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Correlations of three-dimensional motion of chromosomal loci in yeast revealed by the double-helix point spread function microscope.

Backlund MP, Joyner R, Weis K, Moerner WE - Mol. Biol. Cell (2014)

Bottom Line: As controls, we tracked pairs of loci along the same chromosome at various separations, as well as transcriptionally orthogonal genes on different chromosomes.This relative increase has potentially important biological implications, as it might suggest coupling via shared silencing factors or association with decoupled machinery upon activation.We also found that on the time scale studied (∼0.1-30 s), the loci moved with significantly higher subdiffusive mean square displacement exponents than previously reported, which has implications for the application of polymer theory to chromatin motion in eukaryotes.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemistry, Stanford University, Stanford, CA 94305.

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Statistics of  as calculated from both time-ensemble averaging (left of dividing line) and time averaging (right of dividing line). (A, B)  as a function of τ for fixed δ = 1 s (A) and δ = 5 s (B). (C)  as a function of δ for fixed τ = 0, calculated at 1-s intervals. Error bars indicate ± SEM calculated from 10 bootstrapped samples of N track pairs. (D, E) CDFs of  for each condition for δ = 1 s (D) and δ = 5 s (E). Dashed lines give ± SEM for each bin as determined from 100 bootstrapped samples. (F, G) Scatter plots depicting relationship between early-time-averaged interlocus distance and .
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Figure 4: Statistics of as calculated from both time-ensemble averaging (left of dividing line) and time averaging (right of dividing line). (A, B) as a function of τ for fixed δ = 1 s (A) and δ = 5 s (B). (C) as a function of δ for fixed τ = 0, calculated at 1-s intervals. Error bars indicate ± SEM calculated from 10 bootstrapped samples of N track pairs. (D, E) CDFs of for each condition for δ = 1 s (D) and δ = 5 s (E). Dashed lines give ± SEM for each bin as determined from 100 bootstrapped samples. (F, G) Scatter plots depicting relationship between early-time-averaged interlocus distance and .

Mentions: We first consider the T-EAVCC version and its time dependence. Figure 4, A and B, shows the time-ensemble-averaged version of as a function of time lag τ for fixed values of δ = 1 and 5 s, respectively, for all conditions studied. Analogous plots for all δ produced by integral increments used between 1 and 10 s are shown in Supplemental Figure S5. Note that each plot consists of a positive peak at τ = 0 and decay to near zero on either side. Note that two objects undergoing uncorrelated random motion would have zero correlation at all τ. The positive peak at τ = 0 indicates that on average the velocity step occurring in the green channel at a given time is positively correlated with the velocity step occurring in the red channel at the same time. In other words, a kick of one locus is accompanied by a similar kick of the other locus around the same time, suggesting coupling between the two objects. Such behavior is not necessarily expected for two separate chromosomes; it is therefore somewhat surprising that we see a weak but significant correlation at τ = 0 even for our negative controls GAL/PES4 and GAL/RPL9A. The discernible negative-going peaks at τ = ±δ in the cross-talk data are most likely a consequence of the elasticity of the medium (see Mean-squared displacement and velocity autocorrelation section), which is a well-documented effect for bacterial chromosomal loci (Weber et al., 2010a). The deviations from zero at large /τ/ for the other conditions in Figure 4B are due to diminished averaging at these points. Note that the /τ/ at which the correlation curves decay to 0 is dependent on δ due to the inclusion of overlapping time intervals in our average.


Correlations of three-dimensional motion of chromosomal loci in yeast revealed by the double-helix point spread function microscope.

Backlund MP, Joyner R, Weis K, Moerner WE - Mol. Biol. Cell (2014)

Statistics of  as calculated from both time-ensemble averaging (left of dividing line) and time averaging (right of dividing line). (A, B)  as a function of τ for fixed δ = 1 s (A) and δ = 5 s (B). (C)  as a function of δ for fixed τ = 0, calculated at 1-s intervals. Error bars indicate ± SEM calculated from 10 bootstrapped samples of N track pairs. (D, E) CDFs of  for each condition for δ = 1 s (D) and δ = 5 s (E). Dashed lines give ± SEM for each bin as determined from 100 bootstrapped samples. (F, G) Scatter plots depicting relationship between early-time-averaged interlocus distance and .
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Related In: Results  -  Collection

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Figure 4: Statistics of as calculated from both time-ensemble averaging (left of dividing line) and time averaging (right of dividing line). (A, B) as a function of τ for fixed δ = 1 s (A) and δ = 5 s (B). (C) as a function of δ for fixed τ = 0, calculated at 1-s intervals. Error bars indicate ± SEM calculated from 10 bootstrapped samples of N track pairs. (D, E) CDFs of for each condition for δ = 1 s (D) and δ = 5 s (E). Dashed lines give ± SEM for each bin as determined from 100 bootstrapped samples. (F, G) Scatter plots depicting relationship between early-time-averaged interlocus distance and .
Mentions: We first consider the T-EAVCC version and its time dependence. Figure 4, A and B, shows the time-ensemble-averaged version of as a function of time lag τ for fixed values of δ = 1 and 5 s, respectively, for all conditions studied. Analogous plots for all δ produced by integral increments used between 1 and 10 s are shown in Supplemental Figure S5. Note that each plot consists of a positive peak at τ = 0 and decay to near zero on either side. Note that two objects undergoing uncorrelated random motion would have zero correlation at all τ. The positive peak at τ = 0 indicates that on average the velocity step occurring in the green channel at a given time is positively correlated with the velocity step occurring in the red channel at the same time. In other words, a kick of one locus is accompanied by a similar kick of the other locus around the same time, suggesting coupling between the two objects. Such behavior is not necessarily expected for two separate chromosomes; it is therefore somewhat surprising that we see a weak but significant correlation at τ = 0 even for our negative controls GAL/PES4 and GAL/RPL9A. The discernible negative-going peaks at τ = ±δ in the cross-talk data are most likely a consequence of the elasticity of the medium (see Mean-squared displacement and velocity autocorrelation section), which is a well-documented effect for bacterial chromosomal loci (Weber et al., 2010a). The deviations from zero at large /τ/ for the other conditions in Figure 4B are due to diminished averaging at these points. Note that the /τ/ at which the correlation curves decay to 0 is dependent on δ due to the inclusion of overlapping time intervals in our average.

Bottom Line: As controls, we tracked pairs of loci along the same chromosome at various separations, as well as transcriptionally orthogonal genes on different chromosomes.This relative increase has potentially important biological implications, as it might suggest coupling via shared silencing factors or association with decoupled machinery upon activation.We also found that on the time scale studied (∼0.1-30 s), the loci moved with significantly higher subdiffusive mean square displacement exponents than previously reported, which has implications for the application of polymer theory to chromatin motion in eukaryotes.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemistry, Stanford University, Stanford, CA 94305.

Show MeSH
Related in: MedlinePlus