### C. elegans chromosomes connect to centrosomes by anchoring into the spindle network

#### by S. Redemann et. al., to appear in Nature Communications (2017); BioRxiv 060855

Abstract: The mitotic spindle ensures the faithful segregation of chromosomes. To discover the nature of the crucial centrosome-to-chromosome connection during mitosis, we combined the first large-scale serial electron tomography of whole mitotic spindles in early C. elegans embryos with live-cell imaging. Using tomography, we reconstructed the positions of all microtubules in 3D, and identified their plus- and minus-ends. We classified them as kinetochore (KMTs), spindle (SMTs), or astral microtubules (AMTs) according to their positions, and quantified distinct properties of each class. While our light microscopy and mutant studies show that microtubules are nucleated from the centrosomes, we find only a few KMTs are directly connected to the centrosomes. Indeed, by quantitatively analysing several models of microtubule growth, we conclude that minus-ends of KMTs have selectively detached and depolymerized from the centrosome. In toto, our results show that the connection between centrosomes and chromosomes is mediated by an anchoring into the entire spindle network and that any direct connections through KMTs are few and likely very transient.

### Cytoplasmic flows as signatures for the mechanics of mitotic positioning

#### by E. Nazockdast et. al., to appear in Molecular Biology of the Cell (2017); arXiv:1511.02508 [physics.bio-ph].

Abstract: The proper positioning of mitotic spindle in the single-cell Caenorhabditis elegans embryo is achieved initially by the migration and rotation of the pronuclear complex (PNC) and its two associated as- tral microtubules (MTs). Pronuclear migration produces global cytoplasmic flows that couple the mechanics of all microtubules, the PNC, and the cell periphery with each other through their hydrodynamic interactions (HIs). We present the first study that explicitly accounts for detailed HIs between the cytoskeletal components and demonstrate the key consequences of HIs on the mechanics of pronuclear migration. First we show that, because of HIs between the MTs, the cytoplasm-filled astral MTs behave like a porous medium with its permeability decreasing with increasing the number of MTs. We then directly study the dynamics of PNC migration under various force-transduction models, including the pushing or pulling of MTs at the cortex, and the pulling of MTs by cytoplasmically-bound force generators. While achieving proper position and orientation on reasonable time-scales does not uniquely choose a model, we find that each model produces a different signature in its induced cytoplasmic flow. We suggest then that cytoplasmic flows can be used to differentiate between mechanisms.

### A fast platform for simulating semi-flexible fiber suspensions applied to cell mechanics

#### by E. Nazockdast et. al., Journal of Comp. Phys., 329, 173-209 (2017).

Abstract: We present a novel platform for the large-scale simulation of three-dimensional fibrous structures immersed in a Stokesian fluid and evolving under confinement or in free- space in three dimensions. One of the main motivations for this work is to study the dynamics of fiber assemblies within biological cells. For this, we also incorporate the key biophysical elements that determine the dynamics of these assemblies, which include the polymerization and depolymerization kinetics of fibers, their interactions with molecular motors and other objects, their flexibility, and hydrodynamic coupling. This work, to our knowledge, is the first technique to include many-body hydrodynamic interactions (HIs), and the resulting fluid flows, in cellular assemblies of flexible fibers. We use non- local slender body theory to compute the fluid–structure interactions of the fibers and a second-kind boundary integral formulation for other rigid bodies and the confining boundary. A kernel-independent implementation of the fast multipole method is utilized for efficient evaluation of HIs. The deformation of the fibers is described by nonlinear Euler–Bernoulli beam theory and their polymerization is modeled by the reparametrization of the dynamic equations in the appropriate non-Lagrangian frame. We use a pseudo- spectral representation of fiber positions and implicit time-stepping to resolve large fiber deformations, and to allow time-steps not excessively constrained by temporal stiffness or fiber–fiber interactions. The entire computational scheme is parallelized, which enables simulating assemblies of thousands of fibers. We use our method to investigate two important questions in the mechanics of cell division: (i) the effect of confinement on the hydrodynamic mobility of microtubule asters; and (ii) the dynamics of the positioning of mitotic spindle in complex cell geometries. Finally to demonstrate the general applicability of the method, we simulate the sedimentation of a cloud of semi-flexible fibers.

### Active microrheology of colloidal suspensions: simulation and microstructural theory

#### by E. Nazockdast, and J. F. Morris, J. Rheol, 60, 733 (2016).

Abstract: Discrete particle simulations by Accelerated Stokesian Dynamics (ASD) and a microstructural theory are applied to study the structure and viscosity of hard-sphere Brownian suspensions in active microrheology (MR). The work considers moderate to dense suspensions, from near to far from equilibrium conditions. The microscopic theory explicitly considers many-body hydrodynamic interactions in active MR, and is compared with the results of ASD simulations, which include detailed near- and far-field hydrodynamic interactions. We consider probe and bath particles which are spherical and of the same radius a. Two conditions of moving the probe sphere are considered: these apply constant force (CF) and constant velocity (CV), which approximately model magnetic bead and optical tweezer experiments, respectively. The structure is quantified using the probability distribution of colloidal particles around the probe, P

_{b|p(r)}= ng(r), giving the probability of finding a bath particle centered at a vector position r relative to a moving probe particle instantaneously centered at the origin; n is the bath particle number density, and is related to the suspension solid volume fraction, φ, by n = 3φ/4πa

^{3}. The pair distribution function for the bath particles relative to the probe, g(r), is computed as a solution to the pair Smoluchowski equation (SE) for 0.2 ≤ φ ≤ 0.50, and a range of P ́eclet numbers, describing the ratio of external force on the probe to thermal forces and defined as

_{f}= F

^{ext}/(k

_{b}T) and Pe

_{U}= 6πηU

^{ext}a

^{2}/(k

_{b}T) for CF and CV conditions, respectively. Results of simulation and theory demonstrate that a wake zone depleted of bath particles behind the moving probe forms at large P ́eclet numbers, while a boundary-layer accumulation develops upstream and near the probe. The wake length saturates at Pe

_{f}≫ 1 for CF, while it continuously grows with P eU in CV. This contrast in behavior is related to the dispersion in the motion of the probe under CF conditions, while CV motion has no dispersion; the dispersion is a direct result of many-body interactions. This effect is incorporated in the theory as a force-induced diffusion flux in pair SE. We also demonstrate that, despite this difference of structure in the two methods of moving the probe, the probability distribution of particles near the probe is primarily set by the P ́eclet number, for both CF and CV conditions, in agreement with dilute theories; as a consequence, similar values for apparent viscosity are found for the CF and CV conditions. Using the microscopic theory, the structural anisotropy and Brownian viscosity near equilibrium are shown to be quantitatively similar in both CF and CV motions, which is in contrast with the dilute theory which predicts larger distortions and Brownian viscosities in CV, by a factor of two relative to CF microrheology. This difference relative to dilute theory arises due to the determining role of many-body interactions associated with the underlying equilibrium structure in the semi-dilute to concentrated regime.

### Pair-particle dynamics and microstructure in sheared colloidal suspensions: Simulation and Smoluchowski theory

#### by E. Nazockdast, and J. F. Morris, Phys. Fluids, 25, 601 (2013).

Abstract: The Smoluchowski equation (SE) approach reduced to pair level provides an accepted method for analysis of the pairmicrostructure, i.e., the pair distribution function g(r), in sheared colloidal suspensions. Under dilute conditions, the resulting problem is well-defined, but for concentrated suspensions the coefficients of the pair SE are unclear. This work outlines a recently developed theoretical approach for analyti- cal and numerical study of the pair SE for concentrated colloidal suspensions of spheres in shear flow, and then focuses upon evaluation of coefficients and related properties of the problem from Stokesian Dynamics simulation, over a wide range of particle volume fraction , φ, and P´eclet number (ratio of shear to Brownian motion). The pair distribution function determined from the SE theory is in generally good agreement with Stokesian Dynamics, as are the computed viscosity and normal stresses of the material. The primary focus of the work is to consider the pair relative velocity predicted by the theory in comparison to Stokesian Dynamics simulations, as well as to evaluate quantities related to the hydrodynamic dispersion needed in the theoretical approach. The pair dynamics for moderate particle volume fraction,0.20 ≤ φ ≤ 0.35, are found to be remarkably different from the form for an isolated pair of spheres, and at φ ≥ 0.40 a qualitative change is again seen. Agreement of the theory and simulation on the primary features of the particle motion and structure is good, and discrepancies are clearly delineated.

### Effect of repulsive interactions on structure and rheology of sheared colloidal dispersions

#### by E. Nazockdast, and J. F. Morris, Soft Matter , 8, 4223-4234 (2012).

Abstract: A previously developed Smoluchowski theory for concentrated hard-sphere suspensions in shear flow is extended to study
structure and rheology of colloidal suspensions with soft repulsive interactions. Accelerated Stokesian Dynamics simulations
are carried out to provide insight and to enable direct comparison with theoretical predictions. The effect of extended range
repulsive interactions is studied by considering repulsive interactions with different steepness, using identical potentials in simulation and theory,
for varying shear rates characterized in dimensionless form as 0.1 ≤ Pe ≤ 100; here, Pe = 6πηγ^{.}a^{3}/k_{b}T is the ratio of
hydrodynamic to Brownian forces and η is the fluid viscosity, γ^{.} is the shear rate, a is the particle radius and kbT is the thermal energy.
Examples of predicted microstructures and the equivalent simulated results for hard-sphere suspensions at φ =0.40 are also presented for comparison.
The predicted pair distribution function is in good agreement with simulations before the onset of a shear-induced ordering transition in simulations of the soft colloids.
The calculations of shear viscosity based on the predicted microstructure were also in general agreement with simulation results.
The role of hydrodynamic interactions on flow-induced structures is discussed in the context of the proposed theory.

### Microstructural theory and the rheology ofconcentrated colloidal suspensions

#### by E. Nazockdast, and J. F. Morris, J. Fluid Mech., 713, 420-452 (2012).

Abstract: A theory for the analytical prediction of microstructure of concentrated Brownian suspensions of spheres in simple-shear flow is developed.
The computed microstructure is used in a prediction of the suspension rheology. A near-hard-sphere suspension is studied for
solid volume fraction ^{.}a^{3}/k_{b} <100^{.}_{b}

### Linear and nonlinear melt-state viscoelastic properties of Polypropylene/Organoclay nanocomposites

#### by E. Nazockdast et. al., Polym. Eng. Sci., 48, 1230–1249 (2008).

Abstract: Rheological behavior of polypropylene (PP)/organoclay nanocomposites varying in compatibilizer (PP-g-MA)and organoclay concentration was investigated. The samples were prepared by melt intercalation method in an internal mixer. The wide angle X-ray diffraction patterns and results of rheological measurements showed that the compatibilizer had strong inﬂuence in increasing the interlayer spacing. The observed low frequency liquid-like to solid-like transition and apparent yield stress in simple shear ﬂows, along with convergence of transient shear stress to nonzero values in stress relaxation after the cessation of ﬂow experiments, were found to be consistent with formation of a physical network in quiescent conditions which could be easily ruptured with applying low shear rates. The values of stress overshoot strain in ﬂow reversal experiments were independent of shear rate, organoclay, and compatibilizer content. From the results of frequency sweep experiments in different nonlinear strain amplitudes it was shown that extended Cox-Merz analogy was valid in nonlinear dynamic deformations while the shear viscosity showed positive deviation from this analogy with higher deviations at lower shear rates. Results of storage modulus recovery and ﬂow reversal experiments at different shear rates suggested that network structure is reformed with a much slower rate compared to the rotational relaxation of organoclay platelets.