Modeling of energy-utilizing biopolymers

Jared Scripture

(University of Notre Dame, USA)

"Quantification of Microtubule Stutters: Dynamic Instability Behaviors that are Strongly Associated with Catastrophe"

Microtubules (MTs) are cytoskeletal fibers that undergo dynamic instability (DI), a remarkable process involving phases of growth and shortening separated by stochastic transitions called catastrophe and rescue. Dissecting dynamic instability mechanism(s) requires first characterizing and quantifying these dynamics, a subjective process that often ignores complexity in MT behavior. We present a Statistical Tool for Automated Dynamic Instability Analysis (STADIA), which identifies and quantifies not only growth and shortening, but also a category of intermediate behaviors that we term ‘stutters.’ During stutters, the rate of MT length change tends to be smaller in magnitude than during typical growth or shortening phases. Quantifying stutters and other behaviors with STADIA demonstrates that stutters precede most catastrophes in our dimer-scale MT simulations and in vitro experiments, suggesting that stutters are mechanistically involved in catastrophes. Related to this idea, we show that the anti-catastrophe factor CLASP2γ works by promoting the return of stuttering MTs to growth. STADIA enables more comprehensive and data-driven analysis of MT dynamics compared to previous methods. The treatment of stutters as distinct and quantifiable DI behaviors provides new opportunities for analyzing mechanisms of MT dynamics and their regulation by binding proteins.

Diana White

(Clarkson University, USA)

"Modelling microtubule dynamic instability: microtubule growth, shortening and pausing"

Microtubules (MTs) are protein polymers which help form the cytoskeleton of all eukaryotic cells. They are crucial for normal cell development, providing structural support for cells, aiding in cell polarization, as well as aiding in cell motility and division. In order to perform these functions, MTs take on different organizations, in addition to being very dynamic. In particular, MTs go through random periods of relatively slow polymerization (growth) followed by very fast depolymerization (shrinkage), a unique type of dynamics called dynamic instability. The onset of a MT shrinking event is called a catastrophe, while the event at which a MT starts to grow again is called a rescue. Although MT dynamic instability has traditionally been described solely in terms of growth and shortening, MTs have also been shown to pause for extended periods of time. Here, we present a novel mathematical model to describe dynamic instability of MTs in terms of growth, shortening and pausing. Our model is a coupled PDE model, that describes length variations in polymerized tubulin (those growing, shrinking, and pausing), with an ODE model to describe the temporal dynamics of free tubulin. Here, we explore how MT dynamics, and in particular MT catastrophe frequency, is altered in the presence of a pausing/quiescent phase, and compare these results with experimental findings.

Kimberly Weirich

(Clemson University, USA)

"Self-organization and shape change in active biopolymer droplets"

Complex mixtures of macromolecules self-organize to form the soft and active biological materials that structure the cellular cytoplasm. Ordered assemblies of cytoskeletal filaments, such as stress fibers and mitotic spindles, orchestrate the complex mechanical behavior of cells. Key to understanding these exquisite mechanics is elucidating the physical principles of self-organization in these systems. We recently reported dense condensates of cytoskeletal filaments that form liquid crystal condensed phases, where structure arises from the anisotropy of the filaments. Here, we discuss emergent self-organization and shape changes that result from forming composites of these liquid crystals with biological polymers of different rigidities and activity. Our results highlight the role of anisotropy in the self-organization of biological materials and suggest physical mechanisms of controlling shape change in bio-inspired, soft materials.

Sidney Shaw

(Indiana University, USA)

"Extracting local polymer dynamics for global cellular models."

Eukaryotic cells create dynamic polymer systems that affect a wide variety of critical cellular functions. The microtubule polymers in plant cells, for example, form patterns at the cell cortex that template the deposition of cellulose into the nascent primary wall with subsequent effects on the wall material properties that govern cell expansion. A key factor in creating and maintaining the patterned microtubule array is the persistent addition of tubulin subunits to the microtubule ‘plus’ end, with concurrent loss of subunits from the ‘minus’ end, affecting a form of polymer treadmilling that is critical to microtubule array patterning in this system. Prior simulations of this microtubule system coming to a steady-state with a fixed subunit number and cell volume indicated that the frequency of stochastic switching between states of plus-end growth and shortening, termed catastrophe, should critically impact all facets of the steady state polymer system. To further investigate the nature and conditions under which catastrophe occurs, we developed high temporal/spatial in vivo microscopy methods for examining the dynamic properties of cortical microtubules in super-resolved detail. Using model- based tracking algorithms, we observe that polymer growth shows a spectrum of intermediate growth states with transitions from growth to shortening being preceded by a bona fide pause state. Using high temporal resolution data, we find that the decision to resume growth or to catastrophe into depolymerization is temporally consistent with the conversion of GTP-tubulin at the microtubule plus end to GDP-tubulin through stochastic hydrolysis. In cells lacking expression of a known microtubule binding protein, we find evidence that the rate of GTP hydrolysis for tubulin subunits binding to the microtubule plus end differs significantly from wild type. Using computational modeling approaches to compare these systems, we provide evidence that plant cells modulate the tubulin GTPase rate constant in order to control the persistence of plus end growth and the frequency of microtubule catastrophe in this treadmilling system. These data are now being used to revise our cellular scale models for understanding how these microtubule achieve and maintain a steady-state microtubule array.