Morphogenesis as a macroscopic self-organizing process

We start from reviewing different epistemological constructions used for explaining morphogenesis. Among them, we explore the explanatory power of a law-centered approach which includes top-down causation and the basic concepts of a self-organization theory. Within such a framework, we discuss the morphomechanical models based upon the presumption of feedbacks between mechanical stresses imposed onto a given embryo part from outside and those generated within the latter as a kind of active response. A number of elementary morphogenetic events demonstrating that these feedbacks are directed towards hyper-restoration (restoration with an overshoot) of the initial state of mechanical stresses are described. Moreover, we show that these reactions are bound together into the larger scale feedbacks. That permits to suggest a reconstruction of morphogenetic successions in early Metazoan development concentrated around two main archetypes distinguished by the blastopores geometry. The perspectives of applying the same approach to cell differentiation are outlined. By discussing the problem of positional information we suggest that the developmental pathway of a given embryo part depends upon its preceded deformations and the corresponding mechanical stresses rather than upon its static position at any moment of development.     

Comparison of pathways from the geometric targeting method and targeted molecular dynamics in nitrogen regulatory protein C

Geometric targeting (GT) is a recently introduced method for rapidly generating all-atom pathways from one protein state to another, based on geometric rather than energetic considerations. To generate pathways, a bias is applied that gradually moves atoms toward a target structure, while a set of geometric constraints between atoms is enforced to keep the structure stereochemically acceptable. In this work, we compare conformational pathways generated from GT to pathways from the much more computationally intensive and commonly used targeted molecular dynamics (TMD) technique, for a complicated conformational change in the signaling protein nitrogen regulatory protein C. We show that the all-atom pathways from GT are similar to previously reported TMD pathways for this protein, by comparing motion along six progress variables that describe the various structural changes. The results suggest that for nitrogen regulatory protein C, finding an all-atom pathway is primarily a problem of geometry, and that a detailed force field in this case constitutes an unnecessary extra layer of detail. We also show that the pathway snapshots from GT have good structure quality, by measuring various structure quality metrics. Transient hydrogen bonds detected by the two methods show some similarities but also some differences. The results justify the usage of GT as a rapid, approximate alternative to TMD for generating stereochemically acceptable all-atom pathways in highly constrained protein systems.     

Metabolic networks are NP-hard to reconstruct

High-throughput data from various omics and sequencing techniques have rendered the automated metabolic network reconstruction a highly relevant problem. Our approach reflects the inherent probabilistic nature of the steps involved in metabolic network reconstruction. Here, the goal is to arrive at networks which combine probabilistic information with the possibility to obtain a small number of disconnected network constituents by reduction of a given preliminary probabilistic metabolic network. We define automated metabolic network reconstruction as an optimization problem on four-partite graph (nodes representing genes, enzymes, reactions, and metabolites) which integrates: (1) probabilistic information obtained from the existing process for metabolic reconstruction from a given genome, (2) connectedness of the raw metabolic network, and (3) clustering of components in the reconstructed metabolic network. The practical implications of our theoretical analysis refer to the quality of reconstructed metabolic networks and shed light on the problem of finding more efficient and effective methods for automated reconstruction. Our main contributions include: a completeness result for the defined problem, polynomial-time approximation algorithm, and an optimal polynomial-time algorithm for trees. Moreover, we exemplify our approach by the reconstruction of the sucrose biosynthesis pathway in Chlamydomonas reinhardtii.     

Determination of the fluxes in the central metabolism of Corynebacterium glutamicum by nuclear magnetic resonance spectroscopy combined with metabolite balancing

To determine the in vivo fluxes of the central metabolism we have developed a comprehensive approach exclusively based on the fundamental enzyme reactions known to be present, the fate of the carbon atoms of individual reactions, and the metabolite balance of the culture. No information on the energy balance is required, nor information on enzyme activities, or the directionalities of reactions. Our approach combines the power of (1)H-detected (13)C nuclear magnetic resonance spectroscopy to follow individual carbons with the simplicity of establishing carbon balances of bacterial cultures. We grew a lysine-producing strain of Corynebacterium glutamicum to the metabolic and isotopic steady state with [1-(13)C]glucose and determined the fractional enrichments in 27 carbon atoms of 11 amino acids isolated from the cell. Since precursor metabolites of the central metabolism are incorporated in an exactly defined manner in the carbon skeleton of amino acids, the fractional enrichments in carbons of precursor metabolites (oxaloacetate, glyceraldehyde 3-phosphate, erythrose 4-phosphate, etc.) became directly accessible. A concise and generally applicable mathematical model was established using matrix calculus to express all metabolite mass and carbon labeling balances. An appropriate all-purpose software for the iterative solution of the equations is supplied. Applying this comprehensive methodology to C. glutamicum, all major fluxes within the central metabolism were determined. The result is that the flux through the pentose phosphate pathway is 66.4% (relative to the glucose input flux of 1.49 mmol/g dry weight h), that of entry into the tricarboxylic acid cycle 62.2%, and the contribution of the succinylase pathway of lysine synthesis 13.7%. Due to the large amount and high quality of measured data in vivo exchange reactions could also be quantitated with particularly high exchange rates within the pentose phosphate pathway for the ribose 5-phosphate transketolase reaction. Moreover, the total net flux of the anaplerotic reactions was quantitated as 38.0%. Most importantly, we found that in vivo one component within these anaplerotic reactions is a back flux from the carbon 4 units of the tricarboxylic acid cycle to the carbon 3 units of glycolysis of 30.6%. (c) 1996 John Wiley & Sons, Inc.     

Efficient extraction of mapping rules of atoms from enzymatic reaction data.

Many computational problems and methods have been proposed for analysis of biological pathways. Among them, this paper focuses on extraction of mapping rules of atoms from enzymatic reaction data, which is useful for drug design, simulation of tracer experiments, and consistency checking of pathway databases. Most of existing methods for this problem are based on maximal common subgraph algorithms. In this paper, we propose a novel approach based on graph partition and graph isomorphism. We show that this problem is NP-hard in general, but can be solved in polynomial time for wide classes of enzymatic reactions. We also present an O(n(1.5)) time algorithm for a special but fundamental class of reactions, where n is the maximum size of compounds appearing in a reaction. We develop practical polynomial-time algorithms in which the Morgan algorithm is used for computing the normal form of a graph, where it is known that the Morgan algorithm works correctly for most chemical structures. Computational experiments are performed for these practical algorithms using the chemical reaction data stored in the KEGG/LIGAND database. The results of computational experiments suggest that practical algorithms are useful in many cases.     

Network Reconstruction Using Nonparametric Additive ODE Models

Network representations of biological systems are widespread and reconstructing unknown networks from data is a focal problem for computational biologists. For example, the series of biochemical reactions in a metabolic pathway can be represented as a network, with nodes corresponding to metabolites and edges linking reactants to products. In a different context, regulatory relationships among genes are commonly represented as directed networks with edges pointing from influential genes to their targets. Reconstructing such networks from data is a challenging problem receiving much attention in the literature. There is a particular need for approaches tailored to time-series data and not reliant on direct intervention experiments, as the former are often more readily available. In this paper, we introduce an approach to reconstructing directed networks based on dynamic systems models. Our approach generalizes commonly used ODE models based on linear or nonlinear dynamics by extending the functional class for the functions involved from parametric to nonparametric models. Concomitantly we limit the complexity by imposing an additive structure on the estimated slope functions. Thus the submodel associated with each node is a sum of univariate functions. These univariate component functions form the basis for a novel coupling metric that we define in order to quantify the strength of proposed relationships and hence rank potential edges. We show the utility of the method by reconstructing networks using simulated data from computational models for the glycolytic pathway of Lactocaccus Lactis and a gene network regulating the pluripotency of mouse embryonic stem cells. For purposes of comparison, we also assess reconstruction performance using gene networks from the DREAM challenges. We compare our method to those that similarly rely on dynamic systems models and use the results to attempt to disentangle the distinct roles of linearity, sparsity, and derivative estimation.     

Algorithmic approaches to clonal reconstruction in heterogeneous cell populations

Background: The reconstruction of clonal haplotypes and their evolutionary history in evolving populations is a common problem in both microbial evolutionary biology and cancer biology. The clonal theory of evolution provides a theoretical framework for modeling the evolution of clones.Results: In this paper, we review the theoretical framework and assumptions over which the clonal reconstruction problem is formulated. We formally define the problem and then discuss the complexity and solution space of the problem. Various methods have been proposed to find the phylogeny that best explains the observed data. We categorize these methods based on the type of input data that they use (space-resolved or time-resolved), and also based on their computational formulation as either combinatorial or probabilistic. It is crucial to understand the different types of input data because each provides essential but distinct information for drastically reducing the solution space of the clonal reconstruction problem. Complementary information provided by single cell sequencing or from whole genome sequencing of randomly isolated clones can also improve the accuracy of clonal reconstruction. We briefly review the existing algorithms and their relationships. Finally we summarize the tools that are developed for either directly solving the clonal reconstruction problem or a related computational problem.Conclusions: In this review, we discuss the various formulations of the problem of inferring the clonal evolutionary history from allele frequeny data, review existing algorithms and catergorize them according to their problem formulation and solution approaches. We note that most of the available clonal inference algorithms were developed for elucidating tumor evolution whereas clonal reconstruction for unicellular genomes are less addressed. We conclude the review by discussing more open problems such as the lack of benchmark datasets and comparison of performance between available tools.     

Modeling and analysis of biopathways dynamics

Cellular processes are governed and coordinated by a multitude of biopathways. A pathway can be viewed as a complex network of biochemical reactions. The dynamics of this network largely determines the functioning of the pathway. Hence the modeling and analysis of biochemical networks dynamics is an important problem and is an active area of research. Here we review quantitative models of biochemical networks based on ordinary differential equations (ODEs). We mainly focus on the parameter estimation and sensitivity analysis problems and survey the current methods for tackling them. In this context we also highlight a recently developed probabilistic approximation technique using which these two problems can be considerably simplified.     

Validation of metabolic pathway databases based on chemical substructure search

Metabolic pathway databases such as KEGG contain information on thousands of biochemical reactions drawn from the biomedical literature. Ensuring consistency of such large metabolic pathways is essential to their proper use. In this paper, we present a new method to determine consistency of an important class of biochemical reactions. Our method exploits the knowledge of the atomic rearrangement pattern in biochemical reactions, to reduce the automatic atom mapping problem to a series of chemical substructure searches between the substrate and the product of a biochemical reaction. As an illustrative application, we describe the exhaustive validation of a substantial portion from the latest release of the KEGG LIGAND database.     

Genome-scale metabolic representation of Amycolatopsis balhimycina

Infection caused by methicillin-resistant Staphylococcus aureus (MRSA) is an increasing societal problem. Typically, glycopeptide antibiotics are used in the treatment of these infections. The most comprehensively studied glycopeptide antibiotic biosynthetic pathway is that of balhimycin biosynthesis in Amycolatopsis balhimycina. The balhimycin yield obtained by A. balhimycina is, however, low and there is therefore a need to improve balhimycin production. In this study, we performed genome sequencing, assembly and annotation analysis of A. balhimycina and further used these annotated data to reconstruct a genome-scale metabolic model for the organism. Here we generated an almost complete A. balhimycina genome sequence comprising 10,562,587 base pairs assembled into 2,153 contigs. The high GC-genome (～ 69%) includes 8,585 open reading frames (ORFs). We used our integrative toolbox called SEQTOR for functional annotation and then integrated annotated data with biochemical and physiological information available for this organism to reconstruct a genome-scale metabolic model of A. balhimycina. The resulting metabolic model contains 583 ORFs as protein encoding genes (7% of the predicted 8,585 ORFs), 407 EC numbers, 647 metabolites and 1,363 metabolic reactions. During the analysis of the metabolic model, linear, quadratic and evolutionary programming algorithms using flux balance analysis (FBA), minimization of metabolic adjustment (MOMA), and OptGene, respectively were applied as well as phenotypic behavior and improved balhimycin production were simulated. The A. balhimycina model shows a good agreement between in silico data and experimental data and also identifies key reactions associated with increased balhimycin production. The reconstruction of the genome-scale metabolic model of A. balhimycina serves as a basis for physiological characterization. The model allows a rational design of engineering strategies for increasing balhimycin production in A. balhimycina and glycopeptide production in general.     

Construction of an E. Coli genome-scale atom mapping model for MFA calculations

Metabolic flux analysis (MFA) has so far been restricted to lumped networks lacking many important pathways, partly due to the difficulty in automatically generating isotope mapping matrices for genome-scale metabolic networks. Here we introduce a procedure that uses a compound matching algorithm based on the graph theoretical concept of pattern recognition along with relevant reaction information to automatically generate genome-scale atom mappings which trace the path of atoms from reactants to products for every reaction. The procedure is applied to the iAF1260 metabolic reconstruction of Escherichia coli yielding the genome-scale isotope mapping model imPR90068. This model maps 90,068 non-hydrogen atoms that span all 2,077 reactions present in iAF1260 (previous largest mapping model included 238 reactions). The expanded scope of the isotope mapping model allows the complete tracking of labeled atoms through pathways such as cofactor and prosthetic group biosynthesis and histidine metabolism. An EMU representation of imPR90068 is also constructed and made available.     

An evolutionary Monte Carlo algorithm for predicting DNA hybridization

Many DNA-based technologies, such as DNA computing, DNA nanoassembly and DNA biochips, rely on DNA hybridization reactions. Previous hybridization models have focused on macroscopic reactions between two DNA strands at the sequence level. Here, we propose a novel population-based Monte Carlo algorithm that simulates a microscopic model of reacting DNA molecules. The algorithm uses two essential thermodynamic quantities of DNA molecules: the binding energy of bound DNA strands and the entropy of unbound strands. Using this evolutionary Monte Carlo method, we obtain a minimum free energy configuration in the equilibrium state. We applied this method to a logical reasoning problem and compared the simulation results with the experimental results of the wet-lab DNA experiments performed subsequently. Our simulation predicted the experimental results quantitatively.     

MapMaker and PathTracer for tracking carbon in genome‐scale metabolic models

Constraint‐based reconstruction and analysis (COBRA) modeling results can be difficult to interpret given the large numbers of reactions in genome‐scale models. While paths in metabolic networks can be found, existing methods are not easily combined with constraint‐based approaches. To address this limitation, two tools (MapMaker and PathTracer) were developed to find paths (including cycles) between metabolites, where each step transfers carbon from reactant to product. MapMaker predicts carbon transfer maps (CTMs) between metabolites using only information on molecular formulae and reaction stoichiometry, effectively determining which reactants and products share carbon atoms. MapMaker correctly assigned CTMs for over 97% of the 2,251 reactions in an Escherichia coli metabolic model (iJO1366). Using CTMs as inputs, PathTracer finds paths between two metabolites. PathTracer was applied to iJO1366 to investigate the importance of using CTMs and COBRA constraints when enumerating paths, to find active and high flux paths in flux balance analysis (FBA) solutions, to identify paths for putrescine utilization, and to elucidate a potential CO₂ fixation pathway in E. coli. These results illustrate how MapMaker and PathTracer can be used in combination with constraint‐based models to identify feasible, active, and high flux paths between metabolites.     

The RNA chaperone StpA enables fast RNA refolding by destabilization of mutually exclusive base pairs within competing secondary structure elements

In bacteria RNA gene regulatory elements refold dependent on environmental clues between two or more long-lived conformational states each associated with a distinct regulatory state. The refolding kinetics are strongly temperature-dependent and especially at lower temperatures they reach timescales that are biologically not accessible. To overcome this problem, RNA chaperones have evolved. However, the precise molecular mechanism of how these proteins accelerate RNA refolding reactions remains enigmatic. Here we show how the RNA chaperone StpA of Escherichia coli leads to an acceleration of a bistable RNA’s refolding kinetics through the selective destabilization of key base pairing interactions. We find in laser assisted real-time NMR experiments on photocaged bistable RNAs that the RNA chaperone leads to a two-fold increase in refolding rates at low temperatures due to reduced stability of ground state conformations. Further, we can show that upon interaction with StpA, base pairing interactions in the bistable RNA are modulated to favor refolding through the dominant pseudoknotted transition pathway. Our results shed light on the molecular mechanism of the interaction between RNA chaperones and bistable RNAs and are the first step into a functional classification of chaperones dependent on their biophysical mode of operation.     

Pathways,pathway tubes,pathway docking,and propagators in electron transfer proteins

The simplest views of long-range electron transfer utilize flat one-dimensional barrier tunneling models, neglecting structural details of the protein medium. The pathway model of protein electron transfer reintroduces structure by distinguishing between covalent bonds, hydrogen bonds, and van der Waals contacts. These three kinds of interactions in a tunneling pathway each have distinctive decay factors associated with them. The distribution and arrangement of these bonded and nonbonded contacts in a folded protein varies tremendously between structures, adding a richness to the tunneling problem that is absent in simpler views. We review the pathway model and the predictions that it makes for protein electron transfer rates in small proteins, docked proteins, and the photosynthetic reactions center. We also review the formulation of the protein electron transfer problem as an effective two-level system. New multi-pathway approaches and improved electronic Hamiltonians are described briefly as well.     

Solving a Generalized Distance Geometry Problem for Protein Structure Determination

We propose a new approach to the problem of determining an ensemble of protein structures with a set of interatomic distance bounds in NMR protein modeling. Similarly to X-ray crystallography, we assume that the protein has an equilibrium structure and the atoms fluctuate around their equilibrium positions. Then, the problem can be formulated as a generalized distance geometry problem, to find the equilibrium positions and maximal possible fluctuation radii for the atoms in the protein, subject to the condition that the fluctuations should be within the given distance bounds. We describe the scientific background of the work, the motivation of the new approach and the formulation of the problem. We develop a geometric buildup algorithm for an approximate solution to the problem and present some preliminary test results as a first step concept proofing. We also discuss related theoretical and computational issues and potential impacts of this work in NMR protein modeling.     

Towards Kinetic Modeling of Global Metabolic Networks: Methylobacterium extorquens AM1 Growth as Validation

Here we report a systematic method for constructing a large scale kinetic metabolic model and its initial application to the modeling of central metabolism of Methylobacterium extorquens AM1, a methylotrophic and environmental important bacterium. Its central metabolic network includes formaldehyde metabolism, serine cycle, citric acid cycle, pentose phosphate pathway, gluconeogensis, PHB synthesis and acetyl-CoA conversion pathway, respiration and energy metabolism. Through a systematic and consistent procedure of finding a set of parameters in the physiological range we overcome an outstanding difficulty in large scale kinetic modeling: the requirement for a massive number of enzymatic reaction parameters. We are able to construct the kinetic model based on general biological considerations and incomplete experimental kinetic parameters. Our method consists of the following major steps: 1) using a generic enzymatic rate equation to reduce the number of enzymatic parameters to a minimum set while still preserving their characteristics; 2) using a set of steady state fluxes and metabolite concentrations in the physiological range as the expected output steady state fluxes and metabolite concentrations for the kinetic model to restrict the parametric space of enzymatic reactions; 3) choosing enzyme constants K’s and K’eqs optimized for reactions under physiological concentrations, if their experimental values are unknown; 4) for models which do not cover the entire metabolic network of the organisms, designing a dynamical exchange for the coupling between the metabolism represented in the model and the rest not included.     

Structure-Affinity Properties of a High-Affinity Ligand of FKBP12 Studied by Molecular Simulations of a Binding Intermediate

With a view to explaining the structure-affinity properties of the ligands of the protein FKBP12, we characterized a binding intermediate state between this protein and a high-affinity ligand. Indeed, the nature and extent of the intermolecular contacts developed in such a species may play a role on its stability and, hence, on the overall association rate. To find the binding intermediate, a molecular simulation protocol was used to unbind the ligand by gradually decreasing the biasing forces introduced. The intermediate was subsequently refined with 17 independent stochastic boundary molecular dynamics simulations that provide a consistent picture of the intermediate state. In this state, the core region of the ligand remains stable, notably because of the two anchoring oxygen atoms that correspond to recurrent motifs found in all FKBP12 ligand core structures. Besides, the non-core regions participate in numerous transient intermolecular and intramolecular contacts. The dynamic aspect of most of the contacts seems important both for the ligand to retain at least a part of its configurational entropy and for avoiding a trapped state along the binding pathway. Since the transient and anchoring contacts contribute to increasing the stability of the intermediate, as a corollary, the dissociation rate constant of this intermediate should be decreased, resulting in an increase of the affinity constant . The present results support our previous conclusions and provide a coherent rationale for explaining the prevalence in high-affinity ligands of (i) the two oxygen atoms found in carbonyl or sulfonyl groups of dissimilar core structures and of (ii) symmetric or pseudo-symmetric mobile groups of atoms found as non-core moieties. Another interesting aspect of the intermediate is the distortion of the flexible 80 s loop of the protein, mainly in its tip region, that promotes the accessibility to the bound state.