Electrodiffusion with Calcium-Activated Potassium Channels in Dendritic Spine.

We investigate calcium signaling feedback through calcium-activated potassium channels of a dendritic spine by applying the immersed boundary method with electrodiffusion. We simulate the stochastic gating of such ion channels and the resulting spatial distribution of concentration, current, and membrane voltage within the dendritic spine. In this simulation, the permeability to ionic flow across the membrane is regulated by the amplitude of chemical potential barriers. With spatially localized ion channels, chemical potential barriers are locally and stochastically regulated. This regulation represents the ion channel gating with multiple subunits, the open and closed states governed by a continuous-time Markov process. The model simulation recapitulates an inhibitory action on voltage-sensitive calcium channels by the calcium-activated potassium channels in a stochastic manner as a non-local feedback loop. The model predicts amplified calcium influx with more closely placed channel complexes, proposing a potential mechanism of differential calcium handling by channel distributions. This work provides a foundation for future computer simulation studies of dendritic spine motility and structural plasticity.

Electrical Propagation of Vasodilatory Signals in Capillary Networks.

We have developed a computational model to study electrical propagation of vasodilatory signals and arteriolar regulation of blood flow depending on the oxygen tension and agonist distribution in the capillary network. The involving key parameters of endothelial cell-to-cell electrical conductivity and plasma membrane area per unit volume were calibrated with the experimental data on an isolated endothelial tube of mouse skeletal feeding arteries. We have estimated the oxygen saturation parameters in terms of erythrocyte ATP release from the data of a left anterior descending coronary blood perfusion of dog. Regarding the acetylcholine-induced upstream conduction, our model shows that spatially uniform superfusion of acetylcholine attenuates the electrical signal propagation, and blocking calcium-activated potassium channels suppresses that attenuation. On the other hand, a local infusion of acetylcholine induces enhanced electrical propagation that corresponds to physiological relevance. Integrating the electrophysiology of endothelial tube and the electrophysiology/mechanics of a lumped arteriole, we show mechanistically that endothelial purinergic oxygen sensing of ATP released from erythrocytes and local infusion of acetylcholine are individually effective to induce vasodilatory signals to regulate blood flow in arterioles. We have recapitulated the upstream vasomotion in arterioles from the elevated oxygen tension in the downstream capillary domain. This study is a foundation for characterizing effective pharmaceutical strategies for ascending vasodilation and oxygenation.

Computationally modeling mammalian succinate dehydrogenase kinetics identifies the origins and primary determinants of ROS production.

Succinate dehydrogenase (SDH) is an inner mitochondrial membrane protein complex that links the Krebs cycle to the electron transport system. It can produce significant amounts of superoxide ([Formula: see text]) and hydrogen peroxide (H2O2); however, the precise mechanisms are unknown. This fact hinders the development of next-generation antioxidant therapies targeting mitochondria. To help address this problem, we developed a computational model to analyze and identify the kinetic mechanism of [Formula: see text] and H2O2 production by SDH. Our model includes the major redox centers in the complex, namely FAD, three iron-sulfur clusters, and a transiently bound semiquinone. Oxidation state transitions involve a one- or two-electron redox reaction, each being thermodynamically constrained. Model parameters were simultaneously fit to many data sets using a variety of succinate oxidation and free radical production data. In the absence of respiratory chain inhibitors, model analysis revealed the 3Fe-4S iron-sulfur cluster as the primary [Formula: see text] source. However, when the quinone reductase site is inhibited or the quinone pool is highly reduced, [Formula: see text] is generated primarily by the FAD. In addition, H2O2 production is only significant when the enzyme is fully reduced, and fumarate is absent. Our simulations also reveal that the redox state of the quinone pool is the primary determinant of free radical production by SDH. In this study, we showed the importance of analyzing enzyme kinetics and associated side reactions in a consistent, quantitative, and biophysically detailed manner using a diverse set of experimental data to interpret and explain experimental observations from a unified perspective.

Physical Mechanisms of Cancer in the Transition to Metastasis.

Whether a tumor is metastatic is one of the most significant factors that influence the prognosis for a cancer patient. The transition from a nonmetastatic tumor to a metastatic one is accompanied by a number of genetic and proteomic changes within the tumor cells. These protein-level changes conspire to produce behavioral changes in the cells: cells that had been relatively stationary begin to move, often as a group. In this study we ask the question of what cell-level biophysical changes are sufficient to initiate evasion away from an otherwise static tumor. We use a mathematical model developed to describe the biophysics of epithelial tissue to explore this problem. The model is first validated against in vitro wound healing experiments with cancer cell lines. Then we simulate the behavior of a group of mutated cells within a sea of healthy tissue. We find that moderate increases in adhesion between the cell and extracellular matrix (ECM) accompanied by a decrease in cell-cell adhesion and/or Rho family of small GTPase activation can cause a group of cells to break free from a tumor and spontaneously migrate. This result may explain why some metastatic cells have been observed to upregulate integrin, downregulate cadherin, and activate Rho family signaling.

An immersed boundary method for two-phase fluids and gels and the swimming of Caenorhabditis elegans through viscoelastic fluids.

The swimming of microorganisms typically involves the undulation or rotation of thin, filamentary objects in a fluid or other medium. Swimming in Newtonian fluids has been examined extensively, and only recently have investigations into microorganism swimming through non-Newtonian fluids and gels been explored. The equations that govern these more complex media are often nonlinear and require computational algorithms to study moderate to large amplitude motions of the swimmer. Here, we develop an immersed boundary method for handling fluid-structure interactions in a general two-phase medium, where one phase is a Newtonian fluid and the other phase is viscoelastic (e.g., a polymer melt or network). We use this algorithm to investigate the swimming of an undulating, filamentary swimmer in 2D (i.e., a sheet). A novel aspect of our method is that it allows one to specify how forces produced by the swimmer are distributed between the two phases of the fluid. The algorithm is validated by comparing theoretical predictions for small amplitude swimming in gels and viscoelastic fluids. We show how the swimming velocity depends on material parameters of the fluid and the interaction between the fluid and swimmer. In addition, we simulate the swimming of Caenorhabditis elegans in viscoelastic fluids and find good agreement between the swimming speeds and fluid flows in our simulations and previous experimental measurements. These results suggest that our methodology provides an accurate means for exploring the physics of swimming through non-Newtonian fluids and gels.

Heterogeneous mechanics of the mouse pulmonary arterial network.

Individualized modeling and simulation of blood flow mechanics find applications in both animal research and patient care. Individual animal or patient models for blood vessel mechanics are based on combining measured vascular geometry with a fluid structure model coupling formulations describing dynamics of the fluid and mechanics of the wall. For example, one-dimensional fluid flow modeling requires a constitutive law relating vessel cross-sectional deformation to pressure in the lumen. To investigate means of identifying appropriate constitutive relationships, an automated segmentation algorithm was applied to micro-computerized tomography images from a mouse lung obtained at four different static pressures to identify the static pressure-radius relationship for four generations of vessels in the pulmonary arterial network. A shape-fitting function was parameterized for each vessel in the network to characterize the nonlinear and heterogeneous nature of vessel distensibility in the pulmonary arteries. These data on morphometric and mechanical properties were used to simulate pressure and flow velocity propagation in the network using one-dimensional representations of fluid and vessel wall mechanics. Moreover, wave intensity analysis was used to study effects of wall mechanics on generation and propagation of pressure wave reflections. Simulations were conducted to investigate the role of linear versus nonlinear formulations of wall elasticity and homogeneous versus heterogeneous treatments of vessel wall properties. Accounting for heterogeneity, by parameterizing the pressure/distention equation of state individually for each vessel segment, was found to have little effect on the predicted pressure profiles and wave propagation compared to a homogeneous parameterization based on average behavior. However, substantially different results were obtained using a linear elastic thin-shell model than were obtained using a nonlinear model that has a more physiologically realistic pressure versus radius relationship.

Computer simulation of voltage sensitive calcium ion channels in a dendritic spine.

Membrane current through voltage-sensitive calcium ion channels at the postsynaptic density of a dendritic spine is investigated. To simulate the ion channels that carry such current and the resulting temporal and spatial distribution of concentration, current, and voltage within the dendritic spine, the immersed boundary method with electrodiffusion is applied. In this simulation method a spatially continuous chemical potential barrier is used to simulate the influence of the membrane on each species of ion. The amplitudes of these barriers can be regulated to simulate channel gating. Here we introduce this methodology in a one-dimensional setting. First, we study the current-voltage relationship obtained with fixed chemical potential barriers. Next, we simulate stochastic ion-channel gating in a calcium channel with multiple subunits, and observe the diffusive wave of calcium entry within the dendritic spine that follows channel opening. This work lays the foundation for future three-dimensional studies of electrodiffusion and advection electrodiffusion in dendritic spines.

Advent of complex flows in epithelial tissues.

The collective migration of cells in tissue pervades many important biological processes, such as wound healing, organism development, and cancer metastasis. Recent experiments on wound healing show that the collective migratory behavior of cells can be quite complex, including transient vortices and long-range correlations. Here, we explore cellular flows in epithelial tissues using a model that considers the force distribution and polarity of a single cell along with cell-cell adhesion. We show that the dipole nature of a crawling cell's force distribution destabilizes steady cellular motion. We determine the values of the physical parameters that are necessary to produce these complex motions and use numerical simulation to verify the linear analysis and to demonstrate the complex flows. We find that the tendency for cells to align is the dominant physical parameter that determines the stability of steady flows in the epithelium.

Crawling cells can close wounds without purse strings or signaling.

When a gash or gouge is made in a confluent layer of epithelial cells, the cells move to fill in the "wound." In some cases, such as in wounded embryonic chick wing buds, the movement of the cells is driven by cortical actin contraction (i.e., a purse string mechanism). In adult tissue, though, cells apparently crawl to close wounds. At the single cell level, this crawling is driven by the dynamics of the cell's actin cytoskeleton, which is regulated by a complex biochemical network, and cell signaling has been proposed to play a significant role in directing cells to move into the denuded area. However, wounds made in monolayers of Madin-Darby canine kidney (MDCK) cells still close even when a row of cells is deactivated at the periphery of the wound, and recent experiments show complex, highly-correlated cellular motions that extend tens of cell lengths away from the boundary. These experiments suggest a dominant role for mechanics in wound healing. Here we present a biophysical description of the collective migration of epithelial cells during wound healing based on the basic motility of single cells and cell-cell interactions. This model quantitatively captures the dynamics of wound closure and reproduces the complex cellular flows that are observed. These results suggest that wound healing is predominantly a mechanical process that is modified, but not produced, by cell-cell signaling.

The immersed boundary method for advection-electrodiffusion with implicit timestepping and local mesh refinement.

We describe an immersed boundary method for problems of fluid-solute-structure interaction. The numerical scheme employs linearly implicit timestepping, allowing for the stable use of timesteps that are substantially larger than those permitted by an explicit method, and local mesh refinement, making it feasible to resolve the steep gradients associated with the space charge layers as well as the chemical potential, which is used in our formulation to control the permeability of the membrane to the (possibly charged) solute. Low Reynolds number fluid dynamics are described by the time-dependent incompressible Stokes equations, which are solved by a cell-centered approximate projection method. The dynamics of the chemical species are governed by the advection-electrodiffusion equations, and our semi-implicit treatment of these equations results in a linear system which we solve by GMRES preconditioned via a fast adaptive composite-grid (FAC) solver. Numerical examples demonstrate the capabilities of this methodology, as well as its convergence properties.