Molecular dynamics simulations of forced conformational transitions in 1,6-linked polysaccharides

Recent atomic force microscopy stretching measurements of single polysaccharide molecules suggest that their elasticity is governed by force-induced conformational transitions of the pyranose ring. However, the mechanism of these transitions and the mechanics of the pyranose ring are not fully understood. Here we use steered molecular dynamics simulations of the stretching process to unravel the mechanism of forced conformational transitions in 1,6 linked polysaccharides. In contrast to most sugars, 1,6 linked polysaccharides have an extra bond in their inter-residue linkage, C5-C6, around which restricted rotations occur and this additional degree of freedom increases the mechanical complexity of these polymers. By comparing the computational results with the atomic force microscopy data we determine that forced rotations around the C5-C6 bond have a significant and different impact on the elasticity of alpha- and beta-linked polysaccharides. Beta-linkages of a polysaccharide pustulan force the rotation around the C5-C6 bonds and produce a Hookean-like elasticity but do not affect the conformation of the pyranose rings. However, alpha-linkages of dextran induce compound conformational transitions that include simultaneous rotations around the C5-C6 bonds and chair-boat transitions of the pyranose rings. These previously not-recognized transitions are responsible for the characteristic plateau in the force-extension relationship of dextran.     

The Topology of the Energy Landscapes of Macromolecules in the Torsion Angle Space and the Principle of the Minimum Energy Dissipation Rate in Conformational Relaxation

This article discusses some basic problems of structural biology and molecular dynamics simulation methods that need to be taken into account when considering, the protein folding problem, and prediction of 3D-structures for biopolymers. A multidimensional Fourier series expansions were formulated for the energy landscapes of the systems with conformational mobility, These energy landscape representations are correct from the viewpoint of the topology of the macromolecule configuration spaces. The problem of the single global minimum on the energy landscape for proteins is discussed and is formulated in tems of phase rules for the component of Fourier expansions. This rule is formally similar to the problem of diffraction on a multidimensional cubic lattice. The calibration of biopolymer force fields and their correspondence to topologically correct energy landscapes are discussed. Equations of motion were obtained in a matrix form for the relaxation of a representative point position on a multidimensional potential energy surface. The solutions of the equations for conformational relaxation were shown to obey the principle of the minimum energy dissipation rate at a given relaxation rate of potential energy (or folding rate).     

From mutations to mechanisms and dysfunction via computation and mining of protein energy landscapes

Background

The protein energy landscape underscores the inherent nature of proteins as dynamic molecules interconverting between structures with varying energies. Reconstructing a protein’s energy landscape holds the key to characterizing a protein’s equilibrium conformational dynamics and its relationship to function. Many pathogenic mutations in protein sequences alter the equilibrium dynamics that regulates molecular interactions and thus protein function. In principle, reconstructing energy landscapes of a protein’s healthy and diseased variants is a central step to understanding how mutations impact dynamics, biological mechanisms, and function.

Results

Recent computational advances are yielding detailed, sample-based representations of protein energy landscapes. In this paper, we propose and describe two novel methods that leverage computed, sample-based representations of landscapes to reconstruct them and extract from them informative local structures that reveal the underlying organization of an energy landscape. Such structures constitute landscape features that, as we demonstrate here, can be utilized to detect alterations of landscapes upon mutation.

Conclusions

The proposed methods detect altered protein energy landscape features in response to sequence mutations. By doing so, the methods allow formulating hypotheses on the impact of mutations on specific biological activities of a protein. This work demonstrates that the availability of energy landscapes of healthy and diseased variants of a protein opens up new avenues to harness the quantitative information embedded in landscapes to summarize mechanisms via which mutations alter protein dynamics to percolate to dysfunction.

     

Stochastic ensembles, conformationally adaptive teamwork, and enzymatic detoxification

It has been appreciated for a long time that enzymes exist as conformational ensembles throughout multiple stages of the reactions they catalyze, but there is renewed interest in the functional implications. The energy landscape that results from conformationlly diverse poteins is a complex surface with an energetic topography in multiple dimensions, even at the transition state(s) leading to product formation, and this represents a new paradigm. At the same time there has been renewed interest in conformational ensembles, a new paradigm concerning enzyme function has emerged, wherein catalytic promiscuity has clear biological advantages in some cases. "Useful", or biologically functional, promiscuity or the related behavior of "multifunctionality" can be found in the immune system, enzymatic detoxification, signal transduction, and the evolution of new function from an existing pool of folded protein scaffolds. Experimental evidence supports the widely held assumption that conformational heterogeneity promotes functional promiscuity. The common link between these coevolving paradigms is the inherent structural plasticity and conformational dynamics of proteins that, on one hand, lead to complex but evolutionarily selected energy landscapes and, on the other hand, promote functional promiscuity. Here we consider a logical extension of the overlap between these two nascent paradigms: functionally promiscuous and multifunctional enzymes such as detoxification enzymes are expected to have an ensemble landscape with more states accessible on multiple time scales than substrate specific enzymes. Two attributes of detoxification enzymes become important in the context of conformational ensembles: these enzymes metabolize multiple substrates, often in substrate mixtures, and they can form multiple products from a single substrate. These properties, combined with complex conformational landscapes, lead to the possibility of interesting time-dependent, or emergent, properties. Here we demonstrate these properties with kinetic simulations of nonequilibrium steady state (NESS) behavior resulting from energy landscapes expected for detoxification enzymes. Analogous scenarios with other promiscuous enzymes may be worthy of consideration.     

Observations on rate theory for rugged energy landscapes

The potential energy profile for many complex reactions of proteins, such as folding or allosteric conformational change, involves many different scales of molecular motion along the reaction coordinate. Although it is natural to model the dynamics of motion along such rugged energy landscapes as diffusional (the Smoluchowski equation; SE), problems arise because the frictional forces generated by the molecular surround are typically not strong enough to justify the use of the SE. Here, we discuss the fundamental theory behind the SE and note that it may be justified through a master equation when reduced to its continuum limit. However, the SE cannot be used for rough energy landscapes, where the continuum limit is ill defined. Instead, we suggest that one should use a mean first passage time expression derived from a master equation, and show how this approach can be used to glean information about the underlying dynamics of barrier crossing. We note that the potential profile in the SE is that of the microbarriers between conformational substates, and that there is a temperature-dependent, effective friction associated with the long residence time in the microwells that populate the rough landscape. The number of recrossings of the overall barrier is temperature-dependent, governed by the microbarriers and not by the effective friction. We derive an explicit expression for the mean number of recrossings and its temperature dependence. Finally, we note that the mean first passage time can be used as a departure point for measuring the roughness of the landscape.     

Dynamics of pore growth in membranes and membrane stability.

Pores can form and grow in biomembranes because of factors such as thermal fluctuation, transmembrane electrical potential, and cellular environment. We propose a new statistical physics model of the pore growth treated as a non-Markovian stochastic process, with a free energy barrier and memory friction from the membrane matrix treated as a quasi-two-dimensional viscoelastic and dielectric fluid continuum. On the basis of the modern theory of activated barrier crossing, an analytical expression for membrane lifetime and the phase diagram for membrane stability are obtained. The memory effect due to membrane viscoelasticity and the elasticity due to cytoskeletal network are found to induce sharp transitions to membrane stability against pore growth and compete with other factors to manifest rich dynamic transitions over the membrane lifetime.     

Relative microelastic mapping of living cells by atomic force microscopy.

The spatial and temporal changes of the mechanical properties of living cells reflect complex underlying physiological processes. Following these changes should provide valuable insight into the biological importance of cellular mechanics and their regulation. The tip of an atomic force microscope (AFM) can be used to indent soft samples, and the force versus indentation measurement provides information about the local viscoelasticity. By collecting force-distance curves on a time scale where viscous contributions are small, the forces measured are dominated by the elastic properties of the sample. We have developed an experimental approach, using atomic force microscopy, called force integration to equal limits (FIEL) mapping, to produce robust, internally quantitative maps of relative elasticity. FIEL mapping has the advantage of essentially being independent of the tip-sample contact point and the cantilever spring constant. FIEL maps of living Madine-Darby canine kidney (MDCK) cells show that elasticity is uncoupled from topography and reveal a number of unexpected features. These results present a mode of high-resolution visualization in which the contrast is based on the mechanical properties of the sample.     

The force-driven conformations of heparin studied with single molecule force microscopy

Using single molecule force spectroscopy we examine the response of heparin chains to mechanical stretching. We find that at forces below 200 pN heparin behaves as a simple entropic spring. At approximately 200 pN heparin displays a large enthalpic elasticity, which is evident as a pronounced plateau in the force-extension relationship. We determine that this enthalpic elasticity is produced by sugar rings of heparin flipping to more energetic and more extended conformations. We estimate that in vivo, the forces which stretch heparin are comparable to the forces that trigger conformational transitions in our single molecule atomic force microscopy measurements. We hypothesize that these conformational transitions have biological significance in that they provide a mechanism to finely regulate the affinity of various ligands toward heparin, for example, in secretory granules undergoing exocytosis and during the mechanical interactions between cells and the extracellular matrix.     

An Event History Analysis of Parcel Extensification and Household Abandonment in Pays Basque,French Pyrenees, 1830–1958 AD

This paper examines local processes of agricultural abandonment, socioeconomic changes, and associated landscape transition in a Pyrenean mountain village. We analyze the effects of socioeconomic and demographic factors contributing to changes in parcel level land use and ownership from 1830 to 1958. We use an event-history analysis to examine how individual etxe (Basque households) influenced the pace and character of landscape transition through their internal composition and their mediation of market pressures. Contrary to conventional narratives of agricultural transitions, our analysis suggests that more rapid “abandonment” of the landscape was prevented by etxe that were able to both engage in markets and maintain higher fertility rates. We conclude that the capacity of agropastoral landscapes to absorb broad-scale change is directly tied to local institutions, such as the etxe, which ultimately mediate socioeconomic drivers of change.     

The role of landscape texture in conservation biogeography: a case study on birds in south-eastern Australia

The binary classification of landscapes into suitable vs. unsuitable areas underlies several prominent theories in conservation biogeography. However, a binary classification is not always appropriate. The textural discontinuity hypothesis provides an alternative theoretical framework to examine the geographical distribution of species, and does not rely on a binary classification scheme. The texture of a given landscape is the combination of its vertical structural complexity and horizontal spatial grain. The textural discontinuity hypothesis states that biophysical features in the environment are scaled in a discontinuous way, and that discontinuities in the body size distribution of animals mirror these biophysical discontinuities. As a result of this relationship, a complex landscape texture should be associated with small‐bodied animals, whereas a simple landscape texture should be associated with larger‐bodied animals. We examined this hypothesis for birds in five landscapes in south‐eastern Australia that represented a gradient from simple to complex landscape texture. In landscapes with a complex texture, the number of detections of small birds was higher than expected, and the number of detections of larger‐bodied birds was lower than expected. The opposite pattern was found in landscapes with a simple texture. The pattern remained significant when only bird species found in each of the five landscapes were considered, which demonstrated that the association of landscape texture with body size was not an artefact of landscapes differing in their species pools. Understanding the effects of landscape texture on species distribution patterns may be a promising research frontier for conservation biogeography. We hypothesize that the active management of landscape texture may be used to attract or deter animals of certain body sizes. Consistent with other theories, the textural discontinuity hypothesis therefore suggests that managing entire landscapes, rather than only predefined patches, is an important conservation strategy.     

Analysis of the conformational energy landscape of human snRNA with a metric based on tree representation of RNA structures

It is an outstanding problem to clarify how the RNA sequence is related to its structure and biological functions. We developed a simplified definition of a metric for tree representation of RNA secondary structures and analyzed the conformational energy landscapes of human spliceosomal snRNAs. We discuss the structural properties of the biological sequence by calculating the conformational energy landscapes based on the structural distance between each of the pairs in the set of suboptimal structures. The new index value is introduced for estimating the shapes of distribution patterns in conformational energy landscapes. We apply our method to the five human snRNAs and show that U1 snRNA has a multi-valley profile of the landscape, whereas the landscapes of the other four snRNAs have one steep valley. This result reflects different biological functions of these snRNAs in the pre-mRNA splicing process. The results of analyzing tRNAs and rRNAs show that the conformational energy landscapes of these sequences have multi-valley profiles.     

Mechanical unfolding of RNA: from hairpins to structures with internal multiloops

Mechanical unfolding of RNA structures, ranging from hairpins to ribozymes, using laser optical tweezer experiments have begun to reveal the features of the energy landscape that cannot be easily explored using conventional experiments. Upon application of constant force (f), RNA hairpins undergo cooperative transitions from folded to unfolded states whereas subdomains of ribozymes unravel one at a time. Here, we use a self-organized polymer model and Brownian dynamics simulations to probe mechanical unfolding at constant force and constant-loading rate of four RNA structures of varying complexity. For simple hairpins, such as P5GA, application of constant force or constant loading rate results in bistable cooperative transitions between folded and unfolded states without populating any intermediates. The transition state location (DeltaxFTS) changes dramatically as the loading rate is varied. At loading rates comparable to those used in laser optical tweezer experiments, the hairpin is plastic, with DeltaxFTS being midway between folded and unfolded states; whereas at high loading rates, DeltaxFTS moves close to the folded state, i.e., RNA is brittle. For the 29-nucleotide TAR RNA with the three-nucleotide bulge, unfolding occurs in a nearly two-state manner with an occasional pause in a high free energy metastable state. Forced unfolding of the 55 nucleotides of the Hepatitis IRES domain IIa, which has a distorted L-shaped structure, results in well-populated stable intermediates. The most stable force-stabilized intermediate represents straightening of the L-shaped structure. For these structures, the unfolding pathways can be predicted using the contact map of the native structures. Unfolding of a RNA motif with internal multiloop, namely, the 109-nucleotide prohead RNA that is part of the 29 DNA packaging motor, at constant value of rf occurs with three distinct rips that represent unraveling of the paired helices. The rips represent kinetic barriers to unfolding. Our work shows 1), the response of RNA to force is largely determined by the native structure; and 2), only by probing mechanical unfolding over a wide range of forces can the underlying energy landscape be fully explored.     

Exploring the relationship between funneled energy landscapes and two-state protein folding

It should take an astronomical time span for unfolded protein chains to find their native state based on an unguided conformational random search. The experimental observation that folding is fast can be rationalized by assuming that protein energy landscapes are sloped towards the native state minimum, such that rapid folding can proceed from virtually any point in conformational space. Folding transitions often exhibit two-state behavior, involving extensively disordered and highly structured conformers as the only two observable kinetic species. This study employs a simple Brownian dynamics model of "protein particles" moving in a spherically symmetrical potential. As expected, the presence of an overall slope towards the native state minimum is an effective means to speed up folding. However, the two-state nature of the transition is eradicated if a significant energetic bias extends too far into the non-native conformational space. The breakdown of two-state cooperativity under these conditions is caused by a continuous conformational drift of the unfolded proteins. Ideal two-state behavior can only be maintained on surfaces exhibiting large regions that are energetically flat, a result that is supported by other recent data in the literature (Kaya and Chan, Proteins: Struct Funct Genet 2003;52:510-523). Rapid two-state folding requires energy landscapes exhibiting the following features: (i) A large region in conformational space that is energetically flat, thus allowing for a significant degree of random sampling, such that unfolded proteins can retain a random coil structure; (ii) a trapping area that is strongly sloped towards the native state minimum.     

Landscape perspectives on agricultural intensification and biodiversity – ecosystem service management

Understanding the negative and positive effects of agricultural land use for the conservation of biodiversity, and its relation to ecosystem services, needs a landscape perspective. Agriculture can contribute to the conservation of high‐diversity systems, which may provide important ecosystem services such as pollination and biological control via complementarity and sampling effects. Land‐use management is often focused on few species and local processes, but in dynamic, agricultural landscapes, only a diversity of insurance species may guarantee resilience (the capacity to reorganize after disturbance). Interacting species experience their surrounding landscape at different spatial scales, which influences trophic interactions. Structurally complex landscapes enhance local diversity in agroecosystems, which may compensate for local high‐intensity management. Organisms with high‐dispersal abilities appear to drive these biodiversity patterns and ecosystem services, because of their recolonization ability and larger resources experienced. Agri‐environment schemes (incentives for farmers to benefit the environment) need to broaden their perspective and to take the different responses to schemes in simple (high impact) and complex (low impact) agricultural landscapes into account. In simple landscapes, local allocation of habitat is more important than in complex landscapes, which are in total at risk. However, little knowledge of the relative importance of local and landscape management for biodiversity and its relation to ecosystem services make reliable recommendations difficult.     

Protein dynamics and function: insights from the energy landscape and solvent slaving

Protein motions are complex and a good way to describe them is in terms of a very high-dimensional conformation space. We give here a simple explanation of the conformation space and the energy landscape, the conformational motions and protein reactions, based on an analogy to a traffic problem. The analogy provides insight into the slaving of protein processes to bulk solvent fluctuations, in both the native and unfolded states.     

Atomistic View of the Conformational Activation of Src Kinase Using the String Method with Swarms-of-Trajectories

The inactive-to-active conformational transition of the catalytic domain of human c-Src tyrosine kinase is characterized using the string method with swarms-of-trajectories with all-atom explicit solvent molecular dynamics simulations. The activation process occurs in two main steps in which the activation loop (A-loop) opens first, followed by the rotation of the αC helix. The computed potential of mean force energy along the activation pathway displays a local minimum, which allows the identification of an intermediate state. These results show that the string method with swarms-of-trajectories is an effective technique to characterize complex and slow conformational transitions in large biomolecular systems.     

Temporal variability of aphid biological control in contrasting landscape contexts

Landscape complexity may provide ecosystem services to agriculture through the provision of natural enemies of agricultural pests. Strong positive effect of adjacent semi-natural habitats on natural enemies in croplands has been evidenced, but the resulting impact on biological control remains unclear. Taking into account the temporal dynamics of pest and natural enemies in agricultural landscapes provides better resolution to the studies and better understanding of the biological control service.In this study, the population dynamics of aphids and two groups of predators (coccinellid and carabid beetles) were examined. Insects were sampled in 20 wheat fields, surrounded by structurally simple and complex landscapes in Chilean central valley. Considering the whole sampling period, the diversity of aphids and natural enemies were similar in wheat crops surrounded by both types of landscapes, and the abundance of ladybirds was higher in crops in the complex landscapes. The dynamics of predators was more advanced in complex landscapes than in the simple ones, whereas the dynamics of aphids were similar in both types of landscape. Negative correlation between abundance of predators and aphid population growth rate in both landscape contexts were observed suggesting a control of the pest population by the predators. Different temporal patterns were observed in these correlations in the two landscape contexts, which suggests differences in the biological control related to the landscape composition.The present study shows that colonization of crops by natural enemies occurs sooner in structurally complex landscapes and suggests that this early colonization may facilitate an early and efficient control of aphid populations, nevertheless the biological control efficiency seems to be higher in structurally simple landscapes later in the season.     

Spatial configuration and landscape context of wildflower areas determine their benefits to pollinator α- and β-diversity

Wildflower areas have become a staple tool within agro-environmental schemes (AES) to counteract pollinator declines. While their role in providing food resources to resident flower-visiting insects is unambiguous, the conservation effectiveness in a landscape context is less clear. Particularly, how multiple vs. single wildflower area utilization differs between simple and complex landscapes is understudied. We examined colonisation and community dynamics of wild bees and hoverflies in 33 newly established wildflower areas across a gradient of landscape complexity (amount of semi-natural habitat) and connectivity (presence of additional wildflower areas) for seven weeks during three consecutive years (one year during and two after establishment). We recorded more than 25% of the wild bee and hoverfly species of Hesse in an area of approx. 10 ha, substantiating the general benefit of wildflower areas to pollinators. While alpha-diversity increased with landscape complexity in isolated wildflower areas, the opposite pattern was observed for connected areas. The low alpha-diversity in complex landscapes indicated a dilution effect between connected sites. The inverse relationship between alpha and beta diversity among wildflower areas within landscapes suggests interspecific trade-offs between local resource conditions and landscape context. Accordingly, the establishment of multiple wildflower areas within AES is advisable to increase connectivity of suitable habitats in simple landscapes. Moreover, adjusting local conditions (plant diversity) to landscape context likely optimizes conservation effectiveness in modern agroecosystems.