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Spinodal decomposition and the emergence of dissipative transient periodic spatio-temporal patterns in acentrosomal microtubule multitudes of different morphology
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Image of FIG. 1.
FIG. 1.

Microtubule assembly kinetic, morphology, and spontaneous ordering. A. (a) Time-dependent microtubule assembly at MTP concentration of 5 mg/ml, measured by turbidity. (b) When the time dependence of logarithm of turbidity was graphed, it reveals biphasic character. Biphasic character is more pronounced at higher protein concentration. B. Straight microtubule morphology. (a) Single straight microtubule with MAPs—periodic structural features on microtubule wall labeled with white arrow. Bar is 0.05 m. (b) Multitude of straight microtubules may spontaneously form patterns of aligned microtubules (labeled with white arrow). Formation of patterns of aligned microtubules is responsible for appearance of biphasic kinetics graphs (Buljan 2009). The turning point between monophasic and biphasic kinetics may be considered as the beginning of ordered phase formation (Buljan , 2009). Bar is 5.0 m. (c). Microtubule assembly kinetic graphs for the set of MTP concentrations [ml/mg] (0.5, 1.0, 2.0, and 10.0). C Curved microtubule morphology in the presence of excess of 1 mM CaCl2. (a) Single curved microtubule with MAPs—periodic structural features on microtubule wall labeled with white arrow. Bar is 0.05 m. (b).Multitude of curved microtubules—no alignment observed. Bar is 5.0 m.

Image of FIG. 2.
FIG. 2.

The intrinsic durability in the system composed of macroscopically demixed microtubules self-organized and non-organized phase. Macroscopically self-organized phase of multitude of microtubules is spontaneously breaking the symmetry of homogenous space, from which different rudimentary morphological patterns may rise which show remarkable intrinsic durability against mechanical disruption: A. (a) An arbitrary global self-organized pattern in stationary state, 60 min after microtubule assembly initiation, at 3 mg/ml and 36OC. The pattern (a) has undergone strong mechanical perturbation: a pippette was immersed to the bottom of cuvette, then it has been pulled left-right from one side of couvette to the other side and back. Bar is 5 mm. (b). The resulting stationary pattern is different from the initial pattern (a), but the pattern (a) is not completely diminished; moreover, the ratio of the size of ordered phase versus a non-ordered phase is preserved. Bar is 5 mm. B Electron microscopy images of the probes taken from the sample in Fig. 3 at locations: (a) non-birefringence region (white rectangular), and (b) birefringence region (black rectangular). Bars are 5 m. C Model: two straight microtubules in an aligned configuration. Numerous MAPs: they are attached to the outer surface by one of their two ends while they perpendicularly protrude from the surface by their other end. MAPs serve as spacers and joiners for neighboring microtubules. They may ratchet microtubules alignment due to their electrostatic mutual interactions, and increased effective excluded volume of the microtubules. Outer diameter of microtubule is 25 nm, while MAPs protrusion is about 15 nm, thus, it follows that the effective diameter of microtubule + MAPs is 55 nm.

Image of FIG. 3.
FIG. 3.

The spatial extent of microtubules spontaneous self-organized, and non- self-organized phase, versus the concentration of microtubule protein. To see the relation between the spatial extent of microtubule self-organized and non-self-organized phase versus the concentration of microtubule protein concentration, we have used birefringence phenomena. White and black regions correspond to self-organized and non-self-organized phase, respectively. A. Birefringence was observed at temperature of 360 °C, and at stationary state of microtubule assembly, i.e., at 60th min after assembly initiated. Buffer only was used as reference sample (a). Different MTP concentrations (in mg/ml) were applied: (b) 0.5, (c) 1.0, (d) 1.5, () 3.0, (f) 4.0, and (g) 5 mg/ml. The first birefringence spot was observed at 1.0 mg/ml of MTP concentration. The bar is 5.0 mm. B Intensity of transmitted light is sensitive to the presence of self-organized phase within the system: see Materials and Methods (Buljan , 2009). Light (300 nm) transmittance intensity was measured at stationary state of the same MTP preparation as in (A) in MTP concentrations interval 0.2–5.0 in mg/ ml. The corresponding graph shows strong nonlinearity; it is biphasic. A linear least squares fit is shown for each phase of the graph (R2); 0.9! R2!1. The turning point between two phases occurs at MTP concentrations 1.0 ± 0.06 mg/ml.

Image of FIG. 4.
FIG. 4.

The dynamic of transient periodic patterns in the crowded mix of straight and curved microtubules A. The spontaneously formed periodic patterns with spatial periodicity was observed at 90th min after microtubules assembly initiated, at 360 °C, and 5 mg/ml MTP, and observed during the next 215 min. The changes of patterns were recorded at different stages: (a) 90th min, (b) 105th min, (c) 155th min, (d) 215th min, (e) 275th min, and (f) 305th min. Bar is equal 1 mm. Temperature was constant, i.e., 36  °C from stage (a) up to (b), then it was decreased by 50 °C and held constant up to stage (f). Periodic patterns occurred randomly in different locations, they moved by diffusion at another locations and slowly degraded. We have followed four different periodic patterns, labeled with white rectangular, named “the first,” “the second,” “the third,” and “the fourth,” and marked, respectively, as P1, P2, P3, and P4 rectangular. Different locations of patterns are labeled as L1, L2, and L3. Each rectangular captures the area of the same size. B. First pattern P1 (a) At 90th min: location 1(L1)—the first periodic pattern observed. (b) At 105th min: location 1(L1)—the first pattern is still periodic but changed. (c) At 155th min: location 1(L1)—the first pattern is degraded. C. Second pattern P2 (c) At 155th min; location 1(L1)—the second pattern observed. (d) At 215th min: location 1(L1)—the second pattern left location (1) due to diffusion, but the pattern from other location is brought in by diffusion. (e) At 275th min: location 1(L1)—no any pattern, all left due to diffusion. (e) At 275th min; location 2(L2)—the second pattern located but partially degraded. (f) At 305th min, location 3(L3)—the second pattern is degraded. D. Third pattern P3 (d) At 215th min; location 1(L1)—the third initial periodic pattern observed. (e) At 275th min: the third pattern left the location due to diffusion, and the pattern from other location is brought in by diffusion. (f) At 305th min: location 2(L2)—the third pattern located but degraded. E. Fourth pattern P4 (e) At 275th min; location 1(L1)—the initial pattern observed. (f) At 305th min: the initial pattern left the location due to diffusion, and the pattern from other location is brought in by diffusion. (f) At 305th min: location 2(L2)—the initial pattern located but partially degraded.In each image B, C, D, and E, the bar is 0.1 mm.

Image of FIG. 5.
FIG. 5.

Transient patterns dynamic. A. The data collected from the four transient patters, which randomly occurred and disappeared (see Fig. 4 ). B. Duration of different transient patterns. Duration was estimated as the time between moments of initial (sharpest) and final (the blurriest) stage of pattern. Initial and final stage corresponds to the values, less then 0.065 or higher then 0.130, respectively, for the standard deviation of measured average pattern periodicity. If the standard deviation was above 0.130, we consider that pattern is degraded. If pattern disappears before reaching the final stage of critical (highest) standard deviation (*see Table 2; the first pattern), the moment of its final stage was calculated as average value of the time of its last record and the time of recorded disappearance. C. The overall graph represents the transient pattern scale of periodicity changes versus time. It is constituted by the developments of four individual patterns data taken as they occur during the time of observation. D. This graph is constructed by the rates of percentile changes of the scale of periodicity [mm/min] between two stages of each pattern. These rates are faster at longer time scale at which pattern occurs. When compared, the rate associated to the second, third, and fourth pattern are, respectively, twice, sixth, and tenth times higher than the rate of the first pattern. The rate associated to the second pattern is likely controlled by the fall of temperature (from 360 °C to 310 °C), while the rates of the third and fourth patterns are the most likely controlled by the GTP depletion.

Image of FIG. 6.
FIG. 6.

Long (12 h) running demix or a slow isothermal spinodal decomposition segregates aligned domains of straight microtubules from multitude of curved microtubules. The process is energy independent, but is driven by cross-diffusion in conjunction with excluded volume. MAPs are present in the system. At some initial stage, domains of aligned straight microtubules and curved microtubules are distributed randomly and mixed evenly. Hence the system is homogeneous. The final stage is reached after a long running demix (spinodal decomposition), and it is constituted by the two phases which are well separated spatially. One phase is constituted of all domains of aligned microtubules, while the other phase is constituted of all multitudes of entangled curved microtubules. The system is inhomogeneous.

Image of FIG. 7.
FIG. 7.

Transient periodic pattern formation in a closed system and in a heterogeneous microtubule solution space. (a) Formation of a domain of aligned (further just “domain”) straight microtubules is proceeding until there is enough GTP-tubulin to be added to the microtubule ends. During domain formation, microtubules undergo dynamic instability, which is powered by energy obtained from the GTP-hydrolysis. By stochastically causing shrinking and extension of the microtubule length, the dynamic instability enables the microtubules to undertake numerous complex readjustments in order to occupy an optimal location in domain. Dynamic instability is responsible for maintaining the given number of the microtubules in domain. If some microtubule (new comer) which is formed apart from the domain approaches, it will be eliminated by dynamic instability. Formation of domain is arrested when the number of neighboring microtubules reaches certain critical value. Neighboring microtubules consume the GTP-tubulin for their growth, and they mutually compete for the GTP-tubulin during this process. This consumption by microtubules is replenished by the GTP-tubulin diffusion. (b) As the number of neighboring microtubules in domain is increasing, competition is increased as well for the consumption of the GTP-tubulin. At some critical number of neighboring microtubules, the rate of a collective consumption of the GTP-tubulin may overtake the rate of the GTP-tubulin diffusion. The zone in front of domain of straight aligned microtubules may be depleted of the GTP-tubulin. Hence, in this zone, the concentration of GTP-tubulin is decreased below the critical threshold for microtubule assembly. Therefore, the growth of microtubules in domains will be stopped and the growth of the domain will be arrested as well. But, the reached size of the domain may be preserved due to effects of the excluded volume and the mutual interactions of the MAPs. On microtubule sides, there will appear the zones where the concentration of the GTP-tubulin is decreased to a lesser degree. However, this decrease may not lead to the concentration of the GTP-tubulin dropping below the critical threshold. (c) Microtubules with the lower rate of a collective consumption may still continue to grow in these zones. This is the case of a curved microtubules. Since the tips of a neighboring curved microtubules are positioned at a distance, these microtubules, as a collective, have a lower rate of consumption of the GTP-tubulin than aligned straight microtubules in domains. (d) On both sides of domain of straight aligned microtubules, but further behind the multitude of growing entangled curved microtubules is the zone in which diffusion of the GTP-tubulin can pump enough GTP-tubulin, so that the microtubules with a high collective rate of consumption can continue to develop. Indeed, these are the conditions that enable the transient periodic pattern to be formed.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Spinodal decomposition and the emergence of dissipative transient periodic spatio-temporal patterns in acentrosomal microtubule multitudes of different morphology