Recent advances in synthetic biology have led to a wealth of well-characterized genetic parts. As parts libraries grow, so too does the potential to create novel multi-input promoters that integrate disparate signals to determine transcriptional output. Our ability to construct such promoters will outpace our ability to characterize promoter performance, due to the vast number of input combinations. In this study, we examine the input-output relations of recently developed synthetic multi-input promoters and describe two methods for predicting their behavior. The first method uses 1-dimensional induction data obtained from experiments on single-input systems to predict the n-dimensional induction responses of systems with n inputs. We demonstrate that this approach accurately predicts Boolean (on/off) responses of multi-input systems consisting of novel chimeric transcription factors and hybrid promoters in Escherichia coli. The second method uses only a small amount of multi-input response data to accurately predict analog system response over the entire landscape of input combinations. Taken together, these methods facilitate the design of synthetic circuits that utilize multi-input promoters.

Motivation: Advances in experimental and imaging techniques have allowed for unprecedented insights into the dynamical processes within individual cells. However, many facets of intracellular dynamics remain hidden, or can be measured only indirectly. This makes it challenging to reconstruct the regulatory networks that govern the biochemical processes underlying various cell functions. Current estimation techniques for inferring reaction rates frequently rely on marginalization over unobserved processes and states. Even in simple systems this approach can be computationally challenging, and can lead to large uncertainties and lack of robustness in parameter estimates. Therefore we will require alternative approaches to efficiently uncover the interactions in complex biochemical networks.Results: We propose a Bayesian inference framework based on replacing uninteresting or unobserved reactions with time delays. Although the resulting models are non-Markovian, recent results on stochastic systems with random delays allow us to rigorously obtain expressions for the likelihoods of model parameters. In turn, this allows us to extend MCMC methods to efficiently estimate reaction rates, and delay distribution parameters, from single-cell assays. We illustrate the advantages, and potential pitfalls, of the approach using a birth-death model with both synthetic and experimental data, and show that we can robustly infer model parameters using a relatively small number of measurements. We demonstrate how to do so even when only the relative molecule count within the cell is measured, as in the case of fluorescence microscopy. Introduction 1The dynamics of intracellular processes are determined by the structure and rates of interactions between 2 different molecular species. However, stochasticity and limitations of experimental methods make it difficult 3 to infer the characteristics of these interactions from data. On the single-cell level, different molecular 4 species can occur in small number, correlate with phenotype, and localize within different parts of the cell. 5The resulting dynamics can thus be highly variable over time, and across the population. Averaging over 6 such fluctuations can lead to inaccurate representations of the underlying biology [1], and inference methods 7 therefore need to account for stochasticity within individual cells, and variability across the population [2-5].8 Different statistical approaches have been developed to fit stochastic models to data from single-cell 9 assays, offering a window into the dynamical processes within individual cells [6][7][8][9][10][11][12][13]. Among these, Bayesian 10 methods have been particularly promising. To apply Bayesian techniques, one typically assumes a model 11 for the network of interactions, postulates a prior over model parameters, and uses experimental data to 12 determine a posterior and estimates of unknown parameters [6,[13][14][15]. However, Bayesian approaches can 13 suffer from the curse of dimensionality [16], and are thus difficult to i...

A partial differential equation (PDE)-based model combining the effects of surface electromigration and substrate wetting is developed for the analysis of the morphological instability of a monocrystalline metal film in a high temperature environment typical to operational conditions of microelectronic interconnects and nanoscale devices. The model accounts for the anisotropies of the atomic mobility and surface energy. The goal is to describe and understand the timeevolution of the shape of the film surface. The formulation of a nonlinear parabolic PDE problem for the height function h(x, t) of the film in the electric field is presented, followed by the results of the linear stability analysis of a planar surface. Computations of a fully nonlinear evolution equation are presented and discussed.