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PubMed2026

Decoding spatiotemporal fibrotic and cellular immunosuppression of therapeutic T cells in live pancreatic ductal adenocarcinoma.

Pancreatic ductal adenocarcinoma (PDA) is profoundly immunosuppressive. To help define this behavior, we present integrated experimental and computational frameworks to elucidate therapeutic T cell dynamics. Through the development of TME-CARTographer (TME-CART), a computational pipeline integrating high-dimensional data, graph theory, behavior analysis, and deep learning (DL), we present quantitative insights on 4D T cell-TME interactions in live PDA tumors. Mapping physical immunosuppression demonstrates that collagen fiber architectures direct migration while concomitantly limiting off-axis movement, creating immune exclusion zones. Expanding these findings, we establish that the collagen matrix harbors and spatially organizes immunosuppressive myeloid cells to serve as cooperative co-modulators of T cell behaviors, including migration, sampling, repulsion, and sequestration. Consistent with these findings, DL defines both linear and nonlinear collagen matrix and cellular neighborhood interactions as drivers of T cell behavior. The TME-CART DL framework also accurately predicts shifts in immunosuppression following depletion of myeloid cells. Overall, we identify synergistic barriers impeding anti-tumor T cell behaviors and present TME-CART as a discovery platform for interpreting complex 4D data to enhance the understanding and design of immunotherapies.

Journal Article↗
PubMed2000

An integral-geometric approach for the euler-Poincare characteristic of spatial images

The determination of the Euler-Poincare characteristic of a set can be based on observations of a digitized image of that set. In the present paper the correctness of the method is proved due to a strict integral-geometric approach. Our result also provides a link to the methods which are used in image analysis and are based on graph theory.

Journal Article↗
PubMed2003

A structural representation of migraine diagnostic criteria: the experts' view.

OBJECTIVE: To generate an empirically derived structural representation of migraine diagnostic criteria in a group of international headache experts using the Pathfinder network scaling algorithm in order to evaluate the validity of the migraine criteria used in the International Headache Society (IHS) classification system. BACKGROUND: Because it is a disease entity that lacks objective defining markers, developing valid diagnostic criteria for migraine is a challenge. The IHS committee relied on expert consensus to develop their classification system in 1988. Expert consensus also was used to evaluate the validity of the IHS classification system, but further studies employing alternative methods still are needed. METHODS: Headache experts representing the Executive Committee of the IHS and the Board of Directors of the American Headache Society analyzed 14 criteria (7 IHS and 7 non-IHS) considered relevant in diagnosing migraine. Their ratings were submitted to the Pathfinder algorithm to generate a network structure reflecting the experts' conceptualization of migraine diagnostic criteria. RESULTS: The expert network had 3 groupings: headache characteristics (eg, phonophobia, unilateral pain, throbbing pain), biological contributing factors (eg, family history, hormonal relationship, relief with sleep), and triggering factors (eg, worse with stress, food triggers). The IHS criteria were clustered together in the center portion of the network. A t test showed that each IHS criterion was closer conceptually to other IHS criteria than to non-IHS criteria. Graph theory indices revealed that the most central criteria were unilateral pain, moderate/severe intensity, and nausea/vomiting. CONCLUSION: The structural representation of migraine diagnostic criteria from these international headache experts is consistent with the migraine diagnostic criteria set forth in the IHS classification system and thus provides further support for the validity of migraine criteria in the IHS system.

Algorithms↗
PubMed2004

Dissociation of hydrogen fluoride in HF(H(2)O)(7).

We have previously demonstrated that H-bond arrangement has a significant influence on the energetics, structure and chemistry of water clusters. In this work, the effect of H-bond orientation on the dissociation of hydrogen fluoride with seven water molecules is studied by means of graph theory and high level ab initio methods. It is found that cubic structures of HF(H(2)O)(7) are more stable than structures of other topologies reported in the literature. Electronic calculations on all possible H-bond orientations of cubie-HF(H(2)O)(7) show that ionized structures are energetically more favorable than nonionized ones. This is an indication that seven water molecules might be capable of ionizing hydrogen fluoride.

Journal Article↗
PubMed2004

Fluctuation theorem and Onsager reciprocity relations.

The Onsager and higher-order reciprocity relations are derived from a fluctuation theorem for nonequilibrium reactions ruled by the chemical master equation. The fluctuation theorem is obtained for the generating function of the macroscopic fluxes between chemiostats maintaining the system in a nonequilibrium steady state. The macroscopic affinities associated with the fluxes are identified by graph theory. The Yamamoto-Zwanzig formulas for the reaction constants are also derived from the fluctuation theorem.

Journal Article↗
PubMed2005

The effect of proton disorder on the structure of ice-Ih: a theoretical study.

A precise and accurate measurement of the crystal structure of ice-Ih is hindered by its disordered H-bond network. In this work, we carried out first-principle calculations to study the effects of H-bond topology on the structure of ice-Ih with emphasis on the molecular geometry of water and the distortion in oxygen lattice. An analytic algorithm based on group and graph theory is employed to enumerate all possible configurations in a given unit cell and to select a set of structures for detailed examinations. In total we have studied more than 60 ice-Ih structures in a hexagonal unit cell of 48 water molecules by quantum-chemical methods and found a significant amount of static distortion in the oxygen positions from their crystallographic positions which is in good agreements with highly significant higher-order terms obtained from both x-ray and neutron-diffraction data. Much debated structural information such as H-O-H angle and O-H bond length is found to be 106.34+/-0.36 degrees and 0.9997+/-0.0008 A, compared to experimental value of 106.6+/-1.5 degrees and 0.986+/-0.005 A. Detailed benchmarking calculations were carried out to gauge the influence of using different exchange and correlation functionals, pseudopotentials, and unit-cell sizes. Our results have proven that first-principle methods are useful complementary tools to experiments, especially for cases in which experimental accuracy is limited by intrinsic orientational disorder.

Journal Article↗
PubMed2005

Subnets of scale-free networks are not scale-free: sampling properties of networks.

Most studies of networks have only looked at small subsets of the true network. Here, we discuss the sampling properties of a network's degree distribution under the most parsimonious sampling scheme. Only if the degree distributions of the network and randomly sampled subnets belong to the same family of probability distributions is it possible to extrapolate from subnet data to properties of the global network. We show that this condition is indeed satisfied for some important classes of networks, notably classical random graphs and exponential random graphs. For scale-free degree distributions, however, this is not the case. Thus, inferences about the scale-free nature of a network may have to be treated with some caution. The work presented here has important implications for the analysis of molecular networks as well as for graph theory and the theory of networks in general.

Journal Article↗
PubMed2005

The hypergraph regularity method and its applications.

Szemeredi's regularity lemma asserts that every graph can be decomposed into relatively few random-like subgraphs. This random-like behavior enables one to find and enumerate subgraphs of a given isomorphism type, yielding the so-called counting lemma for graphs. The combined application of these two lemmas is known as the regularity method for graphs and has proved useful in graph theory, combinatorial geometry, combinatorial number theory, and theoretical computer science. Here, we report on recent advances in the regularity method for k-uniform hypergraphs, for arbitrary k > or = 2. This method, purely combinatorial in nature, gives alternative proofs of density theorems originally due to E. Szemeredi, H. Furstenberg, and Y. Katznelson. Further results in extremal combinatorics also have been obtained with this approach. The two main components of the regularity method for k-uniform hypergraphs, the regularity lemma and the counting lemma, have been obtained recently: Rodl and Skokan (based on earlier work of Frankl and Rodl) generalized Szemeredi's regularity lemma to k-uniform hypergraphs, and Nagle, Rodl, and Schacht succeeded in proving a counting lemma accompanying the Rodl-Skokan hypergraph regularity lemma. The counting lemma is proved by reducing the counting problem to a simpler one previously investigated by Kohayakawa, Rodl, and Skokan. Similar results were obtained independently by W. T. Gowers, following a different approach.

Journal Article↗
PubMed2000

Compositional genomes: prebiotic information transfer in mutually catalytic noncovalent assemblies.

Mutually catalytic sets of simple organic molecules have been suggested to be capable of self-replication and rudimentary chemical evolution. Previous models for the behavior of such sets have analyzed the global properties of short biopolymer ensembles by using graph theory and a mean field approach. In parallel, experimental studies with the autocatalytic formation of amphiphilic assemblies (e.g., lipid vesicles or micelles) demonstrated self-replication properties resembling those of living cells. Combining these approaches, we analyze here the kinetic behavior of small heterogeneous assemblies of spontaneously aggregating molecules, of the type that could form readily under prebiotic conditions. A statistical formalism for mutual rate enhancement is used to numerically simulate the detailed chemical kinetics within such assemblies. We demonstrate that a straightforward set of assumptions about kinetically enhanced recruitment of simple amphiphilic molecules, as well as about the spontaneous growth and splitting of assemblies, results in a complex population behavior. The assemblies manifest a significant degree of homeostasis, resembling the previously predicted quasi-stationary states of biopolymer ensembles (Dyson, F. J. (1982) J. Mol. Evol. 18, 344-350). Such emergent catalysis-driven, compositionally biased entities may be viewed as having rudimentary "compositional genomes." Our analysis addresses the question of how mutually catalytic metabolic networks, devoid of sequence-based biopolymers, could exhibit transfer of chemical information and might undergo selection and evolution. This computed behavior may constitute a demonstration of natural selection in populations of molecules without genetic apparatus, suggesting a pathway from random molecular assemblies to a minimal protocell.

Catalysis↗
PubMed2004

Column sorting: rapid calculation of the phylogenetic likelihood function.

Likelihood applications have become a central approach for molecular evolutionary analyses since the first computationally tractable treatment two decades ago. Although Felsenstein's original pruning algorithm makes likelihood calculations feasible, it is usually possible to take advantage of repetitive structure present in the data to arrive at even greater computational reductions. In particular, alignment columns with certain similarities have components of the likelihood calculation that are identical and need not be recomputed if columns are evaluated in an optimal order. We develop an algorithm for exploiting this speed improvement via an application of graph theory. The reductions provided by the method depend on both the tree and the data, but typical savings range between 15%and 50%. Real-data examples with time reductions of 80%have been identified. The overhead costs associated with implementing the algorithm are minimal, and they are recovered in all but the smallest data sets. The modifications will provide faster likelihood algorithms, which will allow likelihood methods to be applied to larger sets of taxa and to include more thorough searches of the tree topology space.

Algorithms↗
PubMed2004

A genomewide search using an original pairwise sampling approach for large genealogies identifies a new locus for total and low-density lipoprotein cholesterol in two genetically differentiated isolates of Sardinia.

A powerful approach to mapping the genes for complex traits is to study isolated founder populations, in which genetic heterogeneity and environmental noise are likely to be reduced and in which extended genealogical data are often available. Using graph theory, we applied an approach that involved sampling from the large number of pairwise relationships present in an extended genealogy to reconstruct sets of subpedigrees that maximize the useful information for linkage mapping while minimizing calculation burden. We investigated, through simulation, the properties of the different sets in terms of bias in identity-by-descent (IBD) estimation and power decrease under various genetic models. We applied this approach to a small isolated population from Sardinia, the village of Talana, consisting of a unique large and complex pedigree, and performed a genomewide search through variance-components linkage analysis for serum lipid levels. We identified a region of significant linkage on chromosome 2 for total serum cholesterol and low-density lipoprotein (LDL) cholesterol. Through higher-density mapping, we obtained an increased linkage for both traits on 2q21.2-q24.1, with a LOD score of 4.3 for total serum cholesterol and of 3.9 for LDL cholesterol. A replication study was performed in an independent and larger set from a genetically differentiated isolated population of the same region of Sardinia, the village of Perdasdefogu. We obtained consistent linkage to the region for total serum cholesterol (LOD score 1.4) and LDL cholesterol (LOD score 2.2), with a level of concordance uncommon for complex traits, and refined the location of the quantitative-trait locus. Interestingly, the 2q21.1-22 region has also been linked to premature coronary heart disease in Finns, and, in the adjacent 2q14 region, significant linkage with triglycerides has been reported in Hutterites.

Cholesterol↗
PubMed2006

De novo analysis of peptide tandem mass spectra by spectral graph partitioning.

We report on a new de novo peptide sequencing algorithm that uses spectral graph partitioning. In this approach, relationships between m/z peaks are represented by attractive and repulsive springs, and the vibrational modes of the spring system are used to infer information about the peaks (such as "likely b-ion" or "likely y-ion"). We demonstrate the effectiveness of this approach by comparison with other de novo sequencers on test sets of ion-trap and QTOF spectra, including spectra of mixtures of peptides. On all datasets, we outperform the other sequencers. Along with spectral graph theory techniques, the new de novo sequencer EigenMS incorporates another improvement of independent interest: robust statistical methods for recalibration of time-of-flight mass measurements. Robust recalibration greatly outperforms simple least-squares recalibration, achieving about three times the accuracy for one QTOF dataset.

Algorithms↗
PubMed2006

Antibody quality in old age.

There is very little change in the quantity of antibodies people produce, of any isotype, with age. However, there is a change in the quality of the antibody response. Older people produce fewer antibodies that are specific for the activating pathogen or vaccine. At the same time, the number of nonspecific antibodies increases. Quite often these antibodies have self-reactivity (e.g., anti-dsDNA). The appearance of these antibodies is not associated with pathogenic autoimmune disease, although it is true that the incidence of some autoimmune diseases increases with age. The authors postulate that the process of antibody affinity maturation is compromised in old age. No evidence was found that the process of hypermutation is compromised with age. However, using graph theory to study the dynamics of a germinal center selection process, a decrease in the extent of selection occurring in the germinal centers of mucosal tissue was observed with age. This is a tissue-specific phenomenon because the decrease was not seen in the germinal centers of spleen. Because selection of highly specific cells in the germinal center depends on a number of factors (number and quality of founder cells, help from T cells, and follicular dendritic cells) these need to be investigated further to determine what is needed to improve the affinity mutation process.

Aging↗
PubMed1995

A computer program to aid the sequencing of peptides in collision-activated decomposition experiments.

A computer program named MSEQ, based on graph theory has been implemented to aid the sequencing of peptides from collision-activated decomposition (CAD) spectra. Input data required by this program are: the molecular weight of the peptide, the list of the masses of the daughter ions and the masses of the N- and C-terminal groups. The output comprises a list of the most likely sequences with their respective scores and the assignments of the daughter ions. A set of probabilities for each fragment ion was computed from hundreds of CAD spectra obtained from our mass spectrometer. To date many peptides have been sequenced in our laboratory with the help of this program, and in most of them the real sequence ranks among the five top sequences. The program is able to differentiate isobaric amino acids such as leucine and isoleucine when the side-chain fragmentation appears in the spectrum. A criterion is used to discard those sequences that match the spectrum poorly from the earliest steps. The program is fast and consumes no memory.

Algorithms↗
PubMed2002

Clustering gene expression data using a graph-theoretic approach: an application of minimum spanning trees.

MOTIVATION: Gene expression data clustering provides a powerful tool for studying functional relationships of genes in a biological process. Identifying correlated expression patterns of genes represents the basic challenge in this clustering problem. RESULTS: This paper describes a new framework for representing a set of multi-dimensional gene expression data as a Minimum Spanning Tree (MST), a concept from the graph theory. A key property of this representation is that each cluster of the expression data corresponds to one subtree of the MST, which rigorously converts a multi-dimensional clustering problem to a tree partitioning problem. We have demonstrated that though the inter-data relationship is greatly simplified in the MST representation, no essential information is lost for the purpose of clustering. Two key advantages in representing a set of multi-dimensional data as an MST are: (1) the simple structure of a tree facilitates efficient implementations of rigorous clustering algorithms, which otherwise are highly computationally challenging; and (2) as an MST-based clustering does not depend on detailed geometric shape of a cluster, it can overcome many of the problems faced by classical clustering algorithms. Based on the MST representation, we have developed a number of rigorous and efficient clustering algorithms, including two with guaranteed global optimality. We have implemented these algorithms as a computer software EXpression data Clustering Analysis and VisualizATiOn Resource (EXCAVATOR). To demonstrate its effectiveness, we have tested it on three data sets, i.e. expression data from yeast Saccharomyces cerevisiae, expression data in response of human fibroblasts to serum, and Arabidopsis expression data in response to chitin elicitation. The test results are highly encouraging. AVAILABILITY: EXCAVATOR is available on request from the authors.

Algorithms↗
PubMed1992

Can we recover a sequence, just knowing all its subsequences of given length?

The problem tackled here concerns the feasibility of DNA sequencing using hybridization methods. We establish algorithms for and computational limitations to the reconstruction of a sequence from all its subsequences having the same length: in other words, the building of a string that contains all the words of a given set, and only these ones. Generally there are several possible strings. We refer to graph theory and propose an algorithm to enumerate all the strings that are solutions. We then carried out stimulations using real DNA sequences. They provided some necessary conditions and give some upper bounds to the length of the sequence to recover in relation with the length of oligonucleotides. To avoid limiting ourselves to problems that admit a unique solution, we introduce another algorithm that produces a signature for each solution string. Each signature can be tested to determine which one belongs to the correct sequence.

Algorithms↗
PubMed2003

Protein structure prediction via combinatorial assembly of sub-structural units.

Following the hierarchical nature of protein folding, we propose a three-stage scheme for the prediction of a protein structure from its sequence. First, the sequence is cut to fragments that are each assigned a structure. Second, the assigned structures are combinatorially assembled to form the overall 3D organization. Third, highly ranked predicted arrangements are completed and refined. This work focuses on the second stage of this scheme: the combinatorial assembly. We present CombDock, a combinatorial docking algorithm. CombDock gets an ordered set of protein sub-structures and predicts the inter-contacts that define their overall organization. We reduce the combinatorial assembly to a graph-theory problem, and give a heuristic polynomial solution to this computationally hard problem. We applied CombDock to various examples of structural units of two types: protein domains and building blocks, which are relatively stable sub-structures of domains. Moreover, we tested CombDock using increasingly distorted input, where the native structural units were replaced by similarly folded units extracted from homologous proteins and, in the more difficult cases, from globally unrelated proteins. The algorithm is robust, showing low sensitivity to input distortion. This suggests that CombDock is a useful tool in protein structure prediction that may be applied to large target proteins.

Algorithms↗
PubMed2004

A dynamically growing self-organizing tree (DGSOT) for hierarchical clustering gene expression profiles.

MOTIVATION: The increasing use of microarray technologies is generating large amounts of data that must be processed in order to extract useful and rational fundamental patterns of gene expression. Hierarchical clustering technology is one method used to analyze gene expression data, but traditional hierarchical clustering algorithms suffer from several drawbacks (e.g. fixed topology structure; mis-clustered data which cannot be reevaluated). In this paper, we introduce a new hierarchical clustering algorithm that overcomes some of these drawbacks. RESULT: We propose a new tree-structure self-organizing neural network, called dynamically growing self-organizing tree (DGSOT) algorithm for hierarchical clustering. The DGSOT constructs a hierarchy from top to bottom by division. At each hierarchical level, the DGSOT optimizes the number of clusters, from which the proper hierarchical structure of the underlying dataset can be found. In addition, we propose a new cluster validation criterion based on the geometric property of the Voronoi partition of the dataset in order to find the proper number of clusters at each hierarchical level. This criterion uses the Minimum Spanning Tree (MST) concept of graph theory and is computationally inexpensive for large datasets. A K-level up distribution (KLD) mechanism, which increases the scope of data distribution in the hierarchy construction, was used to improve the clustering accuracy. The KLD mechanism allows the data misclustered in the early stages to be reevaluated at a later stage and increases the accuracy of the final clustering result. The clustering result of the DGSOT is easily displayed as a dendrogram for visualization. Based on a yeast cell cycle microarray expression dataset, we found that our algorithm extracts gene expression patterns at different levels. Furthermore, the biological functionality enrichment in the clusters is considerably high and the hierarchical structure of the clusters is more reasonable. AVAILABILITY: DGSOT is available upon request from the authors.

Algorithms↗