Protein motions visualized by femtosecond time-resolved crystallography: The case of photosensory vs photosynthetic proteins

Proteins are dynamic objects and undergo conformational changes when functioning. These changes range from interconversion between states in equilibrium to ultrafast and coherent structural motions within one perturbed state. Time-resolved serial femtosecond crystallography at free-electron X-ray lasers can unravel structural changes with atomic resolution and down to femtosecond time scales. In this review, we summarize recent advances on detecting structural changes for phytochrome photosensor proteins and a bacterial photosynthetic reaction center. In the phytochrome structural changes are extensive and involve major rearrangements of many amino acids and water molecules, accompanying the regulation of its biochemical activity, whereas in the photosynthetic reaction center protein the structural changes are smaller, more localized, and are optimized to facilitate electron transfer along the chromophores. The detected structural motions underpin the proteins’ function, providing a showcase for the importance of detecting ultrafast protein structural dynamics.     

Parameter estimation in stochastic biochemical reactions

Gene regulatory, signal transduction and metabolic networks are major areas of interest in the newly emerging field of systems biology. In living cells, stochastic dynamics play an important role; however, the kinetic parameters of biochemical reactions necessary for modelling these processes are often not accessible directly through experiments. The problem of estimating stochastic reaction constants from molecule count data measured, with error, at discrete time points is considered. For modelling the system, a hidden Markov process is used, where the hidden states are the true molecule counts, and the transitions between those states correspond to reaction events following collisions of molecules. Two different algorithms are proposed for estimating the unknown model parameters. The first is an approximate maximum likelihood method that gives good estimates of the reaction parameters in systems with few possible reactions in each sampling interval. The second algorithm, treating the data as exact measurements, approximates the number of reactions in each sampling interval by solving a simple linear equation. Maximising the likelihood based on these approximations can provide good results, even in complex reaction systems.     

Combining mechanical and optical approaches to dissect cellular mechanobiology

Mechanical force modulates a wide array of cell physiological processes. Cells sense and respond to mechanical stimuli using a hierarchy of structural complexes spanning multiple length scales, including force-sensitive molecules and cytoskeletal networks. Understanding mechanotransduction, i.e., the process by which cells convert mechanical inputs into biochemical signals, has required the development of novel biophysical tools that allow for probing of cellular and subcellular components at requisite time, length, and force scales and technologies that track the spatio-temporal dynamics of relevant biomolecules. In this review, we begin by discussing the underlying principles and recent applications of atomic force microscopy, magnetic twisting cytometry, and traction force microscopy, three tools that have been widely used for measuring the mechanical properties of cells and for probing the molecular basis of cellular mechanotransduction. We then discuss how such tools can be combined with advanced fluorescence methods for imaging biochemical processes in living cells in the context of three specific problem spaces. We first focus on fluorescence resonance energy transfer, which has enabled imaging of intra- and inter-molecular interactions and enzymatic activity in real time based on conformational changes in sensor molecules. Next, we examine the use of fluorescence methods to probe force-dependent dynamics of focal adhesion proteins. Finally, we discuss the use of calcium ratiometric signaling to track fast mechanotransductive signaling dynamics. Together, these studies demonstrate how single-cell biomechanical tools can be effectively combined with molecular imaging technologies for elucidating mechanotransduction processes and identifying mechanosensitive proteins.     

Case for an RNA–prion world: a hypothesis based on conformational diversity

Prions and other misfolded proteins can impart their structure and functions to normal molecules. Based upon a thorough structural assessment of RNA, prions and misfolded proteins, especially from the perspective of conformational diversity, we propose a case for co-existence of these in the pre-biotic world. Analyzing the evolution of physical aspects of biochemical structures, we put forward a case for an RNA–prion pre-biotic world, instead of, merely, the “RNA World”.     

Conformational selection in protein binding and function

Protein binding and function often involves conformational changes. Advanced nuclear magnetic resonance (NMR) experiments indicate that these conformational changes can occur in the absence of ligand molecules (or with bound ligands), and that the ligands may “select” protein conformations for binding (or unbinding). In this review, we argue that this conformational selection requires transition times for ligand binding and unbinding that are small compared to the dwell times of proteins in different conformations, which is plausible for small ligand molecules. Such a separation of timescales leads to a decoupling and temporal ordering of binding/unbinding events and conformational changes. We propose that conformational‐selection and induced‐change processes (such as induced fit) are two sides of the same coin, because the temporal ordering is reversed in binding and unbinding direction. Conformational‐selection processes can be characterized by a conformational excitation that occurs prior to a binding or unbinding event, while induced‐change processes exhibit a characteristic conformational relaxation that occurs after a binding or unbinding event. We discuss how the ordering of events can be determined from relaxation rates and effective on‐ and off‐rates determined in mixing experiments, and from the conformational exchange rates measured in advanced NMR or single‐molecule fluorescence resonance energy transfer experiments. For larger ligand molecules such as peptides, conformational changes and binding events can be intricately coupled and exhibit aspects of conformational‐selection and induced‐change processes in both binding and unbinding direction.     

Cross–Scale Interactions and Changing Pattern–Process Relationships: Consequences for System Dynamics

Cross–scale interactions refer to processes at one spatial or temporal scale interacting with processes at another scale to result in nonlinear dynamics with thresholds. These interactions change the pattern–process relationships across scales such that fine-scale processes can influence a broad spatial extent or a long time period, or broad-scale drivers can interact with fine-scale processes to determine system dynamics. Cross–scale interactions are increasing recognized as having important influences on ecosystem processes, yet they pose formidable challenges for understanding and forecasting ecosystem dynamics. In this introduction to the special feature, “Cross–scale interactions and pattern–process relationships”, we provide a synthetic framework for understanding the causes and consequences of cross–scale interactions. Our framework focuses on the importance of transfer processes and spatial heterogeneity at intermediate scales in linking fine- and broad-scale patterns and processes. Transfer processes and spatial heterogeneity can either amplify or attenuate system response to broad-scale drivers. Providing a framework to explain cross–scale interactions is an important step in improving our understanding and ability to predict the impacts of propagating events and to ameliorate these impacts through proactive measures.     

Determinants of the steep species–area relationship of coral reef fishes

The increase in species richness with area is known as the species–area relationship (SPAR). Although several mutually non-exclusive processes may produce the SPAR, the null, often ignored, hypothesis states that a SPAR can be generated by random placement alone. The log–log-transformed SPAR of coral reef fishes on small patch-reefs revealed a steep slope of 0.55. However, this slope was dependent on the cumulative area of the reef examined and was therefore affected by random placement. After statistically removing the contribution of random placement from the SPAR, the slope was estimated to be 0.21. This is consistent with estimates from other, mostly terrestrial, systems. Furthermore, a randomization procedure, where the probability of fishes to reach a patch was proportional to reef area, showed that the field measured SPAR did not differ from random placement. In addition, fish assemblages on species poor reefs did not form subsets of species rich reefs (i.e., no nestedness) beyond that expected from random placement. Steep log–log-transformed SPARs can be formed by random placement alone, indicating that caution should be used when assigning an ecological meaning to SPARs generated from small spatial scales.     

Hydrogen bonding and packing density are factors most strongly connected to limiting sites of high flexibility in the 16S rRNA in the 30S ribosome

Background  

Conformational flexibility in structured RNA frequently is critical to function. The 30S ribosomal subunit exists in different conformations in different functional states due to changes in the central part of the 16S rRNA. We are interested in evaluating the factors that might be responsible for restricting flexibility to specific parts of the 16S rRNA using biochemical data obtained from the 30S subunit in solution. This problem was approached taking advantage of the observation that there must be a high degree of conformational flexibility at sites where UV photocrosslinking occurs and a lack of flexibility inhibits photoreactivity at many other sites that are otherwise suitable for reaction.     

Structural States and Dynamics of the D-Loop in Actin

Conformational changes induced by ATP hydrolysis on actin are involved in the regulation of complex actin networks. Previous structural and biochemical data implicate the DNase I binding loop (D-loop) of actin in such nucleotide-dependent changes. Here, we investigated the structural and conformational states of the D-loop (in solution) using cysteine scanning mutagenesis and site-directed labeling. The reactivity of D-loop cysteine mutants toward acrylodan and the mobility of spin labels on these mutants do not show patterns of an α-helical structure in monomeric and filamentous actin, irrespective of the bound nucleotide. Upon transition from monomeric to filamentous actin, acrylodan emission spectra and electron paramagnetic resonance line shapes of labeled mutants are blue-shifted and more immobilized, respectively, with the central residues (residues 43–47) showing the most drastic changes. Moreover, complex electron paramagnetic resonance line shapes of spin-labeled mutants suggest several conformational states of the D-loop. Together with a new (to our knowledge) actin crystal structure that reveals the D-loop in a unique hairpin conformation, our data suggest that the D-loop equilibrates in F-actin among different conformational states irrespective of the nucleotide state of actin.     

A tool for the prediction of structures of complex sugars

In two recent back to back articles(Xia et al., J Chem Theory Comput 3:1620–1628 and 1629–1643, 2007a, b) we have started to address the problem of complex oligosaccharide conformation and folding. The scheme previously presented was based on exhaustive searches in configuration space in conjunction with Nuclear Overhauser Effect (NOE) calculations and the use of a complex rotameric library that takes branching into account. NOEs are extremely useful for structural determination but only provide information about short range interactions and ordering. Instead, the measurement of residual dipolar couplings (RDC), yields information about molecular ordering or folding that is long range in nature. In this article we show the results obtained by incorporation RDC calculations into our prediction scheme. Using this new approach we are able to accurately predict the structure of six human milk sugars: LNF-1, LND-1, LNF-2, LNF-3, LNnT and LNT. Our exhaustive search in dihedral configuration space combined with RDC and NOE calculations allows for highly accurate structural predictions that, because of the non-ergodic nature of these molecules on a time scale compatible with molecular dynamics simulations, are extremely hard to obtain otherwise (Almond et al., Biochemistry 43:5853–5863, 2004). Molecular dynamics simulations in explicit solvent using as initial configurations the structures predicted by our algorithm show that the histo-blood group epitopes in these sugars are relatively rigid and that the whole family of oligosaccharides derives its conformational variability almost exclusively from their common linkage (β-d-GlcNAc-(1→3)-β-d-Gal) which can exist in two distinct conformational states. A population analysis based on the conformational variability of this flexible glycosidic link indicates that the relative population of the two distinct states varies for different human milk oligosaccharides. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Hierarchical thinking in network biology: the unbiased modularization of biochemical networks

As reconstructed biochemical reaction networks continue to grow in size and scope, there is a growing need to describe the functional modules within them. Such modules facilitate the study of biological processes by deconstructing complex biological networks into conceptually simple entities. The definition of network modules is often based on intuitive reasoning. As an alternative, methods are being developed for defining biochemical network modules in an unbiased fashion. These unbiased network modules are mathematically derived from the structure of the whole network under consideration.     

A Markov model for interspike interval distributions of auditory cortical neurons that do not show periodic firings

Spontaneous firing properties of individual auditory cortical neurons are interpreted in terms of local and global order present in functioning brain networks, such as alternating “up” and “down” states. A four-state modulated Markov process is used to model neuronal firings. The system alternates between a bound and an unbound state, both with Poisson-distributed lifetimes. During the unbound state, active and closed states alternate with Poisson-distributed lifetimes. Inside the active state, spikes are generated as a realization of a Poisson process. This combination of processes constitutes a four-state modulated Markov process, determined by five independent parameters. Analytical expressions for the probability density functions (pdfs) that describe the interspike interval (ISI) distribution and autocorrelation function are derived. The pdf for the ISI distribution is shown to be a linear combination of three exponential functions and is expressed through the five system parameters. Through fitting experimental ISI histograms by the theoretical ones, numerical values of the system parameters are obtained for the individual neurons. Both Monte Carlo simulations and goodness-of-fit tests are used to validate the fitting procedure. The values of the estimated system parameters related to the active-closed and bound–unbound processes and their independence on the neurons’ mean firing rate suggest that the underlying quasi-periodic processes reflect properties of the network in which the neurons are embedded. The characteristic times of autocorrelations, determined by the bound–unbound and active-closed processes, are also independent of the neuron’s firing rate. The agreement between experimental and theoretical ISI histograms and autocorrelation functions allows interpretation of the system parameters of the individual neurons in terms of slow and delta waves, and high-frequency oscillations observed in cortical networks. This procedure can identify and track the influence of changing brain states on the single-unit firing patterns in experimental animals.     

Translated Chemical Reaction Networks

Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems of polynomial ordinary differential equations. The steady states of these mass action systems have been analyzed via a variety of techniques, including stoichiometric network analysis, deficiency theory, and algebraic techniques (e.g., Gröbner bases). In this paper, we present a novel method for characterizing the steady states of mass action systems. Our method explicitly links a network’s capacity to permit a particular class of steady states, called toric steady states, to topological properties of a generalized network called a translated chemical reaction network. These networks share their reaction vectors with their source network but are permitted to have different complex stoichiometries and different network topologies. We apply the results to examples drawn from the biochemical literature.     

Analysis of the plant architecture via tree-structured statistical models: the hidden Markov tree models

Plant architecture is the result of repetitions that occur through growth and branching processes. During plant ontogeny, changes in the morphological characteristics of plant entities are interpreted as the indirect translation of different physiological states of the meristems. Thus connected entities can exhibit either similar or very contrasted characteristics. We propose a statistical model to reveal and characterize homogeneous zones and transitions between zones within tree-structured data: the hidden Markov tree (HMT) model. This model leads to a clustering of the entities into classes sharing the same 'hidden state'. The application of the HMT model to two plant sets (apple trees and bush willows), measured at annual shoot scale, highlights ordered states defined by different morphological characteristics. The model provides a synthetic overview of state locations, pointing out homogeneous zones or ruptures. It also illustrates where within branching structures, and when during plant ontogeny, morphological changes occur. However, the labelling exhibits some patterns that cannot be described by the model parameters. Some of these limitations are addressed by two alternative HMT families.     

Bistability and oscillations in chemical reaction networks

Bifurcation theory is one of the most widely used approaches for analysis of dynamical behaviour of chemical and biochemical reaction networks. Some of the interesting qualitative behaviour that are analyzed are oscillations and bistability (a situation where a system has at least two coexisting stable equilibria). Both phenomena have been identified as central features of many biological and biochemical systems. This paper, using the theory of stoichiometric network analysis (SNA) and notions from algebraic geometry, presents sufficient conditions for a reaction network to display bifurcations associated with these phenomena. The advantage of these conditions is that they impose fewer algebraic conditions on model parameters than conditions associated with standard bifurcation theorems. To derive the new conditions, a coordinate transformation will be made that will guarantee the existence of branches of positive equilibria in the system. This is particularly useful in mathematical biology, where only positive variable values are considered to be meaningful. The first part of the paper will be an extended introduction to SNA and algebraic geometry-related methods which are used in the coordinate transformation and set up of the theorems. In the second part of the paper we will focus on the derivation of bifurcation conditions using SNA and algebraic geometry. Conditions will be derived for three bifurcations: the saddle-node bifurcation, a simple branching point, both linked to bistability, and a simple Hopf bifurcation. The latter is linked to oscillatory behaviour. The conditions derived are sufficient and they extend earlier results from stoichiometric network analysis as can be found in (Aguda and Clarke in J Chem Phys 87:3461–3470, 1987; Clarke and Jiang in J Chem Phys 99:4464–4476, 1993; Gatermann et al. in J Symb Comput 40:1361–1382, 2005). In these papers some necessary conditions for two of these bifurcations were given. A set of examples will illustrate that algebraic conditions arising from given sufficient bifurcation conditions are not more difficult to interpret nor harder to calculate than those arising from necessary bifurcation conditions. Hence an increasing amount of information is gained at no extra computational cost. The theory can also be used in a second step for a systematic bifurcation analysis of larger reaction networks. We have added a dedication of the paper to K. Gatermann.     

The model–data fusion pitfall: assuming certainty in an uncertain world

Model–data fusion is a powerful framework by which to combine models with various data streams (including observations at different spatial or temporal scales), and account for associated uncertainties. The approach can be used to constrain estimates of model states, rate constants, and driver sensitivities. The number of applications of model–data fusion in environmental biology and ecology has been rising steadily, offering insights into both model and data strengths and limitations. For reliable model–data fusion-based results, however, the approach taken must fully account for both model and data uncertainties in a statistically rigorous and transparent manner. Here we review and outline the cornerstones of a rigorous model–data fusion approach, highlighting the importance of properly accounting for uncertainty. We conclude by suggesting a code of best practices, which should serve to guide future efforts.     

Hill coefficients,dose–response curves and allosteric mechanisms

Hill coefficients (n _H) derived from four parameter logistic fits to dose–response curves were compared to calculated realistic reaction schemes and related to experimental data: (1) Hill coefficients may give information on the number of interacting sites but cannot distinguish between competitive, non-competitive or ortho-, iso-, or allosteric mechanisms. (2) For enzymatic dose–inhibition curves, Hill coefficients smaller than one do not indicate anticooperative binding but show that at least one ternary complex has enzymatic activity. (3) Hill coefficients different from one are proof for multiple ligand binding. The large variations of reported Hill coefficients corresponds to multiple allosteric binding, where induced conformational changes cause loss of the active conformation. Such a denaturation mechanism is in stark contrast to the desired specificity of drugs. The discussion is open.     

Empirical and theoretical challenges in aboveground–belowground ecology

A growing body of evidence shows that aboveground and belowground communities and processes are intrinsically linked, and that feedbacks between these subsystems have important implications for community structure and ecosystem functioning. Almost all studies on this topic have been carried out from an empirical perspective and in specific ecological settings or contexts. Belowground interactions operate at different spatial and temporal scales. Due to the relatively low mobility and high survival of organisms in the soil, plants have longer lasting legacy effects belowground than aboveground. Our current challenge is to understand how aboveground–belowground biotic interactions operate across spatial and temporal scales, and how they depend on, as well as influence, the abiotic environment. Because empirical capacities are too limited to explore all possible combinations of interactions and environmental settings, we explore where and how they can be supported by theoretical approaches to develop testable predictions and to generalise empirical results. We review four key areas where a combined aboveground–belowground approach offers perspectives for enhancing ecological understanding, namely succession, agro-ecosystems, biological invasions and global change impacts on ecosystems. In plant succession, differences in scales between aboveground and belowground biota, as well as between species interactions and ecosystem processes, have important implications for the rate and direction of community change. Aboveground as well as belowground interactions either enhance or reduce rates of plant species replacement. Moreover, the outcomes of the interactions depend on abiotic conditions and plant life history characteristics, which may vary with successional position. We exemplify where translation of the current conceptual succession models into more predictive models can help targeting empirical studies and generalising their results. Then, we discuss how understanding succession may help to enhance managing arable crops, grasslands and invasive plants, as well as provide insights into the effects of global change on community re-organisation and ecosystem processes.