Shear flow as a tool to distinguish microscopic activities of molecular machines in a chromatin loop

Shear flow as a tool to distinguish microscopic activities of molecular machines in a chromatin loop | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results Shear flow as a tool to distinguish microscopic activities of molecular machines in a chromatin loop Sandeep Kumar , Ranjith Padinhateeri , Snigdha Thakur doi: https://doi.org/10.1101/2024.01.23.576811 Sandeep Kumar 1 Department of Physics, Indian Institute of Science Education and Research Bhopal , Bhopal 462066, India Find this author on Google Scholar Find this author on PubMed Search for this author on this site Ranjith Padinhateeri 2 Department of Biosciences and Bioengineering, Indian Institute of Technology Bombay , Mumbai 400076, India Find this author on Google Scholar Find this author on PubMed Search for this author on this site Snigdha Thakur 1 Department of Physics, Indian Institute of Science Education and Research Bhopal , Bhopal 462066, India Find this author on Google Scholar Find this author on PubMed Search for this author on this site For correspondence: sthakur{at}iiserb.ac.in Abstract Full Text Info/History Metrics Supplementary material Preview PDF Abstract Several types of molecular machines move along biopolymers like chromatin. However, the details about the microscopic activity of these machines and how to distinguish their modes of action are not well understood. We propose that the activity of such machines can be classified by studying looped chromatin under shear flow. Our simulations show that a chromatin-like polymer with two types of activities (constant or local curvature-dependent tangential forces) exhibits very different behavior under shear flow. We show that one can distinguish both activities by measuring the nature of a globule-to-extended coil transition, tank treading, and tumbling dynamics. Spatial organization and biological functions of polymers, like DNA, chromatin, actin, etc., are made possible by various molecular motors/enzymes operating on them [ 1 – 4 ]. The activity of such ATP-dependent molecular machines influences the 3D conformations of DNA/chromatin. Motors on biopolymers perform a diverse set of functions such as reading the genetic code (RNA polymerase), re-organize proteins along DNA (SWI/SNF, CHD, ISWI, etc.), and move along the track transporting appropriate cargo (Kinesin, Dynein, Cohesin, Myosin) [ 2 ]. While performing these tasks, they apply a local force on the track that may bend or distort the polymer [ 5 – 8 ]. The microscopic details of how each motor acts on the filaments can differ. Some of the motors act like force-dipoles tangential to the chain [ 9 – 11 ] while others translocate along the backbone [ 12 , 13 ]. The simultaneous action of such multiple ATP-consuming motors on a biopolymer creates a fascinating active system. For example, loop extruding motors fold chromatin, motors in the SWI/SNF, ISWI family slide nucleosomes leading to activation or repression of genes [ 14 – 16 ], correlated active motion on the chromatin leads to compact domain formation [ 17 , 18 ] and spontaneous segregation in chromosome [ 11 , 19 ]. The precise details of the microscopic action of these motors on the track are poorly understood. Experiments like X-ray crystallography and cryo-electron microscopy typically measure the static/frozen structures and are unable to reveal the dynamics of the motors [ 20 , 21 ]. Light microscopy experiments, on the other hand, do not have sufficient resolution to probe the action of nanometer-sized motors [ 7 , 22 ]. Hence, it will be appropriate to have a macroscopic experimental method combined with physical simulations that can give insight into the microscopic action of these motors on the filament. Shear flow experiments have been used extensively in the past to gain a microscopic understanding of the conformational properties and fluctuations of passive polymers [ 23 – 29 ]. These experiments show that the chain’s local structural properties can influence the polymer’s macroscopic behaviour under shear. However, very little is known about how active polymers behave under shear, given that the underlying motors can have different modes of action. In this letter, we show that active polymer, even with slight differences in microscopic activity, can exhibit distinct collective macroscopic behavior under shear flow. Hence, we propose that studying active ring polymer under shear can help us distinguish between the different modes of microscopic activity of motors. To demonstrate this, we present a model with two types of motors having different tangential activities and show that they behave very differently under shear. We show that, under shear, the polymer undergoes a discontinuous transition from a collapsed to an open state in the presence of one type of activity, while the other type of activity results in a continuous transition. Further, we demonstrate that comparing macroscopic measurements of tumbling and tank-treading frequencies of the polymer can distinguish the two microscopic activities. MODEL AND METHODS We consider a ring polymer of chromatin made of 200 beads (N=200) with neighbouring beads connected by harmonic spring potential and non-neighbouring beads interacting via a purely repulsive WCA potential [ 30 ]. Two sets of such ring polymers are simulated, one with type-I activity and the other with type-II activity, and both are subjected to a simple shear flow. The schematic diagram in Fig. 1 depicts the ring with two activities under shear. In type-I activity, every bead experiences a tangential force that depends solely on the local unit tangent vector. Hence, it has a constant magnitude of the active force on each monomer irrespective of the local shape along the polymer contour [ 31 ], given by where, is the unit vector along tangent for any monomer i with position vector r i . On the other hand, in type-II activity, every bead experiences a tangential force that depends on the length of the tangent vector [ 32 ] given by where, t i = ( r i +1 − r i −1 ) / 2 l, l =| r i +1 − r i | being the bond length. This implies that, unlike type-I, in type-II the local curvature along the contour affects the magnitude of active force. Each of the active r g polymers is subjected to a simple shear flow along the positive x -direction, with the velocity gradient tensor given by: , where the constant shear rate . Download figure Open in new tab FIG. 1: (a) Schematic representation of the active ring under the shear flow (with strength ). The flow is in the x-direction and the gradient is in the y-direction. (b) Type-I activity: constant magnitude of the active force . (c) Type-II activity: magnitude of the active force depends on local curvature. See text for details. Fig. 1 shows the schematic for the active ring under shear. The equation of motion of the i th bead is given by: where U i is the total interaction potential between the beads [ 30 ], F s = β ∇ u · r is the shear force with β being the friction coefficient, and ξ is the white noise [ 30 ]. The strength of the activity is measured by and we use the terms Ac - I (type-I) and Ac - II (type-II) to distinguish the two activities. The standard practice to represent the strength of the shear is to use the dimensionless Weissenberg number , where τ 0 is the longest relaxation time of the passive ring without shear. To determine τ 0 , we initialize the ring to an extended configuration with fractional extension ≈ 0.5. The ring is then allowed to relax without shear and active force. The longest relaxation time τ 0 is then determined by fitting the decay of fractional extension to a single exponential Aexp ( −t/τ 0 ) + B . More details of the model can be found in supplementary material [ 30 ]. RESULTS AND DISCUSSION We quantify the structure of the ring by calculating the gyration tensor , where m, n ∈ {x, y, z} and r i,m is the position of i th monomer in the centre of mass reference frame. The trace of G , , where R g is the gyration radius of the polymer. Fig. 2 shows the heat map of R g by varying Ac and Wi . Download figure Open in new tab FIG. 2: Heat map showing gyration radius R g of the ring for different activity strength ( Ac ) and shear strength ( Wi ): (a) Activity type-I ( Ac - I ) and (b) Activity type-II ( Ac - II ). Type-I activity leads to a more compact configurations than type-II for lower Wi . (c) The component of the gyration tensor G xx as a function of Wi . Without shear The passive ring without shear is in the coiled state [ 33 ]. However, on increasing the activity in the absence of shear, we observe a coil-to-globule transition for both types of activities with subtle differences (see along the y-axis in Fig. 2 (a), (b) ). One observes the transition to globular state for a lower value of Ac - I compared to Ac - II (See Fig. S2a). The collapse of the polymer with activity can be attributed to the emergence of local hairpin structures by the tangential force as characterized by the bond correlation (Fig. S2b). Further, the time for type-I to achieve the collapsed state is lower than type-II (Fig. S2c). Active and passive polymer with shear The coiled passive ring starts to stretch on increasing Wi (see along the x-axis in Fig. 2 (a), (b) ). The increase in R g is by virtue of the monotonic increase in G xx that squeezes the ring along the gradient ( y ) and vorticity ( z ) direction. The scaling of the components of gyration tensor G yy , G zz ∼ Wi − 0.45 (Fig. S3) matches well with previous studies [ 34 , 35 ]. The activity on the ring drives it to be in the globular state, whereas the shear tries to open it up. Hence, there is a stark difference between active and passive cases in the way the compactness of the polymer varies with Wi (compare Ac = 0 with Ac >> 0 in Fig. 2 (a),(b) ). Rings with different activity types unfold differently under shear We observe that the details of the structural transition under shear depend on the type of activity ( Ac - I or Ac - II ). As evident from Fig. 2 , Ac - I supports more compact structure upto a larger Wi than Ac - II . Further, the G xx shows a sudden increase in type-I compared to a gradual increase in type-II ( Fig. 2(c) ) as a function of Wi . Also, a substantial difference is observed in G zz , indicating more swelling in the vorticity direction for type-II (Fig. S3(c)). Simulations give us the time series of the R g (Fig. S4 and Fig. S5). From this, we compute the steady-state probability distribution of R g and plot it in Fig. 3 . The results for the passive case indicate the existence of the open state (a single predominant peak at large R g ) for all Wi ( Fig. 3(a) ). However, comparison of passive P ( R g ) ( Fig. 3 (a)) with either of the active cases ( Fig. 3(b),(c) ) shows a clear difference between the two. For the active case, the P ( R g ) has a single closed state peak at low Wi followed by the double peak at intermediate Wi . The double peak is due to the competition between the activity and shear, resulting in switching between the open and closed states. At this intermediate Wi , we observe the following differences if we compare both activity types. A distinct bimodality in P ( R g ) is observed for Ac - I , showing a microscopic toggling between the open and closed state at intermediate Wi , which then finally goes to the open state. Note that the probability is zero for intermediate R g values (between 30 to 50). However, the type-II activity always possesses finite weight for the intermediate R g s, indicating a gradual transition between closed to open state (also see Fig. 2(c) ). It is this difference — the difference between the microscopic toggling and long-lived switching — is an important feature of our model that helps us differentiate between the two activities. Download figure Open in new tab FIG. 3: Distribution of R g for (a) Passive, (b) Ac - I = 10 and (c) Ac - II = 10. The double peak in (b) and (c) shows the transition of the ring polymer from a collapsed state to a stretched state. Representative configurations of the polymer are shown in blue color. (d) Standard deviation and Binder cumulant of R g suggest that transition under two types of activities are different. To further quantify the difference between the two, we plot the standard deviation ( σ ( R g )) in Fig. 3(d) . It is clear that passive, Ac - I and Ac - II curves are different. For Ac - I , the σ ( R g ) peaks at an intermediate Wi showing the signature of a discontinuous transition. On the other hand, σ ( R g ) for passive case is nearly flat while Ac - II is slightly higher than passive for low Wi . One can also see a clear difference between Ac - I and Ac - II at large Wi , indicating less fluctuations in the open state of type-I active ring. Further, the calculation of Binder cumulant [ 36 – 38 ], a well-known quantity to characterize the type of phase transition, supports the discontinuous nature of transition in type-I activity. The observed differences between the two activities under shear flow can help us experimentally identify the microscopic action of the active motors. Unlike tumbling (TB), tank-treading (TT) is more efficient in differentiating the activities Polymers under shear are known to exhibit tumbling and tank-treading motion [ 26 , 39 – 41 ]. Tumbling is the process where the entire polymer rotates about its centre of mass in the flow-gradient plane (See Movie 1 in [ 30 ]). This results from the net torque experienced by the polymer due to its extension along the gradient direction. The snapshots of the tumbling polymer are presented in Fig. S8. To quantify the tumbling motion, a cross-correlation ( C xy ) between conformational changes along flow and gradient direction is a standard mathematical tool [ 25 , 42 ], defined as: where δ G αα = G αα − ⟨G αα ⟩ and and the angular brackets represent the ensemble average over different t 0 . For a periodic tumbling motion, one would expect the C xy to have an oscillatory behavior whose periodicity would define the tumbling frequency. The inset of Fig. 4 shows the C xy for the two types of activities. The characteristic time of tumbling is obtained by τ tb = 2( t + −t − ), where the times t + > 0 corresponds to the deepest minimum and t − < 0 for highest peak in C xy . In Fig. 4 , we plot the scaled tumbling frequency f tb = τ 0 /τ tb for the passive and active rings. It is interesting to note that f tb shows a power-law scaling as f tb ∼ Wi 0.68 for both active and passive cases at higher Wi . For the passive case, such scaling has been observed before [ 25 – 27 , 35 , 39 , 43 – 46 ]. The same scaling behavior for both types of activities at high Wi indicates the dominance of shear in this regime. Meanwhile, for the lower Wi regime, the two activities differ in two aspects. First, for the same activity strength, type-II exhibits tumbling at a smaller Wi . Secondly, the smoothness of tumbling is superior for type-II activity (see definition and details in [ 30 ]). Therefore, even though the frequency ( f tb ) is weak in differentiating the two activities, the smoothness of tumbling can capture the difference nicely. Download figure Open in new tab FIG. 4: Scaled tumbling frequency f tb for passive and active rings of both types at different Wi values showing the same power law for all cases at large Wi . For lower Wi the distinction between the two activities appear. Inset: Cross-correlation from the conformational fluctuations along the flow and gradient direction C xy for Ac - I, Ac - II = 10. Note the difference between the activities. In non-equilibrium situations like the shear flow, soft objects like vesicles and ring polymers are known to undergo tank-treading motion [ 25 , 47 – 49 ]. In this mode, the polymer is stretched in the flow-gradient plane, forming an elliptical shape with monomers rotating about the center-of-mass along the contour (See Movie 2 in [ 30 ]). To identify and characterize the TT, we track the motion of monomers in the center-of-mass frame. For a given bead i , we define the fractional projection X i = x i /L , where x i = ( r i − r cm ) x is the x-position of i th monomer and L is the distance between the extreme beads along the longitudinal axis of the ring as shown pictorially in Fig. S12. The time auto-correlation of the X i that will enable us to calculate the TT frequency can be defined as: will exhibit an oscillatory motion for a perfect tank-treading. Fig. 5(a) shows distinct behaviors of for the two types of activities. We obtain the characteristic time ( τ tt ) from the secondary peak position (the black dotted vertical line in Fig. 5(a) ) and compute the tank-treading frequency as f tt = τ 0 /τ tt . Fig. 5(b) plots the tank-treading frequency f tt for passive and active rings. It is noteworthy that for passive rings, the f tt ∼Wi 0.72 , similar to the previous works [ 24 , 25 , 46 , 50 ]. We find that even the active case approaches passive scaling at high Wi , suggesting the dominance of shear. At low Wi , both activities support TT, thereby enhancing the f tt compared to its passive counterpart. Download figure Open in new tab FIG. 5: (a) The time auto-correlation of X i ( C x/L ) for Ac - I = Ac - II = 10 and Wi = 3700. Note the difference in periodicity for the two activities. (b) Comparison of tank-treading frequencies ( f tt ) obtained from C x/L for passive and both kinds of activities. The presence/absence of the dip differentiates both the activities. However, at intermediate Wi , we find that both types of activities give very different TT features. This contrasting behaviour can differentiate the two activities. Around Wi≈ 150, f tt starts decreasing for Ac - I , it reaches a minimum and then rises until it approaches the passive curve. Ac - II , on the other hand, does not exhibit such non-monotonic behaviour. The minima in type-I activity correspond to the configurations where the ring polymer almost stops tank-treading and stalls (Fig S13 and Movie 3 in [ 30 ]). This is due to the interplay between the shear-induced TT and tangential force-induced TT. The shift in the minima implies that the stalling point is activity-dependent, suggesting that the shear required to balance it increases with activity. On further increasing Wi , shear overcomes the activity, and the ring tank treads only due to shear. To gain more insights into the absence of minima in type-II, we re-examine the R g distribution in Fig. 3 . The distribution for type-II activity implies rings are more deformable in the open state (note more width around the prominent R g peak) for type-II than type-I. A more flexible open state for type-II will help it to tumble; hence, there is no stalling, and the dynamics are a mix of TB and TT in type-II (Fig. S14 and Movie 4 in [ 30 ]). To further show the distinction between the two types and examine the co-existence of TT and TB, we calculate the power spectral density (PSD) of x i /L time series (Fig. S13 and Fig. S14) by taking the Fourier transform of the time auto-correlation function C xi /L ( t ). The power spectrum is plotted in Fig. 6 for both activities with two different shear strengths. Interestingly, type-I activity exhibits a single peak, whereas type-II shows a double peak in P ( ν ). The underlying feature of the single and double peaks can also be inferred from Fig. 5(a) . The single peak in Ac - I is the evidence of long-lived TT dynamics. Whereas the double peak in Ac - II is the testimony of the co-existence of TB and TT dynamics, where one of the peaks corresponds to f tt and the other is close to f tb . Download figure Open in new tab FIG. 6: Power spectrum of x/L time-series for Ac - I = Ac - II = 10 for different Wi . Note that the Ac - I leads to distributions with a single peak, while the Ac - II contains a double peak in its distribution. In conclusion, we have shown that one can employ shear as a tool to distinguish the dynamics of an active ring under the influence of two different types of microscopic activities. Our results show that the type of activity at the microscopic level strongly affects macroscopic features such as collapsed to open state transition under shear. In particular, the type-I activity exhibits a discontinuous collapse-to-open transition as opposed to a continuous transition for type-II. The dynamical responses of the active polymers under flow are also very different. For intermediate shears, type-II active rings support more tumbling, whereas type-I is more prone to tank treading. Such types of microscopic motor action are common in biological systems, particularly among motors that act on chromatin polymers. Hence, our simulations can be used to design future experiments on chromatin motors to classify their activity. The authors would like to acknowledge the HPC facility at IISER Bhopal for all the computational work. ST acknowledges SERB India. Footnotes ↵ * sandeep19{at}iiserb.ac.in ↵ † ranjithp{at}iitb.ac.in ↵ ‡ sthakur{at}iiserb.ac.in References [1]. ↵ Narlikar , G. J. , Sundaramoorthy , R. & Owen-Hughes , T. Mechanisms and functions of atp-dependent chromatin-remodeling enzymes . Cell 154 , 490 – 503 ( 2013 ). OpenUrl CrossRef PubMed Web of Science [2]. ↵ Alberts , B. Molecular biology of the cell (Garland science , 2017 ). [3]. Michaelis , J. , Muschielok , A. , Andrecka , J. , Kügel , W. & Moffitt , J. R. Dna based molecular motors . Physics of Life Reviews 6 , 250 – 266 ( 2009 ). URL https://www.sciencedirect.com/science/article/pii/S1571064509000323 . OpenUrl [4]. ↵ Clapier , C. R. , Iwasa , J. , Cairns , B. R. & Peterson , C. L. Mechanisms of action and regulation of atp-dependent chromatin-remodelling complexes . Nature reviews Molecular cell biology 18 , 407 – 422 ( 2017 ). OpenUrl CrossRef PubMed [5]. ↵ Wang , H.-Y. , Elston , T. , Mogilner , A. & Oster , G. Force generation in rna polymerase . Biophysical journal 74 , 1186 – 1202 ( 1998 ). OpenUrl CrossRef PubMed Web of Science [6]. Zofall , M. , Persinger , J. , Kassabov , S. R. & Bartholomew , B. Chromatin remodeling by isw2 and swi/snf requires dna translocation inside the nucleosome . Nature structural & molecular biology 13 , 339 – 346 ( 2006 ). OpenUrl [7]. ↵ Ganji , M. et al. Real-time imaging of dna loop extrusion by condensin . Science 360 , 102 – 105 ( 2018 ). OpenUrl Abstract / FREE Full Text [8]. ↵ Dutta , S. , Ghosh , A. & Spakowitz , A. Effect of local active fluctuations on structure and dynamics of flexible biopolymers . Soft Matter ( 2024 ). [9]. ↵ Bruinsma , R. , Grosberg , A. Y. , Rabin , Y. & Zidovska , A. Chromatin hydrodynamics . Biophysical journal 106 , 1871 – 1881 ( 2014 ). OpenUrl CrossRef PubMed [10]. Saintillan , D. , Shelley , M. J. & Zidovska , A. Extensile motor activity drives coherent motions in a model of interphase chromatin . Proceedings of the National Academy of Sciences 115 , 11442 – 11447 ( 2018 ). OpenUrl Abstract / FREE Full Text [11]. ↵ Mahajan , A. , Yan , W. , Zidovska , A. , Saintillan , D. & Shelley , M. J. Euchromatin activity enhances segregation and compaction of heterochromatin in the cell nucleus . Phys. Rev. X 12 , 041033 ( 2022 ). URL https://link.aps.org/doi/10.1103/PhysRevX.12.041033 . OpenUrl [12]. ↵ Terakawa , T. et al. The condensin complex is a mechanochemical motor that translocates along dna . Science 358 , 672 – 676 ( 2017 ). OpenUrl Abstract / FREE Full Text [13]. ↵ Foglino , M. et al. Non-equilibrium effects of molecular motors on polymers . Soft Matter 15 , 5995 – 6005 ( 2019 ). URL doi: 10.1039/C9SM00273A . OpenUrl CrossRef [14]. ↵ Spracklin , G. et al. Diverse silent chromatin states modulate genome compartmentalization and loop extrusion barriers . Nature Structural & Molecular Biology 30 , 38 – 51 ( 2023 ). OpenUrl [15]. Goloborodko , A. , Marko , J. F. & Mirny , L. A. Chromosome compaction by active loop extrusion . Biophysical journal 110 , 2162 – 2168 ( 2016 ). OpenUrl CrossRef PubMed [16]. ↵ Narlikar , G. J. , Sundaramoorthy , R. & Owen-Hughes , T. Mechanisms and functions of atp-dependent chromatin-remodeling enzymes . Cell 154 , 490 – 503 ( 2013 ). OpenUrl CrossRef PubMed Web of Science [17]. ↵ Zidovska , A. , Weitz , D. A. & Mitchison , T. J. Micron-scale coherence in interphase chromatin dynamics . Proceedings of the National Academy of Sciences 110 , 15555 – 15560 ( 2013 ). OpenUrl Abstract / FREE Full Text [18]. ↵ Goychuk , A. , Kannan , D. , Chakraborty , A. K. & Kardar , M. Polymer folding through active processes recreates features of genome organization . Proceedings of the National Academy of Sciences 120 , e2221726120 ( 2023 ). OpenUrl [19]. ↵ Ganai , N. , Sengupta , S. & Menon , G. I. Chromosome positioning from activity-based segregation . Nucleic Acids Research 42 , 4145 – 4159 ( 2014 ). URL doi: 10.1093/nar/gkt1417 . OpenUrl CrossRef PubMed Web of Science [20]. ↵ Wu , H. et al. Reorientation of ino80 on hexasomes reveals basis for mechanistic versatility . Science 381 , 319 – 324 ( 2023 ). OpenUrl [21]. ↵ Shoemaker , S. C. & Ando , N. X-rays in the cryo-electron microscopy era: structural biology’s dynamic future . Biochemistry 57 , 277 – 285 ( 2018 ). OpenUrl CrossRef [22]. ↵ Barth , R. , Bystricky , K. & Shaban , H. Coupling chromatin structure and dynamics by live super-resolution imaging . Science advances 6 , eaaz2196 ( 2020 ). OpenUrl FREE Full Text [23]. ↵ Teixeira , R. E. , Babcock , H. P. , Shaqfeh , E. S. & Chu , S. Shear thinning and tumbling dynamics of single polymers in the flow-gradient plane . Macromolecules 38 , 581 – 592 ( 2005 ). OpenUrl [24]. ↵ Liebetreu , M. , Ripoll , M. & Likos , C. N. Trefoil knot hydrodynamic delocalization on sheared ring polymers . ACS Macro Letters 7 , 447 – 452 ( 2018 ). URL https://doi.org/10.1021/acsmacrolett.8b00059. PMID: 35619341 , doi: 10.1021/acsmacrolett.8b00059 . OpenUrl CrossRef PubMed [25]. ↵ Chen , W. , Chen , J. & An , L. Tumbling and tank-treading dynamics of individual ring polymers in shear flow . Soft Matter 9 , 4312 – 4318 ( 2013 ). URL doi: 10.1039/C3SM50352F . OpenUrl CrossRef [26]. ↵ Schroeder , C. M. , Teixeira , R. E. , Shaqfeh , E. S. G. & Chu , S. Characteristic periodic motion of polymers in shear flow . Phys. Rev. Lett . 95 , 018301 ( 2005 ). URL doi: 10.1103/PhysRevLett.95.018301 . OpenUrl CrossRef PubMed [27]. ↵ Tu , M. Q. , Lee , M. , Robertson-Anderson , R. M. & Schroeder , C. M. Direct observation of ring polymer dynamics in the flow-gradient plane of shear flow . Macromolecules 53 , 9406 – 9419 ( 2020 ). URL https://doi.org/10.1021/acs.macromol.0c01362. 10.1021/acs.macromol.0c01362 . OpenUrl CrossRef [28]. Ladoux , B. et al. Fast kinetics of chromatin assembly revealed by single-molecule videomicroscopy and scanning force microscopy . Proceedings of the National Academy of Sciences 97 , 14251 – 14256 ( 2000 ). OpenUrl Abstract / FREE Full Text [29]. ↵ Matthews , R. , Louis , A. & Yeomans , J. Complex dynamics of knotted filaments in shear flow . Europhysics Letters 92 , 34003 ( 2010 ). OpenUrl [30]. ↵ “See Supplemental Material at URL-will-be-inserted-by-publisher” . [31]. ↵ Locatelli , E. , Bianco , V. & Malgaretti , P. Activity-induced collapse and arrest of active polymer rings . Phys. Rev. Lett . 126 , 097801 ( 2021 ). URL doi: 10.1103/PhysRevLett.126.097801 . OpenUrl CrossRef [32]. ↵ Philipps , C. A. , Gompper , G. & Winkler , R. G. Dynamics of active polar ring polymers . Phys. Rev. E 105 , L062501 ( 2022 ). URL https://link.aps.org/doi/10.1103/PhysRevE.105.L062501 . OpenUrl [33]. ↵ Kumar , S. & Thakur , S. Local polar and long-range isotropic activity assisted swelling and collapse dynamics of an active ring polymer . Macromolecules 56 , 5229 – 5236 ( 2023 ). OpenUrl [34]. ↵ Chen , W. , Chen , J. , Liu , L. , Xu , X. & An , L. Effects of chain stiffness on conformational and dynamical properties of individual ring polymers in shear flow . Macromolecules 46 , 7542 – 7549 ( 2013 ). URL doi: 10.1021/ma401137c . OpenUrl CrossRef [35]. ↵ Chen , W. et al. Effects of excluded volume and hydrodynamic interaction on the deformation, orientation and motion of ring polymers in shear flow . Soft Matter 11 , 5265 – 5273 ( 2015 ). URL doi: 10.1039/C5SM00837A . OpenUrl CrossRef [36]. ↵ Binder , K. Applications of monte carlo methods to statistical physics . Reports on Progress in Physics 60 , 487 ( 1997 ). URL doi: 10.1088/0034-4885/60/5/001 . OpenUrl CrossRef [37]. Aparna , J. , Padinhateeri , R. & Das , D. Signatures of a macroscopic switching transition for a dynamic microtubule . Scientific reports 7 , 45747 ( 2017 ). OpenUrl [38]. ↵ Iino , S. , Morita , S. , Kawashima , N. & Sandvik , A. W. Detecting signals of weakly first-order phase transitions in two-dimensional potts models . Journal of the Physical Society of Japan 88 , 034006 ( 2019 ). OpenUrl [39]. ↵ Gerashchenko , S. & Steinberg , V. Statistics of tumbling of a single polymer molecule in shear flow . Phys. Rev. Lett . 96 , 038304 ( 2006 ). URL doi: 10.1103/PhysRevLett.96.038304 . OpenUrl CrossRef PubMed [40]. Formanek , M. & Moreno , A. J. Single-chain nanoparticles under homogeneous shear flow . Macromolecules 52 , 1821 – 1831 ( 2019 ). OpenUrl [41]. ↵ Li , R. , Gompper , G. & Ripoll , M. Tumbling and vorticity drift of flexible helicoidal polymers in shear flow . Macromolecules 54 , 812 – 823 ( 2021 ). OpenUrl [42]. ↵ Xu , X. , Chen , J. & An , L. Shear thinning behavior of linear polymer melts under shear flow via nonequilibrium molecular dynamics . The Journal of chemical physics 140 ( 2014 ). [43]. ↵ Singh , S. & Kumar , S. Dynamics of a polymer under multi-gradient fields . The Journal of Chemical Physics 150 , 024906 ( 2019 ). URL doi: 10.1063/1.5052219 . OpenUrl CrossRef [44]. Usabiaga , F. B. & Delgado-Buscalioni , R. Characteristic times of polymer tumbling under shear flow . Macromolecular Theory and Simulations 20 , 466 – 471 ( 2011 ). URL https://onlinelibrary.wiley.com/doi/abs/10.1002/mats.201100020 . OpenUrl [45]. Huang , C.-C. , Gompper , G. & Winkler , R. G. Non-equilibrium relaxation and tumbling times of polymers in semidilute solution . Journal of Physics: Condensed Matter 24 , 284131 ( 2012 ). URL doi: 10.1088/0953-8984/24/28/284131 . OpenUrl CrossRef [46]. ↵ Liu , L. , Chen , J. & An , L. Individual circular polyelectrolytes under shear flow . The Journal of Chemical Physics 149 , 163316 ( 2018 ). OpenUrl [47]. ↵ Abkarian , M. , Faivre , M. & Viallat , A. Swinging of red blood cells under shear flow . Phys. Rev. Lett . 98 , 188302 ( 2007 ). URL doi: 10.1103/PhysRevLett.98.188302 . OpenUrl CrossRef PubMed [48]. Noguchi , H. & Gompper , G. Dynamics of fluid vesicles in shear flow: Effect of membrane viscosity and thermal fluctuations . Phys. Rev. E 72 , 011901 ( 2005 ). URL doi: 10.1103/PhysRevE.72.011901 . OpenUrl CrossRef [49]. ↵ Chuphal , P. , p , V. & Thakur , S. Dynamics of diffusiophoretic vesicle under external shear flow . The Journal of Chemical Physics 151 , 064901 ( 2019 ). URL doi: 10.1063/1.5112808 . OpenUrl CrossRef [50]. ↵ Wang , D. , Wen , X. , Zhang , D. , Tan , X. & Tang , J. Single-polymer dynamics of starch-like branched ring polymers in steady shear flow . International Journal of Biological Macromolecules 227 , 173 – 181 ( 2023 ). OpenUrl View the discussion thread. Back to top Previous Next Posted January 25, 2024. Download PDF Supplementary Material Email Thank you for your interest in spreading the word about bioRxiv. NOTE: Your email address is requested solely to identify you as the sender of this article. Your Email * Your Name * Send To * Enter multiple addresses on separate lines or separate them with commas. You are going to email the following Shear flow as a tool to distinguish microscopic activities of molecular machines in a chromatin loop Message Subject (Your Name) has forwarded a page to you from bioRxiv Message Body (Your Name) thought you would like to see this page from the bioRxiv website. Your Personal Message CAPTCHA This question is for testing whether or not you are a human visitor and to prevent automated spam submissions. Share Shear flow as a tool to distinguish microscopic activities of molecular machines in a chromatin loop Sandeep Kumar , Ranjith Padinhateeri , Snigdha Thakur bioRxiv 2024.01.23.576811; doi: https://doi.org/10.1101/2024.01.23.576811 Share This Article: Copy Citation Tools Shear flow as a tool to distinguish microscopic activities of molecular machines in a chromatin loop Sandeep Kumar , Ranjith Padinhateeri , Snigdha Thakur bioRxiv 2024.01.23.576811; doi: https://doi.org/10.1101/2024.01.23.576811 Citation Manager Formats BibTeX Bookends EasyBib EndNote (tagged) EndNote 8 (xml) Medlars Mendeley Papers RefWorks Tagged Ref Manager RIS Zotero Tweet Widget Facebook Like Google Plus One Subject Area Biophysics Subject Areas All Articles Animal Behavior and Cognition (7644) Biochemistry (17728) Bioengineering (13916) Bioinformatics (42037) Biophysics (21489) Cancer Biology (18637) Cell Biology (25553) Clinical Trials (138) Developmental Biology (13401) Ecology (19941) Epidemiology (2067) Evolutionary Biology (24367) Genetics (15622) Genomics (22547) Immunology (17764) Microbiology (40475) Molecular Biology (17208) Neuroscience (88747) Paleontology (667) Pathology (2842) Pharmacology and Toxicology (4834) Physiology (7659) Plant Biology (15175) Scientific Communication and Education (2047) Synthetic Biology (4304) Systems Biology (9835) Zoology (2272)