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Bacterial secretion and the role of diffusive and subdiffusive first passage processes.

Marten F, Tsaneva-Atanasova K, Giuggioli L - PLoS ONE (2012)

Bottom Line: By funneling protein effectors through needle complexes located on the cellular membrane, bacteria are able to infect host cells during type III secretion events.As a result, theoretical predictions of secretion times are still lacking.Here we provide a model that quantifies, depending on the transport characteristics within bacterial cytoplasm, the amount of time for a protein effector to reach either of the available needle complexes.

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering Mathematics, University of Bristol, Bristol, United Kingdom.

ABSTRACT
By funneling protein effectors through needle complexes located on the cellular membrane, bacteria are able to infect host cells during type III secretion events. The spatio-temporal mechanisms through which these events occur are however not fully understood, due in part to the inherent challenges in tracking single molecules moving within an intracellular medium. As a result, theoretical predictions of secretion times are still lacking. Here we provide a model that quantifies, depending on the transport characteristics within bacterial cytoplasm, the amount of time for a protein effector to reach either of the available needle complexes. Using parameters from Shigella flexneri we are able to test the role that translocators might have to activate the needle complexes and offer semi-quantitative explanations of recent experimental observations.

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Dependence of the GMFPT , expressed in seconds, as function of the number  equidistant circular targets on the boundary with two different radius  of the initial localization area : the extreme case when  and when , where  is the disk radius.Panels A and C represent the  case, corresponding to an effector that starts at the origin, whereas panels B and D correspond to an initial particle localization being anywhere inside the bacterium. Each of the panels shows the GMFPT as function of  for four choices of target radius  = 10, 50, 100 and 150 Å (line colour, see legend in panel A). The black curves represent a limiting case in which the entire boundary of the domain is a target; i.e.  becomes the average time required to arrive at the boundary. In the top row we have considered the ‘fast’ model with m/s, whereas the bottom row displays results for the ‘slow’ model with m/s. In all four panels m.
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pone-0041421-g004: Dependence of the GMFPT , expressed in seconds, as function of the number equidistant circular targets on the boundary with two different radius of the initial localization area : the extreme case when and when , where is the disk radius.Panels A and C represent the case, corresponding to an effector that starts at the origin, whereas panels B and D correspond to an initial particle localization being anywhere inside the bacterium. Each of the panels shows the GMFPT as function of for four choices of target radius  = 10, 50, 100 and 150 Å (line colour, see legend in panel A). The black curves represent a limiting case in which the entire boundary of the domain is a target; i.e. becomes the average time required to arrive at the boundary. In the top row we have considered the ‘fast’ model with m/s, whereas the bottom row displays results for the ‘slow’ model with m/s. In all four panels m.

Mentions: where , and . The -dependence of the GMFPT is dominated by the last term in Eq. (2), which is much larger than the term with the -summation. For one can show numerically that this second term in Eq. (2) becomes constant. This inverse proportionality with of the GMFPT can be clearly observed in Fig. 4 where is plotted as function of for different values of target radii and for diffusion coefficient m/s (top panels) and diffusion coefficient m/s. The left and right panels represent the two extreme cases of initial localization: with on the left and on the right, the former implying an initial condition at the center of the disk, whereas the latter implying that the initial condition could be from anywhere within the disk. Although the GMFPT in Fig. 4B and 4D changes rapidly between and targets, if the number of targets is increased above this range, slowly decays to a limit where the entire domain boundary is a target (black curve). We also find that in the range there is little difference between the values of for and (compare Fig. 4B and Fig. 4D). Hence in a disk with less than 10 targets, the initial effector location does not play much of a role: the average time to arrive at any of the targets is roughly the same. We also notice that even in the case of one very small ( = 10 Å) target, reaching a needle complex seems to occur rather rapidly as a particle requires less than 0.7 seconds on average to reach the small target.


Bacterial secretion and the role of diffusive and subdiffusive first passage processes.

Marten F, Tsaneva-Atanasova K, Giuggioli L - PLoS ONE (2012)

Dependence of the GMFPT , expressed in seconds, as function of the number  equidistant circular targets on the boundary with two different radius  of the initial localization area : the extreme case when  and when , where  is the disk radius.Panels A and C represent the  case, corresponding to an effector that starts at the origin, whereas panels B and D correspond to an initial particle localization being anywhere inside the bacterium. Each of the panels shows the GMFPT as function of  for four choices of target radius  = 10, 50, 100 and 150 Å (line colour, see legend in panel A). The black curves represent a limiting case in which the entire boundary of the domain is a target; i.e.  becomes the average time required to arrive at the boundary. In the top row we have considered the ‘fast’ model with m/s, whereas the bottom row displays results for the ‘slow’ model with m/s. In all four panels m.
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Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3412870&req=5

pone-0041421-g004: Dependence of the GMFPT , expressed in seconds, as function of the number equidistant circular targets on the boundary with two different radius of the initial localization area : the extreme case when and when , where is the disk radius.Panels A and C represent the case, corresponding to an effector that starts at the origin, whereas panels B and D correspond to an initial particle localization being anywhere inside the bacterium. Each of the panels shows the GMFPT as function of for four choices of target radius  = 10, 50, 100 and 150 Å (line colour, see legend in panel A). The black curves represent a limiting case in which the entire boundary of the domain is a target; i.e. becomes the average time required to arrive at the boundary. In the top row we have considered the ‘fast’ model with m/s, whereas the bottom row displays results for the ‘slow’ model with m/s. In all four panels m.
Mentions: where , and . The -dependence of the GMFPT is dominated by the last term in Eq. (2), which is much larger than the term with the -summation. For one can show numerically that this second term in Eq. (2) becomes constant. This inverse proportionality with of the GMFPT can be clearly observed in Fig. 4 where is plotted as function of for different values of target radii and for diffusion coefficient m/s (top panels) and diffusion coefficient m/s. The left and right panels represent the two extreme cases of initial localization: with on the left and on the right, the former implying an initial condition at the center of the disk, whereas the latter implying that the initial condition could be from anywhere within the disk. Although the GMFPT in Fig. 4B and 4D changes rapidly between and targets, if the number of targets is increased above this range, slowly decays to a limit where the entire domain boundary is a target (black curve). We also find that in the range there is little difference between the values of for and (compare Fig. 4B and Fig. 4D). Hence in a disk with less than 10 targets, the initial effector location does not play much of a role: the average time to arrive at any of the targets is roughly the same. We also notice that even in the case of one very small ( = 10 Å) target, reaching a needle complex seems to occur rather rapidly as a particle requires less than 0.7 seconds on average to reach the small target.

Bottom Line: By funneling protein effectors through needle complexes located on the cellular membrane, bacteria are able to infect host cells during type III secretion events.As a result, theoretical predictions of secretion times are still lacking.Here we provide a model that quantifies, depending on the transport characteristics within bacterial cytoplasm, the amount of time for a protein effector to reach either of the available needle complexes.

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering Mathematics, University of Bristol, Bristol, United Kingdom.

ABSTRACT
By funneling protein effectors through needle complexes located on the cellular membrane, bacteria are able to infect host cells during type III secretion events. The spatio-temporal mechanisms through which these events occur are however not fully understood, due in part to the inherent challenges in tracking single molecules moving within an intracellular medium. As a result, theoretical predictions of secretion times are still lacking. Here we provide a model that quantifies, depending on the transport characteristics within bacterial cytoplasm, the amount of time for a protein effector to reach either of the available needle complexes. Using parameters from Shigella flexneri we are able to test the role that translocators might have to activate the needle complexes and offer semi-quantitative explanations of recent experimental observations.

Show MeSH
Related in: MedlinePlus