A Molecular Implementation of the Least Mean Squares Estimator

In order to function reliably, synthetic molecular circuits require mechanisms that allow them to adapt to environmental disturbances. Least mean squares (LMS) schemes, such as commonly encountered in signal processing and control, provide a powerful means to accomplish that goal. In this paper we show how the traditional LMS algorithm can be implemented at the molecular level using only a few elementary biomolecular reactions. We demonstrate our approach using several simulation studies and discuss its relevance to synthetic biology.Comment: Molecular circuits, synthetic biology, least mean squares estimator, adaptive system

Path mutual information for a class of biochemical reaction networks

Living cells encode and transmit information in the temporal dynamics of biochemical components. Gaining a detailed understanding of the input-output relationship in biological systems therefore requires quantitative measures that capture the interdependence between complete time trajectories of biochemical components. Mutual information provides such a measure but its calculation in the context of stochastic reaction networks is associated with mathematical challenges. Here we show how to estimate the mutual information between complete paths of two molecular species that interact with each other through biochemical reactions. We demonstrate our approach using three simple case studies.Comment: 6 pages, 2 figure

Uncoupled Analysis of Stochastic Reaction Networks in Fluctuating Environments

The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as for instance the fluctuations in ribsome copy numbers for a gene regulatory network. While several recent studies demonstrate the importance of accounting for such extrinsic components, the resulting models are typically hard to analyze. In this work we develop a general mathematical framework that allows to uncouple the network from its dynamic environment by incorporating only the environment's effect onto the network into a new model. More technically, we show how such fluctuating extrinsic components (e.g., chemical species) can be marginalized in order to obtain this decoupled model. We derive its corresponding process- and master equations and show how stochastic simulations can be performed. Using several case studies, we demonstrate the significance of the approach. For instance, we exemplarily formulate and solve a marginal master equation describing the protein translation and degradation in a fluctuating environment.Comment: 7 pages, 4 figures, Appendix attached as SI.pdf, under submissio

Moment-based analysis of biochemical networks in a heterogeneous population of communicating cells

Cells can utilize chemical communication to exchange information and coordinate their behavior in the presence of noise. Communication can reduce noise to shape a collective response, or amplify noise to generate distinct phenotypic subpopulations. Here we discuss a moment-based approach to study how cell-cell communication affects noise in biochemical networks that arises from both intrinsic and extrinsic sources. We derive a system of approximate differential equations that captures lower-order moments of a population of cells, which communicate by secreting and sensing a diffusing molecule. Since the number of obtained equations grows combinatorially with number of considered cells, we employ a previously proposed model reduction technique, which exploits symmetries in the underlying moment dynamics. Importantly, the number of equations obtained in this way is independent of the number of considered cells such that the method scales to arbitrary population sizes. Based on this approach, we study how cell-cell communication affects population variability in several biochemical networks. Moreover, we analyze the accuracy and computational efficiency of the moment-based approximation by comparing it with moments obtained from stochastic simulations.Comment: 6 pages, 5 Figure

The gift of gab: probing the limits of dynamic concentration-sensing across a network of communicating cells

Many systems in biology and beyond employ collaborative, collective communication strategies for improved efficiency and adaptive benefit. One such paradigm of particular interest is the community estimation of a dynamic signal, when, for example, an epithelial tissue of cells must decide whether to react to a given dynamic external concentration of stress signaling molecules. At the level of dynamic cellular communication, however, it remains unknown what effect, if any, arises from communication beyond the mean field level. What are the limits and benefits to communication across a network of neighbor interactions? What is the role of Poissonian vs. super Poissonian dynamics in such a setting? How does the particular topology of connections impact the collective estimation and that of the individual participating cells? In this letter we construct a robust and general framework of signal estimation over continuous time Markov chains in order to address and answer these questions. Our results show that in the case of Possonian estimators, the communication solely enhances convergence speed of the Mean Squared Error (MSE) of the estimators to their steady-state values while leaving these values unchanged. However, in the super-Poissonian regime, MSE of estimators significantly decreases by increasing the number of neighbors. Surprisingly, in this case, the clustering coefficient of an estimator does not enhance its MSE while reducing total MSE of the population

Stochastic reaction networks in dynamic compartment populations

Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and typically very challenging to analyze computationally. Recent studies have made progress towards addressing this problem in the context of concrete biological systems but general approaches remain lacking. In this work we propose a mathematical framework based on counting processes that allows us to study compartment populations with arbitrary interactions and internal biochemistry. We provide an efficient description of the population dynamics in terms of differential equations which capture moments of the population and their variability. We demonstrate the relevance of our approach using several case studies inspired by biological systems at different scales.Comment: 9 pages, 3 figures, appendix include

Tilivalline- and Tilimycin-Independent Effects of Klebsiella oxytoca on Tight Junction-Mediated Intestinal Barrier Impairment

Klebsiella oxytoca causes antibiotic-associated hemorrhagic colitis and diarrhea. This was attributed largely to its secreted cytotoxins tilivalline and tilimycin, inductors of epithelial apoptosis. To study whether Klebsiella oxytoca exerts further barrier effects, T84 monolayers were challenged with bacterial supernatants derived from tilivalline/tilimycin-producing AHC6 or its isogeneic tilivalline/tilimycin-deficient strain Mut-89. Both preparations decreased transepithelial resistance, enhanced fluorescein and FITC-dextran-4kDa permeabilities, and reduced expression of barrier-forming tight junction proteins claudin-5 and -8. Laser scanning microscopy indicated redistribution of both claudins off the tight junction region in T84 monolayers as well as in colon crypts of mice infected with AHC6 or Mut-89, indicating that these effects are tilivalline/tilimycin-independent. Furthermore, claudin-1 was affected, but only in a tilivalline/tilimycin-dependent manner. In conclusion, Klebsiella oxytoca induced intestinal barrier impairment by two mechanisms: the tilivalline/tilimycin-dependent one, acting by increasing cellular apoptosis and a tilivalline/tilimycin-independent one, acting by weakening the paracellular pathway through the tight junction proteins claudin-5 and -8

Ni-P: Microstructure and micro-compression

Electroless nickel-phosphorus (EN-P) plating is a popular deposition process with widespread applications in microelectronics [1, 2]. Much emphasis has been given on the plating process and on the physical and chemical properties of the EN-P layers; however their mechanical properties down to the sub-micrometer dimensions have not been elucidated systematically. In this work, we study the mechanical properties of EN-P as a function of annealing states using in-situ pillar compression technique [3]. Please click Additional Files below to see the full abstract