Robert Ransom

A topological model of cell division: structure of the computer program.

The general structure of a computer program (CD3D) simulating division in a sheet of cells is presented. The program is based on a topological representation of cell division previously developed by the authors, and the biological background to the model is discussed. The computer modelling of the various elements of the model (i.e. vertices, edges and meshes) is described, and an annotated description of the subroutines making up the program is given in an Appendix. Although the program and model are specifically designed to represent cell division processes, the graph framework may have applicability in other biological subject areas where dynamic relationships between elements are involved.

Simulation and Animation

If you have read through the earlier chapters of this book you will have already learnt many of the fundamental techniques of graphics programming. Some of these techniques involve the most straightforward kinds of movement of graphic data: transformations like rotation, scaling, and translation. You have seen for example in Chapter 10 that application of rotations in real-time can give a dynamic picture of the structure of molecules. The present chapter will consider the general question of how movement of graphic images can be carried out in real-time. Examples of both research simulations and animations suitable for teaching purposes will be discussed with reference to a number of different graphics systems.

Computer Graphics in Biology

1. An Introduction to Computer Graphics.- 1.1 The beginnings of computer graphics.- 1.2 What is computer graphics?.- 1.3 Computer graphics and biology.- 1.4 The elements of a computer graphics system.- 1.5 Computer graphics in perspective.- 1.6 References.- 2. Graphics Hardware.- 2.1 An overview.- 2.2 Input devices.- 2.3 Display devices.- 2.4 Display processors.- 2.5 The computer.- 2.6 References and bibliography.- 3. Graphics Software.- 3.1 Connecting computers and graphic devices.- 3.2 Graphics software packages.- 3.3 Graphics packages on mini computers and mainframe computers.- 3.4 Microcomputer graphics software.- 3.5 Graphics workstations.- 3.6 The applications program.- 3.7 References and bibliography.- 4. Two-dimensional Graphics.- 4.1 The elements of two-dimensional transformations.- 4.2 Representation of points.- 4.3 Straight line transformations.- 4.4 Rotation.- 4.5 Reflection.- 4.6 Multi-operation transformations (composition).- 4.7 Two-dimensional homogeneous coordinates.- 4.8 Two-dimensional rotation about an arbitrary axis.- 4.9 References.- 5. Three-dimensional Graphics.- 5.1 Basic concepts.- 5.2 Three-dimensional homogeneous coordinates.- 5.3 Three-dimensional scaling.- 5.4 Three-dimensional shearing.- 5.5 Three-dimensional rotations.- 5.6 Reflection in three dimensions.- 5.7 Three-dimensional translation.- 5.8 Three-dimensional rotation about an arbitrary axis.- 5.9 Projections.- 5.10 Conclusions.- 5.11 References.- 6. Hidden Lines and Hidden Surfaces.- 6.1 An introduction to hidden lines and surfaces.- 6.2 A simple hidden lines algorithm.- 6.3 The Galimberti and Montanari algorithm.- 6.4 The hidden surface problem.- 6.5 A preliminary classification.- 6.6 Surface representation and hidden surface methods.- 6.7 Conclusions.- 6.8 References and bibliography.- 7. Graphical Representation of Biological Data.- 7.1 Introduction.- 7.2 Graphs and histograms.- 7.3 Point plots and transforms.- 7.4 Graphics data structures.- 7.5 A data structure for hidden lines treatment.- 7.6 References.- 8. Reconstruction Methods for Cell Systems.- 8.1 Tissue reconstruction.- 8.2 The role of computer graphics.- 8.3 Input of data.- 8.4 Two-dimensional analyses.- 8.5 Three-dimensional reconstruction.- 8.6 Three-dimensional reconstruction of neurones (CELL).- 8.7 Three-dimensional reconstruction of non-neural tissue (RECON).- 8.8 Other three-dimensional reconstruction programs.- 8.9 References and bibliography.- 9. Image Capture and Image Analysis.- 9.1 Biological images.- 9.2 Image capture devices.- 9.3 Analysis of periodic images.- 9.4 The Joyce-Loebl Magiscan.- 9.5 Reconstruction from X-ray data.- 9.6 References and bibliography.- 10. Molecular Graphics.- 10.1 An introduction to molecular graphics.- 10.2 Components of a molecular graphics system.- 10.3 Molecular data.- 10.4 Examples of molecular graphics packages.- 10.5 Some existing systems.- 10.6 References and bibliography.- 11. Simulation and Animation.- 11.1 Moving pictures.- 11.2 Hardware for real-time animations.- 11.3 Concepts of graphic animation.- 11.4 Dynamic graph construction.- 11.5 Simulation of cell division and cell interaction processes.- 11.6 Animation of genetic events.- 11.7 References and bibliography.- Appendix 1: Matrix Manipulations.- A1.1 Basic definitions.- A1.2 Vectors.- A1.3 Matrix addition.- A1.4 The trace of a matrix.- A1.5 The determinants of a matrix.- A1.6 Multiplication by a scalar.- A1.7 Matrix multiplication.- A1.8 References.- Appendix 2: A Graphics Glossary.

Quantitative analysis of ventral denticular patterns of Drosophila melanogaster larvae and the regulation of the bithorax complex

A quantitative model of the effect of the bithorax complex on segmentation is presented which could explain the known data of the spatiotemporal regulation of key gene complex during early Drosophila development, in relation to their effects on some of the segmentation landmarks. The model tries to put together the two different genetic levels, the genotypic and the phenotypic. At the genotypic level, a minimal cross-regulatory network of the different genes involved, Antp, Ubx, abd-A and Abd-B which explains the reported levels of expressions of these genes. At the phenotypic level, the pattern of the ventral denticle belts across the larva which are characteristics of the different segments have been compared by calculating a value of the degree of similarity in the case of the wild-type and several mutant combinations. Finally the two parts of the model are combined, showing that a satisfactory agreement between the two can be achieved. Therefore, this work is a first attempt to develop a method which will provide an explanatory solution of the old question in morphogenesis of how the phenotype is directed by the genotype of a cell or organism.

Image Capture and Image Analysis

We saw in the last chapter that computer graphics has been widely used in the reconstruction of sectioned biological material. A prerequisite of this type of analysis is that individual elements should be identifiable on the sections for digitization. Often, however, this kind of analysis is not feasible: the complexity of the data may preclude digitization altogether, for example, and in many cases the computer analysis is itself needed to work out the two-dimensional structure of the section.

Graphical Representation of Biological Data

We have looked at the manipulation of two and three-dimensional data in the last three chapters, concentrating mainly on general methodologies. We will now turn to consider specific biological applications of computer graphics. The present chapter deals with aspects of simple data manipulation, while Chapters 8 to 11 are concerned with areas of specific applications.

Reconstruction Methods for Cell Systems

It is often difficult to analyse biological material at the level of the whole, be it whole organism, whole organ or whole tissue. If subcellular or cellular patterns are to be studied, the relationships of organelles or cells must be considered. Various methods exist for separating components: at the ultrastructural level centrifugation may be used, and at a higher level microdissection is often possible. There are several problems inherent in the use of these methods.

An Introduction to Computer Graphics

In the early days of computing, computer graphics were a novelty rather than a necessity. Part of the reason for this was the very restricted amount of memory available on the first computers, but of course the graphics devices that could be used were few and far between. Early in the 1950s the Whirlwind computer was used to produce simple line drawings using a cathode ray tube display, and the SAGE air defence system also used CRT (cathode ray tube) displays on which the operators pointed at images using light pens. It was not until 1963 that computer graphics really came of age. In that year, the MIT student Ivan Sutherland published the results of his PhD thesis entitled Sketchpad: A Man-Machine Graphical Communication System (Sutherland, 1963). The fundamental ideas developed by Sutherland have formed the basis of much of the interactive computer graphics in use today.

Hidden Lines and Hidden Surfaces

In general the objects that are manipulated in three-dimensional graphics can be classified into two groups: wire frame and true solids. In the wire frame group the objects are described in terms of sets of lines, and in the solid group the objects would be described in terms of surfaces with well-defined properties. While both groups of objects are quite distinct visually, they do share common problems: the removal of unwanted lines and/or surfaces respectively.

Three-dimensional Graphics

In Chapter 4 we considered the basic transformations that are available to us for manipulating planar figures. We now enter the realm of three-dimensional objects in three-dimensional space. This chapter is primarily concerned with the transformations which are applicable to these objects. While most of the information that we discussed in Chapter 4 is relevant to the three-dimensional case, there are substantial differences. These differences arise mainly through the addition of a third axis (at right angles to the existing two). The transformations are similar, but the complexity has increased.