Modeling and Estimation for Real-Time Microarrays

Microarrays are used for collecting information about a large number of different genomic particles simultaneously. Conventional fluorescent-based microarrays acquire data after the hybridization phase. During this phase, the target analytes (e.g., DNA fragments) bind to the capturing probes on the array and, by the end of it, supposedly reach a steady state. Therefore, conventional microarrays attempt to detect and quantify the targets with a single data point taken in the steady state. On the other hand, a novel technique, the so-called real-time microarray, capable of recording the kinetics of hybridization in fluorescent-based microarrays has recently been proposed. The richness of the information obtained therein promises higher signal-to-noise ratio, smaller estimation error, and broader assay detection dynamic range compared to conventional microarrays. In this paper, we study the signal processing aspects of the real-time microarray system design. In particular, we develop a probabilistic model for real-time microarrays and describe a procedure for the estimation of target amounts therein. Moreover, leveraging on system identification ideas, we propose a novel technique for the elimination of cross hybridization. These are important steps toward developing optimal detection algorithms for real-time microarrays, and to understanding their fundamental limitations

Efficiency of polymerase chain reaction processes: A stochastic model

A stochastic model for the efficiency of polymerase chain reaction (PCR) processes is presented. The model is based on the assumption that the i’th nucleotide incorporation on the DNA template takes τi seconds, where τi has an exponential distribution with mean 1/λi. In this paper, given λi that can be obtained from the primer-template sequence, temperature profile, enzyme rate, and other assay conditions [3], we calculate the efficiency of a multi-step PCR process using the distribution of the summation of non-identical exponential distributions

A Spectral-Scanning Nuclear Magnetic Resonance Imaging (MRI) Transceiver

An integrated spectral-scanning nuclear magnetic resonance imaging (MRI) transceiver is implemented in a 0.12 mum SiGe BiCMOS process. The MRI transmitter and receiver circuitry is designed specifically for small-scale surface MRI diagnostics applications where creating low (below 1 T) and inhomogeneous magnetic field is more practical. The operation frequency for magnetic resonance detection and analysis is tunable from 1 kHz to 37 MHz, corresponding to 0-0.9 T magnetization for ^1H (hydrogen). The concurrent measurement bandwidth is approximately one frequency octave. The chip can also be used for conventional narrowband nuclear magnetic resonance (NMR) spectroscopy from 1 kHz up to 250 MHz. This integrated transceiver consists of both the magnetic resonance transmitter which generates the required excitation pulses for the magnetic dipole excitation, and the receiver which recovers the responses of the dipoles

Signal Processing for Real-Time DNA Microarrays

In conventional fluorescent-based microarrays, data is acquired after the completion of the hybridization phase. In this phase the target analytes (i.e., DNA fragments) bind to the capturing probes on the array and supposedly reach a steady state. Accordingly, microarray experiments essentially provide only a single, steady-state data point of the hybridization process. On the other hand, a novel technique (i.e., real-time microarrays) capable of recording the kinetics of hybridization in fluorescent-based microarrays has recently been proposed in [1]. The richness of the information obtained therein promises higher signal-to-noise ratio, smaller estimation error, and broader assay detection dynamic range compared to the conventional microarrays. In the current paper, we model the kinetics of the hybridization process measured by the realtime microarrays, and develop techniques for estimating the amounts of analytes present therein

A Spectral-Scanning Magnetic Resonance Imaging (MRI) Integrated System

An integrated spectral-scanning magnetic resonance imaging (MRI) technique is implemented in a 0.12μm SiGe BiCMOS process. This system is designed for small-scale MRI applications with non-uniform and low magnetic fields. The system is capable of generating customized magnetic resonance (MR) excitation signals, and also recovering the MR response using a coherent direct conversion receiver. The operation frequency is tunable from DC to 37MHz for wide-band MRI and up to 250MHz for narrow-band MR spectroscopy

On noise processes and limits of performance in biosensors

In this paper, we present a comprehensive stochastic model describing the measurement uncertainty, output signal, and limits of detection of affinity-based biosensors. The biochemical events within the biosensor platform are modeled by a Markov stochastic process, describing both the probabilistic mass transfer and the interactions of analytes with the capturing probes. To generalize this model and incorporate the detection process, we add noisy signal transduction and amplification stages to the Markov model. Using this approach, we are able to evaluate not only the output signal and the statistics of its fluctuation but also the noise contributions of each stage within the biosensor platform. Furthermore, we apply our formulations to define the signal-to-noise ratio, noise figure, and detection dynamic range of affinity-based biosensors. Motivated by the platforms encountered in practice, we construct the noise model of a number of widely used systems. The results of this study show that our formulations predict the behavioral characteristics of affinity-based biosensors which indicate the validity of the model

Limits of Performance of Quantitative Polymerase Chain Reaction Systems

Estimation of the DNA copy number in a given biological sample is an important problem in genomics. Quantitative polymerase chain reaction (qPCR) systems detect the target DNA molecules by amplifying their number through a series of thermal cycles and measuring the amount of created amplicons in each cycle. Ideally, the number of target molecules doubles at the end of each cycle. However, in practice, due to biochemical noise the efficiency of the qPCR reaction—defined as the fraction of the target molecules which are successfully copied during a cycle—is always less than 1. In this paper, we formulate the problem of the joint maximum-likelihood estimation of the qPCR efficiency and the initial DNA copy number. Then, we analytically determine the limits of performance of qPCR by deriving the Cramer–Rao lower bound on the mean-square estimation error. As indicated by simulation studies, the performance of the proposed estimator is superior compared to competing statistical approaches. The proposed approach is validated using experimental data

A statistical model for microarrays, optimal estimation algorithms, and limits of performance

DNA microarray technology relies on the hybridization process, which is stochastic in nature. Currently, probabilistic cross hybridization of nonspecific targets, as well as the shot noise (Poisson noise) originating from specific targets binding, are among the main obstacles for achieving high accuracy in DNA microarray analysis. In this paper, statistical techniques are used to model the hybridization and cross-hybridization processes and, based on the model, optimal algorithms are employed to detect the targets and to estimate their quantities. To verify the theory, two sets of microarray experiments are conducted: one with oligonucleotide targets and the other with complementary DNA (cDNA) targets in the presence of biological background. Both experiments indicate that, by appropriately modeling the cross-hybridization interference, significant improvement in the accuracy over conventional methods such as direct readout can be obtained. This substantiates the fact that the accuracy of microarrays can become exclusively noise limited, rather than interference (i.e., cross-hybridization) limited. The techniques presented in this paper potentially increase considerably the signal-to-noise ratio (SNR), dynamic range, and resolution of DNA and protein microarrays as well as other affinity-based biosensors. A preliminary study of the Cramer-Rao bound for estimating the target concentrations suggests that, in some regimes, cross hybridization may even be beneficial-a result with potential ramifications for probe design, which is currently focused on minimizing cross hybridization. Finally, in its current form, the proposed method is best suited to low-density arrays arising in diagnostics, single nucleotide polymorphism (SNP) detection, toxicology, etc. How to scale it to high-density arrays (with many thousands of spots) is an interesting challenge

Real-time DNA microarray analysis

We present a quantification method for affinity-based DNA microarrays which is based on the real-time measurements of hybridization kinetics. This method, i.e. real-time DNA microarrays, enhances the detection dynamic range of conventional systems by being impervious to probe saturation in the capturing spots, washing artifacts, microarray spot-to-spot variations, and other signal amplitude-affecting non-idealities. We demonstrate in both theory and practice that the time-constant of target capturing in microarrays, similar to all affinity-based biosensors, is inversely proportional to the concentration of the target analyte, which we subsequently use as the fundamental parameter to estimate the concentration of the analytes. Furthermore, to empirically validate the capabilities of this method in practical applications, we present a FRET-based assay which enables the real-time detection in gene expression DNA microarrays