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At least 163 records · Page 9Linked to original sources
PubMed1996

Description of interacting channel gating using a stochastic Markovian model.

Single-channel recordings from membrane patches frequently exhibit multiple conductance levels. In some preparations, the steady-state probabilities of observing these levels do not follow a binomial distribution. This behavior has been reported in sodium channels, potassium channels, acetylcholine receptor channels and gap junction channels. A non-binomial distribution suggests interaction of the channels or the presence of channels or the presence of channels with different open probabilities. However, the current trace sometimes exhibits single transitions spanning several levels. Since the probability of simultaneous transitions of independent channels is infinitesimally small, such observations strongly suggest a cooperative gating behavior. We present a Markov model to describe the cooperative gating of channels using only the all-points current amplitude histograms for the probability of observing the various conductance levels. We investigate the steady-state (or equilibrium) properties of a system of N channels and provide a scheme to express all the probabilities in terms of just two parameters. The main feature of our model is that lateral interaction of channels gives rise to cooperative gating. Another useful feature is the introduction of the language of graph theory which can potentially provide a different avenue to study ion channel kinetics. We write down explicit expressions for systems of two, three and four channels and provide a procedure to describe the system of N channels.

Animals↗
PubMed2006

Mathematical tools in analytical mass spectrometry.

Over the last few decades, mass spectrometry has become a powerful tool for exploring various aspects of molecular processes occurring in biological systems. Such exploration is leading to a greater understanding of various complex life processes; unraveling these processes poses the greatest challenge to contemporary bioscience. With due respect to sample preparation, data analysis is rapidly becoming a major obstacle to the conversion of experimental knowledge into valid conclusions. It is interesting to note that many problems related to mass spectrometry can be solved using techniques from computer science, graph theory and discrete mathematics. The aim of this manuscript is to recollect several essays that demonstrate the power and the need to apply such skills to mass spectrometry data interpretation. Special attention is paid to situations where traditional chemical analysis reaches its limits but mathematical reasoning can still allow us to reach valid conclusions.

Journal Article↗
PubMed1992

Three-dimensional structural resemblance between leucine aminopeptidase and carboxypeptidase A revealed by graph-theoretical techniques.

Using 3-D searching techniques based on algorithms derived from graph theory we have established a striking structural similarity between the structure of bovine carboxypeptidase A and that of the C-terminal domain of bovine leucine aminopeptidase. There is no significant sequence homology between the aminopeptidases and the carboxypeptidases but the strong structural relationship detected in this complex fold suggests that there may be a very remote divergent evolutionary relationship between these two enzyme classes.

Animals↗
PubMed1993

Three-dimensional structural resemblance between the ribonuclease H and connection domains of HIV reverse transcriptase and the ATPase fold revealed using graph theoretical techniques.

Using 3D searching techniques based on algorithms derived from graph theory, we have established two previously unreported structural similarities involving the ribonuclease H (RNase H) domain of HIV-1 reverse transcriptase (RT). First, we report that there is a strong similarity between the 3D folds of the RNase H domain of RT and the 'ATPase folds' of hexokinase, the 70 kDa heat-shock cognate protein and actin. Like RNase H, these enzymes are involved in nucleotide binding and metal ion-catalysed cleavage of a phosphodiester bond. Similarities of the folding motif and the position of the metal-binding site in these enzymes suggest possible functional analogies and evolutionary relationships with RNase H. Second, we find there is a strong resemblance between the folds of the RNase H domain and of the p66 and p51 'connection' domains of RT. It is possible that this striking similarity within the RT structure indicates a possible ancestral gene doubling event. The similarity may also indicate that the connection domains possess functional roles in addition to those previously suggested, and they may therefore represent a further target for the design of therapeutic agents.

Adenosine Triphosphatases↗
PubMed1983

The complexity of the overlap method for sequencing biopolymers.

The problem of trying to reconstruct the sequence of a biopolymer by using overlapping fragments obtained from cleaving agents is shown to be computationally intractable. This strongly suggests that any computer program for overlap sequencing, even though it may work well for a limited number of inputs, will not work sufficiently for all inputs. However, if the problem is restricted so that certain crucial fragments are known, called prime strings, a sequence can be found efficiently in all cases. Graph theory techniques for doing so can also be used to count the number of sequences consistent with the fragment data to determine whether a unique sequence has been obtained.

Amino Acid Sequence↗
PubMed1983

Computer simulation of compartment maintenance in the Drosophila wing imaginal disc.

A new method for modelling cell division is reported which uses a cellular representation based on graph theory. This allows us to model the adjacencies of non-regular dividing cells accurately, avoiding the rigid geometrical constraints present in earlier simulations. We use this system to simulate compartment boundary maintenance in the Drosophila wing imaginal disc. We show that a boundary of minimum length between two growing polyclones of cells could depend on sorting between cells in the different polyclones. We also investigate the response of the model to differential cell division rates within polyclones. This is the first demonstration that cell sorting can generate a smooth boundary in a dividing cell mass. We suggest that biological analogs of our computer sorting rules are responsible for the similar straight polyclone borders seen in the real wing disc. A possible strategy for showing the existence of these analogs is also given.

Animals↗
PubMed1984

A return to time, cells, systems and aging: II. Relational and reliability theoretic approaches to the study of senescence in living systems.

In this paper, we approach the problem of attempting to understand senescence by understanding the complexity and hierarchical structure of mammalian organisms. To do this, we make use of some concepts from abstract relational biology; in particular, graph theory. We subsequently utilize these concepts to develop the idea of an irreplaceable element in a mammalian system. We then make use of these elements, and some concepts from reliability theory, to show how senescence processes in mammalian systems may be related to the failure of a critical number of irreplaceable elements. Finally, we show how we may derive formulas for the expected number of elements which fail by a given time, and how this time is related to actual lifespan and expected lifespan of the organism. In particular, we relate this to some recent work by Cutler on the evolution of longevity.

Aging↗
PubMed1995

The topology of the kinetoplast DNA network.

Kinetoplast DNA (kDNA) of trypanosomatid parasites is a network of approximately 5000 catenated DNA minicircles and approximately 25 maxicircles. We developed the following strategy to deduce the topological linkage of the minicircles of the Crithidia fasciculata network. First, we used graph theory to provide precise models of possible network structures. Second, on the basis of these models, we predicted the frequencies of minicircle oligomers expected from random network breakage. Third, we determined the fragmentation pattern of kDNA networks as a function of the extent of digestion. Fourth, by comparison of the results with the predictions, we identified the model that best represents the network. We conclude that each minicircle is linked on average to three other minicircles. A honeycomb arrangement probably results, with each minicircle typically at the vertex of a hexagonal cell. This topology has implications for the assembly, structure, and function of kDNA networks.

Animals↗
PubMed1986

The uses of spatial analysis in medical geography: a review.

This paper is a review of how geographers and others have used spatial analysis to study disease and health care delivery patterns. Point, line, area and surface patterns, as well as map comparisons and relative spaces are discussed. Problems encountered in applying spatial analytic techniques in medical geography are pointed out. The paper is intended to stimulate discussion about where medical geography can and should go in this area of study. Point pattern techniques include standard distance, standard deviational ellipses, gradient analysis and space and space-time clustering. Line methods include random walks, vectors and graph theory or network analysis. Under areas, location quotients, standardized mortality ratios, Poisson probabilities, space and space-time clustering, autocorrelation measures and hierarchical clustering are discussed. Surface techniques mentioned are isolines and trend surfaces. For map comparisons, Lorenz curves, coefficients of areal correspondence and correlation coefficients have been used. Case-control matching, acquaintance networks, multidimensional scaling and cluster analysis are examples of methods that are based on relative or non-metric spaces. The review gives rise to the discussion of several general points: problems encountered in spatial analysis, theory building and verification, the appropriate role of technique and computer use. Some suggestions are made for further use of spatial analytic techniques in medical geography: Monte Carlo simulation of point patterns, network analysis to study referral systems and health care for pastoralists, geographic information systems to assess environmental risk, difference mapping for disease and risk factor map comparisons and multidimensional scaling to measure social distance.

Cross-Sectional Studies↗
PubMed1979

Quantitative analysis of dendritic branching. I. Simple formulae for the quantitative analysis of dendritic branching.

Dendritic branching of neurons may be quantitatively studied using applications of graph theory. Dendritic ramifications may be considered as 'forests' of planted, stemmed, binary 'trees' with simple mathematical properties. Two fundamental numbers, that of dendritic tips and that of dendritic stems, usually suffice to quantify the dendritic branching of one neuron as, in most cases, they allow the computation of all other numbers of dendritic points and segments.

Animals↗
PubMed2006

Kinetic modeling and fitting software for interconnected reaction schemes: VisKin.

Reaction kinetics for complex, highly interconnected kinetic schemes are modeled using analytical solutions to a system of ordinary differential equations. The algorithm employs standard linear algebra methods that are implemented using MatLab functions in a Visual Basic interface. A graphical user interface for simple entry of reaction schemes facilitates comparison of a variety of reaction schemes. To ensure microscopic balance, graph theory algorithms are used to determine violations of thermodynamic cycle constraints. Analytical solutions based on linear differential equations result in fast comparisons of first order kinetic rates and amplitudes as a function of changing ligand concentrations. For analysis of higher order kinetics, we also implemented a solution using numerical integration. To determine rate constants from experimental data, fitting algorithms that adjust rate constants to fit the model to imported data were implemented using the Levenberg-Marquardt algorithm or using Broyden-Fletcher-Goldfarb-Shanno methods. We have included the ability to carry out global fitting of data sets obtained at varying ligand concentrations. These tools are combined in a single package, which we have dubbed VisKin, to guide and analyze kinetic experiments. The software is available online for use on PCs.

Computer Simulation↗
PubMed2025

Interrogating functional connectivity of in vitro neural glia tissue model modulated through integrative control of matrix stiffness and a neurotrophic factor.

Brain function emerges from intricate cellular communication within neural networks. Both In silico neuronal models and primary neuron cells have revealed that the branching architecture of individual neurons determines the bioelectrical signal propagation pattern and dynamics. However, whether stem cell-differentiated neurons can build functional connectivity regulated by neuronal morphology has yet to be determined. Here, we hypothesized that neurite length, branching, or both factors would regulate the functional connectivity of the stem cell-differentiated neural network. We examined this hypothesis by differentiating mouse cortical neural stem cells (NSCs) on Matrigel substrates with varying storage moduli, both with and without basic fibroblast growth factor (bFGF). Interestingly, with bFGF, Matrigel with a storage modulus (G') of 100 Pa drives NSCs to differentiate into neurons with more dendritic branches, while the gel with G' of 50 Pa led to the development of longer neurites with fewer branches. Notably, branch-rich neural networks exhibited an increased frequency of calcium transients. Using a MATLAB-based analysis pipeline incorporating graph theory, we constructed spatial and temporal calcium activity maps, revealing that branching complexity, more than neurite length, correlates with the density and strength of functional neural circuits. Overall, this study demonstrates that the dendritic branching of neurons, modulated with matrix stiffness and neurotrophic factors, is a key element in enhancing the electrophysiological functionality of the stem cell-differentiated neural network. This finding will have a significant impact on efforts to reconstruct functional neural tissue models, advancing both regenerative therapies and unexplored applications, including biological computing.

Animals↗
PubMed2005

EXAMINE: a computational approach to reconstructing gene regulatory networks.

Reverse-engineering of gene networks using linear models often results in an underdetermined system because of excessive unknown parameters. In addition, the practical utility of linear models has remained unclear. We address these problems by developing an improved method, EXpression Array MINing Engine (EXAMINE), to infer gene regulatory networks from time-series gene expression data sets. EXAMINE takes advantage of sparse graph theory to overcome the excessive-parameter problem with an adaptive-connectivity model and fitting algorithm. EXAMINE also guarantees that the most parsimonious network structure will be found with its incremental adaptive fitting process. Compared to previous linear models, where a fully connected model is used, EXAMINE reduces the number of parameters by O(N), thereby increasing the chance of recovering the underlying regulatory network. The fitting algorithm increments the connectivity during the fitting process until a satisfactory fit is obtained. We performed a systematic study to explore the data mining ability of linear models. A guideline for using linear models is provided: If the system is small (3-20 elements), more than 90% of the regulation pathways can be determined correctly. For a large-scale system, either clustering is needed or it is necessary to integrate information in addition to expression profile. Coupled with the clustering method, we applied EXAMINE to rat central nervous system development (CNS) data with 112 genes. We were able to efficiently generate regulatory networks with statistically significant pathways that have been predicted previously.

Algorithms↗
PubMed2004

Searching for functional sites in protein structures.

An ability to assign protein function from protein structure is important for structural genomics consortia. The complex relationship between protein fold and function highlights the necessity of looking beyond the global fold of a protein to specific functional sites. Many computational methods have been developed that address this issue. These include evolutionary trace methods, methods that involve the calculation and assessment of maximal superpositions, methods based on graph theory, and methods that apply machine learning techniques. Such function prediction techniques have been applied to the identification of enzyme catalytic triads and DNA-binding motifs.

Binding Sites↗
PubMed2005

Flexible information storage in MUDR(II) EHR.

An important research task of the EuroMISE Centre is the applied research in the field of electronic health record (EHR) design including electronic medical guidelines and intelligent systems for data mining and decision support. The research in this field was inspired by several European projects. We have proposed a mathematical meta-description of a flexible information storage model based on the experience gathered in cooperation in those projects. In this model, we use two basic structures called a knowledge base and data files. We describe those two structures using the graph theory concepts. Furthermore, we use logical formulas to express conditions that should be valid. Additionally, we present a description of a global system architecture of a 3-tier EHR application with interfaces based on the latest technologies; predominately on Web Services, SOAP, XML, HTTP, CORBA, etc. According to our experience and test results gained from the MUDR EHR usage, we describe an open universal solution, which can be applied as the EHR kernel of hospital information systems. To realize this approach in a daily practice for health professionals we have started a co-operative project with clinical information systems developers. Within that project we are developing a new system for continual shared health care.

Biomedical Research↗
PubMed2005

Structural prediction of peptides bound to MHC class I.

An ab initio structure prediction approach adapted to the peptide-major histocompatibility complex (MHC) class I system is presented. Based on structure comparisons of a large set of peptide-MHC class I complexes, a molecular dynamics protocol is proposed using simulated annealing (SA) cycles to sample the conformational space of the peptide in its fixed MHC environment. A set of 14 peptide-human leukocyte antigen (HLA) A0201 and 27 peptide-non-HLA A0201 complexes for which X-ray structures are available is used to test the accuracy of the prediction method. For each complex, 1000 peptide conformers are obtained from the SA sampling. A graph theory clustering algorithm based on heavy atom root-mean-square deviation (RMSD) values is applied to the sampled conformers. The clusters are ranked using cluster size, mean effective or conformational free energies, with solvation free energies computed using Generalized Born MV 2 (GB-MV2) and Poisson-Boltzmann (PB) continuum models. The final conformation is chosen as the center of the best-ranked cluster. With conformational free energies, the overall prediction success is 83% using a 1.00 Angstroms crystal RMSD criterion for main-chain atoms, and 76% using a 1.50 Angstroms RMSD criterion for heavy atoms. The prediction success is even higher for the set of 14 peptide-HLA A0201 complexes: 100% of the peptides have main-chain RMSD values < or =1.00 Angstroms and 93% of the peptides have heavy atom RMSD values < or =1.50 Angstroms. This structure prediction method can be applied to complexes of natural or modified antigenic peptides in their MHC environment with the aim to perform rational structure-based optimizations of tumor vaccines.

Algorithms↗
PubMed2006

PIPATH: an optimized algorithm for generating alpha-helical structures from PISEMA data.

An optimized algorithm for finding structures and assignments of solid-state NMR PISEMA data obtained from alpha-helical membrane proteins is presented. The description of this algorithm, PIPATH, is followed by an analysis of its performance on simulated PISEMA data derived from synthetic and experimental structures. pipath transforms the assignment problem into a path-finding problem for a directed graph, and then uses techniques of graph theory to efficiently find candidate assignments from a very large set of possibilities.

Algorithms↗
PubMed2006

Gene expression changes in peripheral blood cells provide insight into the biological mechanisms associated with regimen-related toxicities in patients being treated for head and neck cancers.

UNLABELLED: Patients treated with radiotherapy are prone to a constellation of local and systemic toxicities including mucositis, xerostomia, fatigue and anorexia. The biological complexities and similarities underlying the development of toxicities have recently been realized. Mucosal barrier injury is one of the best studied, and gene expression patterns, based on animal tissue samples, have added to its understanding. While investigations gene expression based on tissue samples was valuable, its use precludes more generalizable conclusions relative to common pathogenic mechanisms. Additionally, attempting to define the kinetics of changes in gene expression by sequential sampling is pragmatically unrealistic. Our objectives were: 1. to determine if changes in gene expression could be detected during toxicity development using PBM from patients receiving chemoradiation; 2. to characterize the relationship of expressed genes using graph theory and pathway analysis; and 3. to evaluate potential relationships between the expression of particular genes, canonical pathways, and functional networks in explaining the pathogenesis of regimen-related toxicities. DESIGN: Microarray analysis was performed using PBM-derived cRNA obtained before and 2 weeks after the initiation of chemoradiation in five patients with head and neck cancer who developed documented regimen-related toxicities. We created a database of those genes newly expressed at 2 weeks and evaluated their potential significance relative to toxicity, by canonical pathway analysis, compilation of regional networks around focus genes, and development of a model globalizing the individual functional networks. There was strong concordance between known pathogenic mechanisms of toxicity and the genes, pathways, and networks developed by our data. A role was elicited for unsuspected genes in toxicity development. Our results support the concept that radiation induced toxicities have common underlying mechanisms and demonstrate the utility of PBM as an RNA source for genetic studies. This methodology could be broadly applicable to the study of regimen-related toxicities.

Adult↗