Simons, M, Pellionisz A (2005) Genomics, morphogenesis and biophysics: Triangulation of Purkinje cell development. The Cerebellum. (In Press; submitted 27/04/2005)
Genomics, morphogenesis and biophysics:
Triangulation of Purkinje cell development
Malcolm J Simons1* and András J Pellionisz2**
1 Haplomic Technologies Pty. Ltd., Victoria, Australia
2 HelixoMetry, Sunnyvale, California, USA
*Dr. Malcolm Simons, Haplomic Technologies Pty. Ltd., PO Box 5201, Geelong North, Victoria, 3215, Australia. E-mail: email@example.com
** Dr. András Pellionisz, HelixoMetry, 935 Rosette Court, Sunnyvale, California, 94086, USA. E-mail: firstname.lastname@example.org
The cerebellar Purkinje cells (P-cells) is an organelle that is suitable for combined analysis by morphology and genomics, using biophysical tools. In some unknown way, genomic information specifies the development of P-cells. One of us (AJP) has previously proposed that fractal processes associated with DNA are in a causal relation to the fractal properties of organelles such as P-cells (FractoGene, 2002, patent pending). This fractal postulate predicts that the dendritic arborization of P-cells will be less complex in lower order vertebrates. The prediction can be tested by systematic comparative neuroanatomy of the P-cell in species for whom genome sequences permit inter-species comparison. The Fugu rubripes (fugu), Danio rerio (danio) and other species are lower order vertebrates for whom genome sequences are available and tests could be conducted. Consistent with the fractal prediction, P-cell dendritic arbor is primitive in fugu, much less complex than in Mus musculus and in Homo sapiens. Genomic analysis readily identified PEP19/pcp4, Calbindin-D28k, and GAD67 genes in fugu and in danio that are closely associated with P-cells in Canis familiaris, Rattus norvegicus, Mus musculus and Homo sapiens. Gene L7/pcp2 exhibits strongest association with P-cells in higher vertebrates. L7/pcp2 shows strong protein residue homology with genes greater than 600 residues and including 2-3 GoLoco domains, designated as having G protein signaling modulator function (AGS3-like proteins). Fugu has a short gene with a single GoLoco domain, but it has greatest homology with the AGS3-like proteins. No similar short gene is present in Danio or in Xenopus. Classical L7/pcp2 is only detected in higher vertebrates, suggesting that it may be a marker of more recent evolutionary development of cerebellar P-cells. We expect that a new generation of data mining tools will be required to support recursive fractal geometrical, combinatorial, and neural network models of the genomic basis of morphogenesis.
In ways that are largely unknown, genomic information is presumed to specify the development of cellular systems, distributed as well as discrete. For most of the half century since the discovery of DNA structure it has been assumed that the projected 100,000+ genes were sufficiently responsible for the genesis of dispersed cell systems and of organelles and organs. It has been a major surprise to find that the number of genic units in humans is only of the order of 20,000, and possibly an even greater challenge to comprehend that a similar number is present in most eukaryotic species whose genomes have been sequenced. While recognising that alternative splicing is
exhibited by many genes, augmenting the number of protein varieties, it is becoming widely appreciated, even in generalist publications, that previous concepts of genomic information limited to gene-based dogma need to be reviewed1,2. It is fast becoming recognised that there is genetics beyond genes in which the information content of introns and other non-coding sequences can be expected to contribute important roles. As recently as 2003, Gibbs1 recorded the assertion by Mattick3 that “"the failure to recognize the importance of introns 'may well go down as one of the biggest mistakes in the history of molecular biology'”. One of us (MJS) did not make this mistake. By 1989, 11 years before essential completion of the Human Genome sequencing project in 2000, patents were filed based on the discovery that intron/non-coding sequence variation was sufficiently non-random for haplotype analysis in unrelated subjects4,5,6. Recognition of the utility of linkage disequilibrium-based haplotype structure was a paradigm shift from previous linkage-based pedigree analysis. The central issue was that if the so-called Junk DNA had structure, under Darwinian Theory it could be expected to have function. Proof of application was provided for the most polymorphic and complex component of the genome, the major histocompatibility complex (#6p21.3), in the context of HLA genetic tissue typing7,8. The non-random haplotypic structure of non-coding DNA has been the basis for genome-wide gene discovery by haplotype mapping for more than a decade, and underpins the current international HapMap project. Also in 1989, the second author (AJP), working in a totally different field, and unknown to MJS, recognised that attention would need to be given to the wider genome to understand genetically determined, fractal geometrical development of P-cells9, suggesting that a key to fractal geometry of the P-cell may lie in the genome, while cautioning that an understanding may lie “far in the future9”.
With expansion of genomic horizons beyond genes into non-protein coding DNA, it is timely to consider conceptual frameworks that have the potential of accelerating entry into the post-Gene era. Conceptual frameworks are most useful if they offer the opportunity of mathematization as well as of description, both of the genomic informatics and of derivative cellular and organismal development.
Linguistic features of non-coding DNA were suggested in the 1990’s, prompting the possibility of fractal-like characteristics in the genome10,11,12,13,14. The claims appear to be methodology based, since other investigations reported a failure to detect “well-defined scaling or fractal exponents” 15 or any signs of hidden language in non-coding DNA16.
In 1977, Mandelbrot conjectured that the P-cell might be modelled as a non-Euclidean fractal structure since P-cell arborization has the fractal-like features of scale free, self-similar patterns suggestive of generation by an iterative process17. In 1989, prompted by Mandelbrot’s musing (page 162, ibid), one of us (AJP) developed a fractal model of the P-cell9.
We recognise that a mathematical framework is required for holistic understanding of the contribution of both non-coding and coding genomic components to organelle and organ development. Presently there is a limited choice of conceptual frameworks that also provide a process and a platform. In 2002, one of us (AJP) postulated a causal relationship between fractal genetic structure and fractal P-cell arborization as illustrative of organelle morphogenic complexity (see "FractoGene Fig. 6.” shown as Fig. 3. in this paper18). Thus, our preferred model for a systematic approach to the intrinsic mathematics of genome-directed P-cell arborization development is that of fractal geometry. The simplest notion is that structural DNA is itself fractal, sufficient to encode the information required for development of discrete and distributed cellular systems. Whether or not structural DNA is itself fractal, we propose that nucleic, epinucleic, epistatic and other genetic and genomic mechanisms are considered as conferring fractal characteristics to morphogenic development.
We propose a role for triangulation, a term which has a specific meaning in geometry as the minimum information required to define the precise location of a point in a plane. Genomic contribution and morphological development are two such points. Application of biophysical tools to space-time domain provides the third component to relate the two points. We feel that such an interactive strategy is required to supplement if not supplant current reductionist paradigms that, in the extreme, assume causality between single genes and a phenotype.
Triangulation by mathematization of biology (biophysics) has already proven useful when membrane electrophysiology19 was interrelated with Neuro-morphology by computer modelling of the P-cell20,21. That triangulation successfully explained electrophysiological findings such as how the climbing fiber-evoked "complex spikes" arose from the complex P-cell dendritic tree20. The present task of relating Neuro-morphogenesis and genomics through biophysical concepts and methods is even more challenging. The cerebellum and its notable pathogenetic condition (Friedreich spinocerebellar ataxia) have already been a focus of genetic attention22, including special focus on the P-cell23 (Barski et al., 2002). Morphological studies coupled with biophysical modelling of the P-cell have been elegantly presented21 as depicted in Fig.1, left side.
Of all neurons, P-cells exhibit the most complex dendritic arborization and a most remarkable diversity, yet conserving a pattern of arborization such that morphologists recognize this cell virtually independent of the studied species. The visibly geometrical branching pattern, which is curiously confined to a wafer-thin layer, is strikingly similar across different species, yet distinct in its complexity. The greatest dendritic complexity was first observed in humans almost a Century ago24, see right side of Fig. 1.). Subsequent studies have revealed that the P-cell in frog, mouse, guinea pig (etc) has a less complex pattern than in the human (see frog P-cell histology25, frog P-cell modelling26, P-cell histology for the guinea pig27 and guinea pig P-cell modelling21, see left side of Fig.1.). The well-known but hitherto unexplained exception from an apparent trend is the Mormiryd (an electric fish) in which the "Gigantocerebellum" exhibits a giant P-cell of astounding refinement28.
The genomes of many species have been sequenced. They provide a new opportunity for combining comparative anatomy and genomics, guided by mathematical conceptual frameworks. Hitherto, neurobiological and biophysical studies of P-cells and networks revealed an understanding of the space-time sensorimotor coordination
by the cerebellar neural network29. As yet, the genomic aspects of P-cell development have not been brought into similar focus. Recently, the genomes of the poisonous sea-water puffer fish Takifugu rubripes (hereinafter fugu) and the non-poisonous fresh-water puffer fish Tetraodon nigrivirides (fam. Tetradontidae) have been revealed to be much smaller than higher vertebrates, comprising some 0.365 and 0.385 Gigabases, respectively. They are in stark contrast to the size of the human genome at 3.1 sequenced Gigabases, and even smaller than the 2.6 Gigabases of the mouse genome. The genome of another lower order fish, Danio rerio (common name zebrafish, hereinafter danio), has also been sequenced as smaller than that of human, at 1.56 Gigabases (all data are from Univ. California at Santa Cruz Database). The availability of the genome sequences of fugu (and of danio and other species) promises to offer insights into genomic mechanisms underlying organelle development.
Based on the prediction of "FractoGene, Fig.6. 18" (reproduced in Fig. 3. of this paper) that fugu should exhibit a primitive P-cell arbor, while danio should show an intermediate complexity, one of us suggested (AJP to Prof. G. Székely on 7/4/2003) that a preliminary study be conducted to reveal the facts of neuroanatomy in the fugu, and more recently in the danio. While it is simplistic to imagine that total genome size would correlate linearly with specific organelle complexity, we were curious to examine P-cell presence and dendritic complexity in fugu and danio. That study is to be reported separately30. The authors have permitted us to refer to their results as ‘unpublished observations’ for the fugu. The danio results (only partially available) and other comparisons are expected to blossom as a new branch of research.
[Fig. 2. on fugu is near here]
The P-cell is a specific morphological development platform to be put into the "crossfire of triangulation" similar to earlier syntheses by biophysics of Neuro-morphology and electrophysiology. In particular, we wish to model P-cell morphogenesis based on the genetic control that we assume is inherent in genomic information. Here we begin investigation of the P-cell using the three dimensions of morphological analysis, genomics and biophysics.
We have searched the public genome databases for fugu and (in anticipation of completed morphological studies also for danio) for molecules that are candidate markers of cerebellar P-cells in that they are expressed with varying specificity in P-cells.
Seventeen years ago the earliest report of what became known as L7/Pcp2 was found to be one of three cloned genes associated with P-cell degeneration in the recessive mouse mutant pcd (PCD5) 31.
The L7/Pcp2 marker has been detected only in P-cells and in retinal bipolar neurons, It appears to be the most specific marker of P-cells. L7/Pcp2 is a GoLoco domain protein that functions as a cell-type specific modulator of Galpha(i) and Galpha(o) in G-protein mediated cell signaling. L7/Pcp2 mRNA transcripts have been reported as localizing within the proximal and distal branches of dendrites and in the proximal part of P-cell axons. The strong association of L7/Pcp2 protein and mRNA with P-cells has led to the suggestion of “likely importance in controlling the development and/or motor control function of Purkinje cells.” 32.
The second clone identified 17 years ago31 was Calbindin-D28k. While this molecule is present in neuronal structures outside the cerebellum, among cerebellar elements it is a specific marker of P-cells. Homology BLAST search (NCBI, NIH) of fugu and danio protein databases readily identified Calbindin sequences for both species (fugu CAF99552, CAF96430, CAG00001; danio NP_957012, NP_957005, NP_001005776, AAH59479, AAH59467, AAH83168).
The third of the three genes to be reported was PCD6, an unidentified protein of greater than 500aa. 14 years later33, the gene mutated in the original pcd mouse was identified as Nna1 (Fernandez- Gonzalez 2002). The Nna1 protein is 1,160 aa in mice, and has strong homology to proteins present in fugu (CAG08401 - 997aa; CAF98247 - 538aa; CAG00089 - 774aa), danio (NP_001004113, AAH80248 - 885aa), and Xenopus (AAH77808 - 1225aa; AAH77561 - 678aa).
Other molecules that are expressed in P-cells include PEP19/Pcp4 and glutamic acid decarboxylase 67 (GAD67).
The PEP19/Pcp4 gene product of 62 aa is one of the smallest translation products identified in eukaryotes. Using the human sequence as reference (NP_006189), an unnamed protein of 63 aa is readily identified in Tetraodon nigriviridis (CAF93207) as full length homology. The NCBI, NIH BLAST ‘select organism’ lists Takifugu rubripes, but we have not observed any listing for this organism in the BLAST output. Further, when the T. nigiviridis sequence (CAF93207) is BLASTed against Takifugu ribripes as the selected single organism, no hits were observed. Using the same human sequence as query, an unnamed 72 aa protein (CAE17624) is identified in danio, with homology of less than full length, extending from aa 22 to the 3’ end. Among lower vertebrates, the human gene sequence identified only fugu and danio. No sequences were revealed in xenopus or gallus.
GAD67 is present in both the fugu and danio databases in many entries (fugu: CAF97647, CAG07380, CAG09942, CAG05466; danio: AAH47851, AAC24327, AAD22710, NP_919400).
In view of the ease in which the P-cell markers PEP19/pcp4, Calbindin-D28k, GAD67, and Nna1 homologues are detectable in fugu and danio databases, we were surprised that the most P-cell specific marker, L7/Pcp2, does not appear to be present in danio, and is not readily recognizable in fugu.
At a nucleotide level, BLASTing the promoter region of L7/Pcp2 and exon 2 reveals a homology with sequences restricted to vertebrate species (mouse, rat, dog and cow). By contrast, human exon1 and intron1 nucleotide sequences show no homology with any other species.
BLASTing with a range of vertebrate L7/Pcp2 protein sequences regularly identified all human, murine, rat, canine and bovine homologues with strong identity (Homo: XP_058956, Q8IVA1, AAN52488, AAN52487, AAH38715, XP_058956; Mus: AAH14694, NP_032816, P12660, AAH24853, AAH28982, AAN52485, AAA02989, BAC25015, B34955, AAB19316; Rattus: XP_221787; Canis: XP_542114; Bos: XP_600613).
In humans, L7/Pcp2 exists in two isoforms of 99 and 136 residues as a single GoLoco domain protein that modulates the activation of guanine nucleotide-binding regulatory protein (G protein) subunits Galpha (i) and Galpha(o) in cell signaling. It was therefore of considerable interest that, lower on the L7/Pcp2 list of revealed peptide sequences, were those designated as having G protein signalling modulator function (activator of G-protein signalling 3 [AGS3]-like proteins). These latter proteins, mostly greater than 600 aa in length, included 2-3 GoLoco sequences with which the L7/Pcp2 GoLoco region aligned. It was with this group that fugu (CAG12405, CAF91737, CAG07707, CAG11554) and danio (AAH83520, NP_001005936, NP_001007779, AAU14175, AAH54918, NP_956732) sequences were grouped. We do not know whether the third clone (PCD6) 33 to encode a protein greater than 500aa was an AGS3-like protein.
There was one exception to fugu protein molecules of long length that was identified by vertebrate L7/Pcp2 BLAST query. CAF91737 accession sequence is a 78 residue peptide for which the most homologous sequences were G-protein signalling modulators 1,2 and 3 (activator of G-protein signalling 3-like). Lower on the listing of homologous sequences were the L7/Pcp2 sequences of the vertebrates. The domain showing greatest homology (Homo Q8IVA1 aa 32-53) overlapped with the GoLoc domain (aa 28-42, of 99). However, the corresponding residue positions in the fugu peptide were at the 3’ end of the peptide, at positions 55-76 of the 78 residues. When this domain in fugu CAF91737 was used for BLAST query, the most similar sequences were Pcp2 peptides of the vertebrates. In view of the 3’ end position of the GoLoco domain in the fugu protein, it is notable that the domain is similarly positioned in bovine Pcp2 (aa72-93 of 100), different from all the other Pcp2 molecules. Nonetheless, the primary homology appears to be with AGS3-like molecules, rather than with L7/Pcp2 itself.
The apparent absence of observable cerebellar abnormalities in L7/Pcp2-null mice does not support a necessary role in P-cell development34,35. The genomic database finding that fugu and danio seem to lack the prototypic L7/Pcp2 molecule is in keeping with the non-essentiality of the gene in P-cell development. There is evidence of close interaction between L7/Pcp2 and Galpha(o). Colocalisation in P-cells suggests a functional role in regions of synaptic activity. It is therefore intriguing that, despite lacking a prototypic L7/Pcp2 molecule, both fugu and danio do have molecules exhibiting the GoLoco domains presumably involved in G-protein signalling modulation.
The present study is a first step towards a triangulation by mathematization of the genomic contribution to morphological development guided by biophysical tools. Towards this goal we chose the P-cell as a platform.
The FractoGene postulate of a causal relationship between fractal genetic function and P-cell arborization that prompted the present study was detailed in 200218.
[Fig. 3. (Reproduction of Fig.6. of Reference 18) is near here]
"FractoGene", which is Fig. 3. of this paper, is an actual copy of Figure 6. of the Patent Application18. The legend to the original figure in the Patent stated: "Elements of Prior Art are combined here, to make a complete circle between the demonstrably fractal-like neuron of Purkinje cell and the demonstrably fractal-like sequences of (only illustrative, not necessarily actual Purkinje cell) DNA base-pairs. From this demonstration diagram it is obvious that the four A,C,T,G base-pair segments are not identical, only self-similar."
There were two cited "elements":
(1) The fractal Purkinje model, lifted from the publication9, and
(2) an illustrative DNA sequence as one example from the wide array of "repetitive DNA sequences" in the literature ( http://bssv01.lancs.ac.uk/ADS/BIOS336/336L2.html ).
The "first element" (fractal Purkinje model - top row of Fig. 3. of this paper) shows, in four stages, the increasing complexity of the dendritic tree from B,C,D,to E, representing the fractal steps towards development of the Golgi-stained Guinea Pig Purkinje Cell (F) 27. As described in the original publication, the model 9 utilized an L-string replacement algorithm. It can be seen that the stem (corresponding to stage A that is not shown) and the Y-shaped fractal template remains conserved through the four stages. By contrast, all peripheral twigs are replaced by the fractal template (or ‘primitive’) of stage B. Branchlet characters such as length and thickness need additional information that are not strictly defined but rather are parameters in the template.
An observation in 2002, thirteen years after publication of the fractal organelle model9, of sequence elements that are self-similar but not identical (bottom left field, four consecutive DNA nucleotide sequences) prompted the FractoGene concept to explain the additional information not inherent in the fractal template, namely that the "fractal-like" properties of Purkinje neurons, as well as of other organelles and organs (eg. Cardial coronary arteries36), and the "fractal-like" self-similar repetitions known to be in DNA since 199412, are in a causal relationship, with fractal sets of DNA generating fractal anatomical (structural proteins), physiological (metabolic proteins) and related pathological formations.
FractoGene predicted that the fugu P-cell arbor would take the form of the ‘B’ stage depicted in the ‘FractoGene’diagram (Fig.6 of18, Fig. 3. of this paper).
It is worthy of mentioning that the prediction of the “FractoGene” diagrams for the several subsequent stages of fractal development are not just visually descriptive. Rather, the fractal model is mathematically deterministic. This means that the basic information is contained in the “L-string fractal primitive” of “B-stage” 18.
The morphological findings reported elsewhere and summarised here support the prediction. The P-cell patterning of fugu is clearly the least developed of all organisms reported to date. Danio, based on preliminary observations, is expected to be documented to show an intermediate level of P-cell arbor structure.
[Fig. 4. Comparative neuroanatomy of P-cells is near here]
The complexity of the genomic-morphological nexus is revealed by the apparent absence of a primary candidate gene L7/Pcp2 for P-cell development in fugu and the preliminary observations indicate an interim stage for the danio. The gene is also undetectable in two genera of xenopus (laevis and x.tropicalis) in which P-cell dendritic arbor is distinct25. This finding may relate to the more recent evolutionarily emergence of basket cell neurons (see the so-called ‘Basic Cerebellar Circuit’ notion, based on the lack of basket and Golgi cells described for the frog38). If L7/Pcp2 could be demonstrated in fugu / danio / xenopus by histological, molecular biological or other procedures, then current sequence homology tools would need to be supplemented by a new generation of genomic search tools, based on significant leaps in algorithmic developments, such as triggered by FractoGene18.
The complexity of the relationship between genomic function and morphological development requires experimentation to be guided by concepts such as that of FractoGene, which specifies a process (recursive instructions) and, here, a platform (P-cell). Any viable alternative to the FractoGene model, such as a combinatorial approach39 to DNA, would also need to identify a suitable process and platform.
It can, however, be easily imagined that the fractal approach can be extended to combinatorial concepts. Components of the DNA in most animals are not a single monofractal, as appears to be the case in some simple plants, but are almost certainly multifractal. This seems evident from the different fractal properties of their separable organelles (lung, coronaries, intestines, etc.). Therefore, the FractoGene concept might have to be augmented with methods of sequence analysis.
It can also be predicted that neural network algorithms derived from biological organisms40 and patents41, will serve as novel computational elements to measure the self-similarity by fractals. Indeed, a recent neuronal network study shows already that fractal, neural network, multidimensional/combinatorial approaches to mathematical treatment of recursive and iterative biological processes have commenced42. Interestingly this recent initiation is applied to sensorimotor sequences, which were the historical precursors to geometrization of biology29,9. Application of fractal and combinatorial approaches together with neural network algorithms to genomic information analysis can be expected as the next development.
We regard it to be essential in this post-gene era that biological studies are guided by some mathematical (geometrical) model of genome-morphodevelopment interaction. While the imperative of mathematization may not be yet compelling to some morphologists and even genomists, the cardinal importance of mathematical tools is rapidly becoming understood by practitioners of nanotechnology attempting to create protein-based novel materials. Nanotechnologists recognise that protein-based Nano-construction requires both a quantitative understanding of the full genome, including introns and non-coding DNA, and appropriate quantitative "blueprints"43. For general essays on this issue, see44,45. Indeed, if protein-based Nanotechnology mathematical tools are not provided by Genomics, then Nanotechnology can be expected to generate such tools on their own, outside of a true interdisciplinary cooperation46,47,48.
We are thankful for the use of unpublished observations of Dr G. Szekely and Dr. N.
Matsumoto (“Department of Anatomy, University of Debrecen”, Hungary, and "Kyushu Institute of Technology", Japan). These authors wish to acknowledge the help of Mr. J. Takata and I. Takami, (Marine Laboratory Nagasaki) with the collection of the animals.
Fig. 1. The cerebellar Purkinje cell in the guinea pig (left 21 and on the right in the human24. While the diagram on the left is a modern computer reconstruction of fluorescent-stained P-cell and thus exhibits all details, the classical diagram24 on the right is a drawing based on Golgi silver stain preparation, and thus the actual Purkinje cell dendritic arbour could be even more complex than showed.
Fig. 2. Golgi-stained cerebellar P-cell in the Fugu rubripens (Courtesy of Székely et al.30). Note the primitive template of "arbor". Calibration bar in the upper right corner shows 50 micrometers.
Fig. 3. Postulates of the "FractoGene" diagram, an actual copy of Figure 6 of the Patent Application "FractoGene: Utility to use self-similar repetitions in the language-like genetic information as fractal sets". US Patent Application18 Aug. 1st, 2002. FractoGene postulated a causal relationship between fractal genetic function and P-cell arborization that prompted preliminary morphological study of the Fugu rubripes30, and of the (to be completed) study of Danio rerio, as its genome became available.
Fig. 4. Sketch of the emerging field of comparison of the complexity of the dendritic trees of P-cells, their genomic analysis, calling for biophysical synthesis. Insert B shows the P-cell in the Fugu rubripes (B is courtesy of Székely30), in which the genome size is 0.37 Gigabases. C will show the P-cell in Danio rerio (as it becomes available, according to studies at an early stage to exhibit an interim complexity) in which the genome size is 1.56 Gigabases. D shows the dendritic arbor of the P-cell in the mouse (genome size is 2.6 Gigabases). Insert D is fluorescent-stained photo, courtesy of Prof. Helen Blau37. E shows a computer-reconstruction of the P-cell in the guinea pig21. The genome size in the guinea pig is not known to date, but its sequencing was slated (at Broad Institute and MIT) among other species. Insert H shows the P-cell of the human24. The genome size in the human is 3.1 Gigabases.
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