Threshold Effects of Energy Price Changes

The effectiveness of policies to reduce the use of energy depend on the elasticity of substitution between the various inputs and on the rate of technological progress. This paper presents a theoretical model emphasising energy investments’ characteristics of uncertainty and irreversibility that result in hypotheses concerning the relative values of substitution parameters and rates of technological change in periods of high and increasing energy prices and in periods of low prices. The theoretical model suggests that threshold level effects exist. Firms are induced to substitute away from energy only if prices of energy exceed a certain threshold level and they reverse the technology only if prices are low enough. Using panel data for the Dutch economy we do not find threshold effects in the level of energy prices.

Self-Assembly of Structures with Addressable Complexity.

The self-assembly of structures with "addressable complexity", where every component is distinct and is programmed to occupy a specific location within a target structure, is a promising route to engineering materials with precisely defined morphologies. Because systems with many components are inherently complicated, one might assume that the chances of successful self-assembly are extraordinarily small. Yet recent advances suggest otherwise: addressable structures with hundreds of distinct building blocks have been designed and assembled with nanometer precision. Despite this remarkable success, it is often challenging to optimize a self-assembly reaction to ensure that the intended structure is kinetically accessible. In this Perspective, we focus on the prediction of kinetic pathways for self-assembly and implications for the design of robust experimental protocols. The development of general principles to predict these pathways will enable the engineering of complex materials using a much wider range of building blocks than is currently possible.This work was carried out with support from the Engineering and Physical Sciences Research Council Programme Grant EP/I001352/1. We would like to acknowledge discussions with Aleks Reinhardt, Rebecca Schulman, Thomas Ouldridge, Oleg Gang and Alexei Tkachenko. DF acknowledges the hospitality of the NYU Center for Soft Matter Research.This is the author accepted manuscript. The final version is available from the American Chemical Society via http://dx.doi.org/10.1021/jacs.5b1191

Threshold effects of energy price changes

This paper presents a theoretical model emphasising energy investments’ characteristics of uncertainty and irreversibility. The theoretical model suggests threshold effects. Firms are induced to substitute away from energy only if prices of energy exceed a certain threshold level and they reverse the technology only if energy prices are low enough. Estimating a simple investment relation using panel data for the Dutch economy, we find evidence for threshold effects.

Rational design of self-assembly pathways for complex multicomponent structures.

The field of complex self-assembly is moving toward the design of multiparticle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such "addressable complexity," we need to understand the factors that optimize the yield and the kinetics of self-assembly. Here we use a simple theoretical method to explain the key features responsible for the unexpected success of DNA-brick experiments, which are currently the only demonstration of reliable self-assembly with such a large number of components. Simulations confirm that our theory accurately predicts the narrow temperature window in which error-free assembly can occur. Even more strikingly, our theory predicts that correct assembly of the complete structure may require a time-dependent experimental protocol. Furthermore, we predict that low coordination numbers result in nonclassical nucleation behavior, which we find to be essential for achieving optimal nucleation kinetics under mild growth conditions. We also show that, rather surprisingly, the use of heterogeneous bond energies improves the nucleation kinetics and in fact appears to be necessary for assembling certain intricate 3D structures. This observation makes it possible to sculpt nucleation pathways by tuning the distribution of interaction strengths. These insights not only suggest how to improve the design of structures based on DNA bricks, but also point the way toward the creation of a much wider class of chemical or colloidal structures with addressable complexity.This work was carried out with support from the Eu- ropean Research Council (Advanced Grant 227758) and the Engineering and Physical Sciences Research Council Programme Grant EP/I001352/1. W.M.J. acknowledges support from the Gates Cambridge Trust and the Na- tional Science Foundation Graduate Research Fellowship under Grant No. DGE-1143678.This is the author accepted manuscript. The final version is available from PNAS at http://www.pnas.org/content/112/20/6313.abstract

Phase separation in solutions with specific and nonspecific interactions.

Protein solutions, which tend to be thermodynamically stable under physiological conditions, can demix into protein-enriched and protein-depleted phases when stressed. Using a lattice-gas model of proteins with both isotropic and specific, directional interactions, we calculate the critical conditions for phase separation for model proteins with up to four patches via Monte Carlo simulations and statistical associating fluid theory. Given a fixed specific interaction strength, the critical value of the isotropic energy, which accounts for dispersion forces and nonspecific interactions, measures the stability of the solution with respect to nonspecific interactions. Phase separation is suppressed by the formation of protein complexes, which effectively passivate the strongly associating sites on the monomers. Nevertheless, we find that protein models with three or more patches can form extended aggregates that phase separate despite the assembly of passivated complexes, even in the absence of nonspecific interactions. We present a unified view of the critical behavior of model fluids with anisotropic interactions, and we discuss the implications of these results for the thermodynamic stability of protein solutions.Protein solutions, which tend to be thermodynamically stable under physiological conditions, can demix into protein-enriched and protein-depleted phases when stressed. Using a lattice-gas model of proteins with both isotropic and specific, directional interactions, we calculate the critical conditions for phase separation for model proteins with up to four patches via Monte Carlo simulations and statistical associating fluid theory. Given a fixed specific interaction strength, the critical value of the isotropic energy, which accounts for dispersion forces and nonspecific interactions, measures the stability of the solution with respect to nonspecific interactions. Phase separation is suppressed by the formation of protein complexes, which effectively passivate the strongly associating sites on the monomers. Nevertheless, we find that protein models with three or more patches can form extended aggregates that phase separate despite the assembly of passivated complexes, even in the absence of nonspecific interactions. We present a unified view of the critical behavior of model fluids with anisotropic interactions, and we discuss the implications of these results for the thermodynamic stability of protein solutions.This is the final published version, which can also be found on the publisher's website at: http://scitation.aip.org/content/aip/journal/jcp/140/20/10.1063/1.4878836 © 2014 AIP Publishing LL

Phase Transitions in Biological Systems with Many Components

Biological mixtures such as the cytosol may consist of thousands of distinct components. There is now a substantial body of evidence showing that, under physiological conditions, intracellular mixtures can phase separate into spatially distinct regions with differing compositions. In this article we present numerical evidence indicating that such spontaneous compartmentalization exploits general features of the phase diagram of a multicomponent biomolecular mixture. In particular, we show that demixed domains are likely to segregate when the variance in the intermolecular interaction strengths exceeds a well-defined threshold. Multiple distinct phases are likely to become stable under very similar conditions, which can then be tuned to achieve multiphase coexistence. As a result, only minor adjustments to the composition of the cytosol or the strengths of the intermolecular interactions are needed to regulate the formation of different domains with specific compositions, implying that phase separation is a robust mechanism for creating spatial organization. We further predict that this functionality is only weakly affected by increasing the number of components in the system. Our model therefore suggests that, for purely physico-chemical reasons, biological mixtures are naturally poised to undergo a small number of demixing phase transitions.W.M.J. acknowledges support from the Gates Cambridge Trust and the National Science Foundation Graduate Research Fellowship under grant No. DGE-1143678