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Finis coronat opus
(The end crowns the work.)
________________________- Roman Proverb
This thesis has demonstrated how modelling of self assembling nanometre-scale structures can be achieved. It has outlined the basics of the physical chemistry required, shown a design for a computer simulation program, implemented that program, and used it to simulate a wide variety of biological systems.
The basic theory required to build a nanoscale simulator was discussed in chapter 5. The standard mathematical background to the relevant physical chemistry was covered, along with a discussion of various heuristics that can be used to calculate required details such as the approximate moment of inertia of aggregates of arbitrary shape and size, the rotational behaviour of such aggregates, and the required steps to model Brownian motion and collisions in a computationally non-intensive manner.
In addition, the concepts of protein states and events were introduced, with a discussion of how a computer program might be able to model these features. The various difficulties that must be overcome when translating such theory to a computer program were discussed, such as handling boundary conditions, and the difficulty of simulating large numbers of particles.
A general purpose program implementing the basic theory was created, and is described in Chapter 6. The program must handle a myriad of details, ranging from correct modelling of the theory covered in Chapter 5, through to a large number of purely programmatic details.
Modelling the theory correctly required many mathematical classes to be implemented, including classes for manipulating vectors and matrices. Also required were a large number of data structures for storing, and allowing fast access to, the many physical attributes of the simulated structures.
More difficult than the above was implementing the complex data structures required to represent the objects. The program accesses its simulated proteins in a variety of ways. Sometimes it searches for them by spatial position, which required a 3-D grid data structure. Sometimes it accesses them linearly, requiring them to be kept in a list. Sometimes they are accessed through the transient aggregates they form as they are incorporated into, or expelled from, growing clumps of objects. Since the simulator implements not a static, but a dynamic model, every protein was a small finite state machine, which requires the program to track the state of each protein, in addition to physical position and mechanical properties. The program must also change this state appropriately when specified events occur, such as the collisions that are also monitored.
It was demonstrated that the simulation was consistent with the experimental results obtained for the well understood self-assembling protein actin. The results of Chapter 7 showed the same broad behaviour as is predicted for actin, with polymerisation curves of both the entire simulated volume, and individual actin filaments, behaving as expected. The relatively small number of actin monomers simulated (thousands, rather than thousands of millions), however, meant that bulk comparison was not possible.
Results were also obtained for the more controversial protein tubulin. This was a difficult area of simulation, and two popular models were demonstrated, without a firm decision of which was preferable being reached. The power of the nanosim program was shown, however, in the relative ease with which different models could be trialed, without any necessity to rewrite program code, but simply by modifying the text file (the .pddf file) passed to the program.
To show the breadth of possibilities for the simulator, a number of other (abstracted) self-assembling structures were also demonstrated. Systems such as two-dimensional crystals, three-dimensional crystals, and various simple platonic solids were shown to be easily reproduced by the program.
In addition to these, an attempt was made to model a large, non-trivial system. A virus model, consisting of four distinct protein capsid types, was demonstrated to be able to self-assemble into intact viral capsids. This is an important result, demonstrating that the program can handle heterogenous populations of protein objects with large numbers of links. It also highlighted the difficulty of constructing such complex models by hand, because implementing the virus required a great deal of hand calculation and a very long .pddf file. For future work, a more human-friendly method of creating these data files will be required.
Finally, it was shown how this technique of simulating nanoscale proteins can be extended even further by combining it with other simulation techniques such as image processing and 3-D modelling. Some results of such techniques were presented in Chapter 10, along with an investigation of 'virtual electron micrographs', which attempt to process a 3-D model in an equivalent manner to how a biological structure would be viewed by an electron microscope.
These 'virtual micrographs' were used to study a large, pre-assembled biological structure, the plasmodesmata found in plant cell walls, as well as pre-prepared models of large structures such as actin filaments or microtubules. 'Virtual micrographs' were shown both of raw 3-D models, and of models where the nanosimulator was used to model the deposition of stain.
Although the technique is still in its infancy, it provided some interesting results, and may reward further investigation as another instrument in the scientific modeller's toolkit.
Some limitations of the current approach were discussed, the primary difficulty being obtaining hard data on the behaviour of the inter-protein links, especially the behaviour of multiple links. This is an area that would reward further work, and a more rigorous modelling of the inter-protein interactions would improve the accuracy of the simulation, as would more detailed experimental data.
Despite some limitations, the predictive power and wide scope of this technique show great promise as a tool for both experimentalists and theoreticians grappling with the difficulties of understanding the low level behaviour of proteins and other nanometre-scale objects. Possible beneficiaries include not only biologists, but potentially workers in such disparate fields as medical technology, geology, chemistry, materials engineering, and of course the emerging field of nanotechnology.
It may also be useful as a low-cost 'virtual laboratory' for researchers to trial new techniques, new drugs, and new theories, without the expense in time and materials of lab work. In the same role of 'virtual laboratory' it may be a powerful tool for teaching and learning, allowing students and researchers to interact with virtual molecules, obtaining a more intuitive understanding of the processes involved.
In general, the applications of a computer simulation of this type have a remarkably wide scope for the study of biological systems. Although a variety of simulation techniques have been used on an atomic and molecular level for some time, no equivalent set of tools exists for the protein biologist studying 'large' structures. It is hoped that this thesis may provide a step along the path to producing such simulations, which may, at some stage in the future, reach the ultimate goal of being able to simulate at the protein level all the biological processes necessary to create a 'virtual cell'.
There are a large number of possibilities for extending this program, and this approach in general. This section briefly lists some of the opportunities that exist to use and extend the nanosimulator.
The simulator might be extended to cover a wider range of self-assembling systems. There are a large number of biological systems that might benefit from simulation in this way. The technique could be expanded to cover other self-assembling structures such as membranes, and with the future addition of conformational state changes, might even be used to simulate cellular machinery such as the actin-myosin motor. It is hoped that other researchers will benefit from, and extend, this program, and will be able to use and improve the theoretical techniques it is based upon. The "nanosim" nanoscale simulation program has been deliberately made quite generic, and new proteins and structures can be simulated simply by altering the text-based data files that the program reads in when it first starts operating (Appendix B).
Some benefits might be obtained by modelling the effect of various medicinal chemicals on the growth of biological aggregates. Some anti-virus drugs attempt to inhibit or modify the construction of the viral protein coat. Using the simulator it may be possible to test small modifications to the binding sites of such drugs to determine the most efficient way of disrupting the coat construction. Similarly, several chemicals affect the growth of microtubules, such as colchicine, nocodazole and taxol, most of which are derived from various plants. Since microtubules play an important role in cell division, and hence in the growth of cancerous cells, the less toxic drugs of this type, such as vinblastine (1), and taxol varients (2) are used in cancer treatment. Drugs like these that affect the cytoskeleton might also be usefully modelled using the simulator.
The program and .pddf file structure has been designed with the intention of including changes in the shape of objects, and changes in the positioning of linkage sites, as the objects change state. This would allow more accurate simulation of systems such as the fraying ends of microtubules, and other systems that involve motile components, possibly extending to dynamic protein systems such as actin-myosin complexes (3), or possibly structures such as ionophores and membrane transport carrier proteins. In fact, being able to model motile proteins would allow a very wide field of study to be simulated, with a huge range of biological processes being amenable to this approach.
The simulator could be extended by including movement within bound aggregates: at the moment they are completely rigid, which is physically unrealistic. Including internal motion might also allow the simulation of bending and internal stress in a structure. A more elaborate simulation of the internal dynamics of objects might also be able to model periodic oscillations or waves that may occur in some structures.
The simulator has taken a very high level, abstracted view of the binding process between objects. But there is no reason why a more sophisticated and detailed interaction model could not be incorporated. Ideally this binding code would be separated into a separate class, which could be rewritten by researchers without reference to the rest of the program.
Some features that might be dealt with in more detail by such a model could be:
The nanoscale simulator can be improved programmatically in a number of ways. For example:
It is a straightforward task to improve the reporting from the program on the state of individual aggregates. Internally, the nanosimulator tracks each aggregate very closely, and this data could be easily output to files. But the gigabytes of data that would be produced would require some processing to make this a useful exercise. Currently a small sample gives the histories of just a few randomly selected aggregates - a more extensive data set could produce more interesting statistical information on the model, as well as track unusual events which might reveal either errors in the model, or interesting insights into the modelled process.
The idea of miniature, nanometre scale machines has been an ideal pursued by researchers for some time. Recent experiments have shown the possibility of manipulating individual atoms, while others have been able to use some of the protein structures mentioned in this thesis, such as actin filaments and microtubules, to move very small objects. In order to design and build such tiny systems, computer simulation similar to that presented in this thesis will be required, that is capable of modelling the laws of physics at the intermediary level between quantum and classical mechanics. This will be especially true with nanomachines operating in liquids, such as the medical devices which are the grail of some researchers in this embryonic field.
A simulator of this sort can be useful in providing a conceptual framework for students (and researchers!) to understand the motion of proteins in solution, and to provide insight into the types of reactions they undergo. Concepts such as diffusion, Brownian motion, and self-assembly can be demonstrates, and in the future more complex subjects such as the action of motile proteins could be reproduced, e.g. myosin-actin, microtubule-kinesin and microtubule-dynein motors.
Some highly speculative, but intriguing, models have been proposed wherein simple "game of life" style computation is done using the regular structure of microtubules (4). Using and extending the state model within the nanosimulator, it should be possible to model such hypothesised activity as state changes within the microtubule lattice. This could be seamlessly combined with the traditional modelling of assembly and disassembly, and interactions between the two processes modelled.
It is planned to make the program and these results publically available (the raw code is available at http://www.cs.monash.edu.au/~cbetts/phd/code/index.html, while the rest of the work will be made available online as soon as possible). It is hoped that the ideas presented in this thesis, combined with the generic object-oriented architecture of the program, will make it possible for others to use and extend it. It would give the author great pleasure if, in ten years time, the program was still in use, although not a single line of the original code remained.
As we attempt to understand the world around us, at scales from the gigantically large to the infinitesimally small, computers are playing a larger and larger role in aiding that understanding. This thesis is a first step in providing a computerised tool for understanding the intriguing behaviour of biological systems at the level lying between quantum and classical mechanics, the nanoscale world.
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1. Amos, L.A. and Amos, W.B. (1991) Molecules of the Cytoskeleton, Macmillan, London, p 130.
2. Nicolaou, K.C., Rodney, K.G. and Potier, P. (1996) Taxoids: New Weapons against Cancer, Sci. Am. Vol 274, No. 6, pp 84-88
3. Amos & Amos op. cit.
4. Hammeroff, S. and Watt, R. (1982) Information processing in microtubules, J. Theor. Biol, Vol 98, 549-562