Simplifying the representation of complex free-energy landscapes using sketch-map

A new scheme, sketch-map, for obtaining a low-dimensional representation of the region of phase space explored during an enhanced dynamics simulation is proposed. We show evidence, from an examination of the distribution of pairwise distances between frames, that some features of the free-energy surface are inherently high-dimensional. This makes dimensionality reduction problematic because the data does not satisfy the assumptions made in conventional manifold learning algorithms We therefore propose that when dimensionality reduction is performed on trajectory data one should think of the resultant embedding as a quickly sketched set of directions rather than a road map. In other words, the embedding tells one about the connectivity between states but does not provide the vectors that correspond to the slow degrees of freedom. This realization informs the development of sketch-map, which endeavors to reproduce the proximity information from the high-dimensionality description in a space of lower dimensionality even when a faithful embedding is not possible.

Approximating the Set of Local Minima in Partial RNA Folding Landscapes

Motivation: We study a stochastic method for approximating the set of local minima in partial RNA folding landscapes associated with a bounded-distance neighbourhood of folding conformations. The conformations are limited to RNA secondary structures without pseudoknots. The method aims at exploring partial energy landscapes pL induced by folding simulations and their underlying neighbourhood relations. It combines an approximation of the number of local optima devised by Garnier and Kallel (2002) with a run-time estimation for identifying sets of local optima established by Reeves and Eremeev (2004).

Results: The method is tested on nine sequences of length between 50 nt and 400 nt, which allows us to compare the results with data generated by RNAsubopt and subsequent barrier tree calculations. On the nine sequences, the method captures on average 92% of local minima with settings designed for a target of 95%. The run-time of the heuristic can be estimated by O(n2D?ln?), where n is the sequence length, ? is the number of local minima in the partial landscape pL under consideration and D is the maximum number of steepest descent steps in attraction basins associated with pL.

Using sketch-map coordinates to analyze and bias molecular dynamics simulations

When examining complex problems, such as the folding of proteins, coarse grained descriptions of the system drive our investigation and help us to rationalize the results. Oftentimes collective variables (CVs), derived through some chemical intuition about the process of interest, serve this purpose. Because finding these CVs is the most difficult part of any investigation, we recently developed a dimensionality reduction algorithm, sketch-map, that can be used to build a low-dimensional map of a phase space of high-dimensionality. In this paper we discuss how these machine-generated CVs can be used to accelerate the exploration of phase space and to reconstruct free-energy landscapes. To do so, we develop a formalism in which high-dimensional configurations are no longer represented by low-dimensional position vectors. Instead, for each configuration we calculate a probability distribution, which has a domain that encompasses the entirety of the low-dimensional space. To construct a biasing potential, we exploit an analogy with metadynamics and use the trajectory to adaptively construct a repulsive, history-dependent bias from the distributions that correspond to the previously visited configurations. This potential forces the system to explore more of phase space by making it desirable to adopt configurations whose distributions do not overlap with the bias. We apply this algorithm to a small model protein and succeed in reproducing the free-energy surface that we obtain from a parallel tempering calculation.

Probing the Unfolded Configurations of a β-Hairpin Using Sketch-Map

This work examines the conformational ensemble involved in β-hairpin folding by means of advanced molecular dynamics simulations and dimensionality reduction. A fully atomistic description of the protein and the surrounding solvent molecules is used, and this complex energy landscape is sampled by means of parallel tempering metadynamics simulations. The ensemble of configurations explored is analyzed using the recently proposed sketch-map algorithm. Further simulations allow us to probe how mutations affect the structures adopted by this protein. We find that many of the configurations adopted by a mutant are the same as those adopted by the wild-type protein. Furthermore, certain mutations destabilize secondary-structure-containing configurations by preventing the formation of hydrogen bonds or by promoting the formation of new intramolecular contacts. Our analysis demonstrates that machine-learning techniques can be used to study the energy landscapes of complex molecules and that the visualizations that are generated in this way provide a natural basis for examining how the stabilities of particular configurations of the molecule are affected by factors such as temperature or structural mutations.

Planning for Renewable Energy: Lessons from the UK’s Devolved Administrations

The planning system has been put forward as a key element in facilitating the low carbon transition (Bulkeley 2006, While 2008), by reducing carbon footprints through initiatives such as encouraging less-energy intensive development, reducing the need to travel or promoting sustainable forms of transport. It has also played a key role on encouraging a shift to more renewable sources of energy, through establishing the spatial ‘rules’ for its regulation, consenting of specific projects and acting as the key arena for mediating a range of social concerns over the resulting socio-technical shift. Despite having this key facilitative role, planning is also regularly seen as a key impediment to renewables, particularly on-shore wind (Ellis et al 2009). There is however, little known about what makes the ‘best’ approach to planning for renewables and indeed little discussion on how to judge the effectiveness of a planning regime for this issue – is it one that maximises generating capacity, protects or landscapes or biodiversity, or perhaps one that maximises social acceptance of renewable developments?

The UK offers a useful context for exploring these issues, with its four main territories (England, Northern Ireland, Scotland and Wales) having broadly similar institutional arrangements, but autonomy over spatial planning during the period in which renewables expanded across the landscape. Each of these jurisdictions has sought to use their planning system to encourage renewables with subtlety different discourses, regulations and spatial strategies. Such an ‘experiment’ offers some important insight into what ‘works’.

This paper will draw on a two year study funded by the UK’s Economic and Social Research Council (RES-062-23-2526), which has charted the effects of devolved administrations on policy and delivery of renewable energy from 1990 to 2012. Drawing on more than 80 interviews, documentary analysis and secondary data sources it describes the growth of renewable capacity in each jurisdiction, explores the spatial strategies adopted and analyses the way in which the broader institutional frameworks in which planning for renewables has emerged. The paper uses this analysis to consider the lessons that can be drawn from the comparable experience of the devolved administrations in the UK and points to the ways in which we should evaluate the effectiveness of planning regimes for renewable energy.

Contested landscapes: the moral geographies of light pollution in Britain

This paper considers the concept of light pollution and its connections to moral geographies of landscape in Britain. The paper aims to provide a greater understanding of light pollution in the present day, where the issue connects to policy debates about energy efficiency, crime, health, ecology and night time aesthetics, whilst also engaging with new areas of research in cultural geography. The main sources of investigation are the Campaign to Protect Rural England and the British Astronomical Association’s Campaign for Dark Skies (est. 1990). Using interviews, archival and textual analysis, the paper examines this anti-light-pollution lobby, looking at the lead-up to the formation of the Campaign as well as its ongoing influence. A moral geography of light pollution is identified, drawing on two interconnected discourses – a notion of the ‘astronomical sublime’ and the problem of urbanization. Whilst the former is often invoked, both through visual and linguistic means, by anti-light pollution campaigners, the latter is characterized as a threat to clear night skies, echoing earlier protests against urban sprawl. Complementing a growing area of research, the geographies of light and darkness, this paper considers the light pollution lobby as a way of investigating the fundamental relationship between humankind and the cosmos in the modern age.