High rates of fuel consumption are not required by insulating motifs to suppress retroactivity in biochemical circuits

Retroactivity arises when the coupling of a molecular network $\mathcal{U}$ to a downstream network $\mathcal{D}$ results in signal propagation back from $\mathcal{D}$ to $\mathcal{U}$. The phenomenon represents a breakdown in modularity of biochemical circuits and hampers the rational design of complex functional networks. Considering simple models of signal-transduction architectures, we demonstrate the strong dependence of retroactivity on the properties of the upstream system, and explore the cost and efficacy of fuel-consuming insulating motifs that can mitigate retroactive effects. We find that simple insulating motifs can suppress retroactivity at a low fuel cost by coupling only weakly to the upstream system $\mathcal{U}$. However, this design approach reduces the signalling network's robustness to perturbations from leak reactions, and potentially compromises its ability to respond to rapidly-varying signals.Comment: 26 pages, 19 figures, To appear in Engineering Biolog

Beyond the two-state model of switching in biology and computation

The thesis presents various perspectives on physical and biological computation. Our fundamental object of study in both these contexts is the notion of switching/erasing a bit. In a physical context, a bit is represented by a particle in a double well, whose dynamics is governed by the Langevin equation. We define the notions of reliability and erasing time-scales in addition to the work required to erase a bit for a given family of control protocols. We call bits “optimal” if they meet the required reliability and erasing time requirements with minimal work cost. We find that optimal bits always saturate the erasing time requirement, but may not saturate the reliability time requirement. This allows us to eliminate several regions of parameter space as sub-optimal. In a biological context, our bits are represented by substrates that are acted upon by catalytic enzymes. We define retroactivity as the back-signal propagated by the downstream system when connected to the upstream system. We analyse certain upstream systems that can help mitigate retroactivity. However, these systems require a substantial pool of resources and are therefore not optimal. As a consequence, we turn our attention to insulating networks called push-pull motifs. We find that high rates of energy consumption are not essential to alleviate retroactivity in push-pull motifs; all we need is to couple weakly to the upstream system. However, this approach is not resilient to cross-talk caused by leak reactions in the circuit. Next, we consider a single enzyme-substrate reaction and analyse its mechanism. Our system has two intermediate states (enzyme-substrate complexes). Our main question is “How should we choose binding energies of the intermediates to minimize sequestra- tion of substrates (retroactivity), whilst maintaining a minimum flux at steady-state?”. Choosing very low binding energies increases retroactivity since the system spends a considerable proportion of time in the intermediate states. Choosing binding energies that are very high reduces retroactivity, but hinders the progress of the reaction. As a result, we find that the the optimal binding energies are both moderate, and indeed tuned with each other. In particular, their difference is related to the free energy difference between the products and reactants.Open Acces

Flow Induced Corrosion in 6061-T6 Aluminum Pipes in De-Ionized Water Environments

Flow induced corrosion/erosion of 6061-T6 aluminum in de-ionized (DI) water environments has not been studied widely. Especially, the long-term effects of corrosion/erosion in seemingly benign flow velocity, temperature, and resistivity ranges of 8 ft/s, 85 oF, 3-5 MOhm-cm, respectively. This study concludes that the flow induced corrosion/erosion in the above parameter ranges is minimal. This is detailed by presenting a literature survey, measuring pipe wall samples from a system that has operated in the above parameter range, predict the loss of material in mm/year at the above velocities and at higher temperatures using electric potential values from other experimental studies coupled with wall shear stress simulated using Computational Fluid Dynamic (CFD) analysis

On the Connectivity of the Disguised Toric Locus of a Reaction Network

Complex-balanced mass-action systems are some of the most important types of mathematical models of reaction networks, due to their widespread use in applications, as well as their remarkable stability properties. We study the set of positive parameter values (i.e., reaction rate constants) of a reaction network $G$ that, according to mass-action kinetics, generate dynamical systems that can be realized as complex-balanced systems, possibly by using a different graph $G'$. This set of parameter values is called the disguised toric locus of $G$. The $\mathbb{R}$-disguised toric locus of $G$ is defined analogously, except that the parameter values are allowed to take on any real values. We prove that the disguised toric locus of $G$ is path-connected, and the $\mathbb{R}$-disguised toric locus of $G$ is also path-connected. We also show that the closure of the disguised toric locus of a reaction network contains the union of the disguised toric loci of all its subnetworks.Comment: 18 pages, 2 figure

Effect of a Symmetric Contraction on the Concentration Profiles of a Particleladen Slurry

The effect of a symmetric contraction on the concentration profiles of a xylene- 2 amino, 4, 6 dimethyl pyrimidine (ADP) slurry flowing in a cylindrical pipe were simulated using computational fluid dynamics. ANSYS FLUENT 12.0 was used as the computational fluid dynamic software. Variations in the pipe Reynolds number, initial efflux concentration, and the particle size were considered. An ASME flow nozzle, that served the purpose of a contraction, was incorporated in the fully-developed region of the pipe geometry. The pipe had an L/D ratio of 55. The k-epsilon turbulence model with standard wall functions coupled with the mixture multi-phase model was used to simulate all the test cases. A grid independence study was performed for both the velocity and concentration profiles. The model was validated with experimental data sets available in the literature. The concentration profiles at the exit plane were compared with those registered at the fully-developed region. The present computational model predicts the velocity and the concentration profiles of a slurry with an acceptable degree of accuracy. The accuracy of the simulated results is compromised in the near-wall region. It was found that the concentration profiles in all the test cases displayed reduced spatial variation at the exit plane of the geometric contraction. At higher Reynolds number (ReD) the concentration profiles of 38 m ADP particles realized at the exit plane and the fully-developed region were almost identical. It was found that the gradient of concentration along the vertical diameter of the geometry for heavier particles decreases with an increase in pipe Reynolds number. The turbulence intensity of the flow field at the exit plane of the contraction was found to be lower than that registered at the fully-developed region. Owing to this, the exit plane of the geometric contraction may serve as a suitable location for performing near infra-red and mass spectral analysis of a particle-laden slurry.Mechanical & Aerospace Engineerin

A Lower Bound on the Dimension of the R\mathbb{R}-Disguised Toric Locus of a Reaction Network

Polynomial dynamical systems (i.e. dynamical systems with polynomial right hand side) are ubiquitous in applications, especially as models of reaction networks and interaction networks. The properties of general polynomial dynamical systems can be very difficult to analyze, due to nonlinearity, bifurcations, and the possibility for chaotic dynamics. On the other hand, toric dynamical systems are polynomial dynamical systems that appear naturally as models of reaction networks, and have very robust and stable properties. A disguised toric dynamical system is a polynomial dynamical system generated by a reaction network $\mathcal N$ and some choice of positive parameters, such that (even though it may not be toric with respect to $\mathcal N$) it has a toric realization with respect to some network $\mathcal N'$. Disguised toric dynamical systems enjoy all the robust stability properties of toric dynamical systems. In this paper, we study a larger set of dynamical systems where the rate constants are allowed to take both positive and negative values. More precisely, we analyze the $\mathbb{R}$-disguised toric locus of a reaction network $\mathcal N$, i.e., the subset in the space rate constants (positive or negative) of $\mathcal N$ for which the corresponding polynomial dynamical system is disguised toric. We focus especially on finding a lower bound on the dimension of the $\mathbb{R}$-disguised toric locus.Comment: 25 pages, 4 figure

A Generalized Mathematical model to understand the capacity fading in lithium ion batteries-Effects of solvent and lithium transport

A general mathematical model to study capacity fading in lithium ion batteries is developed. The model assumes that the formation of the Solid Electrolyte Interphase (SEI) layer is the primary reason behind the capacity fading in lithium ion batteries. Previous models have assumed that either the solvent or the lithium plays a key role in the film formation reaction which drives the capacity fading in lithium ion batteries. The current model postulates that the solvent species and lithium ions could play a limiting role in the capacity fade in a lithium ion battery. The model studies the concentration profiles of the solvent species and lithium ions at the electrode/film interphase as a function of diffusion and migration parameters. Model predictions are found to fit experimental data very well