A consistent hierarchy of generalized kinetic equation approximations to the master equation applied to surface catalysis.

We develop a hierarchy of approximations to the master equation for systems that exhibit translational invariance and finite-range spatial correlation. Each approximation within the hierarchy is a set of ordinary differential equations that considers spatial correlations of varying lattice distance; the assumption is that the full system will have finite spatial correlations and thus the behavior of the models within the hierarchy will approach that of the full system. We provide evidence of this convergence in the context of one- and two-dimensional numerical examples. Lower levels within the hierarchy that consider shorter spatial correlations are shown to be up to three orders of magnitude faster than traditional kinetic Monte Carlo methods (KMC) for one-dimensional systems, while predicting similar system dynamics and steady states as KMC methods. We then test the hierarchy on a two-dimensional model for the oxidation of CO on RuO2(110), showing that low-order truncations of the hierarchy efficiently capture the essential system dynamics. By considering sequences of models in the hierarchy that account for longer spatial correlations, successive model predictions may be used to establish empirical approximation of error estimates. The hierarchy may be thought of as a class of generalized phenomenological kinetic models since each element of the hierarchy approximates the master equation and the lowest level in the hierarchy is identical to a simple existing phenomenological kinetic models.

A mechanochemical model for auto-regulation of lung airway surface layer volume.

We develop a proof-of-principle model for auto-regulation of water volume in the lung airway surface layer (ASL) by coupling biochemical kinetics, transient ASL volume, and homeostatic mechanical stresses. The model is based on the hypothesis that ASL volume is sensed through soluble mediators and phasic stresses generated by beating cilia and air drag forces. Model parameters are fit based on the available data on human bronchial epithelial cell cultures. Simulations then demonstrate that homeostatic volume regulation is a natural consequence of the processes described. The model maintains ASL volume within a physiological range that modulates with phasic stress frequency and amplitude. Next, we show that the model successfully reproduces the responses of cell cultures to significant isotonic and hypotonic challenges, and to hypertonic saline, an effective therapy for mucus hydration in cystic fibrosis patients. These results compel an advanced airway hydration model with therapeutic value that will necessitate detailed kinetics of multiple molecular pathways, feedback to ASL viscoelasticity properties, and stress signaling from the ASL to the cilia and epithelial cells.

Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish.

The Scallop theorem states that reciprocal methods of locomotion, such as jet propulsion or paddling, will not work in Stokes flow (Reynolds number=0). In nature the effective limit of jet propulsion is still in the range where inertial forces are significant. It appears that almost all animals that use jet propulsion swim at Reynolds numbers (Re) of about 5 or more. Juvenile squid and octopods hatch from the egg already swimming in this inertial regime. Juvenile jellyfish, or ephyrae, break off from polyps swimming at Re greater than 5. Many other organisms, such as scallops, rarely swim at Re less than 100. The limitations of jet propulsion at intermediate Re is explored here using the immersed boundary method to solve the 2D Navier-Stokes equations coupled to the motion of a simplified jellyfish. The contraction and expansion kinematics are prescribed, but the forward and backward swimming motions of the idealized jellyfish are emergent properties determined by the resulting fluid dynamics. Simulations are performed for both an oblate bell shape using a paddling mode of swimming and a prolate bell shape using jet propulsion. Average forward velocities and work put into the system are calculated for Re between 1 and 320. The results show that forward velocities rapidly decay with decreasing Re for all bell shapes when Re<10. Similarly, the work required to generate the pulsing motion increases significantly for Re<10. When compared to actual organisms, the swimming velocities and vortex separation patterns for the model prolate agree with those observed in Nemopsis bachei. The forward swimming velocities of the model oblate jellyfish after two pulse cycles are comparable to those reported for Aurelia aurita, but discrepancies are observed in the vortex dynamics between when the 2D model oblate jellyfish and the organism. This discrepancy is likely due to a combination of the differences between the 3D reality of the jellyfish and the 2D simplification, as well as the rigidity of the time varying geometry imposed by the idealized model.

Programmable assembly of pressure sensors using pattern-forming bacteria.

Biological systems can generate microstructured materials that combine organic and inorganic components and possess diverse physical and chemical properties. However, these natural processes in materials fabrication are not readily programmable. Here, we use a synthetic-biology approach to assemble patterned materials. We demonstrate programmable fabrication of three-dimensional (3D) materials by printing engineered self-patterning bacteria on permeable membranes that serve as a structural scaffold. Application of gold nanoparticles to the colonies creates hybrid organic-inorganic dome structures. The dynamics of the dome structures' response to pressure is determined by their geometry (colony size, dome height, and pattern), which is easily modified by varying the properties of the membrane (e.g., pore size and hydrophobicity). We generate resettable pressure sensors that process signals in response to varying pressure intensity and duration.