An ERK5-PFKFB3 axis regulates glycolysis and represents a therapeutic vulnerability in pediatric diffuse midline glioma

Metabolic reprogramming in pediatric diffuse midline glioma is driven by gene expression changes induced by the hallmark histone mutation H3K27M, which results in aberrantly permissive activation of oncogenic signaling pathways. Previous studies of diffuse midline glioma with altered H3K27 (DMG-H3K27a) have shown that the RAS pathway, specifically through its downstream kinase, extracellular-signal-related kinase 5 (ERK5), is critical for tumor growth. Further downstream effectors of ERK5 and their role in DMG-H3K27a metabolic reprogramming have not been explored. We establish that ERK5 is a critical regulator of cell proliferation and glycolysis in DMG-H3K27a. We demonstrate that ERK5 mediates glycolysis through activation of transcription factor MEF2A, which subsequently modulates expression of glycolytic enzyme PFKFB3. We show that in vitro and mouse models of DMG-H3K27a are sensitive to the loss of PFKFB3. Multi-targeted drug therapy against the ERK5-PFKFB3 axis, such as with small-molecule inhibitors, may represent a promising therapeutic approach in patients with pediatric diffuse midline glioma.

EPCO-38. TYPE B ULTRA LONG-RANGE INTERACTIONS IN PFAS (TULIPS) ARE RECURRENT EPIGENOMIC FEATURES OF PFA EPENDYMOMA

Posterior Fossa Group A (PFA) ependymomas are pediatric brain tumors with extremely poor survival outcomes. As protein-coding mutations in PFA are exceedingly rare, the underlying etiology of these tumors remains elusive. Elevated CpG island methylation and depletion of H3K27me3 have been described in PFA, leading to the hypothesis that PFA may be driven by a dysregulated epigenetic state. In this study, we sought to determine how three-dimensional (3D) genome features (such as DNA loops, domains, and compartments) differ between pediatric brain tumors. We performed Hi-C sequencing on a collection of 64 patient specimens and patient-derived primary cultures that collectively span multiple subgroups of ependymoma, medulloblastoma, high-grade glioma, and non-neoplastic brain. For certain samples, we further performed RNA-seq, histone modification ChIP-seq, or whole-genome bisulfite sequencing to allow multiomic data integration. Overall, the 3D genome organization of PFA samples appeared distinct from other tumor types. We identified and defined TULIPs: a subset of type B compartments, separated by genomic distances greater than 10 Mbp, that exhibit a striking fivefold increase in reciprocal interaction strength. These TULIPs recurred at the same genomic positions across the vast majority of PFA samples with minimal representation among other tumor or non-tumor samples. TULIPs displayed enrichment for heterochromatic features such as H3K9me3 and late replication timing and were depleted of euchromatic features such as H3K27ac and protein-coding genes. By using immuno-fluorescence for H3K9me3 and oligo-FISH to label TULIP regions, we demonstrated that TULIP regions are more compact in PFA than other tumors. Finally, by applying inhibitors of H3K9 lysine methylation to PFA cultures we showed that TULIPs become more diffuse and cell viability is reduced. Altogether, this work defines TULIPs as highly recurrent epigenetic features of PFA tumors.

TMET-09. LOSS OF MAT2A COMPROMISES METHIONINE METABOLISM AND REPRESENTS A VULNERABILITY IN H3K27M MUTANT GLIOMAS

H3K27-mutant diffuse midline gliomas (DMGs) are defined as grade IV tumors by the World Health Organization. DMGs are inoperable and resistant to chemo/radio therapies. Median survival ranges from 8-11 months, with 2% of patients surviving beyond 5 years. H3K27M mutations lead to global epigenetic and transcriptional reprogramming driven by global loss of negative transcriptional regulator H3K27 trimethylation (H3K27me3). Loss of H3K27me3 is an initiating event in gliomagenesis. This disease lacks appropriate models to predict disease biology and response to treatment. Therefore, we developed a novel syngeneic H3K27M mouse model. An unbiased integrated systems biology approach identified that H3K27M but not isogenic controls relied on the amino acid methionine and the enzyme Methionine Adenosyltransferase 2A (MAT2A). MAT2A is a central regulator of one-carbon metabolism by converting methionine to S-adenosylmethionine (SAM), the universal methyl-donor for protein and nucleotide methylation reactions. In complementary genetic approaches, we applied these findings to patient-derived cell lines with the H3K27M mutation. We hypothesize that MAT2A abrogation, genetic/pharmacological, would alter DMG viability by disrupting the methylome. The current MAT2A sensitivity paradigm is based on Methylthioadenosine Phosphorylase (MTAP) deletion through a synthetic lethal mechanism. We provide a novel mechanism whereby H3K27M cells are sensitive to MAT2A loss, independent of MTAP and through Adenosylmethionine Decarboxylase 1 (AMD1) overexpression disrupting MAT2A regulation. This results in H3K27M cells having lower MAT2A protein levels, conferring a sensitivity by inhibiting residual MAT2A. Genetic/pharmacological aberrations to MAT2A resulted in reduced proliferation. Parallel H3K36me3 ChIP and RNA-sequencing identified loss of oncogenic and developmental transcriptional programs associated with MAT2A loss. In vivo syngeneic and patient-derived xenograft models with both inducible MAT2A knockdown or methionine restricted diets showed extended survival. These results suggest novel interactions between methionine metabolism and the epigenome of H3K27M gliomas and provide evidence that MAT2A, presents exploitable therapeutic vulnerabilities in histone mutant gliomas.

Loss of MAT2A compromises methionine metabolism and represents a vulnerability in H3K27M mutant glioma by modulating the epigenome

Diffuse midline gliomas (DMGs) bearing driver mutations of histone 3 lysine 27 (H3K27M) are incurable brain tumors with unique epigenomes. Here, we generated a syngeneic H3K27M mouse model to study the amino acid metabolic dependencies of these tumors. H3K27M mutant cells were highly dependent on methionine. Interrogating the methionine cycle dependency through a short-interfering RNA screen identified the enzyme methionine adenosyltransferase 2A (MAT2A) as a critical vulnerability in these tumors. This vulnerability was not mediated through the canonical mechanism of MTAP deletion; instead, DMG cells have lower levels of MAT2A protein, which is mediated by negative feedback induced by the metabolite decarboxylated S-adenosyl methionine. Depletion of residual MAT2A induces global depletion of H3K36me3, a chromatin mark of transcriptional elongation perturbing oncogenic and developmental transcriptional programs. Moreover, methionine-restricted diets extended survival in multiple models of DMG in vivo. Collectively, our results suggest that MAT2A presents an exploitable therapeutic vulnerability in H3K27M gliomas.

ZFTA-RELA Dictates Oncogenic Transcriptional Programs to Drive Aggressive Supratentorial Ependymoma

More than 60% of supratentorial ependymomas harbor a ZFTA-RELA (ZRfus) gene fusion (formerly C11orf95-RELA). To study the biology of ZRfus, we developed an autochthonous mouse tumor model using in utero electroporation (IUE) of the embryonic mouse brain. Integrative epigenomic and transcriptomic mapping was performed on IUE-driven ZRfus tumors by CUT&RUN, chromatin immunoprecipitation sequencing, assay for transposase-accessible chromatin sequencing, and RNA sequencing and compared with human ZRfus-driven ependymoma. In addition to direct canonical NFκB pathway activation, ZRfus dictates a neoplastic transcriptional program and binds to thousands of unique sites across the genome that are enriched with PLAGL family transcription factor (TF) motifs. ZRfus activates gene expression programs through recruitment of transcriptional coactivators (Brd4, Ep300, Cbp, Pol2) that are amenable to pharmacologic inhibition. Downstream ZRfus target genes converge on developmental programs marked by PLAGL TF proteins, and activate neoplastic programs enriched in Mapk, focal adhesion, and gene imprinting networks. SIGNIFICANCE: Ependymomas are aggressive brain tumors. Although drivers of supratentorial ependymoma (ZFTA- and YAP1-associated gene fusions) have been discovered, their functions remain unclear. Our study investigates the biology of ZFTA-RELA-driven ependymoma, specifically mechanisms of transcriptional deregulation and direct downstream gene networks that may be leveraged for potential therapeutic testing.This article is highlighted in the In This Issue feature, p. 2113.

ZFTA Translocations Constitute Ependymoma Chromatin Remodeling and Transcription Factors

ZFTA (C11orf95)-a gene of unknown function-partners with a variety of transcriptional coactivators in translocations that drive supratentorial ependymoma, a frequently lethal brain tumor. Understanding the function of ZFTA is key to developing therapies that inhibit these fusion proteins. Here, using a combination of transcriptomics, chromatin immunoprecipitation sequencing, and proteomics, we interrogated a series of deletion-mutant genes to identify a tripartite transformation mechanism of ZFTA-containing fusions, including: spontaneous nuclear translocation, extensive chromatin binding, and SWI/SNF, SAGA, and NuA4/Tip60 HAT chromatin modifier complex recruitment. Thereby, ZFTA tethers fusion proteins across the genome, modifying chromatin to an active state and enabling its partner transcriptional coactivators to promote promiscuous expression of a transforming transcriptome. Using mouse models, we validate further those elements of ZFTA-fusion proteins that are critical for transformation-including ZFTA zinc fingers and partner gene transactivation domains-thereby unmasking vulnerabilities for therapeutic targeting. SIGNIFICANCE: Ependymomas are hard-to-treat brain tumors driven by translocations between ZFTA and a variety of transcriptional coactivators. We dissect the transforming mechanism of these fusion proteins and identify protein domains indispensable for tumorigenesis, thereby providing insights into the molecular basis of ependymoma tumorigenesis and vulnerabilities for therapeutic targeting.This article is highlighted in the In This Issue feature, p. 2113.

EPEN-01. C11ORF95-RELA DICTATES ONCOGENIC TRANSCRIPTIONAL PROGRAMS TO DRIVE AGGRESSIVE SUPRATENTORIAL EPENDYMOMA

Over 60% of supratentorial (ST) ependymomas harbor a gene fusion between C11orf95, an uncharacterized gene, and RELA (also known as p65), a main component of the NF-ĸB family of transcription factors. While its sufficiency to drive tumor has been established, the mechanism of tumorigenesis remains elusive. To tackle this question, we developed a natively forming mouse tumor model using in utero electroporation (IUE) of the embryonic mouse brain and performed integrative epigenomic and transcriptomic mapping. Our findings indicate that in addition to direct canonical NF-ĸB pathway activation, C11orf95-RELA (CRfus) dictates a neoplastic transcriptional program and binds to unique sites across the genome enriched with Plagl family transcription factor motifs. CRfus modulates the transcriptional landscape by recruiting transcription co-activators (Brd4, EP300, Cbp, Pol2) which are amenable to pharmacologic inhibition. Downstream CRfus target genes converge on developmental programs marked by Plagl family of transcription factors and activate neoplastic programs enriched in Mapk, focal adhesion, and gene imprinting networks, many of which contain previously unreported therapeutic leads in C11orf95-RELA ependymoma.

EPEN-30. C11ORF95-RELA FUSION PROTEIN ENGAGES NOVEL GENOMIC LOCI TO DRIVE MURINE EPENDYMOMA GROWTH

RATIONALE

Over 70% of supratentorial (ST) ependymoma are characterized by an oncogenic fusion between C11ORF95 and RELA. C11ORF95-RELA fusion is frequently the sole genetic driver detected in ST ependymoma, thus ranking this genomic event as a lead target for therapeutic investigation. RELA is a transcription factor (TF) central to mediating NF-kB pathway activation in processes such as inflammation, cellular metabolism, and chemotaxis. HYPOTHESIS: We posited that C11ORF95-RELA acts as an oncogenic TF that aberrantly shapes the tumor epigenome to drive aberrant transcription. Approach: To this end we developed an in utero electroporation (IUE) mouse model of ependymoma to express C11ORF95-RELA during embryonic development. Our IUE approach allowed us to develop C11ORF95-RELA driven tumor models and cell lines. We comprehensively characterized the epigenome and transcriptome of C11ORF95-RELA fusion driven mouse cells by H3K27ac ChIP-seq, ATAC-seq, and RNA-seq.

RESULTS

This data revealed that: 1) C11ORF95-RELA directly engages ‘open’ chromatin and is enriched at regions with known RELA TF binding sites as well as novel genomic loci/motifs, 2) C11ORF95-RELA preferentially binds to both H3K27ac (active) enhancers and promoters, and 3) Bound C11ORF95-RELA promoter loci are associated with increased transcription of genes shared with human ependymoma.

CONCLUSION

Our findings shed light on the transcriptional mechanisms of C11ORF95-RELA, and reveal downstream targets that may represent cancer dependency genes and molecular targets.

A High-Quality Assembly of the Nine-Spined Stickleback (Pungitius pungitius) Genome

The Gasterosteidae fish family hosts several species that are important models for eco-evolutionary, genetic, and genomic research. In particular, a wealth of genetic and genomic data has been generated for the three-spined stickleback (Gasterosteus aculeatus), the "ecology's supermodel," whereas the genomic resources for the nine-spined stickleback (Pungitius pungitius) have remained relatively scarce. Here, we report a high-quality chromosome-level genome assembly of P. pungitius consisting of 5,303 contigs (N50 = 1.2 Mbp) with a total size of 521 Mbp. These contigs were mapped to 21 linkage groups using a high-density linkage map, yielding a final assembly with 98.5% BUSCO completeness. A total of 25,062 protein-coding genes were annotated, and about 23% of the assembly was found to consist of repetitive elements. A comprehensive analysis of repetitive elements uncovered centromere-specific tandem repeats and provided insights into the evolution of retrotransposons. A multigene phylogenetic analysis inferred a divergence time of about 26 million years ago (Ma) between nine- and three-spined sticklebacks, which is far older than the commonly assumed estimate of 13 Ma. Compared with the three-spined stickleback, we identified an additional duplication of several genes in the hemoglobin cluster. Sequencing data from populations adapted to different environments indicated potential copy number variations in hemoglobin genes. Furthermore, genome-wide synteny comparisons between three- and nine-spined sticklebacks identified chromosomal rearrangements underlying the karyotypic differences between the two species. The high-quality chromosome-scale assembly of the nine-spined stickleback genome obtained with long-read sequencing technology provides a crucial resource for comparative and population genomic investigations of stickleback fishes and teleosts.

A High-Quality Assembly of the Nine-Spined Stickleback (Pungitius pungitius) Genome

The Gasterosteidae fish family hosts several species that are important models for eco-evolutionary, genetic, and genomic research. In particular, a wealth of genetic and genomic data has been generated for the three-spined stickleback (Gasterosteus aculeatus), the "ecology's supermodel," whereas the genomic resources for the nine-spined stickleback (Pungitius pungitius) have remained relatively scarce. Here, we report a high-quality chromosome-level genome assembly of P. pungitius consisting of 5,303 contigs (N50 = 1.2 Mbp) with a total size of 521 Mbp. These contigs were mapped to 21 linkage groups using a high-density linkage map, yielding a final assembly with 98.5% BUSCO completeness. A total of 25,062 protein-coding genes were annotated, and about 23% of the assembly was found to consist of repetitive elements. A comprehensive analysis of repetitive elements uncovered centromere-specific tandem repeats and provided insights into the evolution of retrotransposons. A multigene phylogenetic analysis inferred a divergence time of about 26 million years ago (Ma) between nine- and three-spined sticklebacks, which is far older than the commonly assumed estimate of 13 Ma. Compared with the three-spined stickleback, we identified an additional duplication of several genes in the hemoglobin cluster. Sequencing data from populations adapted to different environments indicated potential copy number variations in hemoglobin genes. Furthermore, genome-wide synteny comparisons between three- and nine-spined sticklebacks identified chromosomal rearrangements underlying the karyotypic differences between the two species. The high-quality chromosome-scale assembly of the nine-spined stickleback genome obtained with long-read sequencing technology provides a crucial resource for comparative and population genomic investigations of stickleback fishes and teleosts.

Switching on the light: using metagenomic shotgun sequencing to characterize the intestinal microbiome of Atlantic cod

Atlantic cod (Gadus morhua) is an ecologically important species with a wide-spread distribution in the North Atlantic Ocean, yet little is known about the diversity of its intestinal microbiome in its natural habitat. No geographical differentiation in this microbiome was observed based on 16S rRNA amplicon analyses, yet such finding may result from an inherent lack of power of this method to resolve fine-scaled biological complexity. Here, we use metagenomic shotgun sequencing to investigate the intestinal microbiome of 19 adult Atlantic cod individuals from two coastal populations in Norway-located 470 km apart. Resolving the species community to unprecedented resolution, we identify two abundant species, Photobacterium iliopiscarium and Photobacterium kishitanii, which comprise over 50% of the classified reads. Interestingly, the intestinal P. kishitanii strains have functionally intact lux genes, and its high abundance suggests that fish intestines form an important part of its ecological niche. These observations support a hypothesis that bioluminescence plays an ecological role in the marine food web. Despite our improved taxonomical resolution, we identify no geographical differences in bacterial community structure, indicating that the intestinal microbiome of these coastal cod is colonized by a limited number of closely related bacterial species with a broad geographical distribution.

The Chromosome-Level Genome Assembly of European Grayling Reveals Aspects of a Unique Genome Evolution Process Within Salmonids

Salmonids represent an intriguing taxonomical group for investigating genome evolution in vertebrates due to their relatively recent last common whole genome duplication event, which occurred between 80 and 100 million years ago. Here, we report on the chromosome-level genome assembly of European grayling (Thymallus thymallus), which represents one of the earliest diverged salmonid subfamilies. To achieve this, we first generated relatively long genomic scaffolds by using a previously published draft genome assembly along with long-read sequencing data and a linkage map. We then merged those scaffolds by applying synteny evidence from the Atlantic salmon (Salmo salar) genome. Comparisons of the European grayling genome assembly to the genomes of Atlantic salmon and Northern pike (Esox lucius), the latter used as a nonduplicated outgroup, detailed aspects of the characteristic chromosome evolution process that has taken place in European grayling. While Atlantic salmon and other salmonid genomes are portrayed by the typical occurrence of numerous chromosomal fusions, European grayling chromosomes were confirmed to be fusion-free and were characterized by a relatively large proportion of paracentric and pericentric inversions. We further reported on transposable elements specific to either the European grayling or Atlantic salmon genome, on the male-specific sdY gene in the European grayling chromosome 11A, and on regions under residual tetrasomy in the homeologous European grayling chromosome pairs 9A-9B and 25A-25B. The same chromosome pairs have been observed under residual tetrasomy in Atlantic salmon and in other salmonids, suggesting that this feature has been conserved since the subfamily split.

The Grayling Genome Reveals Selection on Gene Expression Regulation after Whole-Genome Duplication

Whole-genome duplication (WGD) has been a major evolutionary driver of increased genomic complexity in vertebrates. One such event occurred in the salmonid family ∼80 Ma (Ss4R) giving rise to a plethora of structural and regulatory duplicate-driven divergence, making salmonids an exemplary system to investigate the evolutionary consequences of WGD. Here, we present a draft genome assembly of European grayling (Thymallus thymallus) and use this in a comparative framework to study evolution of gene regulation following WGD. Among the Ss4R duplicates identified in European grayling and Atlantic salmon (Salmo salar), one-third reflect nonneutral tissue expression evolution, with strong purifying selection, maintained over ∼50 Myr. Of these, the majority reflect conserved tissue regulation under strong selective constraints related to brain and neural-related functions, as well as higher-order protein–protein interactions. A small subset of the duplicates have evolved tissue regulatory expression divergence in a common ancestor, which have been subsequently conserved in both lineages, suggestive of adaptive divergence following WGD. These candidates for adaptive tissue expression divergence have elevated rates of protein coding- and promoter-sequence evolution and are enriched for immune- and lipid metabolism ontology terms. Lastly, lineage-specific duplicate divergence points toward underlying differences in adaptive pressures on expression regulation in the nonanadromous grayling versus the anadromous Atlantic salmon. Our findings enhance our understanding of the role of WGD in genome evolution and highlight cases of regulatory divergence of Ss4R duplicates, possibly related to a niche shift in early salmonid evolution.

Assessment of the efficacy and tolerability of a fixed dose combination of atorvastatin 10 mg + metformin SR 500 mg in diabetic dyslipidaemia in adult Indian patients

Type 2 diabetes mellitus is associated with a marked increase in the risk of coronary heart disease (CHD) or stroke (by a factor of two to three compared with non-diabetic patients), and cardiovascular disease (CVD) accounts for the majority of deaths among patients with diabetes. A new fixed dose combination containing atorvastatin 10 mg + metformin SR 500 mg is being introduced in the Indian market for the treatment of dyslipidaemia in diabetic patients. The present study was therefore undertaken to assess efficacy, safety and tolerability of a fixed dose combination of atorvastatin 10mg + metformin SR 500mg in adult Indian patients with diabetic dyslipidaemia. The final protocol was approved by relevant ethics committee before the initiation of study. Informed consent was obtained from all the patients prior to enrollment in study. The total duration of study was 14 weeks including two weeks dietary run in period. Patients fulfilling the selection criteria received a single oral tablet of fixed dose combination of atorvastatin 10mg + metformin SR 500mg once daily for 12 weeks. The primary efficacy parameters were assessed by evaluating reduction in fasting and postprandial plasma glucose concentration levels at baseline and thereafter at each follow up visit at 2, 4, 8 and 12 weeks and plasma lipid profile and glycosylated Hb levels at baseline and end of study. The secondary efficacy parameters were assessed by evaluating percentage change from baseline at the end of the study (week 12) in the plasma concentration of the various lipid parameters such as total, HDL-, LDL- and very low density (VLDL)-cholesterol, triglycerides, Apo B, Apo A1, TC/LDL ratio, LDL/ HDL ratio, and percentage of patients achieving LDL-cholesterol goals as per NCEP ATP III guidelines. A total of 213 patients were enrolled in the study. Of these seven patients were lost to follow-up and considered as drop-outs. Therapy with the fixed dose combination of atorvastatin 10 mg + metformin SR 500 mg resulted in a significant reduction in the mean plasma fasting and postprandial glucose levels (35 and 38.8% respectively). There was a steep fall in the HbA1c levels from baseline levels of 8.76% to 6.74% (23.1%). There was also a significant (p < 0.05) reduction in mean total cholesterol (31.2%), LDL cholesterol (35.4%), VLDL-cholesterol (19.6%) and a significant increase HDL-cholesterol (9.5%). Thus there appeared to be trend towards reducing atherosclerosis following therapy with the fixed dose combination of atorvastatin 10 mg + metformin SR 500 mg. Mean body mass index was significantly reduced in the patients in the present study following therapy with the study drugs. The fixed dose combination of atorvastatin with metformin was well tolerated with mostly gastro-intestinal adverse events being reported in the current study. Moreover, most of the adverse events were mild to moderate in intensity and disappeared with continued treatment. In conclusion, the results of the present study suggest that, the fixed dose combination of atorvastatin 10 mg + metformin SR 500 mg is efficacious and well tolerated therapeutic modality in patients with diabetic dyslipidaemia. Furthermore this combination offers dosage convenience to the patient and by virtue of its dual mode of action is a useful addition to the therapeutic armamentarium for patients with diabetic dyslipidaemia.

Involvement of delta-aminolaevulinate synthase encoded by the parasite gene in de novo haem synthesis by Plasmodium falciparum

The malaria parasite can synthesize haem de novo. In the present study, the expression of the parasite gene for delta-aminolaevulinate synthase (Pf ALAS ) has been studied by reverse transcriptase PCR analysis of the mRNA, protein expression using antibodies to the recombinant protein expressed in Escherichia coli and assay of ALAS enzyme activity in Plasmodium falciparum in culture. The gene is expressed through all stages of intra-erythrocytic parasite growth, with a small increase during the trophozoite stage. Antibodies to the erythrocyte ALAS do not cross-react with the parasite enzyme and vice versa. The recombinant enzyme activity is inhibited by ethanolamine and the latter inhibits haem synthesis in P. falciparum and growth in culture. The parasite ALAS is localized in the mitochondrion and its import into mitochondria in a cell-free import assay has been demonstrated. The import is blocked by haemin. On the basis of these results, the following conclusions are arrived at: PfALAS has distinct immunological identity and inhibitor specificity and is therefore a drug target. The malaria parasite synthesizes haem through the mitochondrion/cytosol partnership, and this assumes significance in light of the presence of apicoplasts in the parasite that may be capable of independent haem synthesis. The Pf ALAS gene is functional and vital for parasite haem synthesis and parasite survival.

Expression for aberration coefficients using nonlinear transforms--extension to spherocylindrical surfaces

Previously we have used a matrix method to do nonlinear calculations and presented exact expressions for the third and fifth order aberration coefficients for a general conic surface as functions of the latus rectum and eccentricity. In this paper we show how the method can be extended to include the case of a general spherocylindrical surface.

Expressions for aberration coefficients using nonlinear transforms

A matrix method to do nonlinear calculations is described. This is possible only under the special condition when a transformation maps a zero vector onto a zero vector. Geometrical optics conform to this condition and hence matrix methods can be applied to calculate aberrations. Methods to reduce computational complexities using symmetry arguments are provided. The formalism is applied to study refraction by a conic surface. Aberration coefficients, up to fifth order, are obtained as functions of eccentricity and the latus rectum of the conic surface. The method can be used to model corneal aberrations.

Ray vector fields, prentice's equation, and Fourier representation of spherocylindrical lenses

AIM

To illustrate how the concept of ray vector fields can be used to demonstrate the elementary properties of thin lenses.

METHODS

Principles of matrix algebra are used.

RESULTS

Using simple geometry we give a generalization of Prentice's rule to include thick astigmatic lenses. Starting from the ray vector fields we show the connection between various representations of spherocylindrical lenses (Fourier representation, expansion in terms of the cross-cylinders). We suggest two clinical areas to which these concepts can be applied.

Ray vector fields and representation of thin spherocylindrical lenses

PURPOSE

To introduce the concept of the ray vector field and apply it to a problem in ophthalmic optics.

METHODS

Matrix and linear algebra are used to relate ray vector fields and a representation of thin spherocylindrical lenses.

RESULTS

Equations were derived relating ray vector fields and a particular coordinate system recommended previously. The method is illustrated with a simple example from ophthalmic optics, namely, addition of spherocylindrical lenses. We also illustrate the method by considering two spherocylinders separated by a distance.

CONCLUSIONS

Ray vector fields are intuitively simple and can be used to solve complex ophthalmic optics problems.