Simulation methods for spatiotemporal models of biochemical signaling networks

Cells use signaling networks consisting of multiple interacting proteins to respond to changes in their environment. In many situations, such as chemotaxis, spatial and temporal information must be transmitted through a signaling network. Recent computational studies have emphasized the importance of cellular geometry in signal transduction, but have been limited in their ability to accurately represent complex cell morphologies. We present a finite volume method that addresses this problem. Our method uses Cartesian cut cells in a differential algebraic formulation to handle the complex boundary dynamics encountered in biological systems. The method is second order in space and time. Several models of signaling systems are simulated in realistic cell morphologies obtained from live cell images. We then examine the effects of geometry on signal transduction. External signals can trigger cells to polarize and move in a specific direction. During migration, spatially localized activity of proteins is maintained. To investigate the effects of morphological changes on intracellular signaling, we present a numerical scheme consisting of a cut cell finite volume spatial discretization coupled with level set methods to simulate the resulting advection-reaction-diffusion equation. We then show that shape deformations drive a Turing-type system into an unstable regime. The method is also applied to a model of a signaling network in a migrating fibroblast. Determining the signaling mechanisms used by membrane proteins that interact with the cytoskeleton is important for understanding phenomena such as T-cell activation and viral infection. To investigate these interactions, recent experiments have tracked the movements of single lipids and glycosyl-phosphatidylinositol (GPI) anchored protein clusters tagged with 40 nm gold particles. These experiments reveal regions of transient confinement and transient anchorage of the particles. The distribution of transient anchorage release times exhibits a long tail. We developed a stochastic model of the system to explain the transient anchorage release times and the underlying biochemical reaction system

A cut-cell method for simulating spatial models of biochemical reaction networks in arbitrary geometries

Cells use signaling networks consisting of multiple interacting proteins to respond to changes in their environment. In many situations, such as chemotaxis, spatial and temporal information must be transmitted through the network. Recent computational studies have emphasized the importance of cellular geometry in signal transduction, but have been limited in their ability to accurately represent complex cell morphologies. We present a finite volume method that addresses this problem. Our method uses Cartesian cut cells and is second order in space and time. We use our method to simulate several models of signaling systems in realistic cell morphologies obtained from live cell images and examine the effects of geometry on signal transduction

Simulating Biochemical Signaling Networks in Complex Moving Geometries

Signaling networks regulate cellular responses to environmental stimuli through cascades of protein interactions. External signals can trigger cells to polarize and move in a specific direction. During migration, spatially localized activity of proteins is maintained. To investigate the effects of morphological changes on intracellular signaling, we developed a numerical scheme consisting of a cut cell finite volume spatial discretization coupled with level set methods to simulate the resulting advection-reaction-diffusion system. We then apply the method to several biochemical reaction networks in changing geometries. We found that a Turing instability can develop exclusively by cell deformations that maintain constant area. For a Turing system with a geometry-dependent single or double peak solution, simulations in a dynamically changing geometry suggest that a single peak solution is the only stable one, independent of the oscillation frequency. The method is also applied to a model of a signaling network in a migrating fibroblast

Simulation methods for spatiotemporal models of biochemical signaling networks

Cells use signaling networks consisting of multiple interacting proteins to respond to changes in their environment. In many situations, such as chemotaxis, spatial and temporal information must be transmitted through a signaling network. Recent computational studies have emphasized the importance of cellular geometry in signal transduction, but have been limited in their ability to accurately represent complex cell morphologies. We present a finite volume method that addresses this problem. Our method uses Cartesian cut cells in a differential algebraic formulation to handle the complex boundary dynamics encountered in biological systems. The method is second order in space and time. Several models of signaling systems are simulated in realistic cell morphologies obtained from live cell images. We then examine the effects of geometry on signal transduction. External signals can trigger cells to polarize and move in a specific direction. During migration, spatially localized activity of proteins is maintained. To investigate the effects of morphological changes on intracellular signaling, we present a numerical scheme consisting of a cut cell finite volume spatial discretization coupled with level set methods to simulate the resulting advection-reaction-diffusion equation. We then show that shape deformations drive a Turing-type system into an unstable regime. The method is also applied to a model of a signaling network in a migrating fibroblast. Determining the signaling mechanisms used by membrane proteins that interact with the cytoskeleton is important for understanding phenomena such as T-cell activation and viral infection. To investigate these interactions, recent experiments have tracked the movements of single lipids and glycosyl-phosphatidylinositol (GPI) anchored protein clusters tagged with 40 nm gold particles. These experiments reveal regions of transient confinement and transient anchorage of the particles. The distribution of transient anchorage release times exhibits a long tail. We developed a stochastic model of the system to explain the transient anchorage release times and the underlying biochemical reaction syste

Actin Turnover Required for Adhesion-Independent Bleb Migration

Cell migration is critical for many vital processes, such as wound healing, as well as harmful processes, such as cancer metastasis. Experiments have highlighted the diversity in migration strategies employed by cells in physiologically relevant environments. In 3D fibrous matrices and confinement between two surfaces, some cells migrate using round membrane protrusions, called blebs. In bleb-based migration, the role of substrate adhesion is thought to be minimal, and it remains unclear if a cell can migrate without any adhesion complexes. We present a 2D computational fluid-structure model of a cell using cycles of bleb expansion and retraction in a channel with several geometries. The cell model consists of a plasma membrane, an underlying actin cortex, and viscous cytoplasm. Cellular structures are immersed in viscous fluid which permeates them, and the fluid equations are solved using the method of regularized Stokeslets. Simulations show that the cell cannot effectively migrate when the actin cortex is modeled as a purely elastic material. We find that cells do migrate in rigid channels if actin turnover is included with a viscoelastic description for the cortex. Our study highlights the non-trivial relationship between cell rheology and its external environment during migration with cytoplasmic streaming

Actin Turnover Required for Adhesion-Independent Bleb Migration

Cell migration is critical for many vital processes, such as wound healing, as well as harmful processes, such as cancer metastasis. Experiments have highlighted the diversity in migration strategies employed by cells in physiologically relevant environments. In 3D fibrous matrices and confinement between two surfaces, some cells migrate using round membrane protrusions, called blebs. In bleb-based migration, the role of substrate adhesion is thought to be minimal, and it remains unclear if a cell can migrate without any adhesion complexes. We present a 2D computational fluid-structure model of a cell using cycles of bleb expansion and retraction in a channel with several geometries. The cell model consists of a plasma membrane, an underlying actin cortex, and viscous cytoplasm. Cellular structures are immersed in viscous fluid which permeates them, and the fluid equations are solved using the method of regularized Stokeslets. Simulations show that the cell cannot effectively migrate when the actin cortex is modeled as a purely elastic material. We find that cells do migrate in rigid channels if actin turnover is included with a viscoelastic description for the cortex. Our study highlights the non-trivial relationship between cell rheology and its external environment during migration with cytoplasmic streaming

Intracellular Pressure Dynamics in Blebbing Cells

Blebs are pressure-driven protrusions that play an important role in cell migration, particularly in three-dimensional environments. A bleb is initiated when the cytoskeleton detaches from the cell membrane, resulting in the pressure-driven flow of cytosol toward the area of detachment and local expansion of the cell membrane. Recent experiments involving blebbing cells have led to conflicting hypotheses regarding the timescale of intracellular pressure propagation. The interpretation of one set of experiments supports a poroelastic model of the cytoplasm that leads to slow pressure equilibration when compared to the timescale of bleb expansion. A different study concludes that pressure equilibrates faster than the timescale of bleb expansion. To address this discrepancy, a dynamic computational model of the cell was developed that includes mechanics of and the interactions among the cytoplasm, the actin cortex, the cell membrane, and the cytoskeleton. The model results quantify the relationship among cytoplasmic rheology, pressure, and bleb expansion dynamics, and provide a more detailed picture of intracellular pressure dynamics. This study shows the elastic response of the cytoplasm relieves pressure and limits bleb size, and that both permeability and elasticity of the cytoplasm determine bleb expansion time. Our model with a poroelastic cytoplasm shows that pressure disturbances from bleb initiation propagate faster than the timescale of bleb expansion and that pressure equilibrates slower than the timescale of bleb expansion. The multiple timescales in intracellular pressure dynamics explain the apparent discrepancy in the interpretation of experimental results