On joint maximum-likelihood estimation of PCR efficiency and initial amount of target

We consider the problem of estimating unknown parameters of the real-time polymerase chain reaction (RTPCR) from noisy observations. The joint ML estimator of the RT-PCR efficiency and the initial number of DNA target molecules is derived. The mean-square error performance of the estimator is studied via simulations. The simulation results indicate that the proposed estimator significantly outperforms a competing technique

ML Estimation of DNA Initial Copy Number in Polymerase Chain Reaction (PCR) Processes

Estimation of DNA copy number in a given biological sample is an extremely important problem in genomics. This problem is especially challenging when the number of the DNA strands is minuscule, which is often the case in applications such as pathogen and genetic mutation detection. A recently developed technique, real-time polymerase chain reaction (PCR), amplifies the number of initial target molecules by replicating them through a series of thermal cycles. Ideally, the number of target molecules doubles at the end of each cycle. However, in practice, due to biochemical noise the efficiency of the PCR reaction, defined as the fraction of target molecules which are successfully copied during a cycle, is always less than 1. In this paper, we formulate the problem of joint maximum-likelihood estimation of the PCR efficiency and the initial DNA copy number. As indicated by simulation studies, the performance of the proposed estimator is superior with respect to competing statistical approaches. Moreover, we compute the Cramer-Rao lower bound on the mean-square estimation error

On Limits of Performance of DNA Microarrays

DNA microarray technology relies on the hybridization process which is stochastic in nature. Probabilistic cross-hybridization of non-specific targets, as well as the shot-noise originating from specific targets binding, are among the many obstacles for achieving high accuracy in DNA microarray analysis. In this paper, we use statistical model of hybridization and cross-hybridization processes to derive a lower bound (viz., the Cramer-Rao bound) on the minimum mean-square error of the target concentrations estimation. A preliminary study of the Cramer-Rao bound for estimating the target concentrations suggests that, in some regimes, cross-hybridization may, in fact, be beneficial—a result with potential ramifications for probe design, which is currently focused on minimizing cross-hybridization

Modeling the kinetics of hybridization in microarrays

Conventional fluorescent-based microarrays acquire data after the hybridization phase. In this phase the targets 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., realtime microarrays) capable of recording the kinetics of hybridization in fluorescent-based microarrays has recently been proposed in [5]. 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 develop a probabilistic model of the kinetics of hybridization and describe a procedure for the estimation of its parameters which include the binding rate and target concentration. This probabilistic model is an important step towards developing optimal detection algorithms for the microarrays which measure the kinetics of hybridization, and to understanding their fundamental limitations

On estimation in real-time microarrays

Conventional fluorescent-based microarrays acquire data after the hybridization phase. During this phase, the target analytes 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 in (Hassibi, 2007). 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 the current paper, 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

Signal Processing Aspects of Real-Time DNA Microarrays

Data acquisition in conventional fluorescent-based microarrays takes place after the completion of a hybridization phase. During the hybridization phase, target analytes bind to their corresponding capturing probes on the array. The conventional microarrays attempt to detect presence and quantify amounts of the targets by collecting a single data point, supposedly taken after the hybridization process has reached its steady-state. Recently, so-called real-time microarrays capable of acquiring not only the steady-state data but the entire kinetics of hybridization have been proposed in [1]. The richness of the information obtained by the real-time microarrays 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 study the signal processing aspects of the real-time microarray data acquisition

Weighted ℓ_1 minimization for sparse recovery with prior information

In this paper we study the compressed sensing problem of recovering a sparse signal from a system of underdetermined linear equations when we have prior information about the probability of each entry of the unknown signal being nonzero. In particular, we focus on a model where the entries of the unknown vector fall into two sets, each with a different probability of being nonzero. We propose a weighted ℓ_1 minimization recovery algorithm and analyze its performance using a Grassman angle approach. We compute explicitly the relationship between the system parameters (the weights, the number of measurements, the size of the two sets, the probabilities of being non-zero) so that an iid random Gaussian measurement matrix along with weighted ℓ_1 minimization recovers almost all such sparse signals with overwhelming probability as the problem dimension increases. This allows us to compute the optimal weights. We also provide simulations to demonstrate the advantages of the method over conventional ℓ_1 optimization

Divide-and-conquer: Approaching the capacity of the two-pair bidirectional Gaussian relay network

The capacity region of multi-pair bidirectional relay networks, in which a relay node facilitates the communication between multiple pairs of users, is studied. This problem is first examined in the context of the linear shift deterministic channel model. The capacity region of this network when the relay is operating at either full-duplex mode or half-duplex mode for arbitrary number of pairs is characterized. It is shown that the cut-set upper-bound is tight and the capacity region is achieved by a so called divide-and-conquer relaying strategy. The insights gained from the deterministic network are then used for the Gaussian bidirectional relay network. The strategy in the deterministic channel translates to a specific superposition of lattice codes and random Gaussian codes at the source nodes and successive interference cancelation at the receiving nodes for the Gaussian network. The achievable rate of this scheme with two pairs is analyzed and it is shown that for all channel gains it achieves to within 3 bits/sec/Hz per user of the cut-set upper-bound. Hence, the capacity region of the two-pair bidirectional Gaussian relay network to within 3 bits/sec/Hz per user is characterized.Comment: IEEE Trans. on Information Theory, accepte

Estimation over Communication Networks: Performance Bounds and Achievability Results

This paper considers the problem of estimation over communication networks. Suppose a sensor is taking measurements of a dynamic process. However the process needs to be estimated at a remote location connected to the sensor through a network of communication links that drop packets stochastically. We provide a framework for computing the optimal performance in the sense of expected error covariance. Using this framework we characterize the dependency of the performance on the topology of the network and the packet dropping process. For independent and memoryless packet dropping processes we find the steady-state error for some classes of networks and obtain lower and upper bounds for the performance of a general network. Finally we find a necessary and sufficient condition for the stability of the estimate error covariance for general networks with spatially correlated and Markov type dropping process. This interesting condition has a max-cut interpretation