(A) Close-up and (B) full network analysis of vein radius dynamics and associated shear rate in P. polycephalum. (i) Bright-field images of reorganizing specimens allow us to record vein dynamics. (i…
(A) Principle of the cross-correlation in time between the delayed time-averaged shear rate and the time-averaged radius change . The plot shows the delayed curve with the best score. (B) …
(A) Translation of (i) a bright field image of specimen into (ii) vein networks; each vein is modeled as a flow circuit link. (iii) Reduction of (ii) via Northon’s theorem into an equivalent and …
Full network maps of the same specimen as in Figure 1B, at the beginning of the observation, of (A) the average fluid pressure in a vein and (B) of the relative resistance . The fluid pressure is defined up to an additive constant. Grey veins in (B) correspond to bottleneck veins or dangling ends for which can not be defined. The color scales indicate the magnitude of each variable in each colored vein. For example, in (B), the red arrow indicates a vein with large relative resistance .
(A–C) (i) determining factors mapped out from experimental data for the specimen of Figure 1B and (ii) typical trajectories from data. All pink (respectively blue) arrows indicate shrinking …
(A) Time series of network reorganization. Each vein is colored according to the ratio between the resistance of an individual vein and the rest of the network in each vein. Red arrows …
(A) Time zoom of a close-up data set (that of Figure 1A.iii, #K) showing the doubling of the frequency of the shear rate compared to the radius. (B) Minimal model example with short timescale and …
The letters indicate the data set names, and are used consistently throughout the manuscript. Typical classification of vein dynamics is indicated for each plot.
The veins shown are chosen randomly but distributed throughout the network. The network sketch on the right hand side shows circles indicating at their center the location of each vein, with …
(A - B) Bright field images of a specimen with long time dynamics of vanishing veins, specimen 2. (c) Mean shear rate , (D) pressure and (E) relative resistance at the initial stage. (F) …
(A–B) Bright field images of a specimen with long time dynamics of vanishing veins, specimen . (c) Mean shear rate , (D) pressure and (E) relative resistance at the initial stage. (F) Time …
We also present maps of the connected resistance in (C) and of the vein outflow in (F). The color scales indicate the magnitude of each variable in each colored vein. All cross-correlations …
(A) Time delays measured without extracting trends from data (same plot as Figure 2C but without extracting trends). (B) Extracting the time delay for model data with (i) model data and extracted …
Distribution of best time delays for all veins in the network (#1, with about 10,000 vein segments and #2 and #3, both of which have about 30,000 vein segments). (insets). Network maps – not to scale.
(Left hand side) Time-averaged shear rate (red) and radius change () with time for each vein (#E, #F, #G, #K), as well as time delayed shear right producing the best cross correlation . …
In the left column the distribution of the obtained time delays using Equation 1 and Equation 2 over a distribution of time windows is depicted. To obtain time windows of approximately constant …
The obtained fit parameters are reported in Appendix 2—table 2. All shear rate and radius data presented is time-averaged.
The corresponding fitted parameters are reported in Appendix 2—table 3. The vein positions correspond to those indicated in Appendix 1—figure 3.
The networks are different in all cases except networks D-E-F are the same. D-E-F differ in which vein is under scrutiny. For each case, equivalent resistances of the rest of the network relative …
Frame sequence: 5 frames at 600 ms and 1 frame at 2.5 s. Scale 0.353 μm/pix.
Frame sequence: 5 frames at 600 ms and 1 frame at 5 s. Scale 0.25 μm/pix.
Frame rate 6 s and scale 5.03 μm/pix.
Frame sequence: 5 frames at 60 ms and 1 frame at 5 s. Scale 0.574 μm/pix.
Frame sequence: 5 frames at 60 ms and 1 frame at 2.5 s. Scale 0.48 μm/pix.
Frame sequence: 5 frames at 60 ms and 1 frame at 2.5 s. Scale 0.408 μm/pix.
Frame sequence: 5 frames at 600 ms and 1 frame at 2.5 s. Scale 0.25 μm/pix.
Frame sequence: 5 frames at 60 ms and 1 frame at 2.5 s. Scale 1.06 μm/pix.
Frame sequence: 5 frames at 600 ms and 1 frame at 2.5 s. Scale 0.513 μm/pix.
Frame rate 6s and scale 5.36 μm/pix.
Frame rate 6 s and scale 12.26 μm/pix.
Short length scale variations correspond to variables that can vary strongly from one vein to a neighboring vein, while long length scale variations vary smoothly throughout the network. Variables …
Variable | Significance | Length scale variations | Timescale variations |
---|---|---|---|
Radius of a vein | Short | Short and long | |
Relative contraction amplitude | – | – | |
Length of a vein | – | – | |
Inner fluid viscosity | Long | Long | |
Contraction frequency | – | – | |
Inner fluid pressure | Long | Short and long | |
Atmospheric pressure | – | – | |
Fluid flow pervading a vein | Short | Short and long | |
Fluid flow generated by peristaltic contractions in a vein | Short | Short and long | |
Fluid flow generated by the rest of the network | Short | Short and long | |
Resistance of a vein, | Short | Short and long | |
Resistance of the rest of the network attached to a vein at both vein ends | Short | Short and long | |
Shear rate on a vein’s inner wall | Short | Short and long | |
Sensed shear rate for adaptation | Short | Long | |
Steady state shear rate, | Long | Long | |
Active contribution to , due to energetic consumption from the actomyosin cortex to maintain contractions | Long | Long | |
Time | – | – | |
Long-time adaptation timescale | Long | Long | |
Delay between adaptation and shear rate | Long | Long | |
Peristaltic contraction period | – | – | |
Long-time average of | – | Long |
These fits include fitting of . The fits are done over a range in time .
Experiment | |||||
---|---|---|---|---|---|
data set G∗ | 69 ± 3 | 903 ± 190 | 5.4 ± 0.04 | 25–46 | 1.6 % |
data set F∗ | 82 ± 3 | 335 ± 8 | 5.7 ± 0.03 | 90–102 | 0.17 % |
data set E∗ | 352 ± 7 | 798 ± 3 | 3.07 ± 0.02 | 67–104 | 0.6 % |
data set K∗ | 76 ± 4 | 85 ± 4 | 3.63 ± 0.01 | 50–90 | 2.7 % |
Note that when a data set name is repeated, it corresponds to fitting results over different time ranges for the same data set.
Experiment | ||||
---|---|---|---|---|
data set A | 2682 ± 831 | 1.48 ± 0.17 | 0–17 | 0.13 % |
data set A | 220 ± 10 | 0.44 ± 0.00 | 17–33 | 0.22 % |
data set A | 246 ± 960 | 1.21 ± 0.59 | 67–83 | 0.68 % |
data set B | 1195 ± 20 | 1.43 ± 0.00 | 10–75 | 1.4 % |
data set C | 5948 ± 122 | 0.97 ± 0.00 | 0–83 | 1.9 % |
data set D | 1531 ± 69 | 0.58 ± 0.01 | 0–33 | 2.0 % |
data set D | 377 ± 6 | 0.79 ± 0.00 | 8–50 | 3.2 % |
data set E | 1312 ± 37 | 1.46 ± 0.01 | 0–21 | 0.93 % |
data set E | 1894 ± 49 | 3.05 ± 0.02 | 58–83 | 0.66 % |
data set F | 4323 ± 319 | 3.30 ± 0.06 | 0–42 | 1.9 % |
data set F | 4323 ± 319 | 3.30 ± 0.06 | 0–42 | 1.9 % |
data set F | 910 ± 24 | 5.08 ± 0.03 | 83–100 | 0.27 % |
data set G | 1153 ± 51 | 6.07 ± 0.04 | 12–29 | 0.38 % |
data set G | 1808 ± 322 | 1.00 ± 0.09 | 42–54 | 0.61 % |
data set G | 1233 ± 54 | 6.68 ± 0.07 | 83–100 | 0.31 % |
data set H | 355 ± 8 | 2.35 ± 0.02 | 0–25 | 1.4 % |
data set I | 274 ± 5 | 2.27 ± 0.01 | 0–25 | 1.6 % |
data set J | 601 ± 132 | 1.41 ± 0.09 | 0–25 | 3.1 % |
data set K | 278 ± 6 | 3.16 ± 0.00 | 8–67 | 2.0 % |
data set K | 85 ± 2 | 3.70 ± 0.00 | 45–75 | 0.6 % |
data set K | 862 ± 119 | 3.40 ± 0.13 | 67–108 | 1.5 % |
data set K | 123 ± 2 | 4.18 ± 0.00 | 108–133 | 0.53 % |
data set L | 2553 ± 248 | 0.27 ± 0.01 | 6–23 | 1.3 % |
was established with cross-correlation, while and were obtained through linear least-squares fitting. Error bars correspond to the 95% confidence interval and N.R. corresponds to non …
Vein index in full network | |||||
---|---|---|---|---|---|
a | 24 | 1800 ± 250 | 0.76 ± 0.02 | 8.1% | 7.9% |
b | 78 | 1520 ± 40 | 0.89 ± 0.02 | 2.6% | 2.9% |
c | 360 | 1500 ± 150 | N.R. | 1.4% | 1.4% |
d | 120 | 1800 ± 100 | N.R. | 17% | 23% |
e | 120 | 900 ± 70 | 0.2 ± 0.05 | 7.4% | 11% |
f | 186 | 2750 ± 100 | 0.38 ± 0.05 | 5.2% | 6.3% |
g | 42 | 2450 ± 50 | 0.94 ± 0.03 | 5.0% | 5.1% |
h | 246 | N.R. | 0.26 ± 0.03 | 8% | 11% |
i | 186 | 870 ± 40 | 0.26 ± 0.01 | 3.3% | 6.9% |
j | 54 | 2200 ± 100 | 1.1 ± 0.2 | 5.2% | 5.0% |
k | 288 | 730 ± 50 | 4.0 ± 1.0 | 4.7% | 6.7% |
l | 108 | 4050 ± 200 | N.R. | 1.1% | 1.2% |
m | 360 | 10000 ± 3000 | 0.62 ± 0.1 | 6.1% | 8.0% |
n | 18 | 2050 ± 200 | 0.73 ± 0.02 | 3.7% | 3.8% |
o | 54 | 7300 ± 3000 | 0.48 ± 0.12 | 6.5% | 6.8% |