Michael Knudsen

A bimodular mechanism of calcium control in eukaryotes

Calcium ions (Ca2+) have an important role as secondary messengers in numerous signal transduction processes, and cells invest much energy in controlling and maintaining a steep gradient between intracellular (∼0.1-micromolar) and extracellular (∼2-millimolar) Ca2+ concentrations. Calmodulin-stimulated calcium pumps, which include the plasma-membrane Ca2+-ATPases (PMCAs), are key regulators of intracellular Ca2+ in eukaryotes. They contain a unique amino- or carboxy-terminal regulatory domain responsible for autoinhibition, and binding of calcium-loaded calmodulin to this domain releases autoinhibition and activates the pump. However, the structural basis for the activation mechanism is unknown and a key remaining question is how calmodulin-mediated PMCA regulation can cover both basal Ca2+ levels in the nanomolar range as well as micromolar-range Ca2+ transients generated by cell stimulation. Here we present an integrated study combining the determination of the high-resolution crystal structure of a PMCA regulatory-domain/calmodulin complex with in vivo characterization and biochemical, biophysical and bioinformatics data that provide mechanistic insights into a two-step PMCA activation mechanism mediated by calcium-loaded calmodulin. The structure shows the entire PMCA regulatory domain and reveals an unexpected 2:1 stoichiometry with two calcium-loaded calmodulin molecules binding to different sites on a long helix. A multifaceted characterization of the role of both sites leads to a general structural model for calmodulin-mediated regulation of PMCAs that allows stringent, highly responsive control of intracellular calcium in eukaryotes, making it possible to maintain a stable, basal level at a threshold Ca2+ concentration, where steep activation occurs.

An algebraic approach to signaling cascades with N layers.

Posttranslational modification of proteins is key in transmission of signals in cells. Many signaling pathways contain several layers of modification cycles that mediate and change the signal through the pathway. Here, we study a simple signaling cascade consisting of n layers of modification cycles such that the modified protein of one layer acts as modifier in the next layer. Assuming mass-action kinetics and taking the formation of intermediate complexes into account, we show that the steady states are solutions to a polynomial in one variable and in fact that there is exactly one steady state for any given total amounts of substrates and enzymes.We demonstrate that many steady-state concentrations are related through rational functions that can be found recursively. For example, stimulus-response curves arise as inverse functions to explicit rational functions. We show that the stimulus-response curves of the modified substrates are shifted to the left as we move down the cascade. Further, our approach allows us to study enzyme competition, sequestration, and how the steady state changes in response to changes in the total amount of substrates.Our approach is essentially algebraic and follows recent trends in the study of posttranslational modification systems.

The CATH database

The CATH database provides hierarchical classification of protein domains based on their folding patterns. Domains are obtained from protein structures deposited in the Protein Data Bank and both domain identification and subsequent classification use manual as well as automated procedures. The accompanying website http://www.cathdb.info provides an easy-to-use entry to the classification, allowing for both browsing and downloading of data. Here, we give a brief review of the database, its corresponding website and some related tools.

Computational discovery of specificity-conferring sites in non-ribosomal peptide synthetases

MOTIVATION By using a class of large modular enzymes known as Non-Ribosomal Peptide Synthetases (NRPS), bacteria and fungi are capable of synthesizing a large variety of secondary metabolites, many of which are bioactive and have potential, pharmaceutical applications as e.g. antibiotics. There is thus an interest in predicting the compound synthesized by an NRPS from its primary structure (amino acid sequence) alone, as this would enable an in silico search of whole genomes for NRPS enzymes capable of synthesizing potentially useful compounds. RESULTS NRPS synthesis happens in a conveyor belt-like fashion where each individual NRPS module is responsible for incorporating a specific substrate (typically an amino acid) into the final product. Here, we present a new method for predicting substrate specificities of individual NRPS modules based on occurrences of motifs in their primary structures. We compare our classifier with existing methods and discuss possible biological explanations of how the motifs might relate to substrate specificity. AVAILABILITY AND IMPLEMENTATION SEQL-NRPS is available as a web service implemented in Python with Flask at http://services.birc.au.dk/seql-nrps and source code available at https://bitbucket.org/dansondergaard/seql-nrps/. CONTACT micknudsen@gmail.com or cstorm@birc.au.dk SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.

An Algebro-topological description of protein domain structure.

The space of possible protein structures appears vast and continuous, and the relationship between primary, secondary and tertiary structure levels is complex. Protein structure comparison and classification is therefore a difficult but important task since structure is a determinant for molecular interaction and function. We introduce a novel mathematical abstraction based on geometric topology to describe protein domain structure. Using the locations of the backbone atoms and the hydrogen bonds, we build a combinatorial object – a so-called fatgraph. The description is discrete yet gives rise to a 2-dimensional mathematical surface. Thus, each protein domain corresponds to a particular mathematical surface with characteristic topological invariants, such as the genus (number of holes) and the number of boundary components. Both invariants are global fatgraph features reflecting the interconnectivity of the domain by hydrogen bonds. We introduce the notion of robust variables, that is variables that are robust towards minor changes in the structure/fatgraph, and show that the genus and the number of boundary components are robust. Further, we invesigate the distribution of different fatgraph variables and show how only four variables are capable of distinguishing different folds. We use local (secondary) and global (tertiary) fatgraph features to describe domain structures and illustrate that they are useful for classification of domains in CATH. In addition, we combine our method with two other methods thereby using primary, secondary, and tertiary structure information, and show that we can identify a large percentage of new and unclassified structures in CATH.

Exact analysis of intrinsic qualitative features of phosphorelays using mathematical models.

Phosphorelays are a class of signaling mechanisms used by cells to respond to changes in their environment. Phosphorelays (of which two-component systems constitute a special case) are particularly abundant in prokaryotes and have been shown to be involved in many fundamental processes such as stress response, osmotic regulation, virulence, and chemotaxis. We develop a general model of phosphorelays extending existing models of phosphorelays and two-component systems. We analyze the model analytically under the assumption of mass-action kinetics and prove that a phosphorelay has a unique stable steady-state. Furthermore, we derive explicit functions relating stimulus to the response in any layer of a phosphorelay and show that a limited degree of ultrasensitivity in the bottom layer of a phosphorelay is an intrinsic feature which does not depend on any reaction rates or substrate amounts. On the other hand, we show how adjusting reaction rates and substrate amounts may lead to higher degrees of ultrasensitivity in intermediate layers. The explicit formulas also enable us to prove how the response changes with alterations in stimulus, kinetic parameters, and substrate amounts. Aside from providing biological insight, the formulas may also be used to replace the time-consuming simulations in numerical analyses.

Fungal NRPS-dependent siderophores: from function to prediction

Iron is an essential, yet often limiting element for the growth of many organisms. In response to iron limitation, fungi have developed siderophores that provide a high-affinity iron uptake system and safe intracellular storage and transport mechanisms to gain a competitive advantage. Here, we discuss the function of siderophores in relation to fungal iron uptake mechanisms and their importance for coexistence with host organisms. The chemical nature of the major groups of siderophores and their regulation is described along with the function and architecture of the large multi-domain enzymes responsible for siderophore synthesis, namely the non-ribosomal peptide synthetases (NRPSs). Finally, we present the most recent advances in our understanding of the structural biology of fungal NRPSs and discuss opportunities for the development of a fungal NRPS prediction server.

A Markov Chain Approach to Randomly Grown Graphs

A Markov chain approach to the study of randomly grown graphs is proposed and applied to some popular models that have found use in biology and elsewhere. For most randomly grown graphs used in biology, it is not known whether the graph or properties of the graph converge (in some sense) as the number of vertices becomes large. Particularly, we study the behaviour of the degree sequence, that is, the number of vertices with degree in large graphs, and apply our results to the partial duplication model. We further illustrate the results by application to real data.

Combined price and event-based demand response using two-stage model predictive control

Demand Response is a key enabler for the shift from a generation-oriented system towards a consumption-oriented electrical grid known as the Smart Grid. This paper proposes a Model Predictive Control scheme enabling a combination of both price and event-based Demand Response. The controller is divided into two stages where the first consists of an optimization which takes dynamic prices into account, whereas the second stage calculates power reduction offers for an Aggregator. The proposed method is validated through a simulation case study, where a single apartment is modeled in EnergyPlus and an electric heater is regulated by the two-stage controller. The results show that the first stage shifts consumption from high to low-price periods, leading to an 8% increase in energy consumption but a 7% reduction in energy costs. The second stage continuously provides hourly power reduction offers for a 24 hours period. The offering price of these bids depends largely on the notification time and the baseline consumption. Results show that in certain time periods these bids can be provided at a very low cost compared to the average energy cost.

Signaling Cascades: Consequences of Varying Substrate and Phosphatase Levels

We study signaling cascades with an arbitrary number of layers of one-site phosphorylation cycles. Such cascades are abundant in nature and integrated parts of many pathways. Based on the Michaelis-Menten model of enzyme kinetics and the law of mass-action, we derive explicit analytic expressions for how the steady state concentrations and the total amounts of substrates, kinase, and phosphatates depend on each other. In particular, we use these to study how the responses (the activated substrates) vary as a function of the available amounts of substrates, kinase, and phosphatases. Our results provide insight into how the cascade response is affected by crosstalk and external regulation.