Spatio-temporal modelling is the emerging approach to the analysis of pro- tein transport and targeting processes. Much of our biological knowledge of protein targeting comes from inherently non-spatialin vitrobiochemical
Figure 1.1: Chloroplast import and targeting pathways. Immature forms of chloroplast proteins are shown at the top, outside the chloroplast, and labelled with their functional destinations. The transit peptides are shown as grey bars and these allow entry to the chloroplast by the translocons at the inner and outer chloroplast envelopes (the Toc and Tic complexes). The stromal processing peptidase is shown as scissors cleaving the grey transit peptide. Various methods of membrane protein insertion into the inner and outer envelopes are shown, and a protein destined to reside in the stroma is depicted as folded on entry. The four thylakoid-related pathways are shown with the Sec and Tat pathways for lumenal proteins, and the SRP and spontaneous pathways for thylakoid membrane proteins. The Sec signal peptide is shown in light blue to match the Sec translocase; and the Tat signal peptide is shown in red to match the Tat translocase. Both the Sec and Tat signal peptides are cleaved by the lumenal thylakoid processing peptidase shown as scissors. The SRP pathway is shown as a GTP-dependent pathway. Figure reproduced from Current Biology (Jarvis and Robinson,2004).
Figure 1.2: Citation relationship for Tat and fluorescent proteins. Current analyses are static rather than dynamic. In contrast to some areas of biology, there has been no attempt at spatial modelling and simulation for the Tat pathway and this is a key motivation for the current work.
Clark and Theg(1997) Transport of folded protein
Chaddock et al.(1995) Twin-arginine motif
Mould et al.(1991b) Stromal requirement in thylakoid import
Spence et al.(2003) Synechocystis PCC6803 Tat-targeted GFP Mullineaux et al.(2006) GFP diffusion in E. coli Marques et al.(2004) Chloroplast Tat-targeted GFP Marques et al.(2003) Chloroplast Tat-targeted GFP Thomas et al.(2001) E. coli Tat-targeted GFP
Mould and Robinson(1991) Proton motive force in thylakoid import
di Cola and Robinson(2005) Tat translocation reversal
Table 1.1: Fluorescence mobility and photobleaching techniques. New techniques and novel modifications of old techniques are developed to tackle a specific biological application before further refinement and dis- cussion of wider applications. The work presented in this thesis is an ex- ample of an application-driven employment and adaptation of techniques with a greater emphasis on spatial inhomogeneity in protein targeting.
Name Distinguishing features Reference(s)
(unnamed) observation of fluorophore Frye and Edidin(1970)
intermixing
Fluorescence bleach region of varied Peters et al.(1974); recovery after sizes and shapes Lopez et al.(1988) photobleaching
(FRAP)
Fluorescence spot bleach, resolving flow Axelrod et al.(1976) photobleaching and diffusion processes
recovery (FPR)
Continuous prolonged spot bleaching Peters et al.(1981) fluorescence
microphotolysis (CFM)
Fluorescence fluorescence loss outside Cole et al.(1996) loss in bleach region measured
photobleaching (FLIP)
Line-scanning line bleaching and Wedekind et al.(1996) microphotolysis monitoring for high
Table 1.2: Photobleaching analysis and determination of mobility. There is an emphasis on deriving numbers, some with and some without intervals to indicate the uncertainty, as the final output of the analysis. The nature of our experimental system requires us to take a more explorative approach rather than deriving a number from some lesser, as low as three, or greater number of data points.
Approximation Reference(s)
Spherical diffusion and Peters et al.(1974) Legendre polynomials expansions
2D planar diffusion, Axelrod et al.(1976) three point fitting,
and scaling of variables
Uniform circular Soumpasis(1983) laser beam
Analytical solutions Lopez et al.(1988) and finite differences
Constrained diffusion Feder et al.(1996)
3D finite difference Kubitscheck et al.(1998) and line-scanning
Table 1.3: Continuous photobleaching – selected articles. The technique of continuous photobleaching makes a measurement in a small part of a particular sample, so care must be taken when the sample is highly inho- mogeneous and the measurement at one location may not be representative of other locations or other samples.
Title Reference
Continuous fluorescence microphotolysis: Peters et al.(1981) a sensitive method for study of
diffusion processes in single cells.
Analyzing intracellular binding and Wachsmuth et al.(2003) diffusion with continuous
fluorescence photobleaching.
Derivation of a closed form analytical Endress et al.(2005) expression for fluorescence recovery
after photo bleaching in the case of continuous bleaching during read out.
Continuous photobleaching in vesicles Delon et al.(2006) and living cells: a measure of
diffusion and compartmentation.
Continuous fluorescence microphotolysis Arkhipov et al.(2007) and correlation spectroscopy using
methods such as the finite difference and finite element methods. For our simulations later, we will make use of the reported diffusion coefficients shown in table1.4although we keep in mind that many such results rely on methods developed for expedience: an example being curve fitting methods using a small numbers of graph points. Some of the concerns and recommendations regarding assumptions made in expedient methods are shown in table1.5.
We point out a selection of the more sophisticated biological spatial simulations in table1.6which includes the use of a particle-based method that is of the same class of methods that we will employ.