Stephen W. Davies

A genetic circuit amplifier: design and simulation

A genetic circuit amplifier is designed using an electronic inverting amplifier as a starting point. Two simulation methods are used to analyze circuit performance in terms of the impulse and sinusoidal responses of electrical engineering. The first method is an exact stochastic simulation based on a kinetic model of the circuit. The second method incorporates statistical thermodynamic analysis. The simulations are used to analyze amplifier performance in response to classical systems analysis stimuli: impulses and sine waves. Degradation reactions, analogous to leakage off circuit capacitors, are found to have considerable impact on circuit response. For the nonlinear gain element used in our exemplary circuit, the selection of bias level based on controlling protein degradation rate plays an important role in determining circuit behavior. A parameter without electronic analog, the circuit plasmid copy number, is crucial to circuit operation. These simulations suggest that the copy number must be less than 50 for desired circuit operation.

DNA microarray stochastic model

A stochastic model of the DNA microarray image pixels is presented. The model includes spot pixel intensity distribution, interpixel correlations and the intensity distribution of background noise. The data is indicative of a small exponential additive noise process and a larger Gaussian fluctuation that scales with spot intensity. Correlations are observed among pixels in the spot and between test and control images. The correlated fluctuations may be attributed to variations across each spot in the amount of DNA placed on the spot during the array fabrication process. The model may be used in gene expression estimation algorithm development, both to test new algorithms through simulation and to develop optimum algorithms. The model should also be easily adapted to new array based technologies in proteomics.

Genetic circuit design from an electronics perspective

Synthetic genetic circuits are examined from an electronic circuit design perspective. The design of an amplifier is used to explore interactions between genetic elements used as circuit components. A stochastic simulation is developed. This is used to analyze performance in terms of elementary notions of feedback, gain and noise. Degradation reactions, analogous to leakage off circuit capacitors, are found to have considerable impact on circuit response. For the non-linear gain element used in our exemplary circuit, the selection of bias level plays an important role in determining circuit behavior.

Visualizing Genetic Circuits Using Concepts Borrowed from Electronics

Biology features genetic circuits that are analogous to electronic circuits. A major goal of synthetic biology is the engineering of new genetic circuits. Inspired by electronic circuit diagrams, this paper proposes a means of representing these genetic circuits that facilitates analysis and effectively communicates circuit properties.

Consequences of deterministic and stochastic modeling of a promoter

For an engineered genetic oscillator, deterministic analysis indicates sustained oscillations and stochastic simulations show irregular or absent oscillations. Since the major difference is in the modeling of the promoters, we have performed a detailed analysis of a generic repressible promoter system. Deterministic, stochastic, thermodynamic, and hybrid models were developed for the promoter. The average behavior of the stochastic model converged to the thermodynamic model. The deterministic model is a special case of the thermodynamic model. The hybrid model could lock into the off state. Adding an unrelated background reaction allowed it to exit that state. Increasing the background rate allowed the hybrid model to converge to thermodynamic and stochastic model. Adding a background reaction to the stochastic oscillator simulation noticeably improved its performance.

Models of local behavior of DNA electrophoresis peak parameters

Many base calling algorithms implicitly or explicitly rely on predictions of local sequence parameters such as amplitude, peak time and peak width. For example, an algorithm may search for the next peak about a predicted peak time formed by adding the mean peak separation to the last position measurement. In this paper, covariance models are presented which characterize the dependence of peak parameters on those of other peaks. Based on experimental measurements, the model features an exponential decay in peak time jitter covariance with respect to base separation. Both peak amplitude and peak width are modelled as being uncorrelated with those of adjacent bases. In the model, linear expressions are given to describe the growth in peak time jitter and peak width as a function of base position while other parameters, such as amplitude variance, are modeled by constants. Together, these results form a simple model which may be used in the derivation of new sequencing algorithms or in simulations for the testing of such algorithms. We suggest that the correlation of the peak times is related to the Kuhn length of the single‐stranded DNA fragments.

Design of a Genetic Differential Amplifier

A genetic differential amplifier is made using the control elements of genes. The output mRNA level is proportional to the difference between the concentrations of two input proteins. The active element is engineered from the right operator of bacteriophage lambda. Mutations are introduced to yield the correct gain characteristic and to provide a bias level; the latter allows for the representation of negative differences. Simulation is used to aid the design process. A test circuit has been constructed. Preliminary experimental results indicate excellent results for the inverting input and lower gain for the non-inverting input

Optimal estimation of gene expression

Classical stochastic signal modeling is applied to DNA microarray images to obtain an estimator for gene expression level in the infinite SNR case. The derivation of an estimator is shown for both the single-pixel case and the multiple-pixel case. The optimal estimator is a pair of low-order polynomials that are solved simultaneously to produce an estimate.

A novel hypothesis-testing technique for resolving overlapping peaks in DNA sequencing

The accuracy of determining the Deoxyribo Nucleic Acid (DNA) sequence is limited by overlapping peaks of the same base-type (A, C, G or T). Commonly used iterative method to resolve these peaks tends to generate false peaks and has limited resolution. This paper presents a novel hypothesis-testing method, which uses a statistical model of DNA time series, to estimate position and amplitude of the overlapping peaks. The new method has better resolution than the iterative method and does not generate false peaks.

Near optimal DNA sequencing

DNA sequencing is limited by the resolution of peaks in data series produced by chemical processing and gel electrophoresis. In the clinical application, resolution is expected to be poorer due to a need for fast results. A near optimum sequencing algorithm is found to yield excellent performance for such data.