a distance of about 82 nm in the case of the homozygote genotype; and upon 61 measured pairs at a distance of about 158 nm in the case of the heterozygote. In the case of the homozygote the preferred interval follows immediately upon the termination of the forbidden interval, but after a short gap in the case of the heterozygote. With the pattern observed on the homozygote cell surface it would be possible to postulate that an originally random pattern had been perturbed through a subsequent artifactual mutual separation of close pairs, the shortest distances having simply been separated to about 82 nm. However, the fact that this distance falls within the forbidden
Rh Antigens on Red Cell Surfaces
541
zone on the heterozygotc cell, and the fact that the heterozygote cell has a preferred distance at almost twice this interval, is evidence against such a mechanism. It would be useful, for these reasons, if an alternative method of visualizing D-sites could be devised. In fact, Romano et a1 (1975) have devised a method in which the antiglobulins were prepared in the horsc and labelled with colloidal gold instead of with ferritin, but there are still a t least two globulin molecules involved. In addition, the method is less precise in that the sites arc less densely marked, often with a single gold particle, and some, presumably, are unmarked. It is also much more difficult in the photographs to discern whether two modcrately close markers should be regarded as a single D-site, or as two. The authors provide relatively little photographic material, and no negative control material, and their published data cannot be satisfactorily analysed by the methods described in the present study. For the time being the pattern of inter-pair distances revealed in the analysis of Nicolson et al’s data is most readily interpreted as evidence for the existence of short-range order, although the precise pattern cannot be exactly inferred. O n e reasonable speculation may, however, be allowed. If the difference between the homozygote and the heterozygote cell is regarded as a reflection of the fact that about halfof the antigenic sites in the latter are ‘invisible’, then the fact that the forbidden zone for the heterozygote extends into the preferred zone for the homozygote, implies a systematic alternation of the maternally and paternally derived elements. It suggests that they are linked on a I-to-I basis, at least as couplets and, probably, that the ordering of the elements extends beyond a simple pairing arrangement in the form of chains or as a two-dimensional mesh. REFERENCES
K N O X ,E.G. (1968) A notional structure for the rhcsus antigens. British Journal Of HAPmAtOlOgy, 12, I 05. NICOLSON. G.L., MASOUREDIS S.P. & SINGER S.J. (1971) Quantitative two-dimensional ultra-structural distributionof Rh(D) antigenic sites on human erythrocyte membranes. Proceedings ofrhe National Academy of Sciences of the United States of America, 68, 1416.
ROMANO,E.L., STOLINSKI, C. & HUGHES-JONES, N.C. (1975)Distribution and mobility of the A, D and c antigens on human cell membranes: studies with a gold-labelled antiglobulin reagent. BritishJournal of HAPmAtOlOgy, 3 0 , 507.
STURGEON, P. (1970) Haematological observations of the anemia associated with blood type Rh.-null. Blood, 3 6 , 3 10.
T w o distinct approaches to the study of cell surfaces can be recognized. The first considers the cell surface in section, which is currently characterized as a bilipid layer with each leaf of the membrane consisting of tightly packed elongated molecules standing perpendicular to the surface. Between the layers is a series of larger molecules, mainly proteins, protruding through the lipid. The second approach views the surface in plan rather than in section and asks questions about the organization of the proteins. Are they free to move, or are they fixed? Are they packed or perhaps linked in a regular arrangement? Does the arrangement of one class of molecule constrain the arrangements of the others? Knox (1966)assembled evidence which indicated a regular pattern for the rhesus antigen sites on the red cell. The hypothesis arose out of the observed difference in antigenicity of the R l r and the RZrgenotypes in haemolytic disease of the newborn, a difference manifest both in the risk ofinitial maternal isoimmunization, and in the severity of the disease. It was postulated that the antigenic-complex C occupied more surface-space than the complex c, so that for R l r there was room for fewer D-sites on each cell. It follows that the molecules responsible for rhesus antigenicity were either packed together, or linked into a mesh. The known limitation of the anti-f (anti-ce) antibody/antigen reactions to genotypes where c and e are represented on the same chromosome, indicated that maternally and paternally determined antigenic complexes maintained their separate identities on the surface of the cell. One possibility, therefore, was a mesh built up of these complexes, either in a random order or in the form of alternating maternal and paternal complexes. There are several ways in which such a mesh could be assembled. Further evidence of structure was adduced from the observed genetic linkage between the Correspondence:Professor E. G. Knox, Health Services Research Centre, Department of Social Medicine, The Medical School, Edgbaston, Birmingham BI5 zTJ.
537
538
E. G. Knox
rhesus gene loci and the locus responsible for elliptocytosis. It was suggested that elliptocytc represented a structural aberration, just as the rhesus characteristics represented antige variation, of an otherwise common material. Another mechanical correlate of the rhesus blc groups has since been discovered by Sturgeon (1970),namely the occurrence of haemolj anaemia and of deformed cells (stomatocytes) in people without Rh antigens (Rh-null disea Recent work by Nicolson et a1 (1971)attempted to display the surface arrangements of rhesus antigens directly. Anti-D globulins were attached to the surfaces of red cells and the c subsequently exposed to antiglobulins prepared in the goat, and labelled with ferritin. T enabled goat antibody to be located by electron microscopy, and Nicolson et al concluded t the distribution was aperiodic. This conclusion differs from that suggested by circumstantial evidence reviewed by Knox. The question therefore arises how one may reliably recognize an aperiodic arrangement fundamentally regular arrangement of the rhesus gene sites might be obscured in several wa First, the antigenic locations might suffer elastic perturbation around a central positil secondly, the main part of the anti-D globulin might be offset from a point of attachment 2 random angle by some (unknown) fixed or variable distance; thirdly, the attachment of goat antibody to the human globulin and of the ferritin to the goat antibody might redistrib the visible sites through further circles of uncertainty. In these circumstances it might reqt considerable effort and analysis to detect an underlying pattern which was truly present anc separate it from the random overlay. The present paper reports an analysis of Nicolson et al’s published photographic plates i manner which, given sufficient material, should be capable of detecting the presence of underlying regular arrangement. MATERIALS, METHODS AND RESULTS The materials used are photographs of red cells surfaces taken from the publication of Nicol! et al (1971)and marked with clusters of ferritin grains in the manner described earl Duplicates were taken in the form of transparencies and the centres of the grain clust estimated by eye, and marked with a dot. The transparencies were laid upon graph papei that the marked points could be expressed in terms of coordinates, and they were recorded the nearest 0.5 mm. The corners of the photographs and the scale marks were also record Two photographs were used (Figs 2 and 5 of Nicolson et al). The first is a rectangle approximately 90 x I I 5 mm (representing 950 x 1200nm) from a cell of genotype R2r; 1 D-sites are marked. The second photograph measures approximately 90 x 105m m (950x I nm) from a red cell of genotype RIRl; 260 D-sites are marked. The coordinates were prepa on punch cards for computer input and analysis. The method of analysis consisted in examining every possible pair of points within boundary of the figure, measuring the distances between these pairs, and assembling distances into a frequency distribution. A search was then made for oscillations of frequenc! varying inter-point distances. To this end, the observed frequency distribution was compa with the frequency distribution which would have been expected if the points had bc scattered in a truly random fashion within the rectangles. Pairs exhibiting ‘preferred’ distan are the minimum structured element of all higher-order patterns, and a positive finding wo
R h Antigens on R e d Cell Surfaces
539
indicate the presence of short-range order, and the possible presence of longer-range order such as would occur if there were a regular network, o r a regular packing pattern. If more than one 'preferred' distance were found it might be possible to draw inferences o n the form of such a pattern although, with the limited data available, it might be over-optimistic to expect to demonstrate more than the existence of a 'primary' connectivity. The approach is, in effect, a spcctral (Fourrier) analysis, carried out in two dimensions, with the objective o f testing for the cxistcnce of a dominant 'frequency'. The main technical problem encountered related to the frequency distribution appropriate to a random distribution ofpoints. This is required for comparative purposes (see above), but is
+ '1
E Y
- - _heterozygous _
-hOmOzygOuS
- 7
10
i.5
'
35.5' 6i.s'
67.5 ' i27.5. 157.5'
ib7.5
217.5 247.5' 237.5' 307.5' 337.5' 387.5' 397.5 427.5' 467.5' 487.5
Interval
(nm)
FIG I . Frequency distribution of inter-pair distances.
difficult to calculate. For an inddinite (unbounded) plane each increment of distance from an index point is rcprcsented as a ring, or an expanding ripple, i.e. the difference between the areas of a larger and a smaller concentric circle. The area of the ring is proportional to the mean radius, so that frequencies a t increasing distances rise linearly with the distance itself, as a straight line. However, the boundaries of a finite plane modify this picture and the longer distances are progressively censored by the boundaries of the rectangle. For instance, the maximum distance for random points within the material studied corresponds with the diagonals of the rectangles. Unfortunately, the exact form of the randomly expected distribution proved to be elusive, and failing a mathematical solution it was necessary to assemble an empirical distribution using computational rather than purely mathematical methods. First, the total number of possible pairs is easily calculated as n ( n - 1)/2,for n observations. Next, for the shorter range of distances from index points, where interference from the
540
E.C.Knox
boundaries of the rectangle is minimal, it is possible to calculate approximate expectations on a mathematical basis, namely as the product of the overall density of D-sites per unit area, and the increment of area represented by each increment of distance (i.e. density x n(d22-d12). Finally, the overall distribution of the shorter (calculated) distances, and the actual numbers of longer distances, were ‘smoothed’ repeatedly, using a five-point moving mean applied on 10 occasions. This produced a curve of expectations which was smooth to the eye. The observations themselves could then be expressed in terms of their departure from this curve and Fig I expresses the results. The departures are expressed in numbers of Standard Errors, the Standard Error being taken as the square root of the expected value. Two curves are represented, one corresponding with the homozygote (DD) genotype, and the other with the heterozygote (Dd) genotype, as obtained from Nicolson et al’s figures. The numbers of pairs upon which the different points are based, are given in some cases. Both curves are clearly non-random. For each there is a short-distance ‘forbidden-zone’, where the density of observations falls far below the random expectation. The forbidden zone is more extensive in the heterozygote than in the homozygote. Second, both forbidden zones are followed by a zone of ‘preferred intervals’, the preference being shorter in the homozygote than in the heterozygote; in the homozygote the preferred interval follows immediately upon the forbidden zone while in the heterozygote it follows after a short gap. The evidence for the existence of ‘preferred intervals’ is less convincing than that for the ‘forbidden zones’ but the peaks correspond with 2.70 and 3.04 Standard Errors, respectively. The first is expected to occur by chance about once in 300 samples; the second about once in 800 samples. For the remaining zone covered by the Figure, the points do not deviate significantly from the expectations of a random distribution. DISCUSSION The analysis permits the conclusion that the distribution of the ferritin markers is not random, exhibiting both proximity constraints and preferred distances. The simplest interpretation of the proximity constraints is one due to the physical size of the molecules, but there are several reasons for supposing that this is not simply a function of their being packed together on the surface. First, the forbidden intervals vary between homozygote and heterozygote cells, the distance for the former being about 65 nm, while that for the latter is about 85 nm. Both values are substantially more than the diameter of an immune globulin complex, about 9 nm. Even if we allow that the ferritin clusters are attached to the D-site through at least two immunoglobulin molecules, it is unlikely that their mutual repulsion from each other, at ranges of 65-86 nm, can be accounted for entirely in this way. The evidence for ‘preferred intervals’ is based upon 122measured pairs at a distance of about 82 nm in the case of the homozygote genotype; and upon 61 measured pairs at a distance of about 158 nm in the case of the heterozygote. In the case of the homozygote the preferred interval follows immediately upon the termination of the forbidden interval, but after a short gap in the case of the heterozygote. With the pattern observed on the homozygote cell surface it would be possible to postulate that an originally random pattern had been perturbed through a subsequent artifactual mutual separation of close pairs, the shortest distances having simply been separated to about 82 nm. However, the fact that this distance falls within the forbidden
Rh Antigens on Red Cell Surfaces
541
zone on the heterozygotc cell, and the fact that the heterozygote cell has a preferred distance at almost twice this interval, is evidence against such a mechanism. It would be useful, for these reasons, if an alternative method of visualizing D-sites could be devised. In fact, Romano et a1 (1975) have devised a method in which the antiglobulins were prepared in the horsc and labelled with colloidal gold instead of with ferritin, but there are still a t least two globulin molecules involved. In addition, the method is less precise in that the sites arc less densely marked, often with a single gold particle, and some, presumably, are unmarked. It is also much more difficult in the photographs to discern whether two modcrately close markers should be regarded as a single D-site, or as two. The authors provide relatively little photographic material, and no negative control material, and their published data cannot be satisfactorily analysed by the methods described in the present study. For the time being the pattern of inter-pair distances revealed in the analysis of Nicolson et al’s data is most readily interpreted as evidence for the existence of short-range order, although the precise pattern cannot be exactly inferred. O n e reasonable speculation may, however, be allowed. If the difference between the homozygote and the heterozygote cell is regarded as a reflection of the fact that about halfof the antigenic sites in the latter are ‘invisible’, then the fact that the forbidden zone for the heterozygote extends into the preferred zone for the homozygote, implies a systematic alternation of the maternally and paternally derived elements. It suggests that they are linked on a I-to-I basis, at least as couplets and, probably, that the ordering of the elements extends beyond a simple pairing arrangement in the form of chains or as a two-dimensional mesh. REFERENCES
K N O X ,E.G. (1968) A notional structure for the rhcsus antigens. British Journal Of HAPmAtOlOgy, 12, I 05. NICOLSON. G.L., MASOUREDIS S.P. & SINGER S.J. (1971) Quantitative two-dimensional ultra-structural distributionof Rh(D) antigenic sites on human erythrocyte membranes. Proceedings ofrhe National Academy of Sciences of the United States of America, 68, 1416.
ROMANO,E.L., STOLINSKI, C. & HUGHES-JONES, N.C. (1975)Distribution and mobility of the A, D and c antigens on human cell membranes: studies with a gold-labelled antiglobulin reagent. BritishJournal of HAPmAtOlOgy, 3 0 , 507.
STURGEON, P. (1970) Haematological observations of the anemia associated with blood type Rh.-null. Blood, 3 6 , 3 10.
