Regulation of Microtubule Disassembly by Spatially Heterogeneous Patterns of Acetylation

Microtubules (MTs) are bio-polymers, composed of tubulin proteins, involved in several functions such as cell division, transport of cargoes within cells, maintaining cellular structures etc. Their kinetics are often affected by chemical modifications on the filament known as Post Translational Modifications (PTMs). Acetylation is a PTM which occurs on the luminal surface of the MT lattice and has been observed to reduce the lateral interaction between tubulins on adjacent protofilaments. Depending on the properties of the acetylase enzyme αTAT1 and the structural features of MTs, the patterns of acetylation formed on MTs are observed to be quite diverse. In this study, we present a multi-protofilament model with spatially heterogenous patterns of acetylation, and investigate how the local kinetic differences arising from heterogeneity affect the global kinetics of MT filaments. From the computational study we conclude that a filament with spatially uniform acetylation is least stable against disassembly, while ones with more clustered acetylation patterns may provide better resistance against disassembly. The increase in disassembly times for clustered pattern as compared to uniform pattern can be upto fifty percent for identical amounts of acetylation. Given that acetylated MTs affect several cellular functions as well as diseases such as cancer, our study indicates that spatial patterns of acetylation need to be focussed on, apart from the overall amount of acetylation. Author Summary Microtubules (MTs) form a crucial part of the cytoskeletal machinery which regulates several cellular processes. The basic building block of MTs are tubulin proteins. These proteins assemble in lateral and longitudinal directions to form a hollow cylindrical structure of a MT. There are chemical modifications on tubulin, known as Post Translational Modifications (PTMs), which affect the stability and dynamics of MT filaments. We computationally study how one such PTM, namely acetylation, affects the kinetics of disassembly of a MT filament. We propose a model which incorporates spatially heterogeneous patterns of acetylation on MT filament and study how they may regulate the disassembly times and velocities, a factor hitherto unexplored in studies. We conclude that there are significant differences of disassembly velocities and their fluctuations depending on the differnces in spatial patterns of acetylation.

Microtubules constitute an important class of bio-polymers that are essential for cell 2 division, transport of vesicles, cell motility and for maintaining the structure and shape 3 of the cell [1][2][3][4][5]. In order to fulfil certain cellular functions, during the corresponding 4 stage of the cell cycle, MTs may have to polymerise and maintain stable structures. 5 However, at other times, certain other cellular functions call for these filaments to 6 depolymerise into free protein subunits, before entering into another period of stable 7 assembly or bout of rapid dynamics. How MTs regulate the dynamics in these different 8 states, and the switch between them, is an important question. It is known that certain 9 chemical modifications on the polymer and various MT-binding proteins play crucial 10 roles in regulating the stability and dynamics of the filaments. While there have been 11 many models for investigating the dynamics of MTs alone, assembled in vitro, we know 12 very little about how MT dynamics is influenced by the chemical modifications on the 13 polymer. The focus of this work is to study the role of chemical modifications in 14 deciding certain aspects of MT polymer dynamics. 15 The effect of these chemical modifications, known as Post-Translational 16 Modifications (PTMs), on MT filaments depends on the structure and composition of 17 the filaments. MT filaments exist as hollow cylinders of multiple protofilaments aligned 18 laterally. Each protofilament consists of α-β-tubulin dimers (subunits). After tubulin 19 subunits in a GTP-associated form polymerise to form MT filaments, the GTP molecule 20 can undergo hydrolysis with a certain rate, to create GDP-associated tubulin subunits 21 on the filament. In the absence of stabilizing external proteins, the higher 22 depolymerisation rate of GDP-tubulin and the irreversibility of hydrolysis give rise to 23 the phenomenon of "dynamic instability" in MTs, characterised by successive rapid 24 shortening events (catastrophes) and slow growth events (rescues) [6]. The interaction 25 of a variety of Microtubule Associated Proteins (MAPs) and PTMs on MT filaments 26 may either alter the parameters associated with dynamic instability or altogether shift 27 the filament into either a stable state which resists disassembly or an unstable state of 28 enhanced disassembly [7]. 29 There are a variety of enzymes which cause distinct modifications on tubulins such 30 as acetylation, detyrosination, polyglutamylation, polyglycylation, polyamination etc. 31 Tubulin subunits on a MT filament may exist in a variety of states with respect to the 32 presence of each PTM. The extent to which each type of PTM is present on individual 33 MTs correlates with the structure formed by these MTs, cell type and stages of the cell 34 cycle [8,9]. Mitotic spindle, centrioles and midbody show high levels of acetylation, 35 detyrosination and polyglutamylation. Neurons also have high levels of these PTMs, 36 with detyrosination being more abundant on the axons than growth cones. Axonemes, 37 which form part of cilia and flagella, also have abundance of these PTMs, in addition to 38 high levels of glycylation. However, PTMs are less abundant in astral MTs. Altering Primary position of tubulin acetylation is the Lys40 residue on α tubulin and the 53 enzyme responsible is called α-tubulin acetyltransferase (αTAT1). αTAT1 has been 54 shown to preferentially acetylate tubulins which are part of the MT filament rather 55 than free tubulins in the solution [9]. If the lumen of the filament is presumed to be less 56 accessible by proteins, aggravated by the decreased diffusion inside the cylinder [15], it 57 can result in two scenarios.  [18]. Their findings favour a model in which acetylation is limited by low 72 affinity of αTAT1 (high dissociation constant) for its substrate as well as a low catalytic 73 rate. The low affinity enables the enzyme to diffuse to farther distances on the inner 74 surface before catalysing acetylation, resulting in a more random pattern of acetylation 75 along the filament length. This conclusion is in sharp contrast to the diffusion limited  These results are also supported by the experiments of Nathalie et al [15], which 81 observed that in vivo MTs tend to have acetylation patches concentrated on the tips, 82 whereas in vitro MTs showed random patches along the MTs. They attribute the 83 presence of the random patches to defects along the filament and lateral entry of the 84 enzyme through them.

85
These set of experiments suggest to us that several acetylation patterns can be 86 formed on MT lattices depending on filament geometry as well as the binding and 87 catalytic rates of the acetyltransferase. Given that this variability also exists in the case 88 of in vivo MT filaments [16], it would be interesting to see whether these patterns have a 89 direct impact in regulating the dynamics of MTs.

90
To understand the effect of acetylation on the stability of MT lattice, it is essential 91 to know how this modification affects the mechanical and kinetic parameters of MTs.

92
There have been some earlier experimental studies which mapped the overall changes in 93 MT population caused by altering the amount of acetylation. Experiments on touch 94 receptive neurons (TRN) of C. elegans [20,21] observed that suppression of acetylation 95 on MTs results in shorter filaments with protofilament number varying between [10][11][12][13][14][15][16]96 whereas, the wild-type cells mostly contain long MT filaments with 15 protofilaments.

97
Recent experiments using cryo-electron microscopy [22] probed potential differences in 98 MT structure caused by acetylation. They observe that the state of tubulin acetylation 99 does not cause any discernible variation in the helical structure of MTs, retaining the 100 same lateral and longitudinal spacing in acetylated and deacteylated MTs. Neither do 101 they find significant differences in the structure of the tubulin dimer at a fairly high coarse-graining and the type of parameters used in them [23]. One set of extensive 134 coarse-grained theoretical models that study MT dynamics, use the four 135 phenomenological parameters associated with "dynamic instability". These minimal set 136 of parameters are the mean velocities of growth and shrinkage and the frequencies of 137 catastrophes and rescues [24]. Another set of models explicitly include microscopic 138 kinetic rates associated with processes such as polymerisation, depolymerisation and 139 hydrolysis [25][26][27][28][29]. This type of models are coarse-grained to some extent since the 140 knietic rates (whose values are measured from experiments) are input parameters rather 141 than emerging from the mechanical and chemical properties of tubulin proteins. using a linear polymer model, we observe that the differential polymerisation rate at the 146 open MT tip containing a GTP-tubulin versus a GDP-tubulin can regulate the 147 multi-step mechanism behind age-dependent catastrophes [30]. In another category of 148 models, the multi-protofilament structure of MT filaments, which may include bond 149 energies between subunits and elastic properties of protofilaments, is accounted for in 150 detail [31][32][33][34][35][36][37][38][39]. The choice of employment of the level of coarse-graining in theoretical 151 models depends on the aspect of MT dynamics that they seek to answer.

152
It is known that acetylation alters the lateral interaction between tubulin subunits 153 on adjacent protofilaments and thereby the kinetics of these subunits [14]. Hence, given 154 In the model we employ, MT filament is represented by an N -protofilament lattice 164 (with N =13), as shown in the schematic (Fig 1(a)). Each α-β-tubulin dimer is  Hence, in this study, the filament lattice consists of GDP-tubulins, on which acetylation 180 can be thought to have introduced local spatial disorders. Experimental evidences show 181 that at these points of disorder, lateral interaction energy between subunits of 182 neighbouring protofilaments is reduced [14]. Hence, in the model, the lateral interaction 183 energy (g l ) between subunits can assume two values; g l = g 0 l in the absence of The value of lateral interaction energy (g l ) associated with the subunit at (i, n) 190 depends on the status of acetylation of subunits at (i, n), (i − 1, n), (i, n − 1) and 191 (i, n + 1). Hence, we focus on the set variables. In order to determine the rates of polymerisation and depolymerisation at 193 position (i, n), the lateral interaction energy shared with the neighbours is determined 194 as, if any a j,r ∈ I = 1 (either subunit i or atleast one of its neighbours is acetylated). g 0 l , if all a j,r ∈ I = 0 (neither subunit i nor any of its neighbours is acetylated). (2)

Lateral bond
Longitudinal bond In addition, note that, when any of the nearest neighbours of i (marked → 'x') is acetylated, this also corresponds to w i = R d e . R a is linearly proportional to the concentration of free tubulin.

201
However, since our focus in this paper is on the disassembly profiles of the filament, we 202 simulate the filament in the absence of free tubulin in the solution. Hence, u i = 0 203 throughout the study, while the rate of depolymerisation is given by,

6/22
Here m i is the number of lateral neighbours shared by the subunit at position i which 205 can take values 0, 1 or 2 (see Fig 1(b)). The constants α and 1 − α represent the relative 206 fractional contribution of the lateral interaction energy to the rates of polymerisation 207 and depolymerisation, respectively. We use kinetic Monte Carlo simulations to model 208 the kinetics of the system [42]. The parameters and their values used in the simulations 209 are listed in Table 1  Supporting Information (SI)).

Parameters
Values Parameter is chosen such that w i is consistent with the mean disassembly rate of a GTP lattice measured from experiments ≈ 0.5µm min −1 [43].
Parameter is determined such that w i is consistent with the mean disassembly rate of GDP lattice measured from experiments ≈ 8µm min −1 [14].
Parameter is determined such that under complete acetylation of the MT lattice, w i is consistent with the mean disassembly rate of ≈ 20µ m min −1 (a three fold increase compared to the case of complete deacetylation as measured by Portran et al [14]). Also see SI. from differences in the mechanism of αTAT1 entry, diffusion and catalysis. In this work, 216 we incorporate distinct preformed acetylation patterns onto the GDP-tubulin lattice, in 217 accordance with these earlier experimental observations. At various points in the cell 218 cycle, a stable filament is required to undergo rapid disassembly before the next 219 assembly event begins [16]. There are also various dilution assay experiments which 220 study the disassembly dynamics of filaments. A combination of these factors serve as  An important parameter to consider is the total fraction of acetylation ρ ac , defined 242 as the number of acetylated subunits on the filament divided by the total number of 243 subunits on the filament. In Fig 2(a)-(c), ρ ac = 0.5. Note that when the pattern of 244 acetylation is clusterd (Fig 2(c)), there is an additional parameter which needs to be considered which is represented by ρ ld . This parameter represents the fraction of 246 positions, along the axis of the filament, on which a defect is assumed to be present.

247
Defects are MT lattice openings through which the TAT enzyme may enter the luminal 248 space. Note that ld stands for defect layer. For the clustered pattern, likelihood of 249 acetylation is maximum at defect layers. In other words, these are the layers at which 250 maximum number of subunits are acetylated. Descrition of three distinct patterns of 251 acetylation considered in this study are provided in the following paragraphs. neighbours is acetylated. This procedure continues until the total number of acetylated 293 subunits reaches the number = ρ ac × N × L. Note that since the state of acetylation of 294 a subunit depends on those of its neighbours, acetylated clusters arise around the defect 295 layers. In order to form acetylation patterns in the case of ρ ac < ρ ld , a minimum of subunits are acetylated at each defect layer. Note that the positions 297 of these subunits along that particular layer are chosen randomly. For further 298 acetylation, a subunit is chosen randomly and it is acetylated if it belongs to a defect 299 layer. As before, this procedure continues until the total number of acetylated subunits 300 reaches the number stipulated by ρ ac .

302
We use kinetic Monte-Carlo [42] simulations on the multi-protofilament model and 303 generate length versus time data during disassembly. Using these data, distributions of 304 disassembly times and velocities are measured for an ensemble of 3 × 10 4 filaments.

305
Stability of the filaments with various patterns of acetylation are explored using 306 statistical quantities measured from the corresponding distributions, as explained in the 307 following subsections.

308
Total disassembly times are regulated by acetylation patterns 309 In this section, we investigate whether the time it takes for an ensemble of filaments to 310 convert from the polymeric form to the dimeric form be regulated by the inclusion of 311 different patterns of acetylation. In Fig 3(a)-(b), length of the filament (measured as 312 the length of the longest protofilament at every step) is plotted as a function of time as 313 the disassembly progresses. The pattern of acetylation is uniform in Fig 3(a) and (b).

314
In Fig 3(a), the two curves show distinct paths of disassembly followed by the filament 315 starting from identical patterns of acetylation. The differences arise due to the 316 stochasticity inherent in the kinetics of the process due to thermal fluctuations. In 317 kinetic Monte-Carlo, the times of every next event in the process is drawn from an 318 exponential distribution and the events themselves are chosen with a probability 319 proportional to their kinetic rates. In Fig 3(b), the purple curve is retained from (a).

320
However, the black curve corresponds to a filament where the positions of acetylated 321 subunits have been altered, although the overall pattern is still uniform. Note that, in 322 this figure, the differences between the paths followed by the two curves arise due to the 323 spatial stochasticity associated with the distribution of disorders of acetylation across 324 the filament lattice. In reality, stochasticity in the length versus time data arises due to 325 both these factors -the spatial variation of acetylation as well as thermal fluctuations. 326 All the measurements in this study, hence, invoke averages over these two sources of   Since τ is a random variable, it is associated with fluctuations, which may be 351 quantified through the variance of the distribution of τ . In Fig 4(c), the variance of τ 352 (measured as τ 2 -τ 2 ) is plotted as a function of ρ ac . In the case of uniform (green) 353 and exponential (magenta) patterns, the variance monotonically decreases with increase 354 in ρ ac until it reaches a saturation value for higher values of ρ ac . This can be contrasted 355 with the variance curve of the clustered pattern (blue), where the variance initially   4. (a) Mean of τ ( τ ) is plotted as a function of total fraction of acetylation ρ ac for uniform (green), exponential (magenta) and clustered (with ρ ld = 0.1 (blue)) patterns. In (b), the curves show τ as a function of ρ ac , for different clustered patterns with ρ ld = 0.1 (blue), ρ ld = 0.2 (black) and ρ ld = 0.3 (brown). In (c), variance of τ (measured as τ 2 -τ 2 ) of filaments is plotted as a function of ρ ac for uniform (green), exponential (magenta) and clustered (with ρ ld = 0.1 (blue)) patterns. pattern.

360
Disassembly velocities characterise the underlying acetylation 361 pattern 362 We calculate disassembly velocities (v) for individual filaments, over an interval of every 363 1/60 min, from the length versus time data corresponding to various realisations, for a 364 given value of ρ ac and ρ ld . In Fig 5(a), v obtained from one realisation is plotted as a 365 function of time, for uniform pattern of acetylation (green) and clustered pattern of 366 acetylation with ρ ld = 0.1 (blue), with ρ ac = 0.5 in both cases. Since, v is a stochastic 367 variable, each realisation gives rise to a distinct trajectory of v as a function of time.

368
The probability distribution of v calculated from velocity vs time curves, from an 369 ensemble of 3 × 10 4 filaments (or realisations), is plotted in Fig 5(b). Here, each v is  In Fig 5(c), v values calculated from the probability distributions are plotted as a 375 function of the corresponding ρ ac values. The uniform acetylation pattern (green) has a 376 distinctly higher v compared to the clustered acetylation patterns (blue, black, brown) 377

380
The difference in disorder created on the lattice due to acetylation patterns not only 381 affects the mean of v, but strongly alters the fluctuations associated with v as well.

382
This is expressed as the variance of v (calculated as v 2 -v 2 ) plotted in Fig 5(d) as a 383 function of ρ ac , corresponding to uniform and clustered acetylation patterns. For all ρ ac , 384 variance is the least for uniform acetylation pattern (green). Among the clustered 385 acetylation patterns, ρ ld = 0.1 (with least number of defect layers) has a distinctly 386 higher variance compared to others.

387
Next, we verify the disassembly profile of the filament with exponential acetylation 388 pattern.  distance from tip (µm) Fig 6. Mean velocities expected (black) from the exponential acetylation pattern are compared with mean velocities calculated (measured for an interval of (1/60) min from the length versus time data) from simulations (red) performed with the exponential acetylation pattern, both plotted as a function of the distance from the open tip of the filament, for ρ ac = 0.5. The larger values of mean disassembly velocities obtained from simulations (red) arise as a result of decresed stability caused by random distribution of acetylated subunits along each lateral layer of protofilaments. A scaled exponential pattern of acetylation (magenta) is plotted as a marker.
v exp(−bl) + v 0 as l increases (Fig 6 (black)). However, the v of the filament 398 calculated from simulations (red) are much higher than the expected velocities along the 399 length of the filament. This decreased stability of the filament can be attributed to 400 acetylated subunits being distributed randomly along each layer. As a result, even when 401 only a few subunits on each layer are acetylated, the decrease in their lateral interaction 402 energies ensures that their neighbours also (and by extension the layer itself) have less 403 resistance against disassembly. This cooperative behaviour is discussed in detail below. 404 Cooperativity on a lateral layer affects the observed kinetics subunits -sampling is done over an ensemble of multiple filaments. Here, ρ ac = 0.5 for 412 both uniform acetylation pattern (green) and clustered acetylation pattern (blue).

413
The stability of every lateral layer depends on the fraction and relative positions of 414 acetylated subunits in them. Since, the effect of acetylation is to reduce the lateral 415 interaction energy between subunits on neighbouring protofilaments, it follows that in a 416 lateral layer, a deacetylated subunit has a reduced lateral interaction energy (g ac l ) when 417 atleast one of its neighbours is acetylated. When a minimum of approximately half the 418 layer is acetylated (k = 6), this influence from acetylated neighbours gives rise to a 419 cooperative decrease in lateral energy and increase in local disassembly velocity of the 420 entire lateral layer. On the other hand, lateral layers which contain less than k = 6 421 acetylated subunits have higher chances of containing three or more consecutive 422 deacetylated subunits. This is marked by a decrease in neighbour-induced cooperative 423 disassembly at those layers. Hence, the local disassembly velocity at these layers is acetylated subunits is plotted in the y-axis as a function of k in the x-axis. Here, ρ ac = 0.5 and the curves correspond to uniform pattern (green) and clustered pattern with ρ ld = 0.1 (blue). For uniform pattern, fraction is unimodal and the peak appears at k = 6 ≈ N ρ ac , where N = 13. For the clustered pattern, fraction is bimodal; the peak at k = 13 arises due to the assumption that each defect layer is completely acetylated when ρ ac ρ ld and the one at k = 0 signifies the large number of completely deacetylated lattice layers.
smaller compared to the former case.

425
In the case of uniform pattern, the randomness in the distribution of acetylated

449
The difference in variance of disassembly velocities (Fig 5(d)) between uniform and 450 clustered patterns of acetylation can also be understood in terms of the fractions in  Theoretical studies have not so far, to the best of our knowledge, investigated the 504 effect of acetylation on MT dynamics within a multi-protofilament model. In this study, 505 we incorporate patterns of acetylation as a heterogeneous disorder distribution of 506 tubulin subunits on the MT lattice. It can be discerned from the results of this study 507 that the inclusion of multiple protofilaments is crucial since the size and spatial 508 distribution of domains of acetylation can regulate the phenomenological parameters 509 associated with filament disassembly.

510
Suggested experiments in the context of this study 511 The distinct patterns of acetylation used in our study are based on observations of the 512 same by in vitro experiments under different physiological conditions [15,18,19]. Hence, 513 suitable experiments can generate MT filaments with specific patterns of acetylation 514 with the aid of α-TAT1 enzymes. In our study, we investigate the disassembly of MT 515 filaments with preformed acetylation patterns, when the free tubulin concentration in 516 the solution is zero. The disassembly dynamics of filaments can be investigated in 517 experiments by diluting the free tubulin concentration to zero (dilution assay), and 518 measuring the times and velocities of shrinkage. However, in order for acetylation 519 patterns to be gradually formed on MTs, these filaments have to be stabilised against 520 disassembly using external proteins while acetylation is in progress. Hence, in order to 521 initiate shrinkage and track the disassembly profiles, the stabilising proteins should also 522 be eliminated from the assay along with free tubulins. From the simulations we obtain 523 differences in mean disassembly velocities upto ≈ 6µm/min and variance of disassembly 524 velocities upto ≈ 15µm 2 /min 2 , between the uniform pattern and clustered pattern 525 (with ρ ld = 0.1). These differences are large enough to be measured in dilution assay 526 experiments of MT filaments with distinct preformed acetylation patterns.

527
Experiments on acetylation have not studied its formation on filaments which 528 undergo polymerisation-depolymerisation kinetics in the absence external stabilising 529 proteins. Although, polymerisation was present in the experiments of Portran et al [14], 530 the free tubulin subunits were either completely acetylated or completely deacetylated. 531 While in vivo acetylation is predominantly observed on stable MTs, it is also observed 532 to be present to some extent in dynamic MTs as well [44]. The formation of acetylation 533 on a dynamic filament can generate varied patterns of acetylation which can regulate 534 the filament's shrinkage state. Hence, it is of interest to investigate the coupling of 535 acetylation to the whole polymerisation-depolymerisation kinetics of filaments in future 536 experimental and theoretical studies.

537
Defects or lattice openings are channels through which the acetyltransferase enzymes 538 may enter the lumen of the filament. Apart from these enzymes, defects are also 539 observed to be the prefered positions at which katanin (a MT severing protein) binds in 540 order to sever the filaments [45]. Moreover, this has been suspected as a mechanism for 541 cells to disassemble the older MTs which have accumulated several defects and also to 542 maintain specific lengths of MTs. Also, in vivo experiments have observed a strong 543 preference for katanin to bind to MT filaments with higher levels of acetylation in 544 fibroblasts and dendrites, while not showing the same dependence for axonal MTs [46]. 545 The mean times before severing measured for katanin in Davis et al [45] (3.3 ± 2.2min 546 for 180µm filament and 290nM katanin; 8.5 ± 4.9min for 73µm filament and 5.7nM 547 katanin) are comparable with the maximum difference in disassembly times (≈ 3min) 548 between uniform and clustered acetylation patterns on filaments of ≈ 100µm in our 549 study. Hence, there may be an interesting interplay between the destabilising effects of 550 acetylation and severing proteins on MTs since the distribution of both are affected by 551 the presence of defects. This could be an interesting area of future study.

552
Biophysical significance of the study 553 Transitions between different stages of cell cycle is marked by a distinct shift in MT 554 lengths and numbers. Inadequate disassembly of MT during the prophase has been 555 observed to cause disruption in spindle formation [47]. Various MAPs and severing 556 proteins have been associated with regulating MT stability and disassembly during the 557 various stages of cell cycle.

558
In this study we have analysed the role of various patterns of acetylation and its 559 total fraction in regulating the stability of filaments against disassembly. It can be 560 discerned from the results that a difference in acetylation patterns can give rise to large 561 differences in MT filament stability, even when the total fraction of acetylation per 562 filament is kept fixed. This becomes more interesting given that under various external 563 conditions, αT AT 1 turn over rates have been measured to vary by as much as 50 564 folds [17,[48][49][50]. An interplay between this and the effective diffusion constant of the 565 enzyme inside the MT lumen will give rise to various patterns of acetylation. Infact, 566 cytoplasmic MTs have been observed to show variability in acetylation patterns. For 567 example, experiments on human fibroblast cells observed that, while a large fraction of 568 cytoplasmic MTs contained acetylated "domains" along the length as well as at the tip, 569 a smaller fraction contained completely uniformly distributed patterns [16]. Results 570 from our study reveal differences in means and variances of disassembly times and 571 velocities between various acetylation patterns. These differences show that preformed 572 patterns of instabilities on stable lattices can be utilised to regulate response of the 573 lattice to cues to disassemble, as required. Hence, the formation of spatially 574 heterogeneous acetylation patterns can be compared to decisions made by the cell 575 regarding the regulation of filament disassembly before it is triggered.

576
The state of acetylation of tubulin subunits on MT filaments are observed to affect 577 many cellular structures and functions such as the touch sensation of Touch Receptor 578 Neurons in C.elegans, dynamics of actin filaments, growth of invadopodia, cell 579 migration [48, 51] etc. Kinesin-1 proteins preferentially interact with acetylated tubulins 580 on MTs [52]. Proteins have been observed to preferentially interact with tubulins in 581 other PTM states as well [8,11]. Based on this, it is proposed that a tubulin "code" 582 may exist, which can be read by proteins associated with MT filaments [53,54], which 583 can in turn be used for transport or regulation of filament dynamics. However, our 584 results show that, apart from this multifarious effect, characteristic acetylation patterns 585 accumulated under different conditions themselves have signatures which can variably 586 regulate filament disassembly. Hence, in the context of filament disassembly, patterns of 587 acetylation may be a manifestation of the "code" which regulate the phenomenological 588 parameters associated with the MT filament.

589
Supporting Information 590 S1 text. Determining the parameters used in the simulations.

591
In this text we discuss how the parameters used in this work are obtained.