The extent of enthalpy-entropy compensation in protein-ligand interactions

The extent of enthalpy–entropy compensation in protein–ligand interactions has long been disputed because negatively correlated enthalpy (ΔH) and entropy (TΔS) changes can arise from constraints imposed by experimental and analytical procedures as well as through a physical compensation mechanism. To distinguish these possibilities, we have created quantitative models of the effects of experimental constraints on isothermal titration calorimetry (ITC) measurements. These constraints are found to obscure any compensation that may be present in common data representations and regression analyses (e.g., in ΔH vs. –TΔS plots). However, transforming the thermodynamic data into ΔΔ-plots of the differences between all pairs of ligands that bind each protein diminishes the influence of experimental constraints and representational bias. Statistical analysis of data from 32 diverse proteins shows a significant and widespread tendency to compensation. ΔΔH versus ΔΔG plots reveal a wide variation in the extent of compensation for different ligand modifications. While strong compensation (ΔΔH and −TΔΔS opposed and differing by < 20% in magnitude) is observed for 22% of modifications (twice that expected without compensation), 15% of modifications result in reinforcement (ΔΔH and −TΔΔS of the same sign). Because both enthalpy and entropy changes arise from changes to the distribution of energy states on binding, there is a general theoretical expectation of compensated behavior. However, prior theoretical studies have focussed on explaining a stronger tendency to compensation than actually found here. These results, showing strong but imperfect compensation, will act as a benchmark for future theoretical models of the thermodynamic consequences of ligand modification

The thermodynamics of protein–ligand interaction and solvation: insights for ligand design

Isothermal titration calorimetry is able to provide accurate information on the thermodynamic contributions of enthalpy and entropy changes to free energies of binding. The Structure/Calorimetry of Reported Protein Interactions Online database of published isothermal titration calorimetry studies and structural information on the interactions between proteins and small-molecule ligands is used here to reveal general thermodynamic properties of protein–ligand interactions and to investigate correlations with changes in solvation. The overwhelming majority of interactions are found to be enthalpically favoured. Synthetic inhibitors and biological ligands form two distinct subpopulations in the data, with the former having greater average affinity due to more favourable entropy changes on binding. The greatest correlation is found between the binding free energy and apolar surface burial upon complex formation. However, the free-energy contribution per unit area buried is only 30–50% of that expected from earlier studies of transfer free energies of small molecules. A simple probability-based estimator for the maximal affinity of a binding site in terms of its apolar surface area is proposed. Polar surface area burial also contributes substantially to affinity but is difficult to express in terms of unit area due to the small variation in the amount of polar surface buried and a tendency for cancellation of its enthalpic and entropic contributions. Conventionally, the contribution of apolar desolvation to affinity is attributed to gain of entropy due to solvent release. Although data presented here are supportive of this notion, because the correlation of entropy change with apolar surface burial is relatively weak, it cannot, on present evidence, be confidently considered to be correct. Further, thermodynamic changes arising from small differences between ligands binding to individual proteins are relatively large and, in general, uncorrelated with changes in solvation, suggesting that trends identified across widely differing proteins are of limited use in explaining or predicting the effects of ligand modifications

Kilombo: a Kilobot simulator to enable effective research in swarm robotics

The Kilobot is a widely used platform for investigation of swarm robotics. Physical Kilobots are slow moving and require frequent recalibration and charging, which significantly slows down the development cycle. Simulators can speed up the process of testing, exploring and hypothesis generation, but usually require time consuming and error-prone translation of code between simulator and robot. Moreover, code of different nature often obfuscates direct comparison, as well as determination of the cause of deviation, between simulator and actual robot swarm behaviour. To tackle these issues we have developed a C-based simulator that allows those working with Kilobots to use the same programme code in both the simulator and the physical robots. Use of our simulator, coined Kilombo, significantly simplifies and speeds up development, given that a simulation of 1000 robots can be run at a speed 100 times faster than real time on a desktop computer, making high-throughput pre-screening possible of potential algorithms that could lead to desired emergent behaviour. We argue that this strategy, here specifically developed for Kilobots, is of general importance for effective robot swarm research. The source code is freely available under the MIT license

Kilombo: a Kilobot simulator to enable effective research in swarm robotics

The Kilobot is a widely used platform for investigation of swarm robotics. Physical Kilobots are slow moving and require frequent recalibration and charging, which significantly slows down the development cycle. Simulators can speed up the process of testing, exploring and hypothesis generation, but usually require time consuming and error-prone translation of code between simulator and robot. Moreover, code of different nature often obfuscates direct comparison, as well as determination of the cause of deviation, between simulator and actual robot swarm behaviour. To tackle these issues we have developed a C-based simulator that allows those working with Kilobots to use the same programme code in both the simulator and the physical robots. Use of our simulator, coined Kilombo, significantly simplifies and speeds up development, given that a simulation of 1000 robots can be run at a speed 100 times faster than real time on a desktop computer, making high-throughput pre-screening possible of potential algorithms that could lead to desired emergent behaviour. We argue that this strategy, here specifically developed for Kilobots, is of general importance for effective robot swarm research. The source code is freely available under the MIT license