Interpretation support for multistage MS: a mathematical method for theoretical generation of glycan fragments and calculation of their masses

Glycan fragmentation forms an integral part of the current research in glycomics. Creation of a database of glycan fragments and their masses for known glycan structures is an important step in the interpretation of mass spectra for the identification of unknown glycan structures. This paper introduces the concept of positional nomenclature, gives a systematic representation of glycan structure of any size, and hence develops a method for theoretically generating all possible first and second generation fragments resulting from glycosidic and cross ring cleavages. Matrix equations are developed for the calculation of theoretical masses. Algorithm is presented for iterative generation of all fragments and calculation of their masses. This method is applicable to glycan analytical techniques using MS, MS/MS, and multistage MS (MSn) with different ionization methods, derivatives, or ions used. The method is adaptable to computer program and has been verified for theoretical masses reported in literature. Rules for the theoretical validation of the fragments are presented.     

Quasi-steady-state kinetics at enzyme and substrate concentrations in excess of the Michaelis-Menten constant

In vitro enzyme reactions are traditionally conducted under conditions of pronounced substrate excess since this guarantees that the bound enzyme is at quasi-steady-state (QSS) with respect to the free substrate, thereby justifying the Briggs-Haldane approximation (BHA). In contrast, intracellular reactions, amplification assays, allergen digestion assays and industrial applications span a range of enzyme-to-substrate ratios for which the BHA is invalid, including the extreme of enzyme excess. The quasi-equilibrium approximation (QEA) is valid for a subset of enzyme excess states. Previously, we showed that the total QSSA (tQSSA) overlaps and extends the validity of the BHA and the QEA, and that it is at least roughly valid for any total substrate and enzyme concentrations. The analysis of the tQSSA is hampered by square root nonlinearity. Previous simplifications of the tQSSA rate law are valid in a parameter domain that overlaps the validity domains of the BHA and the QEA and only slightly extends them. We now integrate the tQSSA rate equation in closed form, without resorting to further approximations. Moreover, we introduce a complimentary simplification of the tQSSA rate law that is valid in states of enzyme excess when the absolute difference between total enzyme and substrate concentrations greatly exceeds the Michaelis-Menten constant. This includes a wide range of enzyme and substrate concentrations where both the BHA and the QEA are invalid and allows us to define precisely the conditions for zero-order and first-order product formation. Remarkably, analytical approximations provided by the tQSSA closely match the expected stochastic kinetics for as few as 15 reactant molecules, suggesting that the conditions for the validity of the tQSSA and for its various simplifications are also of relevance at low molecule numbers.     

Improved analysis of bacterial CGH data beyond the log-ratio paradigm

Background

While the theory of enzyme kinetics is fundamental to analyzing and simulating biochemical systems, the derivation of rate equations for complex mechanisms for enzyme-catalyzed reactions is cumbersome and error prone. Therefore, a number of algorithms and related computer programs have been developed to assist in such derivations. Yet although a number of algorithms, programs, and software packages are reported in the literature, one or more significant limitation is associated with each of these tools. Furthermore, none is freely available for download and use by the community.

Results

We have implemented an algorithm based on the schematic method of King and Altman (KA) that employs the topological theory of linear graphs for systematic generation of valid reaction patterns in a GUI-based stand-alone computer program called KAPattern. The underlying algorithm allows for the assumption steady-state, rapid equilibrium-binding, and/or irreversibility for individual steps in catalytic mechanisms. The program can automatically generate MathML and MATLAB output files that users can easily incorporate into simulation programs.

Conclusion

A computer program, called KAPattern, for generating rate equations for complex enzyme system is a freely available and can be accessed at http://www.biocoda.org.     

Calculating pKa values in enzyme active sites

The ionization properties of the active-site residues in enzymes are of considerable interest in the study of the catalytic mechanisms of enzymes. Knowledge of these ionization constants (pKa values) often allows the researcher to identify the proton donor and the catalytic nucleophile in the reaction mechanism of the enzyme. Estimates of protein residue pKa values can be obtained by applying pKa calculation algorithms to protein X-ray structures. We show that pKa values accurate enough for identifying the proton donor in an enzyme active site can be calculated by considering in detail only the active-site residues and their immediate electrostatic interaction partners, thus allowing for a large decrease in calculation time. More specifically we omit the calculation of site-site interaction energies, and the calculation of desolvation and background interaction energies for a large number of pairs of titratable groups. The method presented here is well suited to be applied on a genomic scale, and can be implemented in most pKa calculation algorithms to give significant reductions in calculation time with little or no impact on the accuracy of the results. The work presented here has implications for the understanding of enzymes in general and for the design of novel biocatalysts.     

Difficulties encountered with an ultrafiltration method for measuring the binding of ligands to protein

The ultrafiltration method of Paulus has been used to study the binding of aspartate and ITP to the catalytic subunit of aspartate transcarbamylase. Markedly different estimates of dissociation constants and of the number of moles of ligand bound per mole of enzyme have been obtained using different batches of UM 10 Diaflo membranes. Estimates derived using Visking membranes are presented for comparison.For both an amino acid and a nucleotide invalid results have been obtained using UM 10 Diaflo membranes in conjunction with this enzyme. The importance of excluding artifacts in any system studied by this method is emphasized.     

Calculation of steady-state rate equations and the fluxes between substrates and products in enzyme reactions.

1. Two methods are described for deriving the steady-state velocity of an enzyme reaction from a consideration of fluxes between enzyme intermediates. The equivalent-reaction technique, in which enzyme intermediates are systematically eliminated and replaced by equivalent reactions, appears the most generally useful. The methods are applicable to all enzyme mechanisms, including three-substrate and random Bi Bi Ping Pong mechanisms. Solutions are obtained in algebraic form and these are presented for the common random Bi Bi mechanisms. The steady-state quantities of the enzyme intermediates may also be calculated. Additional steps may be introduced into enzyme mechanisms for which the steady-state velocity equation is already known. 2. The calculation of fluxes between substrates and products in three-substrate and random Bi Bi Ping Pong mechanisms is described. 3. It is concluded that the new methods may offer advantages in ease of calculation and in the analysis of the effects of individual steps on the overall reaction. The methods are used to show that an ordered addition of two substrates to an enzyme which is activated by another ligand will not necessarily give hyperbolic steady-state-velocity kinetics or the flux ratios characteristic of an ordered addition, if the dissociation of the ligand from the enzyme is random.     

Dynamic simulation and metabolic re-design of a branched pathway using linlog kinetics

This paper presents a new mathematical framework for modeling of in vivo dynamics and for metabolic re-design: the linlog approach. This approach is an extension of metabolic control analysis (MCA), valid for large changes of enzyme and metabolite levels. Furthermore, the presented framework combines MCA with kinetic modeling, thereby also combining the merits of both approaches. The linlog framework includes general expressions giving the steady-state fluxes and metabolite concentrations as a function of enzyme levels and extracellular concentrations, and a metabolic design equation that allows direct calculation of required enzyme levels for a desired steady state when control and response coefficients are available. Expressions giving control coefficients as a function of the enzyme levels are also derived. The validity of the linlog approximation in metabolic modeling is demonstrated by application of linlog kinetics to a branched pathway with moiety conservation, reversible reactions and allosteric interactions. Results show that the linlog approximation is able to describe the non-linear dynamics of this pathway very well for concentration changes up to a factor 20. Also the metabolic design equation was tested successfully.     

A systematic method for the compilation of the King & Altman graphs of a steady-state enzyme model suitable for manual or computer use

The schematic way of computing the King & Altman (1956) patterns for complex enzyme models is rather tedious. In this paper, a systematic method for the compilation of these patterns is proposed. This method ensures the generation of all the King & Altman patterns including those containing cycles. The importance of such patterns for an automatic recognition of the cyclic pathways of a given model is emphasized. The suggested algorithm is suitable for manual or computer processing.     

Express Attentional Re-Engagement but Delayed Entry into Consciousness Following Invalid Spatial Cues in Visual Search

Background

In predictive spatial cueing studies, reaction times (RT) are shorter for targets appearing at cued locations (valid trials) than at other locations (invalid trials). An increase in the amplitude of early P1 and/or N1 event-related potential (ERP) components is also present for items appearing at cued locations, reflecting early attentional sensory gain control mechanisms. However, it is still unknown at which stage in the processing stream these early amplitude effects are translated into latency effects.

Methodology/Principal Findings

Here, we measured the latency of two ERP components, the N2pc and the sustained posterior contralateral negativity (SPCN), to evaluate whether visual selection (as indexed by the N2pc) and visual-short term memory processes (as indexed by the SPCN) are delayed in invalid trials compared to valid trials. The P1 was larger contralateral to the cued side, indicating that attention was deployed to the cued location prior to the target onset. Despite these early amplitude effects, the N2pc onset latency was unaffected by cue validity, indicating an express, quasi-instantaneous re-engagement of attention in invalid trials. In contrast, latency effects were observed for the SPCN, and these were correlated to the RT effect.

Conclusions/Significance

Results show that latency differences that could explain the RT cueing effects must occur after visual selection processes giving rise to the N2pc, but at or before transfer in visual short-term memory, as reflected by the SPCN, at least in discrimination tasks in which the target is presented concurrently with at least one distractor. Given that the SPCN was previously associated to conscious report, these results further show that entry into consciousness is delayed following invalid cues.     

Phase Coexistence Curves for Off-lattice Polymer-Solvent Mixtures: Gibbs-Duhem Integration Simulations

The Gibbs-Duhem integration scheme is combined with the osmotic Gibbs-ensemble simulation method presented in previous work [Brennan, J.K. and Madden, W.G. "Phase coexistence curves for off-lattice polymer-solvent mixtures: Gibbs-ensemble simulations." Macromolecules , 2002, 35, 2827.] to calculate the phase coexistence of a polymer-solvent mixture. Gibbs-Duhem integration simulations are carried out at temperatures for which the osmotic Gibbs-ensemble method is not valid because the solvent-rich phase contains a significant amount of polymer. This combined strategy allows for the calculation of the full coexistence curve for polymer-solvent systems in the continuum. An alternative formulation of the Gibbs-Duhem integration algorithm is also presented. A major strength of the technique is that neither chain insertions nor deletions are required. The method allows for the calculation of the phase behavior of polymer-solvent mixtures containing long chains or branched and networked chains not previously possible.     

Disease-related concept mining by knowledge-based two-dimensional gene mapping

There is a strong need to systematically organize and comprehend the rapidly expanding stores of biomedical knowledge to formulate hypotheses on disease mechanisms. However, no method is available that automatically structuralizes fragmentary knowledge along with domain-specific expressions for a large-scale integration. A method presented here, cross-subspace analysis (CSA), produces a holistic view of over 3,000 human genes with a two-dimensional (2D) arrangement. The genes are plotted in relation to functions determined by machine learning from the occurrence patterns of various biomedical terms in MEDLINE abstracts. By focusing on the 2D distributions of gene plots that share the same biomedical concepts, as defined by databases such as Gene Ontology, relevant biomedical concepts can be computationally extracted. In an analysis where myocardial infarction and ischemic stroke were taken as examples, we found valid relations with lifestyle, diet-related metabolism, and host immune responses, all of which are known risk factors for the diseases. These results demonstrate that systematizing accumulated gene knowledge can lead to hypothesis generation and knowledge discovery, regardless of the area of inquiry or discipline.     

A kinetic analysis of enzyme systems involving four substrates

A treatment of kinetic data for enzyme mechanisms involving four substrates is described. The initial-rate equations and product-inhibition patterns for such mechanisms are presented. The treatment is extended to include analysis of enzyme mechanisms involving three substrates in which two molecules of one substrate are used.     

Constant-ratio alternative substrate approach for differentiation of enzyme mechanisms

A new kinetic approach using alternative substrates as a tool for studying enzyme mechanisms is described. In this method the substrate to alternative substrate ratio is maintained constant and the common product (or summation of product analogs) is measured. The double-reciprocal plots so obtained at several constant ratios generate different patterns for various mechanisms, thus permitting a choice of kinetic model. In some cases, secondary intercept plots are utilized as a diagnostic aid. Another feature of this approach is that most of the resultant plots are linear. The graphical patterns for four cases of two-substrate, two-product reactions are presented as examples. These patterns allow one to differentiate several mechanisms which are not distinguishable by conventional alternative substrate, competitive inhibitor, or product inhibition studies alone. When used in combination with other methods, various mechanisms involving isomerization and abortive complex formation can be differentiated even if only one alternative substrate is available.     

Enzyme deactivation

Enzyme deactivation kinetics is often first-order. Different examples of first-order deactivation kinetics exhibited by different enzymes under a wide variety of conditions are presented. Examples of both soluble and immobilized enzymes are presented. The influence of different parameters, chemical modification of specific residues, inhibitors, inactivators, protecting agents, induced conformational changes by external agents, enzyme concentration, and different substrates on the first-order inactivation kinetics of different enzymes is analyzed. The different examples presented from a variety of different areas provides a judicious framework and collection demonstrating the wide applicability of first-order deactivation kinetics. Examples of reversible first-order deactivation kinetics and deactivation-disguise kinetics are also presented.Different mechanisms are also presented to model complex enzyme deactivations. The non-series type mechanisms are emphasized and these involve the substrate and chemical modifiers. Substrate-dependent deactivation rate expressions that are of "separable" and "non-separable" type are presented. Rate expressions involving time-dependent rate constants along with their corresponding mechanisms are presented. Examples of enzymes that exhibit a deactivation-free grace period are also given. An interesting case of enzyme inactivation is the loss of activity in the presence of an auto-decaying reagent. The method is presented by which the intrinsic inactivation rate constants may be obtained. Examples of pH-dependent enzyme inactivation are presented that may be modelled by a five-step (or a simplified two-step) mechanism, and also by a single-step mechanism involving residual activity for the final state. Appropriate examples of enzyme inactivation are presented in each case to highlight the different mechanisms involved.     

Generation of unexpected editing patterns in Leishmania tarentolae mitochondrial mRNAs: misediting produced by misguiding.

We have analyzed the generation of unexpected patterns of RNA editing, i.e., those not following a strict 3' to 5' progression, which occur in junction regions between fully edited and preedited sequences. Evidence is presented that these patterns are generated by misediting due to specific events of misguiding. Misediting can occur through the interaction of inappropriate gRNAs with mRNAs or appropriate gRNAs in an incorrect fashion. Four possible mechanisms for the generation of misedited sequences are presented. Chimeric molecules have been detected in steady-state mitochondrial RNAs that are composed of misguiding gRNAs covalently linked to mRNAs at misediting sites by the 3' oligo(U) tail. We propose that misediting within junction regions can be corrected by appropriately acting gRNAs.     

The steady-state kinetics of isotope exchange for one substrate–one product enzymic reactions

Steady-state kinetic equations for isotope exchange are derived for a number of one substrate-one product enzymic mechanisms in which two molecules of substrate or product can be combined with an enzyme molecule at the one time (e.g. allosteric mechanisms). The usual assumption, that the radioactive material is distributed among the substrate and product components according to a first-order law, is not valid. One can recognize whether isotope-exchange kinetics of an enzyme reaction follows first-order behaviour by using various initial concentrations of the labelled substance added to a mixture.     

基于小波的心电信号有效性检测方法

目的：检测采集到的信号是否为有效心电信号,提高后续心电诊断和分析的准确率。方法：将采集到的信号进行预处理,即去噪处理,主要抑制基线漂移,50Hz工频及其谐波干扰和肌电干扰;取滑动窗长度为4s,检测该段内信号是否有效。为了验证算法的准确率及对不同心电波形是否具有普遍适用性,对MIT-BIH Arrhythmia Database中48个记录,CU及MIT-BIH Noise Stress Test Database中部分记录进行了仿真、验证。结果：仿真实验证明该方法能正确区分有效和无效信号,错检率较低,实现简单,适合实时处理。结论：本方法准确率高,能减少后续心电诊断和分析的计算量并提高准确率,特别是对室颤检测,符合心电分析的要求。     

Following autolysis in proteases by NMR: insights into multiple unfolding pathways and mutational plasticities

Recently there has been significant interest in deducing the form of the rate laws for chemical reactions occurring in the intracellular environment. This environment is typically characterized by low-dimensionality and a high macromolecular content; this leads to a spatial heterogeneity not typical of the well stirred in vitro environments. For this reason, the classical law of mass action has been presumed to be invalid for modeling intracellular reactions. Using lattice-gas automata models, it has recently been postulated [H. Berry, Monte Carlo simulations of enzyme reactions in two dimensions: Fractal kinetics and spatial segregation, Biophys. J. 83 (2002) 1891-1901; S. Schnell, T.E. Turner, Reaction kinetics in intracellular environments with macromolecular crowding: simulations and rate laws, Prog. Biophys. Mol. Biol. 85 (2004) 235-260] that the reaction kinetics is fractal-like. In this article we systematically investigate for the first time how the rate laws describing intracellular reactions vary as a function of: the geometry and size of the intracellular surface on which the reactions occur, the mobility of the macromolecules responsible for the crowding effects, the initial reactant concentrations and the probability of reaction between two reactant molecules. We also compare the rate laws valid in heterogeneous environments in which there is an underlying spatial lattice, for example crystalline alloys, with the rate laws valid in heterogeneous environments where there is no such natural lattice, for example in intracellular environments. Our simulations indicate that: (i) in intracellular environments both fractal kinetics and mass action can be valid, the major determinant being the probability of reaction, (ii) the geometry and size of the intracellular surface on which reactions are occurring does not significantly affect the rate law, (iii) there are considerable differences between the rate laws valid in heterogeneous non-living structures such as crystals and those valid in intracellular environments. Deviations from mass action are less pronounced in intracellular environments than in a crystalline material of similar heterogeneity.     

Visual Benefits in Apparent Motion Displays: Automatically Driven Spatial and Temporal Anticipation Are Partially Dissociated

Many behaviourally relevant sensory events such as motion stimuli and speech have an intrinsic spatio-temporal structure. This will engage intentional and most likely unintentional (automatic) prediction mechanisms enhancing the perception of upcoming stimuli in the event stream. Here we sought to probe the anticipatory processes that are automatically driven by rhythmic input streams in terms of their spatial and temporal components. To this end, we employed an apparent visual motion paradigm testing the effects of pre-target motion on lateralized visual target discrimination. The motion stimuli either moved towards or away from peripheral target positions (valid vs. invalid spatial motion cueing) at a rhythmic or arrhythmic pace (valid vs. invalid temporal motion cueing). Crucially, we emphasized automatic motion-induced anticipatory processes by rendering the motion stimuli non-predictive of upcoming target position (by design) and task-irrelevant (by instruction), and by creating instead endogenous (orthogonal) expectations using symbolic cueing. Our data revealed that the apparent motion cues automatically engaged both spatial and temporal anticipatory processes, but that these processes were dissociated. We further found evidence for lateralisation of anticipatory temporal but not spatial processes. This indicates that distinct mechanisms may drive automatic spatial and temporal extrapolation of upcoming events from rhythmic event streams. This contrasts with previous findings that instead suggest an interaction between spatial and temporal attention processes when endogenously driven. Our results further highlight the need for isolating intentional from unintentional processes for better understanding the various anticipatory mechanisms engaged in processing behaviourally relevant stimuli with predictable spatio-temporal structure such as motion and speech.