Cortical dynein drives centrosome clustering in cells with centrosome amplification.

During cell division, the microtubule nucleating and organizing organelle, known as the centrosome, is a critical component of the mitotic spindle. In cells with two centrosomes, each centrosome functions as an anchor point for microtubules, leading to the formation of a bipolar spindle and progression through a bipolar cell division. When extra centrosomes are present, multipolar spindles form and the parent cell may divide into more than two daughter cells. Cells that are born from multipolar divisions are not viable, and hence clustering of extra centrosomes and progression to a bipolar division are critical determinants of viability in cells with extra centrosomes. We combine experimental approaches with computational modeling to define a role for cortical dynein in centrosome clustering. We show that centrosome clustering fails and multipolar spindles dominate when cortical dynein distribution or activity is experimentally perturbed. Our simulations further reveal that centrosome clustering is sensitive to the distribution of dynein on the cortex. Together, these results indicate that dynein's cortical localization alone is insufficient for effective centrosome clustering and, instead, dynamic relocalization of dynein from one side of the cell to the other throughout mitosis promotes timely clustering and bipolar cell division in cells with extra centrosomes.

Modeling reveals cortical dynein-dependent fluctuations in bipolar spindle length.

Proper formation and maintenance of the mitotic spindle is required for faithful cell division. Although much work has been done to understand the roles of the key molecular components of the mitotic spindle, identifying the consequences of force perturbations in the spindle remains a challenge. We develop a computational framework accounting for the minimal force requirements of mitotic progression. To reflect early spindle formation, we model microtubule dynamics and interactions with major force-generating motors, excluding chromosome interactions that dominate later in mitosis. We directly integrate our experimental data to define and validate the model. We then use simulations to analyze individual force components over time and their relationship to spindle dynamics, making it distinct from previously published models. We show through both model predictions and biological manipulation that rather than achieving and maintaining a constant bipolar spindle length, fluctuations in pole-to-pole distance occur that coincide with microtubule binding and force generation by cortical dynein. Our model further predicts that high dynein activity is required for spindle bipolarity when kinesin-14 (HSET) activity is also high. To the best of our knowledge, our results provide novel insight into the role of cortical dynein in the regulation of spindle bipolarity.

A Bayesian Framework to Estimate Fluid and Material Parameters in Micro-swimmer Models.

To advance our understanding of the movement of elastic microstructures in a viscous fluid, techniques that utilize available data to estimate model parameters are necessary. Here, we describe a Bayesian uncertainty quantification framework that is highly parallelizable, making parameter estimation tractable for complex fluid-structure interaction models. Using noisy in silico data for swimmers, we demonstrate the methodology's robustness in estimating fluid and elastic swimmer parameters, along with their uncertainties. We identify correlations between model parameters and gain insight into emergent swimming trajectories of a single swimmer or a pair of swimmers. Our proposed framework can handle data with a spatiotemporal resolution representative of experiments, showing that this framework can be used to aid in the development of artificial micro-swimmers for biomedical applications, as well as gain a fundamental understanding of the range of parameters that allow for certain motility patterns.

A Hybrid Model of Cartilage Regeneration Capturing the Interactions Between Cellular Dynamics and Porosity.

To accelerate the development of strategies for cartilage tissue engineering, models are necessary to investigate the interactions between cellular dynamics and the local microenvironment. We use a discrete framework to capture the individual behavior of cells, modeling experiments where cells are seeded in a porous scaffold or hydrogel and over the time course of a month, the scaffold slowly degrades while cells divide and synthesize extracellular matrix constituents. The movement of cells and the ability to proliferate is a function of the local porosity, defined as the volume fraction of fluid in the surrounding region. A phenomenological approach is used to capture a continuous profile for the degrading scaffold and accumulating matrix, which will then change the local porosity throughout the construct. We parameterize the model by first matching total cell counts in the construct to chondrocytes seeded in a polyglycolic acid scaffold (Freed et al. in Biotechnol Bioeng 43:597-604, 1994). We investigate the influence of initial scaffold porosity on the total cell count and spatial profiles of cell and ECM in the construct. Cell counts were higher at day 30 in scaffolds of lower initial porosity, and similar cell counts were obtained using different models of scaffold degradation and matrix accumulation (either uniform or cell-specific). Using this modeling framework, we study the interplay between a phenomenological representation of scaffold architecture and porosity as well as the potential continuous application of growth factors. We determine parameter regimes where large cellular aggregates occur, which can hinder matrix accumulation and cellular proliferation. The developed modeling framework can easily be extended and can be used to identify optimal scaffolds and culture conditions that lead to a desired distribution of extracellular matrix and cell counts throughout the construct.

A computational reaction-diffusion model for biosynthesis and linking of cartilage extracellular matrix in cell-seeded scaffolds with varying porosity.

Cartilage tissue engineering is commonly initiated by seeding cells in porous materials such as hydrogels or scaffolds. Under optimal conditions, the resulting engineered construct has the potential to fill regions where native cartilage has degraded or eroded. Within a cell-seeded scaffold supplied by nutrients and growth factors, extracellular matrix accumulation should occur concurrently with scaffold degradation. At present, the interplay between cell-mediated synthesis and linking of matrix constituents and the evolving scaffold properties is not well understood. We develop a computational model of extracellular matrix accumulation in a cell-seeded scaffold based on a continuum reaction-diffusion system with inhomogeneous inclusions representing individual cells. The effects of porosity on engineered tissue outcomes is accounted for via the use of mixture variables capturing the spatiotemporal dynamics of both bound and unbound system constituents. The unbound constituents are the nutrients and unlinked extracellular matrix, while the bound constituents are the scaffold and the linked extracellular matrix. The linking model delineates binding of matrix constituents to either existing bound extracellular matrix or to scaffold. Results on a representative domain exhibit bound matrix trapping (vs spreading) around cells in scaffolds with lower (vs higher) initial porosity, similar to experimental results obtained by Erickson et al. (Osteoarthr Cartil 17:1639-1648, 2009). Significant alterations in the spatiotemporal accumulation of bound matrix are observed when, among the set of all model parameters, only the initial scaffold porosity is varied. The model presented herein proposes a methodology to investigate coupling between cell-mediated biosynthesis and linking of extracellular matrix in porous, cell-seeded scaffolds that has the potential to aid in the design of optimal tissue-engineered cartilage constructs.

Emergent three-dimensional sperm motility: coupling calcium dynamics and preferred curvature in a Kirchhoff rod model.

Changes in calcium concentration along the sperm flagellum regulate sperm motility and hyperactivation, characterized by an increased flagellar bend amplitude and beat asymmetry, enabling the sperm to reach and penetrate the ovum (egg). The signalling pathways by which calcium increases within the flagellum are well established. However, the exact mechanisms of how calcium regulates flagellar bending are still under investigation. We extend our previous model of planar flagellar bending by developing a fluid-structure interaction model that couples the 3D motion of the flagellum in a viscous Newtonian fluid with the evolving calcium concentration. The flagellum is modelled as a Kirchhoff rod: an elastic rod with preferred curvature and twist. The calcium dynamics are represented as a 1D reaction-diffusion model on a moving domain, the flagellum. The two models are coupled assuming that the preferred curvature and twist of the sperm flagellum depend on the local calcium concentration. To investigate the effect of calcium on sperm motility, we compare model results of flagellar bend amplitude and swimming speed for three cases: planar, helical (spiral with equal amplitude in both directions), and quasi-planar (spiral with small amplitude in one direction). We observe that for the same parameters, the planar swimmer is faster and a turning motion is more clearly observed when calcium coupling is accounted for in the model. In the case of flagellar bending coupled to the calcium concentration, we observe emergent trajectories that can be characterized as a hypotrochoid for both quasi-planar and helical bending.

Swimming speeds of filaments in viscous fluids with resistance.

Many microorganisms swim in a highly heterogeneous environment with obstacles such as fibers or polymers. To better understand how this environment affects microorganism swimming, we study propulsion of a cylinder or filament in a fluid with a sparse, stationary network of obstructions modeled by the Brinkman equation. The mathematical analysis of swimming speeds is investigated by studying an infinite-length cylinder propagating lateral or spiral displacement waves. For fixed bending kinematics, we find that swimming speeds are enhanced due to the added resistance from the fibers. In addition, we examine the work and the torque exerted on the cylinder in relation to the resistance. The solutions for the torque, swimming speed, and work of an infinite-length cylinder in a Stokesian fluid are recovered as the resistance is reduced to zero. Finally, we compare the asymptotic solutions with numerical results for the Brinkman flow with regularized forces. The swimming speed of a finite-length filament decreases as its length decreases and planar bending induces an angular velocity that increases linearly with added resistance. The comparisons between the asymptotic analysis and computation give insight on the effect of the length of the filament, the permeability, and the thickness of the cylinder in terms of the overall performance of planar and helical swimmers.

Compartment calcium model of frog skeletal muscle during activation.

Skeletal muscle contraction is triggered by a rise in calcium (Ca(2+)) concentration in the myofibrillar space. The objective of this study was to develop a voltage dependent compartment model of Ca(2+) dynamics in frog skeletal muscle fibers. The compartment model corresponds to the myofibrillar space (MS) and a calcium store, the sarcoplasmic reticulum (SR). Ca(2+) is released from the SR to the MS based on the voltage and is able to bind to several proteins in the MS. We use a detailed model to account for voltage dependent Ca(2+) release and inactivation. With this model, we are able to match previous experimental data for Ca(2+) release and binding to proteins for an applied (fixed) voltage. We explore the sensitivity of parameters in the model and illustrate the importance of inactivation of the SR; during a long depolarization, the SR must be inactivated in order to achieve realistic Ca(2+) concentrations in the MS. A Hodgkin Huxley type model was also developed to describe voltage at the surface membrane using electrophysiological data from previous experiments. This voltage model was then used as the time dependent voltage to determine Ca(2+) release from the SR. With this fully coupled model, we were able to match previous experimental results for Ca(2+) concentrations for a given applied current. Additionally, we examined simulated Ca(2+) concentrations in the case of twitch and tetanus, corresponding to different applied currents. The developed model is robust and reproduces many aspects of voltage dependent calcium signaling in frog skeletal muscle fibers. This modeling framework provides a platform for future studies of excitation contraction coupling in skeletal muscle fibers.

Nonlinear dynamics of a rotating elastic rod in a viscous fluid.

The dynamics of an elastic rod in a viscous fluid at zero Reynolds number is investigated when the bottom end of the rod is tethered at a point in space and rotates at a prescribed angular frequency, while the other part of the rod freely moves through the fluid. A rotating elastic rod, which is intrinsically straight, exhibits three dynamical motions: twirling, overwhirling, and whirling. The first two motions are stable, whereas the last motion is unstable. The stability of dynamical motions is determined by material and geometrical properties of the rod, fluid properties, and the angular frequency of the rod. We employ the regularized Stokes flow to describe the fluid motion and the Kirchhoff rod model to describe the elastic rod. Our simulation results display subcritical Hopf bifurcation diagrams indicating the bistability region. We also investigate the whirling motion generated by the rotation of an intrinsically bent rod. It is observed that the angular frequency determines the handedness of the whirling rod and thus the flow direction and that there is a critical frequency which separates the positive (upward) flow at frequencies above it from the negative (downward) flow at frequencies below it.

Fluid dynamic model of invertebrate sperm chemotactic motility with varying calcium inputs.

In a marine environment, invertebrate sperm are able to adjust their trajectory in response to a gradient of chemical factors released by the egg in a process called chemotaxis. In response to this chemical factor, a signaling cascade is initiated that causes an increase in intracellular calcium (Ca(2+)). This increase in Ca(2+) causes the sperm flagellar curvature to change, and a change in swimming direction ensues. In previous experiments, sperm swimming in a gradient of chemoattractant have exhibited Ca(2+) oscillations of varying peaks and frequency. Here, we model a simplified sperm flagellum with mechanical forces, including a passive stiffness component and an active bending component that is coupled to the time varying Ca(2+) input. The flagellum is immersed in a viscous, incompressible fluid and we use a fluid dynamic model to investigate emergent trajectories. We investigate the sensitivity of the model to the frequency of Ca(2+) oscillations. In this coupled model, we observe that longer periods of Ca(2+) oscillation corresponds to circular paths with greater drift. In contrast, shorter periods of Ca(2+) oscillations corresponded to tighter search patterns. These outcomes shed light on the relation between Ca(2+) oscillations and different searching trajectories and strategies that invertebrate sperm may utilize to reach and fertilize the egg in a marine environment.

Coupling biochemistry and hydrodynamics captures hyperactivated sperm motility in a simple flagellar model.

Hyperactivation in mammalian sperm is characterized by highly asymmetrical waveforms and an increase in the amplitude of flagellar bends. It is important for the sperm to be able to achieve hyperactivated motility in order to reach and fertilize the egg. Calcium (Ca(2+)) dynamics are known to play a large role in the initiation and maintenance of hyperactivated motility. Here we present an integrative model that couples the CatSper channel mediated Ca(2+) dynamics of hyperactivation to a mechanical model of an idealized sperm flagellum in a 3-d viscous, incompressible fluid. The mechanical forces are due to passive stiffness properties and active bending moments that are a function of the local Ca(2+) concentration along the length of the flagellum. By including an asymmetry in bending moments to reflect an asymmetry in the axoneme's response to Ca(2+), we capture the transition from activated motility to hyperactivated motility. We examine the effects of elastic properties of the flagellum and the Ca(2+) dynamics on the overall swimming patterns. The swimming velocities of the model flagellum compare well with data for hyperactivated mouse sperm.

A model of CatSper channel mediated calcium dynamics in mammalian spermatozoa.

CatSpers are calcium (Ca(2+)) channels that are located along the principal piece of mammalian sperm flagella and are directly linked to sperm motility and hyperactivation. It has been observed that Ca(2+) entry through CatSper channels triggers a tail to head Ca(2+) propagation in mouse sperm, as well as a sustained increase of Ca(2+) in the head. Here, we develop a mathematical model to investigate this propagation and sustained increase in the head. A 1-d reaction-diffusion model tracking intracellular Ca(2+) with flux terms for the CatSper channels, a leak flux, and plasma membrane Ca(2+) clearance mechanism is studied. Results of this simple model exhibit tail to head Ca(2+) propagation, but no sustained increase in the head. Therefore, in this model, a simple plasma membrane pump-leak system with diffusion in the cytosol cannot account for these experimentally observed results. It has been proposed that Ca(2+) influx from the CatSper channels induce additional Ca(2+) release from an internal store. We test this hypothesis by examining the possible role of Ca(2+) release from the redundant nuclear envelope (RNE), an inositol 1,4,5-trisphosphate (IP(3)) gated Ca(2+) store in the neck. The simple model is extended to include an equation for IP(3) synthesis, degradation, and diffusion, as well as flux terms for Ca(2+) in the RNE. When IP(3) and the RNE are accounted for, the results of the model exhibit a tail to head Ca(2+) propagation as well as a sustained increase of Ca(2+) in the head.

Anti-CD3 x anti-epidermal growth factor receptor (EGFR) bispecific antibody redirects T-cell cytolytic activity to EGFR-positive cancers in vitro and in an animal model.

PURPOSE: Targeting epidermal growth factor receptor (EGFR) overexpressed by many epithelial-derived cancer cells with anti-EGFR monoclonal antibodies (mAb) inhibits their growth. A limited number of clinical responses in patients treated with the anti-EGFR mAb, (cetuximab), may reflect variability in EGFR type or signaling in neoplastic cells. This study combines EGFR-targeting with the non-MHC-restricted cytotoxicity of anti-CD3 activated T cells (ATC) to enhance receptor-directed cytotoxicity. EXPERIMENTAL DESIGN: ATC from normal and patient donors were expanded ex vivo. Specific cytolytic activity of ATC armed with anti-CD3 x anti-EGFR (EGFRBi) against EGFR-expressing cancer cells derived from lung, pancreas, colon, prostate, brain, skin, or EGFR-negative breast cancer cells was evaluated in (51)Cr release assays. In vivo studies comparing tumor growth delay induced by EGFRBi-armed ATCs or cetuximab were done in severe combined immunodeficient/Beige mice (SCID-Beige) bearing COLO 356/FG pancreatic and LS174T colorectal tumors. RESULTS: At effector/target ratios from 3.125 to 50, both EGFRBi-armed normal and patient ATC were significantly more cytotoxic, by 23% to 79%, against EGFR-positive cells over ATC, cetuximab, anti-CD3 alone, or ATC armed with irrelevant BiAb directed at CD20. EGFRBi-armed ATC also secreted significantly higher levels of some T(H1)/T(H2) cytokines compared with ATC alone. In mice, i.v. infusions of EGFRBi-armed ATC (0.001 mg equivalent/infusion) were equally effective as cetuximab (1 mg/infusion) alone for significantly delaying growth of established COLO 356/FG but not LS174T tumors compared with mice that received ATC alone or vehicle (P < 0.001). CONCLUSIONS: Combining EGFR antibody targeting with T cell-mediated cytotoxicity may overcome some limitations associated with EGFR-targeting when using cetuximab alone.