The rational parameterisation theorem for multisite post-translational modification systems

Post-translational modification of proteins plays a central role in cellular regulation but its study has been hampered by the exponential increase in substrate modification forms (“modforms”) with increasing numbers of sites. We consider here biochemical networks arising from post-translational modification under mass-action kinetics, allowing for multiple substrates, having different types of modification (phosphorylation, methylation, acetylation, etc.) on multiple sites, acted upon by multiple forward and reverse enzymes (in total number L), using general enzymatic mechanisms. These assumptions are substantially more general than in previous studies. We show that the steady-state modform concentrations constitute an algebraic variety that can be parameterised by rational functions of the L free enzyme concentrations, with coefficients which are rational functions of the rate constants. The parameterisation allows steady states to be calculated by solving L algebraic equations, a dramatic reduction compared to simulating an exponentially large number of differential equations. This complexity collapse enables analysis in contexts that were previously intractable and leads to biological predictions that we review. Our results lay a foundation for the systems biology of post-translational modification and suggest deeper connections between biochemical networks and algebraic geometry.     

Positional Information Generated by Spatially Distributed Signaling Cascades

The temporal and stationary behavior of protein modification cascades has been extensively studied, yet little is known about the spatial aspects of signal propagation. We have previously shown that the spatial separation of opposing enzymes, such as a kinase and a phosphatase, creates signaling activity gradients. Here we show under what conditions signals stall in the space or robustly propagate through spatially distributed signaling cascades. Robust signal propagation results in activity gradients with long plateaus, which abruptly decay at successive spatial locations. We derive an approximate analytical solution that relates the maximal amplitude and propagation length of each activation profile with the cascade level, protein diffusivity, and the ratio of the opposing enzyme activities. The control of the spatial signal propagation appears to be very different from the control of transient temporal responses for spatially homogenous cascades. For spatially distributed cascades where activating and deactivating enzymes operate far from saturation, the ratio of the opposing enzyme activities is shown to be a key parameter controlling signal propagation. The signaling gradients characteristic for robust signal propagation exemplify a pattern formation mechanism that generates precise spatial guidance for multiple cellular processes and conveys information about the cell size to the nucleus.     

Lysosomal enzymes possess a common antigenic determinant in the cellular slime mold, Dictyostelium discoideum

Antisera have been prepared against two lysosomal enzymes of the cellular slime mold, Dictyostelium discoideum. The two purified enzyme preparations used for immunization, N-acetylglucosaminidase and beta-glucosidase-1, show no cross-contamination with each other and no significant contamination by other lysosomal enzymes. However, antisera raised against either enzyme bind equally well to seven different lysosomal enzymes and show no preference for the enzyme against which they were raised. A total of 10 different antisera have been examined and all show similar results. Preadsorption of antisera with either purified enzyme removes all antibody activity against the other enzyme. Evidence is presented which indicates that the same species of antibodies are responsible for the precipitation of seven lysosomal enzymes. These data are discussed in terms of the proposal that the antigen that is shared by the lysosomal enzymes is a post-translational modification of the enzyme proteins. We have sought to further characterize the distribution of this common antigen among cellular proteins. We show that N-acetylglucosaminidase and beta-glucosidase-1 represent less than 5% of the total common antigen containing proteins in the cell. Precipitation of 35S-labeled cellular proteins from vegetative cells indicates that as much as 15-30% of the total cell protein may possess the common antigen. Preadsorption experiments confirm that all of the proteins immunoprecipitated in these experiments are recognized by the same antibodies that precipitate the lysosomal enzyme activities. Most of the labeled proteins are secreted into the medium along with the lysosomal enzyme activities during axenic growth. During the developmental phase of the life cycle of Dictyostelium, the total amount of the common antigen decreases about 2-fold relative to total cell protein. However, the synthesis of antigenic proteins continues throughout most of development.     

Algebraic dependency models of protein signal transduction networks from time-series data

Signal transduction networks are crucial for inter- and intra-cellular signaling. Signals are often transmitted via covalent modification of protein structure, with phosphorylation/dephosphorylation as the primary example. In this paper, we apply a recently described method of computational algebra to the modeling of signaling networks, based on time-course protein modification data. Computational algebraic techniques are employed to construct next-state functions. A Monte Carlo method is used to approximate the Deegan-Packel Index of Power corresponding to the respective variables. The Deegan-Packel Index of Power is used to conjecture dependencies in the cellular signaling networks. We apply this method to two examples of protein modification time-course data available in the literature. These experiments identified protein carbonylation upon exposure of cells to sub-lethal concentrations of copper. We demonstrate that this method can identify protein dependencies that might correspond to regulatory mechanisms to shut down glycolysis in a reverse, step-wise fashion in response to copper-induced oxidative stress in yeast. These examples show that the computational algebra approach can identify dependencies that may outline signaling networks involved in the response of glycolytic enzymes to the oxidative stress caused by copper.     

Changes in the post-translational modification of lysosomal enzymes during development of Dictyostelium

The form of post-translational modification present on two lysosomal enzymes--acid phosphatase and alpha-mannosidase--changes as part of the developmental program of Dictyostelium discoideum. Prior to 8 h of development, all enzyme molecules are of a single modification type (early form enzyme). Starting at 8 h of development, enzyme molecules with a second type of modification (late-form enzymes) begin to appear in the cell. We separated the early and late forms of these enzymes from each other by chromatography on DEAE-cellulose. We found that the change in protein modification affects the enzymes' in vitro properties. The early and late forms of both of these enzymes differ in thermostability and susceptibility to proteolytic inactivation. We also found that the late form of alpha-mannosidase is preferentially secreted. We suggest that by synthesizing molecules with a second form of modification, the cell confers new characteristics to its lysosomal enzymes.     

S100A7, S100A10, and S100A11 are transglutaminase substrates

S100 proteins are a family of 10-14 kDa EF-hand-containing calcium binding proteins that function to transmit calcium-dependent cell regulatory signals. S100 proteins have no intrinsic enzyme activity but bind in a calcium-dependent manner to target proteins to modulate target protein function. Transglutaminases are enzymes that catalyze the formation of covalent epsilon-(gamma-glutamyl)lysine bonds between protein-bound glutamine and lysine residues. In the present study we show that transglutaminase-dependent covalent modification is a property shared by several S100 proteins and that both type I and type II transglutaminases can modify S100 proteins. We further show that the reactive regions are at the solvent-exposed amino- and carboxyl-terminal ends of the protein, regions that specify S100 protein function. We suggest that transglutaminase-dependent modification is a general mechanism designed to regulate S100 protein function.     

Job contenders: roles of the β‐barrel assembly machinery and the translocation and assembly module in autotransporter secretion

Billions of years of evolution have yielded today's complex metabolic networks driven by efficient and highly specialized enzymes. In contrast, the metabolism of the earliest cellular life forms was likely much simpler with only a few enzymes of comparatively low activity. It has been speculated that these early enzymes had low specificities and in turn were able to perform multiple functions. In this issue of Molecular Microbiology, Ferla et al. describe examples of enzymes that catalyze chemically distinct reactions while using the same active site. Most importantly, the authors demonstrated that the comparatively weak activities of these multifunctional enzymes are each physiologically relevant. These findings contrast with simply promiscuous enzyme activities, which have been described numerous times but are not physiologically relevant. Ferla et al. elegantly combined initial bioinformatics searches for enzyme candidates with sound kinetic measurements, evolutionary considerations and even structural discussions. The phenomenon of multifunctionality appears to be a mechanism for bacteria with reduced genomes to compensate for their lack of certain enzymes. In the broader context of evolution, these organisms could be considered living model systems to study features of long‐extinct early cellular life.     

N-lysine propionylation controls the activity of propionyl-CoA synthetase

Reversible protein acetylation is a ubiquitous means for the rapid control of diverse cellular processes. Acetyltransferase enzymes transfer the acetyl group from acetyl-CoA to lysine residues, while deacetylase enzymes catalyze removal of the acetyl group by hydrolysis or by an NAD(+)-dependent reaction. Propionyl-coenzyme A (CoA), like acetyl-CoA, is a high energy product of fatty acid metabolism and is produced through a similar chemical reaction. Because acetyl-CoA is the donor molecule for protein acetylation, we investigated whether proteins can be propionylated in vivo, using propionyl-CoA as the donor molecule. We report that the Salmonella enterica propionyl-CoA synthetase enzyme PrpE is propionylated in vivo at lysine 592; propionylation inactivates PrpE. The propionyl-lysine modification is introduced by bacterial Gcn-5-related N-acetyltransferase enzymes and can be removed by bacterial and human Sir2 enzymes (sirtuins). Like the sirtuin deacetylation reaction, sirtuin-catalyzed depropionylation is NAD(+)-dependent and produces a byproduct, O-propionyl ADP-ribose, analogous to the O-acetyl ADP-ribose sirtuin product of deacetylation. Only a subset of the human sirtuins with deacetylase activity could also depropionylate substrate. The regulation of cellular propionyl-CoA by propionylation of PrpE parallels regulation of acetyl-CoA by acetylation of acetyl-CoA synthetase and raises the possibility that propionylation may serve as a regulatory modification in higher organisms.     

Covalent Modification Cycles through the Spatial Prism

Covalent modification cycles are basic units and building blocks of posttranslational modification and cellular signal transduction. We systematically explore different spatial aspects of signal transduction in covalent modification cycles by starting with a basic temporal cycle as a reference and focusing on steady-state signal transduction. We consider, in turn, the effect of diffusion on spatial signal transduction, spatial analogs of ultrasensitive behavior, and the interplay between enzyme localization and substrate diffusion. Our analysis reveals the need to explicitly account for kinetics and diffusional transport (and localization) of enzymes, substrates, and complexes. It demonstrates a complex and subtle interplay between spatial heterogeneity, diffusion, and localization. Overall, examining the spatial dimension of covalent modification reveals that 1), there are important differences between spatial and temporal signal transduction even in this cycle; and 2), spatial aspects may play a substantial role in affecting and distorting information transfer in modules/networks that are usually studied in purely temporal terms. This has important implications for the systematic understanding of signaling in covalent modification cycles, pathways, and networks in multiple cellular contexts.     

Covalent Modification Cycles through the Spatial Prism

Covalent modification cycles are basic units and building blocks of posttranslational modification and cellular signal transduction. We systematically explore different spatial aspects of signal transduction in covalent modification cycles by starting with a basic temporal cycle as a reference and focusing on steady-state signal transduction. We consider, in turn, the effect of diffusion on spatial signal transduction, spatial analogs of ultrasensitive behavior, and the interplay between enzyme localization and substrate diffusion. Our analysis reveals the need to explicitly account for kinetics and diffusional transport (and localization) of enzymes, substrates, and complexes. It demonstrates a complex and subtle interplay between spatial heterogeneity, diffusion, and localization. Overall, examining the spatial dimension of covalent modification reveals that 1), there are important differences between spatial and temporal signal transduction even in this cycle; and 2), spatial aspects may play a substantial role in affecting and distorting information transfer in modules/networks that are usually studied in purely temporal terms. This has important implications for the systematic understanding of signaling in covalent modification cycles, pathways, and networks in multiple cellular contexts.     

Global sequencing of proteolytic cleavage sites in apoptosis by specific labeling of protein N termini

The nearly 600 proteases in the human genome regulate a diversity of biological processes, including programmed cell death. Comprehensive characterization of protease signaling in complex biological samples is limited by available proteomic methods. We have developed a general approach for global identification of proteolytic cleavage sites using an engineered enzyme to selectively biotinylate free protein N termini for positive enrichment of corresponding N-terminal peptides. Using this method to study apoptosis, we have sequenced 333 caspase-like cleavage sites distributed among 292 protein substrates. These sites are generally not predicted by in vitro caspase substrate specificity but can be used to predict other physiological caspase cleavage sites. Structural bioinformatic studies show that caspase cleavage sites often appear in surface-accessible loops and even occasionally in helical regions. Strikingly, we also find that a disproportionate number of caspase substrates physically interact, suggesting that these dimeric proteases target protein complexes and networks to elicit apoptosis.     

The enzymatic and metabolic capabilities of early life

We introduce the concept of metaconsensus and employ it to make high confidence predictions of early enzyme functions and the metabolic properties that they may have produced. Several independent studies have used comparative bioinformatics methods to identify taxonomically broad features of genomic sequence data, protein structure data, and metabolic pathway data in order to predict physiological features that were present in early, ancestral life forms. But all such methods carry with them some level of technical bias. Here, we cross-reference the results of these previous studies to determine enzyme functions predicted to be ancient by multiple methods. We survey modern metabolic pathways to identify those that maintain the highest frequency of metaconsensus enzymes. Using the full set of modern reactions catalyzed by these metaconsensus enzyme functions, we reconstruct a representative metabolic network that may reflect the core metabolism of early life forms. Our results show that ten enzyme functions, four hydrolases, three transferases, one oxidoreductase, one lyase, and one ligase, are determined by metaconsensus to be present at least as late as the last universal common ancestor. Subnetworks within central metabolic processes related to sugar and starch metabolism, amino acid biosynthesis, phospholipid metabolism, and CoA biosynthesis, have high frequencies of these enzyme functions. We demonstrate that a large metabolic network can be generated from this small number of enzyme functions.     

Comparison of the multiple deoxyribonucleic acid-dependent ribonucleic acid polymerase forms of whole rat liver and a minimal-deviation rat hepatoma cell line

To investigate the possibility that the pattern of multiple DNA-dependent RNA polymerases of an animal cell exerts a controlling influence on its nature, the activities of these enzymes were compared in differentiated rat liver and in a rapidly growing minimal-deviation rat hepatoma cell line by using established techniques of enzyme extraction, separation and determination. Relative to the DNA content of the tissues, RNA polymerase activities of forms AI, AII and B were approx. ninefold, twofold and twofold higher respectively in the cell line than in the liver. Tests indicated that these results could not be explained by differences in extraction efficiency or by the presence of unbound inhibitors or stimulators of polymerase activity in the final enzyme preparations. New forms of the enzyme were not detected in either tissue. The significance of these findings with respect to the possible role of multiple RNA polymerases in the control of cellular activities is discussed.     

Evolutionarily conserved linkage between enzyme fold, flexibility, and catalysis

Proteins are intrinsically flexible molecules. The role of internal motions in a protein''s designated function is widely debated. The role of protein structure in enzyme catalysis is well established, and conservation of structural features provides vital clues to their role in function. Recently, it has been proposed that the protein function may involve multiple conformations: the observed deviations are not random thermodynamic fluctuations; rather, flexibility may be closely linked to protein function, including enzyme catalysis. We hypothesize that the argument of conservation of important structural features can also be extended to identification of protein flexibility in interconnection with enzyme function. Three classes of enzymes (prolyl-peptidyl isomerase, oxidoreductase, and nuclease) that catalyze diverse chemical reactions have been examined using detailed computational modeling. For each class, the identification and characterization of the internal protein motions coupled to the chemical step in enzyme mechanisms in multiple species show identical enzyme conformational fluctuations. In addition to the active-site residues, motions of protein surface loop regions (>10 Å away) are observed to be identical across species, and networks of conserved interactions/residues connect these highly flexible surface regions to the active-site residues that make direct contact with substrates. More interestingly, examination of reaction-coupled motions in non-homologous enzyme systems (with no structural or sequence similarity) that catalyze the same biochemical reaction shows motions that induce remarkably similar changes in the enzyme–substrate interactions during catalysis. The results indicate that the reaction-coupled flexibility is a conserved aspect of the enzyme molecular architecture. Protein motions in distal areas of homologous and non-homologous enzyme systems mediate similar changes in the active-site enzyme–substrate interactions, thereby impacting the mechanism of catalyzed chemistry. These results have implications for understanding the mechanism of allostery, and for protein engineering and drug design.

Author''s Summary

Enzymes are nature''s molecular machines that catalyze biochemical reactions with remarkable efficiency. Recent evidence suggests that enzyme function may involve not only direct structural interactions between the enzyme and its substrate, but also internal motions of the enzyme itself. Here, we describe a computational investigation of three classes of enzymes that catalyze completely different biochemical reactions. Remarkably, the mobile enzyme regions and the nature of these motions are the same across species ranging from single-celled organisms to complex life-forms. Also surprisingly, non-homologous enzymes that catalyze the same chemical reaction but do not share sequence or structural similarity reveal a similar impact of enzyme motions on their reaction mechanisms. Flexible enzyme regions are found to be connected by conserved networks of coupled interactions that connect surface regions to active-site residues. These networks may provide a mechanism for the solvent on an enzyme''s surface to couple to the reaction catalyzed by the enzyme. These results have implications for understanding the mechanism of allostery (long-range effects), and for protein engineering and drug design.     

The importance of post-translational modifications in regulating Saccharomyces cerevisiae metabolism

Regulation of the flow of mass and energy through cellular metabolic networks is fundamental to the operation of all living organisms. Such metabolic fluxes are determined by the concentration of limiting substrates and by the amount and kinetic properties of the enzymes. Regulation of the amount of enzyme can be exerted, on a long-term scale, at the level of gene and protein expression. Enzyme regulation by post-translational modifications (PTMs) and noncovalent binding of allosteric effectors are shorter-term mechanisms that modulate enzyme activity. PTMs, in particular protein phosphorylation, are increasingly being recognized as key regulators in many cellular processes, including metabolism. For example, about half of the enzymes in the Saccharomyces cerevisiae metabolic network have been detected as phosphoproteins, although functional relevance has been demonstrated only in a few cases. Direct regulation of enzymes by PTMs provides one of the fastest ways for cells to adjust to environmental cues and internal stimulus. This review charts the so far identified metabolic enzymes undergoing reversible PTMs in the model eukaryote S. cerevisiae and reviews their underlying mechanistic principles - both at the individual enzyme level and in the context of the entire metabolic network operation.     

Sensitivity and control analysis of periodically forced reaction networks using the Green's function method

A general sensitivity and control analysis of periodically forced reaction networks with respect to small perturbations in arbitrary network parameters is presented. A well-known property of sensitivity coefficients for periodic processes in dynamical systems is that the coefficients generally become unbounded as time tends to infinity. To circumvent this conceptual obstacle, a relative time or phase variable is introduced so that the periodic sensitivity coefficients can be calculated. By employing the Green's function method, the sensitivity coefficients can be defined using integral control operators that relate small perturbations in the network's parameters and forcing frequency to variations in the metabolite concentrations and reaction fluxes. The properties of such operators do not depend on a particular parameter perturbation and are described by the summation and connectivity relationships within a control-matrix operator equation. The aim of this paper is to derive such a general control-matrix operator equation for periodically forced reaction networks, including metabolic pathways. To illustrate the general method, the two limiting cases of high and low forcing frequency are considered. We also discuss a practically important case where enzyme activities and forcing frequency are modulated simultaneously. We demonstrate the developed framework by calculating the sensitivity and control coefficients for a simple two reaction pathway where enzyme activities enter reaction rates linearly and specifically.     

A Conserved Deubiquitinating Enzyme Uses Intrinsically Disordered Regions to Scaffold Multiple Protein Interaction Sites

In the canonical view of protein function, it is generally accepted that the three-dimensional structure of a protein determines its function. However, the past decade has seen a dramatic growth in the identification of proteins with extensive intrinsically disordered regions (IDRs), which are conformationally plastic and do not appear to adopt single three-dimensional structures. One current paradigm for IDR function is that disorder enables IDRs to adopt multiple conformations, expanding the ability of a protein to interact with a wide variety of disparate proteins. The capacity for many interactions is an important feature of proteins that occupy the hubs of protein networks, in particular protein-modifying enzymes that usually have a broad spectrum of substrates. One such protein modification is ubiquitination, where ubiquitin is attached to proteins through ubiquitin ligases (E3s) and removed through deubiquitinating enzymes. Numerous proteomic studies have found that thousands of proteins are dynamically regulated by cycles of ubiquitination and deubiquitination. Thus, how these enzymes target their wide array of substrates is of considerable importance for understanding the function of the cell''s diverse ubiquitination networks. Here, we characterize a yeast deubiquitinating enzyme, Ubp10, that possesses IDRs flanking its catalytic protease domain. We show that Ubp10 possesses multiple, distinct binding modules within its IDRs that are necessary and sufficient for directing protein interactions important for Ubp10''s known roles in gene silencing and ribosome biogenesis. The human homolog of Ubp10, USP36, also has IDRs flanking its catalytic domain, and these IDRs similarly contain binding modules important for protein interactions. This work highlights the significant protein interaction scaffolding abilities of IDRs in the regulation of dynamic protein ubiquitination.