Analysis of flow cytometric aneuploid DNA histograms: validation of an automatic procedure against ad hoc experimental data

In this paper we present an improved version of a method for the automatic analysis of flow cytometric DNA histograms from samples containing a mixture of two cell populations. The procedure is tested against two sets of ad hoc experimental data, obtained by mixing cultures of cell lines in different known proportions. The potentialities of the method are enlightened and discussed with regard to its capability of recovering the population percentages, the DNA index and the G0/G1, S, G2+M phase fractions of each population. On the basis of the obtained results, the procedure appears to be a promising tool in the flow cytometric data analysis and, in particular, in problems of diagnosis and prognosis of tumor diseases

Global convergence technique for the Newton method with periodic Hessian evaluation.

The problem of globalizing the Newton method when the actual Hessian matrix is not used at every iteration is considered. A stabilization technique is studied that employs a new line search strategy for ensuring the global convergence under mild assumptions. Moreover, an implementable algorithmic scheme is proposed, where the evaluation of the second derivatives is conditioned to the behavior of the algorithm during the minimization process and the local convexity properties of the objective function. This is done in order to obtain a significant computational saving, while keeping acceptable the unavoidable degradation in convergence speed. The numerical results reported indicate that the method described may be employed advantageously in all applications where the computation of the Hessian matrix is highly time consuming

Efficient training of RBF neural networks for pattern recognition.

The problem of training a radial basis function (RBF) neural network for distinguishing two disjoint sets in Rn is considered. The network parameters can be determined by minimizing an error function that measures the degree of success in the recognition of a given number of training patterns. In this paper, taking into account the specific feature of classification problems, where the goal is to obtain that the network outputs take values above or below a fixed threshold, we propose an approach alternative to the classical one that makes us of the least-squares error function. In particular, the problem is formulated in terms of a system of nonlinear inequalities, and a suitable error function, which depends only on the violated inequalities, is defined. Then, a training algorithm based on this formulation is presented. Finally, the results obtained by applying the algorithm to two test problems are compared with those derived by adopting the commonly used least-squares error function. The results show the effectiveness of the proposed approach in RBF network training for pattern recognition, mainly in terms of computational time saving

Continuous global optimization for protein structure analysis

Optimization methods are a powerful tool in protein structure analysis. In this paper we show that they can be profitably used to solve relevant problems in drug design such as the comparison and recognition of protein binding sites and the protein-peptide docking. Binding sites recognition is generally based on geometry often combined with physico-chemical properties of the site whereas the search for correct protein-peptide docking is often based on the minimization of an interaction energy model. We show that continuous global optimization methods can be used to solve the above problems and show some computational results

Threshold-Free Population Analysis Identifies Larger DRG Neurons to Respond Stronger to NGF Stimulation

Sensory neurons in dorsal root ganglia (DRG) are highly heterogeneous in terms of cell size, protein expression, and signaling activity. To analyze their heterogeneity, threshold-based methods are commonly used, which often yield highly variable results due to the subjectivity of the individual investigator. In this work, we introduce a threshold-free analysis approach for sparse and highly heterogeneous datasets obtained from cultures of sensory neurons. This approach is based on population estimates and completely free of investigator-set parameters. With a quantitative automated microscope we measured the signaling state of single DRG neurons by immunofluorescently labeling phosphorylated, i.e., activated Erk1/2. The population density of sensory neurons with and without pain-sensitizing nerve growth factor (NGF) treatment was estimated using a kernel density estimator (KDE). By subtraction of both densities and integration of the positive part, a robust estimate for the size of the responsive subpopulations was obtained. To assure sufficiently large datasets, we determined the number of cells required for reliable estimates using a bootstrapping approach. The proposed methods were employed to analyze response kinetics and response amplitude of DRG neurons after NGF stimulation. We thereby determined the portion of NGF responsive cells on a true population basis. The analysis of the dose dependent NGF response unraveled a biphasic behavior, while the study of its time dependence showed a rapid response, which approached a steady state after less than five minutes. Analyzing two parameter correlations, we found that not only the number of responsive small-sized neurons exceeds the number of responsive large-sized neurons—which is commonly reported and could be explained by the excess of small-sized cells—but also the probability that small-sized cells respond to NGF is higher. In contrast, medium-sized and large-sized neurons showed a larger response amplitude in their mean Erk1/2 activity

Analysis of DNA Distributions from Flow Cytometry By Means of an Optimization Procedure

In this paper the problem is considered of FCM histogram processing in the case of mixtures of two or more cell populations, which appears of great interest in diagnosis and treatment of tumor diseases. A suitable mathematical model is first developed in order to represent the pattern of DNA and fluorescence distribution in the samples. An optimization procedure is then proposed for the automatic estimation of the unknown model parameters, which employs a version of Newton's method

Global Optimization of Protein–peptide Docking by a Filling Function Method

Molecular docking programs play a crucial role in drug design and development. In recent years, much attention has been devoted to the protein–peptide docking problem in which docking of a flexible peptide with a given protein is sought. In this work, we present a docking algorithm which is based on the use of a filling function method for continuous global optimization. In particular, the protein–peptide docking position is found by minimizing the conformational potential free energy function based on a new approximate mathematical model. The resulting global optimization problem presents some difficulties, since it is a large-scale one and the objective function is non-convex, so that it has many local minima. To solve the problem, we adopt a global optimization method based on the use of a filling function to escape from local solutions. Moreover, in order to obtain more accurate results, we search the correct docking position by performing a two-phase optimization process. In particular, in a first step, only the carbon Cα atoms of the protein and peptide are considered, thus obtaining an approximate docking solution. Then, the energy function is completed by considering all the peptide and protein atoms so that, starting from the solution of the first phase, the new minimization process gives a more accurate result. We present numerical results on a set of benchmark docking pairs and their comparison with those obtained by the known software package PacthDock for molecular docking