Comparison of ABM and ODE time course data.

<p>Comparison of time-course data from an agent based model of molecular binding to that of the numerical solution of the ordinary differential equation for the same event. Probability selection using the relationship in Eq. 11 produces similar behavior to that of the numerical solution in a well-mixed system at multiple rate constants with the addition of stochasticity that is expected from natural systems.</p

Transport rate as a function of cytoplasmic affinity.

<p>Transport rate appears insensitive to cytoplasmic Nup-Impβ affinity as opposed to central channel and nuclear basket Nup-Impβ affinity. An increase or decrease to affinity in the cytoplasmic region by an order of magnitude results in a change in transport rate that is within a standard error. (CC: Central Channel, Nuc: Nuclear basket)</p

Transport rate as a function of cytoplasmic, central channel, and nuclear basket Nup-Impβ affinity.

<p>Impβ transport rate (z-axis) as a function of cytoplasmic (x-axis) and central channel (y-axis) Nup-Impβ affinity ranging from 2 µM to 2 mM. The four three-dimensional surfaces represent a range of nuclear basket affinities ranging from 0.2 µM to 200 µM. Transport rates appear to be least sensitive to cytoplasmic affinities and most sensitive to central channel and nuclear basket affinities. Varying central channel affinities results in biphasic behavior with maximum transport at K_D≈200 µM. Transport rates appear to increase as nuclear basket affinity is increased up to K_D≈10 µM and don't appear to show significant increase at higher affinities.</p

Impβ transport rate through a pore with Nups of uniform affinity.

<p>Transport rates for ABM simulations of Impβ through a nuclear pore containing Nups with uniform affinity (no gradient). Nup-Impβ affinity is varied from 100 nM to 4 mM. The transport rate exhibits biphasic behavior as a function of affinity. At very high affinities (low K_D), Impβ is tightly bound to Nups, resulting in slow transport rates as the Nups become saturated. At very low affinities, Impβ isn't able to bind Nups as efficiently, reducing its resident time at the pore periphery and subsequently excluding it from the pore interior as a result of steric effects. Peak transport of 86.24±1.68 transports per second were observed at a Nup-Impβ affinity of 200 µM. Pores containing Nup bound Impβ agents that are capable of diffusing locally exhibit increased transport rate compared to simulation configurations where Impβ becomes immobile once bound to an FG-Nup.</p

Summary of affinity gradients and <i>in silico</i> derived transport rates.

<p>Summary of <i>in vitro</i> affinity gradients for yeast and vertebrates and the agent based model derived transport rate corresponding to each affinity gradient. The model optimum affinity gradient is included for comparison. The ratio of gradients between yeast and model optimum are comparable while the magnitude of the individual affinities is approximately 1000 times weaker in the model optimum.</p

Transport rate as a function of central channel affinity.

<p>Impβ transport rate appears most sensitive to central channel affinity, regardless of nuclear basket affinity, with a peak transport rate when Nup-Impβ affinities are on the order of 100 µM. (Cyt: Cytoplasmic periphery, Nuc: Nuclear basket)</p

Schematic of the nuclear pore complex.

<p>The pore is anchored to the nuclear envelope by a membrane layer that surrounds the scaffold layer. This scaffold layer provides structure and serves as an anchor for Nups that contain both structured domains as well as highly unstructured domains that are thought to form a barrier that excludes non-interacting molecules while allowing for selective transport of others. This central channel exhibits eight-fold rotational symmetry and has eight cytoplasmic filaments as well as eight nuclear filaments protruding into the cytoplasm and nucleoplasm respectively. The nuclear filaments are bound via a ring, resulting in a basket structure.</p

Simplified representation of the agent based model.

<p>Abstract cartoon representation of the nuclear pore structure environment (not to scale) projected onto a simplified, 2-dimensional, on-lattice ABM with agents representing proteins that move within the system and interact with other agents within their von-Neumann neighborhood. The actual model consists of a three-dimensional representation of the NPC structure and physiologically relevant concentrations of biochemical factors and channel dimensions. In our model, the purple region representing the cytoplasmic periphery is treated as a compartmentalized volume containing non-interacting Nup and Impβ-interacting FG-Nup agents. Similarly, central channel (blue) and nuclear basket (green) regions are represented by compartmentalized volumes, containing both non-interacting and interacting Nup agents at physiologically meaningful concentrations. Grey regions of the diagram represent the scaffold and nuclear envelope regions of the model that are impermeable to diffusing species.</p

Transport rate as a function of nuclear basket affinity.

<p>Transport rates are very sensitive to nuclear basket Nup-Impβ affinity, with maximum transport rates emerging in the presence of a high affinity target for Impβ in the nuclear basket. Transport rates peak at an affinity of ∼2 µM with a slight decrease in transport rate as affinities are increased beyond that. This peak in transport rate doesn't appear to be due to a lack of RanGTP to terminate transport at the nuclear periphery of the pore since there aren't significant changes to transport rate under very high nuclear RanGTP concentrations. Conversely, when nuclear RanGTP concentrations are much lower than physiological values, the effect on transport rate is more noticeable.</p

The Interaction of Vinculin with Actin

<div><p>Vinculin can interact with F-actin both in recruitment of actin filaments to the growing focal adhesions and also in capping of actin filaments to regulate actin dynamics. Using molecular dynamics, both interactions are simulated using different vinculin conformations. Vinculin is simulated either with only its vinculin tail domain (Vt), with all residues in its closed conformation, with all residues in an open I conformation, and with all residues in an open II conformation. The open I conformation results from movement of domain 1 away from Vt; the open II conformation results from complete dissociation of Vt from the vinculin head domains. Simulation of vinculin binding along the actin filament showed that Vt alone can bind along the actin filaments, that vinculin in its closed conformation cannot bind along the actin filaments, and that vinculin in its open I conformation can bind along the actin filaments. The simulations confirm that movement of domain 1 away from Vt in formation of vinculin 1 is sufficient for allowing Vt to bind along the actin filament. Simulation of Vt capping actin filaments probe six possible bound structures and suggest that vinculin would cap actin filaments by interacting with both S1 and S3 of the barbed-end, using the surface of Vt normally occluded by D4 and nearby vinculin head domain residues. Simulation of D4 separation from Vt after D1 separation formed the open II conformation. Binding of open II vinculin to the barbed-end suggests this conformation allows for vinculin capping. Three binding sites on F-actin are suggested as regions that could link to vinculin. Vinculin is suggested to function as a variable switch at the focal adhesions. The conformation of vinculin and the precise F-actin binding conformation is dependent on the level of mechanical load on the focal adhesion.</p></div