A theorem proving approach for automatically synthesizing visualizations of flow cytometry data.

BACKGROUND: Polychromatic flow cytometry is a popular technique that has wide usage in the medical sciences, especially for studying phenotypic properties of cells. The high-dimensionality of data generated by flow cytometry usually makes it difficult to visualize. The naive solution of simply plotting two-dimensional graphs for every combination of observables becomes impractical as the number of dimensions increases. A natural solution is to project the data from the original high dimensional space to a lower dimensional space while approximately preserving the overall relationship between the data points. The expert can then easily visualize and analyze this low-dimensional embedding of the original dataset. RESULTS: This paper describes a new method, SANJAY, for visualizing high-dimensional flow cytometry datasets. This technique uses a decision procedure to automatically synthesize two-dimensional and three-dimensional projections of the original high-dimensional data while trying to minimize distortion. We compare SANJAY to the popular multidimensional scaling (MDS) approach for visualization of small data sets drawn from a representative set of benchmarks, and our experiments show that SANJAY produces distortions that are 1.44 to 4.15 times smaller than those caused due to MDS. Our experimental results show that SANJAY also outperforms the Random Projections technique in terms of the distortions in the projections. CONCLUSIONS: We describe a new algorithmic technique that uses a symbolic decision procedure to automatically synthesize low-dimensional projections of flow cytometry data that typically have a high number of dimensions. Our algorithm is the first application, to our knowledge, of using automated theorem proving for automatically generating highly-accurate, low-dimensional visualizations of high-dimensional data.

Exploring behaviors of stochastic differential equation models of biological systems using change of measures.

Stochastic Differential Equations (SDE) are often used to model the stochastic dynamics of biological systems. Unfortunately, rare but biologically interesting behaviors (e.g., oncogenesis) can be difficult to observe in stochastic models. Consequently, the analysis of behaviors of SDE models using numerical simulations can be challenging. We introduce a method for solving the following problem: given a SDE model and a high-level behavioral specification about the dynamics of the model, algorithmically decide whether the model satisfies the specification. While there are a number of techniques for addressing this problem for discrete-state stochastic models, the analysis of SDE and other continuous-state models has received less attention. Our proposed solution uses a combination of Bayesian sequential hypothesis testing, non-identically distributed samples, and Girsanov's theorem for change of measures to examine rare behaviors. We use our algorithm to analyze two SDE models of tumor dynamics. Our use of non-identically distributed samples sampling contributes to the state of the art in statistical verification and model checking of stochastic models by providing an effective means for exposing rare events in SDEs, while retaining the ability to compute bounds on the probability that those events occur.

Symbolic approaches for finding control strategies in Boolean Networks.

We present an exact algorithm, based on techniques from the field of Model Checking, for finding control policies for Boolean Networks (BN) with control nodes. Given a BN, a set of starting states, I, a set of goal states, F, and a target time, t, our algorithm automatically finds a sequence of control signals that deterministically drives the BN from I to F at, or before time t, or else guarantees that no such policy exists. Despite recent hardness-results for finding control policies for BNs, we show that, in practice, our algorithm runs in seconds to minutes on over 13,400 BNs of varying sizes and topologies, including a BN model of embryogenesis in Drosophila melanogaster with 15,360 Boolean variables. We then extend our method to automatically identify a set of Boolean transfer functions that reproduce the qualitative behavior of gene regulatory networks. Specifically, we automatically learn a BN model of D. melanogaster embryogenesis in 5.3 seconds, from a space containing 6.9 x 10(10) possible models.

Development and validation of an electrochemiluminescent ELISA for quantitation of oral insulin tregopil in diabetes mellitus serum.

AIM: Tregopil, a novel PEGylated human insulin is in clinical development for oral delivery in diabetes treatment. The aim of the study was to develop and validate a sensitive and specific ELISA method for quantitating Tregopil in diabetes subjects on basal Glargine, since most commercially available insulin kits either do not detect Tregopil or show significant reactivity to Glargine. METHODS: An electrochemiluminescent ELISA was developed and validated for Tregopil quantitation in diabetes serum. RESULTS: The method has a LLOQ of 0.25 ng/ml, shows minimum cross-reactivity to Glargine and was successfully tested using a subset of samples from Tregopil-dosed Type 1 diabetes mellitus patients. CONCLUSION: The ELISA method is sensitive and can be used to support accurate measurement of Tregopil with no cross-reactivity to Glargine and its metabolites in clinical studies.

Discovering rare behaviours in stochastic differential equations using decision procedures: applications to a minimal cell cycle model.

Stochastic Differential Equation (SDE) models are used to describe the dynamics of complex systems with inherent randomness. The primary purpose of these models is to study rare but interesting or important behaviours, such as the formation of a tumour. Stochastic simulations are the most common means for estimating (or bounding) the probability of rare behaviours, but the cost of simulations increases with the rarity of events. To address this problem, we introduce a new algorithm specifically designed to quantify the likelihood of rare behaviours in SDE models. Our approach relies on temporal logics for specifying rare behaviours of interest, and on the ability of bit-vector decision procedures to reason exhaustively about fixed-precision arithmetic. We apply our algorithm to a minimal parameterised model of the cell cycle, and take Brownian noise into account while investigating the likelihood of irregularities in cell size and time between cell divisions.

Synthesis of insulin pump controllers from safety specifications using Bayesian model validation.

Insulin pump controllers seek to alleviate the chronic suffering caused by diabetes that affects over 6% of the world population. The design of control laws for insulin pump controllers has been well studied. However, the parameters involved in the control law are difficult to synthesize. Traditionally, ad hoc approaches using animal models and random sampling have been used to construct these parameters. We suggest a synthesis algorithm that uses Bayesian statistical model validation to reduce the number of simulations needed. We apply this algorithm to the problem of insulin pump controller synthesis using in silico simulation of the glucose-insulin metabolism model.