Compressive sensing DNA microarrays

Reconstruction of sparse recurrent connectivity and inputs from the nonlinear dynamics of neuronal networks

Reconstructing the recurrent structural connectivity of neuronal networks is a challenge crucial to address in characterizing neuronal computations. While directly measuring the detailed connectivity structure is generally prohibitive for large networks, we develop a novel framework for reverse-engineering large-scale recurrent network connectivity matrices from neuronal dynamics by utilizing the widespread sparsity of neuronal connections. We derive a linear input-output mapping that underlies the irregular dynamics of a model network composed of both excitatory and inhibitory integrate-and-fire neurons with pulse coupling, thereby relating network inputs to evoked neuronal activity. Using this embedded mapping and experimentally feasible measurements of the firing rate as well as voltage dynamics in response to a relatively small ensemble of random input stimuli, we efficiently reconstruct the recurrent network connectivity via compressive sensing techniques. Through analogous analysis, we then recover high dimensional natural stimuli from evoked neuronal network dynamics over a short time horizon. This work provides a generalizable methodology for rapidly recovering sparse neuronal network data and underlines the natural role of sparsity in facilitating the efficient encoding of network data in neuronal dynamics.

New insights into binocular rivalry from the reconstruction of evolving percepts using model network dynamics

When the two eyes are presented with highly distinct stimuli, the resulting visual percept generally switches every few seconds between the two monocular images in an irregular fashion, giving rise to a phenomenon known as binocular rivalry. While a host of theoretical studies have explored potential mechanisms for binocular rivalry in the context of evoked model dynamics in response to simple stimuli, here we investigate binocular rivalry directly through complex stimulus reconstructions based on the activity of a two-layer neuronal network model with competing downstream pools driven by disparate monocular stimuli composed of image pixels. To estimate the dynamic percept, we derive a linear input-output mapping rooted in the non-linear network dynamics and iteratively apply compressive sensing techniques for signal recovery. Utilizing a dominance metric, we are able to identify when percept alternations occur and use data collected during each dominance period to generate a sequence of percept reconstructions. We show that despite the approximate nature of the input-output mapping and the significant reduction in neurons downstream relative to stimulus pixels, the dominant monocular image is well-encoded in the network dynamics and improvements are garnered when realistic spatial receptive field structure is incorporated into the feedforward connectivity. Our model demonstrates gamma-distributed dominance durations and well obeys Levelt's four laws for how dominance durations change with stimulus strength, agreeing with key recurring experimental observations often used to benchmark rivalry models. In light of evidence that individuals with autism exhibit relatively slow percept switching in binocular rivalry, we corroborate the ubiquitous hypothesis that autism manifests from reduced inhibition in the brain by systematically probing our model alternation rate across choices of inhibition strength. We exhibit sufficient conditions for producing binocular rivalry in the context of natural scene stimuli, opening a clearer window into the dynamic brain computations that vary with the generated percept and a potential path toward further understanding neurological disorders.

Aluminum Microcomb Electrodes on Silicon Wafer for Detecting Val66Met Polymorphism in Brain-Derived Neurotrophic Factor

OBJECTIVE

Brain-derived neurotrophic factor (BDNF) dysregulation is widely related with various psychiatric and neurological disorders, including schizophrenia, depression, Rett syndrome, and addiction, and the available evidence suggests that BDNF is also highly correlated with Parkinson's and Alzheimer's diseases.

METHODS

The BDNF target sequence was detected on a capture probe attached on aluminum microcomb electrodes on the silicon wafer surface. A capture-target-reporter sandwich-type assay was performed to enhance the detection of the BDNF target.

RESULTS

The limit of detection was noticed to be 100 aM. Input of a reporter sequence at concentrations >10 aM improved the detection of the target sequence by enhancing changes in the generated currents. Control experiments with noncomplementary and single- and triple-mismatches of target and reporter sequences did not elicit changes in current levels, indicating the selective detection of the BDNF gene sequence.

CONCLUSION

The above detection strategy will be useful for the detection and quantification of BDNF, thereby aiding in the provision of suitable treatments for BDNF-related disorders.

To Petabytes and beyond: recent advances in probabilistic and signal processing algorithms and their application to metagenomics

As computational biologists continue to be inundated by ever increasing amounts of metagenomic data, the need for data analysis approaches that keep up with the pace of sequence archives has remained a challenge. In recent years, the accelerated pace of genomic data availability has been accompanied by the application of a wide array of highly efficient approaches from other fields to the field of metagenomics. For instance, sketching algorithms such as MinHash have seen a rapid and widespread adoption. These techniques handle increasingly large datasets with minimal sacrifices in quality for tasks such as sequence similarity calculations. Here, we briefly review the fundamentals of the most impactful probabilistic and signal processing algorithms. We also highlight more recent advances to augment previous reviews in these areas that have taken a broader approach. We then explore the application of these techniques to metagenomics, discuss their pros and cons, and speculate on their future directions.

Collaborative representation-based classification of microarray gene expression data

Microarray technology is important to simultaneously express multiple genes over a number of time points. Multiple classifier models, such as sparse representation (SR)-based method, have been developed to classify microarray gene expression data. These methods allocate the gene data points to different clusters. In this paper, we propose a novel collaborative representation (CR)-based classification with regularized least square to classify gene data. First, the CR codes a testing sample as a sparse linear combination of all training samples and then classifies the testing sample by evaluating which class leads to the minimum representation error. This CR-based classification approach is remarkably less complex than traditional classification methods but leads to very competitive classification results. In addition, compressive sensing approach is adopted to project the high-dimensional gene expression dataset to a lower-dimensional space which nearly contains the whole information. This compression without loss is beneficial to reduce the computational load. Experiments to detect subtypes of diseases, such as leukemia and autism spectrum disorders, are performed by analyzing the gene expression. The results show that the proposed CR-based algorithm exhibits significantly higher stability and accuracy than the traditional classifiers, such as support vector machine algorithm.

Universal microbial diagnostics using random DNA probes

Early identification of pathogens is essential for limiting development of therapy-resistant pathogens and mitigating infectious disease outbreaks. Most bacterial detection schemes use target-specific probes to differentiate pathogen species, creating time and cost inefficiencies in identifying newly discovered organisms. We present a novel universal microbial diagnostics (UMD) platform to screen for microbial organisms in an infectious sample, using a small number of random DNA probes that are agnostic to the target DNA sequences. Our platform leverages the theory of sparse signal recovery (compressive sensing) to identify the composition of a microbial sample that potentially contains novel or mutant species. We validated the UMD platform in vitro using five random probes to recover 11 pathogenic bacteria. We further demonstrated in silico that UMD can be generalized to screen for common human pathogens in different taxonomy levels. UMD's unorthodox sensing approach opens the door to more efficient and universal molecular diagnostics.

Improved Compressive Sensing of Natural Scenes Using Localized Random Sampling

Compressive sensing (CS) theory demonstrates that by using uniformly-random sampling, rather than uniformly-spaced sampling, higher quality image reconstructions are often achievable. Considering that the structure of sampling protocols has such a profound impact on the quality of image reconstructions, we formulate a new sampling scheme motivated by physiological receptive field structure, localized random sampling, which yields significantly improved CS image reconstructions. For each set of localized image measurements, our sampling method first randomly selects an image pixel and then measures its nearby pixels with probability depending on their distance from the initially selected pixel. We compare the uniformly-random and localized random sampling methods over a large space of sampling parameters, and show that, for the optimal parameter choices, higher quality image reconstructions can be consistently obtained by using localized random sampling. In addition, we argue that the localized random CS optimal parameter choice is stable with respect to diverse natural images, and scales with the number of samples used for reconstruction. We expect that the localized random sampling protocol helps to explain the evolutionarily advantageous nature of receptive field structure in visual systems and suggests several future research areas in CS theory and its application to brain imaging.

Compressed sensing methods for DNA microarrays, RNA interference, and metagenomics

Compressed sensing (CS) is a sparse signal sampling methodology for efficiently acquiring and reconstructing a signal from relatively few measurements. Recent work shows that CS is well-suited to be applied to problems in genomics, including probe design in microarrays, RNA interference (RNAi), and taxonomic assignment in metagenomics. The principle of using different CS recovery methods in these applications has thus been established, but a comprehensive study of using a wide range of CS methods has not been done. For each of these applications, we apply three hitherto unused CS methods, namely, l1-magic, CoSaMP, and l1-homotopy, in conjunction with CS measurement matrices such as randomly generated CS m matrix, Hamming matrix, and projective geometry-based matrix. We find that, in RNAi, the l1-magic (the standard package for l1 minimization) and l1-homotopy methods show significant reduction in reconstruction error compared to the baseline. In metagenomics, we find that l1-homotopy as well as CoSaMP estimate concentration with significantly reduced time when compared to the GPSR and WGSQuikr methods.

Sparsity and compressed coding in sensory systems

Considering that many natural stimuli are sparse, can a sensory system evolve to take advantage of this sparsity? We explore this question and show that significant downstream reductions in the numbers of neurons transmitting stimuli observed in early sensory pathways might be a consequence of this sparsity. First, we model an early sensory pathway using an idealized neuronal network comprised of receptors and downstream sensory neurons. Then, by revealing a linear structure intrinsic to neuronal network dynamics, our work points to a potential mechanism for transmitting sparse stimuli, related to compressed-sensing (CS) type data acquisition. Through simulation, we examine the characteristics of networks that are optimal in sparsity encoding, and the impact of localized receptive fields beyond conventional CS theory. The results of this work suggest a new network framework of signal sparsity, freeing the notion from any dependence on specific component-space representations. We expect our CS network mechanism to provide guidance for studying sparse stimulus transmission along realistic sensory pathways as well as engineering network designs that utilize sparsity encoding.

In forming a mental percept of the surrounding world, sensory information is processed and transmitted through a wide array of neuronal networks of various sizes and functionalities. Despite, and perhaps because of, this, sensory systems are able to render highly accurate representations of stimuli. In the retina, for example, photoreceptors transform light into electric signals, which are later processed by a significantly smaller network of ganglion cells before entering the optic nerve. How then is sensory information preserved along such a pathway? In this work, we put forth a possible answer to this question using compressed sensing, a recent advance in the field of signal processing that demonstrates how sparse signals can be reconstructed using very few samples. Through model simulation, we discover that stimuli can be recovered from ganglion-cell dynamics, and demonstrate how localized receptive fields improve stimulus encoding. We hypothesize that organisms have evolved to utilize the sparsity of stimuli, demonstrating that compressed sensing may be a universal information-processing framework underlying both information acquisition and retention in sensory systems.

Convergence and Stability of a Class of Iteratively Re-weighted Least Squares Algorithms for Sparse Signal Recovery in the Presence of Noise

In this paper, we study the theoretical properties of a class of iteratively re-weighted least squares (IRLS) algorithms for sparse signal recovery in the presence of noise. We demonstrate a one-to-one correspondence between this class of algorithms and a class of Expectation-Maximization (EM) algorithms for constrained maximum likelihood estimation under a Gaussian scale mixture (GSM) distribution. The IRLS algorithms we consider are parametrized by 0 < ν ≤ 1 and ε > 0. The EM formalism, as well as the connection to GSMs, allow us to establish that the IRLS(ν, ε) algorithms minimize ε-smooth versions of the ℓ _ν 'norms'. We leverage EM theory to show that, for each 0 < ν ≤ 1, the limit points of the sequence of IRLS(ν, ε) iterates are stationary point of the ε-smooth ℓ _ν 'norm' minimization problem on the constraint set. Finally, we employ techniques from Compressive sampling (CS) theory to show that the class of IRLS(ν, ε) algorithms is stable for each 0 < ν ≤ 1, if the limit point of the iterates coincides the global minimizer. For the case ν = 1, we show that the algorithm converges exponentially fast to a neighborhood of the stationary point, and outline its generalization to super-exponential convergence for ν < 1. We demonstrate our claims via simulation experiments. The simplicity of IRLS, along with the theoretical guarantees provided in this contribution, make a compelling case for its adoption as a standard tool for sparse signal recovery.

A computational model for compressed sensing RNAi cellular screening

BACKGROUND

RNA interference (RNAi) becomes an increasingly important and effective genetic tool to study the function of target genes by suppressing specific genes of interest. This system approach helps identify signaling pathways and cellular phase types by tracking intensity and/or morphological changes of cells. The traditional RNAi screening scheme, in which one siRNA is designed to knockdown one specific mRNA target, needs a large library of siRNAs and turns out to be time-consuming and expensive.

RESULTS

In this paper, we propose a conceptual model, called compressed sensing RNAi (csRNAi), which employs a unique combination of group of small interfering RNAs (siRNAs) to knockdown a much larger size of genes. This strategy is based on the fact that one gene can be partially bound with several small interfering RNAs (siRNAs) and conversely, one siRNA can bind to a few genes with distinct binding affinity. This model constructs a multi-to-multi correspondence between siRNAs and their targets, with siRNAs much fewer than mRNA targets, compared with the conventional scheme. Mathematically this problem involves an underdetermined system of equations (linear or nonlinear), which is ill-posed in general. However, the recently developed compressed sensing (CS) theory can solve this problem. We present a mathematical model to describe the csRNAi system based on both CS theory and biological concerns. To build this model, we first search nucleotide motifs in a target gene set. Then we propose a machine learning based method to find the effective siRNAs with novel features, such as image features and speech features to describe an siRNA sequence. Numerical simulations show that we can reduce the siRNA library to one third of that in the conventional scheme. In addition, the features to describe siRNAs outperform the existing ones substantially.

CONCLUSIONS

This csRNAi system is very promising in saving both time and cost for large-scale RNAi screening experiments which may benefit the biological research with respect to cellular processes and pathways.

Linear program relaxation of sparse nonnegative recovery in compressive sensing microarrays

Compressive sensing microarrays (CSM) are DNA-based sensors that operate using group testing and compressive sensing principles. Mathematically, one can cast the CSM as sparse nonnegative recovery (SNR) which is to find the sparsest solutions subjected to an underdetermined system of linear equations and nonnegative restriction. In this paper, we discuss the l₁ relaxation of the SNR. By defining nonnegative restricted isometry/orthogonality constants, we give a nonnegative restricted property condition which guarantees that the SNR and the l₁ relaxation share the common unique solution. Besides, we show that any solution to the SNR must be one of the extreme points of the underlying feasible set.

Compressed sensing, sparsity, and dimensionality in neuronal information processing and data analysis

The curse of dimensionality poses severe challenges to both technical and conceptual progress in neuroscience. In particular, it plagues our ability to acquire, process, and model high-dimensional data sets. Moreover, neural systems must cope with the challenge of processing data in high dimensions to learn and operate successfully within a complex world. We review recent mathematical advances that provide ways to combat dimensionality in specific situations. These advances shed light on two dual questions in neuroscience. First, how can we as neuroscientists rapidly acquire high-dimensional data from the brain and subsequently extract meaningful models from limited amounts of these data? And second, how do brains themselves process information in their intrinsically high-dimensional patterns of neural activity as well as learn meaningful, generalizable models of the external world from limited experience?

A compressed sensing based approach for subtyping of leukemia from gene expression data

With the development of genomic techniques, the demand for new methods that can handle high-throughput genome-wide data effectively is becoming stronger than ever before. Compressed sensing (CS) is an emerging approach in statistics and signal processing. With the CS theory, a signal can be uniquely reconstructed or approximated from its sparse representations, which can therefore better distinguish different types of signals. However, the application of CS approach to genome-wide data analysis has been rarely investigated. We propose a novel CS-based approach for genomic data classification and test its performance in the subtyping of leukemia through gene expression analysis. The detection of subtypes of cancers such as leukemia according to different genetic markups is significant, which holds promise for the individualization of therapies and improvement of treatments. In our work, four statistical features were employed to select significant genes for the classification. With our selected genes out of 7,129 ones, the proposed CS method achieved a classification accuracy of 97.4% when evaluated with the cross validation and 94.3% when evaluated with another independent data set. The robustness of the method to noise was also tested, giving good performance. Therefore, this work demonstrates that the CS method can effectively detect subtypes of leukemia, implying improved accuracy of diagnosis of leukemia.

Open-target sparse sensing of biological agents using DNA microarray

Background

Current biosensors are designed to target and react to specific nucleic acid sequences or structural epitopes. These 'target-specific' platforms require creation of new physical capture reagents when new organisms are targeted. An 'open-target' approach to DNA microarray biosensing is proposed and substantiated using laboratory generated data. The microarray consisted of 12,900 25 bp oligonucleotide capture probes derived from a statistical model trained on randomly selected genomic segments of pathogenic prokaryotic organisms. Open-target detection of organisms was accomplished using a reference library of hybridization patterns for three test organisms whose DNA sequences were not included in the design of the microarray probes.

Results

A multivariate mathematical model based on the partial least squares regression (PLSR) was developed to detect the presence of three test organisms in mixed samples. When all 12,900 probes were used, the model correctly detected the signature of three test organisms in all mixed samples (mean(R²)) = 0.76, CI = 0.95), with a 6% false positive rate. A sampling algorithm was then developed to sparsely sample the probe space for a minimal number of probes required to capture the hybridization imprints of the test organisms. The PLSR detection model was capable of correctly identifying the presence of the three test organisms in all mixed samples using only 47 probes (mean(R²)) = 0.77, CI = 0.95) with nearly 100% specificity.

Conclusions

We conceived an 'open-target' approach to biosensing, and hypothesized that a relatively small, non-specifically designed, DNA microarray is capable of identifying the presence of multiple organisms in mixed samples. Coupled with a mathematical model applied to laboratory generated data, and sparse sampling of capture probes, the prototype microarray platform was able to capture the signature of each organism in all mixed samples with high sensitivity and specificity. It was demonstrated that this new approach to biosensing closely follows the principles of sparse sensing.

Identification of rare alleles and their carriers using compressed se(que)nsing

Identification of rare variants by resequencing is important both for detecting novel variations and for screening individuals for known disease alleles. New technologies enable low-cost resequencing of target regions, although it is still prohibitive to test more than a few individuals. We propose a novel pooling design that enables the recovery of novel or known rare alleles and their carriers in groups of individuals. The method is based on a Compressed Sensing (CS) approach, which is general, simple and efficient. CS allows the use of generic algorithmic tools for simultaneous identification of multiple variants and their carriers. We model the experimental procedure and show via computer simulations that it enables the recovery of rare alleles and their carriers in larger groups than were possible before. Our approach can also be combined with barcoding techniques to provide a feasible solution based on current resequencing costs. For example, when targeting a small enough genomic region (∼100 bp) and using only ∼10 sequencing lanes and ∼10 distinct barcodes per lane, one recovers the identity of 4 rare allele carriers out of a population of over 4000 individuals. We demonstrate the performance of our approach over several publicly available experimental data sets.

poolMC: smart pooling of mRNA samples in microarray experiments

BACKGROUND

Typically, pooling of mRNA samples in microarray experiments implies mixing mRNA from several biological-replicate samples before hybridization onto a microarray chip. Here we describe an alternative smart pooling strategy in which different samples, not necessarily biological replicates, are pooled in an information theoretic efficient way. Further, each sample is tested on multiple chips, but always in pools made up of different samples. The end goal is to exploit the compressibility of microarray data to reduce the number of chips used and increase the robustness to noise in measurements.

RESULTS

A theoretical framework to perform smart pooling of mRNA samples in microarray experiments was established and the software implementation of the pooling and decoding algorithms was developed in MATLAB. A proof-of-concept smart pooled experiment was performed using validated biological samples on commercially available gene chips. Differential-expression analysis of the smart pooled data was performed and compared against the unpooled control experiment.

CONCLUSIONS

The theoretical developments and experimental demonstration in this paper provide a useful starting point to investigate smart pooling of mRNA samples in microarray experiments. Although the smart pooled experiment did not compare favorably with the control, the experiment highlighted important conditions for the successful implementation of smart pooling - linearity of measurements, sparsity in data, and large experiment size.