Combinatorial Possibilities Research Articles

Life, information, entropy, and time: Vehicles for semantic inheritance

Attempts to understand how information content can be included in an accounting of the energy flux of the biosphere have led to the conclusion that, in information transmission, one component, the semantic content, or "the meaning of the message," adds no thermodynamic burden over and above costs arising from coding, transmission and translation. In biology, semantic content has two major roles. For all life forms, the message of the genotype encoded in DNA specifies the phenotype, and hence the organism that is tested against the real world through the mechanisms of Darwinian evolution. For human beings, communication through language and similar abstractions provides an additional supra-phenotypic vehicle for semantic inheritance, which supports the cultural heritages around which civilizations revolve. The following three postulates provide the basis for discussion of a number of themes that demonstrate some important consequences. (i) Information transmission through either pathway has thermodynamic components associated with data storage and transmission. (ii) The semantic content adds no additional thermodynamic cost. (iii) For all semantic exchange, meaning is accessible only through translation and interpretation, and has a value only in context. (1) For both pathways of semantic inheritance, translational and copying machineries are imperfect. As a consequence both pathways are subject to mutation and to evolutionary pressure by selection. Recognition of semantic content as a common component allows an understanding of the relationship between genes and memes, and a reformulation of Universal Darwinism. (2) The emergent properties of life are dependent on a processing of semantic content. The translational steps allow amplification in complexity through combinatorial possibilities in space and time. Amplification depends on the increased potential for complexity opened by 3D interaction specificity of proteins, and on the selection of useful variants by evolution. The initial interpretational steps include protein synthesis, molecular recognition, and catalytic potential that facilitate structural and functional roles. Combinatorial possibilities are extended through interactions of increasing complexity in the temporal dimension. (3) All living things show a behavior that indicates awareness of time, or chronognosis. The ∼4 billion years of biological evolution have given rise to forms with increasing sophistication in sensory adaptation. This has been linked to the development of an increasing chronognostic range, and an associated increase in combinatorial complexity. (4) Development of a modern human phenotype and the ability to communicate through language, led to the development of archival storage, and invention of the basic skills, institutions and mechanisms that allowed the evolution of modern civilizations. Combinatorial amplification at the supra-phenotypical level arose from the invention of syntax, grammar, numbers, and the subsequent developments of abstraction in writing, algorithms, etc. The translational machineries of the human mind, the "mutation" of ideas therein, and the "conversations" of our social intercourse, have allowed a limited set of symbolic descriptors to evolve into an exponentially expanding semantic heritage. (5) The three postulates above open interesting epistemological questions. An understanding of topics such dualism, the élan vital, the status of hypothesis in science, memetics, the nature of consciousness, the role of semantic processing in the survival of societies, and Popper's three worlds, require recognition of an insubstantial component. By recognizing a necessary linkage between semantic content and a physical machinery, we can bring these perennial problems into the framework of a realistic philosophy. It is suggested, following Popper, that the ∼4 billion years of evolution of the biosphere represents an exploration of the nature of reality at the physicochemical level, which, together with the conscious extension of this exploration through science and culture, provides a firm epistemological underpinning for such a philosophy.

Analysis of the TCR α-chain rearrangement profile in human T lymphocytes

The size of the available human αβ T cell repertoire is difficult to determine and is open to debate. Empirical analysis of TCR β-chain diversity reveals ∼10 6 different β chains in peripheral blood. Due in part to locus complexity, comparable information for TCRα is lacking. Rather, current estimates for human TCRα diversity, and hence, total repertoire diversity, are based on theoretical analyses that assume equal probabilities of rearrangement between any Vα gene and Jα gene. Here, we report on a systematic locus-wide rearrangement analysis of the TCR α-chain in human T cells. We first demonstrate that the V-Jα recombination in the thymus is not random but depends on the reciprocal Vα and Jα position within the locus. Characterization of the frequency of gene usage combined with identification of five previously unrecognized pseudogenes enables us to empirically estimate the human TCRα combinatorial repertoire. The number of V-Jα combinations achieved is ∼44–56% of the total combinatorial possibilities, significantly lower than theoretical estimates. We also demonstrate that TCR α-chain diversity in peripheral T lymphocytes mimics the same general patterns of rearrangement as observed in the thymus, and these patterns appear conserved among different individuals. This unexpected observation indicates that, unlike the TCRβ locus, the human TCR α-chain repertoire is primarily predetermined by genetic recombination and its size is restricted by limits on the combinatorial repertoire rather than post-thymic selection.

Assignment of polar states for protein amino acid residues using an interaction cluster decomposition algorithm and its application to high resolution protein structure modeling

We have developed a new method (Independent Cluster Decomposition Algorithm, ICDA) for creating all-atom models of proteins given the heavy-atom coordinates, provided by X-ray crystallography, and the pH. In our method the ionization states of titratable residues, the crystallographic mis-assignment of amide orientations in Asn/Gln, and the orientations of OH/SH groups are addressed under the unified framework of polar states assignment. To address the large number of combinatorial possibilities for the polar hydrogen states of the protein, we have devised a novel algorithm to decompose the system into independent interacting clusters, based on the observation of the crucial interdependence between the short range hydrogen bonding network and polar residue states, thus significantly reducing the computational complexity of the problem and making our algorithm tractable using relatively modest computational resources. We utilize an all atom protein force field (OPLS) and a Generalized Born continuum solvation model, in contrast to the various empirical force fields adopted in most previous studies. We have compared our prediction results with a few well-documented methods in the literature (WHATIF, REDUCE). In addition, as a preliminary attempt to couple our polar state assignment method with real structure predictions, we further validate our method using single side chain prediction, which has been demonstrated to be an effective way of validating structure prediction methods without incurring sampling problems. Comparisons of single side chain prediction results after the application of our polar state prediction method with previous results with default polar state assignments indicate a significant improvement in the single side chain predictions for polar residues.

Classification of hexagonal adlayer arrangements by means of collective geometrical properties

Unequal-sphere packing model is applied for the simulation of large number of hexagonal adlayer structures with surface coverage between theta=13 and theta=1 on the hexagonal substrate, with atomic radius of the adsorbate and substrate atoms as the only input. Each structure is characterized with respect to collective adlayer properties: the average adlayer height and the adlayer roughness. The distribution of hexagonal arrangements is presented in a special plot, which can be used for identification and characterization of hexagonal adlayers of different surface coverages and atomic registries. The most likely structures are related to the extreme values of our model parameters. The usefulness of this methodology is successfully demonstrated by comparison with some real adsorbate-substrate systems, i.e., halogens and rare gases adsorbed on (111) surface. Besides the agreement with experimental results, our model offers new insight into the formation of atomic adlayers and detailed analysis of the atomic registry. We believe that our approach will be of use for identification of probable structures among the large number of combinatorial possibilities in theoretical studies and for better interpretation of experimental results (i.e., scanning-tunneling microscopy images of atomic adlayers).

The golden spur: innovation independence

PurposeThe authors argue that the “freedom to explore” factor is essential to innovation. And innovation is essential to sustained competitiveness. Today's leadership challenge is learning to manage the independent thinkers who refuse the constraints of professionalism and instead innovate on their own terms – in other words, as amateurs.Design/methodology/approachThe authors believe that only amateurs can move from field to field, finding creativity in the convergence of technology and the combinatorial possibilities found when crossing different industries and professional specialties.FindingsAt a leading nationwide retailer, a group of people has formed an initiative to create a market place of ideas and talent. Anyone can pitch a project and invite others to join it. The hypothesis is that such an avenue for ideas and commitment will increase productivity and address an endemic scarcity of resources. This freedom is facilitated by communications technologies that enable individuals to participate increasingly on their own terms.Practical implicationsCompanies need to unleash their human talent and raise their level of innovation so that they can compete globally. To accomplish this, managers must respect their employees' independence – the very source of innovation.Originality/valueThe authors argue that the case for innovation is the case for the labor of love, that is, the work of passionate amateurs.

The mammalian transcriptome and the cellular complexity of the brain

The mammalian transcriptome and the cellular complexity of the brain

Three allele combinations associated with Multiple Sclerosis

BackgroundMultiple sclerosis (MS) is an immune-mediated disease of polygenic etiology. Dissection of its genetic background is a complex problem, because of the combinatorial possibilities of gene-gene interactions. As genotyping methods improve throughput, approaches that can explore multigene interactions appropriately should lead to improved understanding of MS.Methods286 unrelated patients with definite MS and 362 unrelated healthy controls of Russian descent were genotyped at polymorphic loci (including SNPs, repeat polymorphisms, and an insertion/deletion) of the DRB1, TNF, LT, TGFβ1, CCR5 and CTLA4 genes and TNFa and TNFb microsatellites. Each allele carriership in patients and controls was compared by Fisher's exact test, and disease-associated combinations of alleles in the data set were sought using a Bayesian Markov chain Monte Carlo-based method recently developed by our group.ResultsWe identified two previously unknown MS-associated tri-allelic combinations:-509TGFβ1*C, DRB1*18(3), CTLA4*G and -238TNF*B1,-308TNF*A2, CTLA4*G, which perfectly separate MS cases from controls, at least in the present sample. The previously described DRB1*15(2) allele, the microsatellite TNFa9 allele and the biallelic combination CCR5Δ32, DRB1*04 were also reidentified as MS-associated.ConclusionThese results represent an independent validation of MS association with DRB1*15(2) and TNFa9 in Russians and are the first to find the interplay of three loci in conferring susceptibility to MS. They demonstrate the efficacy of our approach for the identification of complex-disease-associated combinations of alleles.

Scheduling dual gripper robotic cell: One-unit cycles

We consider the scheduling problem of cyclic production in a bufferless dual-gripper robot cell processing a family of identical parts. The objective is to find an optimal sequence of robot moves so as to maximize the long-run average throughput rate of the cell. While there has been a considerable amount of research dealing with single-gripper robot cells, there are only a few papers devoted to scheduling in dual-gripper robotic cells. From the practical point of view, the use of a dual gripper offers the attractive prospect of an increase in the cell productivity. At the same time, the increase in the combinatorial possibilities associated with a dual-gripper robot severely complicates its theoretical analysis. The purpose of this paper is to extend the existing conceptual framework to the dual-gripper situation, and to provide some insight into the problem. We provide a notational and modelling framework for cyclic production in a dual-gripper robotic cell. Focusing on the so-called active cycles, we discuss the issues of feasibility and explore the combinatorial aspects of the problem. The main attention is on 1-unit cycles, i.e., those that restore the cell to the same initial state after the production of each unit. For an m-machine robotic cell served by a dual-gripper robot, we describe a complete family of 1-unit cycles, and derive an analytical formula to estimate their total number for a given m. In the case when the gripper switching time is sufficiently small, we identify an optimal 1-unit cycle. This special case is of particular interest as it reflects the most frequently encountered situation in real-life robotic systems. Finally, we establish the connection between a dual-gripper cell and a single-gripper cell with machine output buffers of one-unit capacity and compare the cell productivity for these two models.

Combinatorial chromatin modifications and memory storage: A code for memory?: Figure 1.

Combinatorial chromatin modifications and memory storage: A code for memory?: Figure 1.

Depicting combinatorial complexity with the molecular interaction map notation

To help us understand how bioregulatory networks operate, we need a standard notation for diagrams analogous to electronic circuit diagrams. Such diagrams must surmount the difficulties posed by complex patterns of protein modifications and multiprotein complexes. To meet that challenge, we have designed the molecular interaction map (MIM) notation (http://discover.nci.nih.gov/mim/). Here we show the advantages of the MIM notation for three important types of diagrams: (1) explicit diagrams that define specific pathway models for computer simulation; (2) heuristic maps that organize the available information about molecular interactions and encompass the possible processes or pathways; and (3) diagrams of combinatorially complex models. We focus on signaling from the epidermal growth factor receptor family (EGFR, ErbB), a network that reflects the major challenges of representing in a compact manner the combinatorial complexity of multimolecular complexes. By comparing MIMs with other diagrams of this network that have recently been published, we show the utility of the MIM notation. These comparisons may help cell and systems biologists adopt a graphical language that is unambiguous and generally understood.

Su.48. Stomatin-Like Protein 2 Stabilizes Tcr-Dependent Signalling Microclusters in Effector T-Cells

Despite significant recent advances in molecular and structural studies of G protein-coupled receptors (GPCRs), an understanding of transmembrane signal transduction with chemical precision requires new approaches. Simple binary receptor–ligand or receptor–G protein complex models cannot adequately describe the relevant macromolecular signaling machineries. GPCR signalosomes undergo complex dynamic assembly–disassembly reactions to create allosteric signaling conduits whose properties cannot necessarily be predicted from individual elements alone. The combinatorial possibilities inherent in a system with hundreds of potential components suggest that high-content miniaturized experimental platforms and computational approaches will be required. To study allosteric effects involved in signalosome reaction pathways, a bottom-up approach using multicolor single-molecule detection fluorescence experiments in biochemically defined systems and complemented by molecular dynamics models of macromolecular complexes is proposed. In bridging the gap between molecular and systems biology, this synthetic approach suggests a way forward from the flatlands to multi-dimensional data collection.

Methyl‐Blocked Dimeric α,γ‐Peptide Nanotube Segments: Formation of a Peptide Heterodimer through Backbone–Backbone Interactions

Cyclic peptides can dimerize through β-sheet-like hydrogen bonding. Heterodimerization is favored over homodimerization, which creates interesting combinatorial possibilities without detriment to the functionalization of amino acid side chains. These dimers represent a new class of self-assembling peptide nanotubes in which the hydrophobicity of the internal cavity (see picture) can be controlled.

Cooperative requirement of the Gli proteins in neurogenesis

The Gli proteins are critical components of multiple processes in development, homeostasis and disease, including neurogenesis and tumorigenesis. However, it is unclear how the Gli code, the sum of their combinatorial positive and negative functions, dictates cell fate and behavior. Using an antisense approach to knockdown gene function in vivo, we find that each of the three Gli proteins is required for the induction of all primary neurons in the amphibian neural plate and regulates the bHLH/Notch neurogenic cascade. Analyses of endogenous Gli function in Gli-mediated neurogenesis and tumorigenesis, and in animal cap assays, reveal specific requirements that are context specific. Nuclear colocalization and binding studies suggest the formation of complexes, with the first two zinc fingers of the Gli five zinc-finger domain acting as a protein-protein interaction site. The Gli proteins therefore appear to form a dynamic physical network that underlies cooperative function, greatly extending the combinatorial possibilities of the Gli code, which may be further fine-tuned in cell fate specification by co-factor function.

Proteolytic cleavage of ALF into α- and β-subunits that form homologous and heterologous complexes with somatic TFIIA and TRF2 in male germ cells

Male germ cells specifically express paralogues of components of the general transcription apparatus including ALF a paralogue of TFIIAα/β. We show that endogenous ALF is proteolytically cleaved to give α- and β-subunits and we map the proteolytic cleavage site by mass spectrometry. Immunoprecipitations show that ALFα- and β-subunits form a series of homologous and heterologous complexes with somatic TFIIA which is coexpressed in male germ cells. In addition, we show that ALF is coexpressed in late pachytene spermatocytes and in haploid round spermatids with transcription factor TRF2, and that these proteins form stable complexes in testis extracts. Our observations highlight how cleavage of ALF and coexpression with TFIIA and TRF2 increases the combinatorial possibilities for gene regulation at different developmental stages of spermatogenesis.

The Spread of Contingent Work in the Knowledge-Based Economy

Permanent employment, typical of industrial societies and bolstered by numerous social guaranties, has been declining in the past 2 decades. There has been a steady expansion of various forms of contingent work. The decomposition of traditional work is a logical consequence of the characteristic patterns of the knowledge-based economy. According to the logic of information technology, changeable modules are key characteristics of production processes and economic organizations. Each module leads a life of its own, with infinite combinatory possibilities. As a consequence, static and “safe” economic arrangements are replaced by dynamic and uncertain institutions. Employees (except for key personnel) become interchangeable, disposable, recallable, and transferable. Consequently, the portfolio of workers’ capabilities and knowledge should be adjusted to the requirements of changing workplaces. For companies, the return on investments in employees’ knowledge is uncertain; thus, contingent workers have to undertake, at least partly, the responsibility and costs of their own training.

The discovery of zinc fingers and their development for practical applications in gene regulation

An account is given of the discovery in 1985 of the classical Cys 2 His 2 (C 2 H 2 ) zinc finger, aris- ing from the interpretation of biochemical studies on the interaction of the Xenopus protein transcription factor IIIA with 5S RNA, and of subsequent structural studies on its 3D structure and its interaction with DNA. Each finger constitutes a self-contained domain stabilized by a zinc ion ligated to a pair of cysteines and a pair of histidines, and by an inner structural hydrophobic core. This work showed not only a new pro- tein fold but also a novel principle of DNA recognition. Whereas other DNA binding proteins generally make use of the two-fold symmetry of the double helix, functioning as homo- or heterodimers, zinc fingers can be linked linearly in tandem to recognize nucleic acid sequences of different lengths. This modular design offers a large number of combinatorial possibilities for the specific recognition of DNA (or RNA). It is therefore not surprising that this zinc finger is found widespread in nature, in 3% of the genes of the human genome. It had long been the goal of molecular biologists to design DNA binding proteins for control of gene expres- sion and we have adopted the zinc finger design and principle for this purpose. We demonstrated that the zinc finger design is ideally suited for such purposes, discriminating between closely related DNA sequences both in vitro and in vivo, and we have therefore adapted this natural design for engineering zinc finger proteins for targeting specific genes. The first example of the potential of the method was published in 1994 when a three-finger protein was constructed to block the expression of an oncogene transformed into a mouse cell line. In the same paper we also showed that we could activate a reporter gene by target- ing a nine base pair promoter which we had inserted. Thus by fusing zinc finger peptides to repression or activation domains, genes can be selectively switched off or on. By combining the targeting zinc fingers with other effector or functional domains e.g. from nucleases or integrases, to form chimeric proteins, genomes can be manipulated or modified. Several applications of such engineered zinc finger proteins are described here, including some of potential therapeutic importance.

Probabilistic cross‐link analysis and experiment planning for high‐throughput elucidation of protein structure

Emerging high-throughput techniques for the characterization of protein and protein-complex structures yield noisy data with sparse information content, placing a significant burden on computation to properly interpret the experimental data. One such technique uses cross-linking (chemical or by cysteine oxidation) to confirm or select among proposed structural models (e.g., from fold recognition, ab initio prediction, or docking) by testing the consistency between cross-linking data and model geometry. This paper develops a probabilistic framework for analyzing the information content in cross-linking experiments, accounting for anticipated experimental error. This framework supports a mechanism for planning experiments to optimize the information gained. We evaluate potential experiment plans using explicit trade-offs among key properties of practical importance: discriminability, coverage, balance, ambiguity, and cost. We devise a greedy algorithm that considers those properties and, from a large number of combinatorial possibilities, rapidly selects sets of experiments expected to discriminate pairs of models efficiently. In an application to residue-specific chemical cross-linking, we demonstrate the ability of our approach to plan experiments effectively involving combinations of cross-linkers and introduced mutations. We also describe an experiment plan for the bacteriophage lambda Tfa chaperone protein in which we plan dicysteine mutants for discriminating threading models by disulfide formation. Preliminary results from a subset of the planned experiments are consistent and demonstrate the practicality of planning. Our methods provide the experimenter with a valuable tool (available from the authors) for understanding and optimizing cross-linking experiments.

Towards therapeutic applications of engineered zinc finger proteins

It has long been the goal of molecular biologists to design DNA-binding proteins for the specific control of gene expression. The zinc finger design is ideally suited for such purposes, discriminating between closely related sequences both in vitro and in vivo. Whereas other DNA-binding proteins generally make use of the 2-fold symmetry of the double helix, zinc fingers do not and so can be linked linearly in tandem to recognize DNA sequences of different lengths, with high fidelity. This modular design offers a large number of combinatorial possibilities for the specific recognition of DNA. By fusing zinc finger peptides to repression or activation domains, genes can be selectively targeted and switched off and on. Several recent applications of such engineered zinc finger proteins (ZFPs) are described, including the activation of vascular endothelial growth factor (VEGF) in a human cell line and an animal model. Clinical trials have recently begun on using VEGF-activating ZFPs to treat human peripheral arterial disease, by stimulating vascular growth. Also in progress are pre-clinical studies using ZFPs to target the defective genes in two monogenic disorders, SCID and SCA. The aim is to replace them in each case by a correct copy from an extrachromosomal DNA donor by means of homologous recombination. Promising results are reported.

Letters

Being German, I love the unsurpassed combinatorial possibilities of our language. Stan Kelly-Bootle’s “From this Moment On” (June 2004), however, contains a construction, “Entunternehhmangenausstreckenisierung,” that defies my linguistic capabilities. Ent... what?

Context of Thought and Context of Utterance: A Note on Free Indirect Discourse and the Historical Present

Abstract: Based on the analysis of narrations in Free Indirect Discourse and the Historical Present, I argue (building in particular on (Banfield, 1982) and (Doron, 1991)) that the grammatical notion of context of speech should be ramified into a Context of Thought and a Context of Utterance. Tense and person depend on the Context of Utterance, while all other indexicals (including here, now and the demonstratives) are evaluated with respect to the Context of Thought. Free Indirect Discourse and the Historical Present are analyzed as special combinatorial possibilities that arise when the two contexts are distinct, and exactly one of them is presented as identical to the physical point at which the sentence is articulated.