Evaluating boundary dependent errors in QM/MM simulations.

Hybrid quantum mechanics/molecular mechanics (QM/MM) simulations provide a powerful tool for studying chemical reactions, especially in complex biochemical systems. In most works to date, the quantum region is kept fixed throughout the simulation and is defined in an ad hoc way based on chemical intuition and available computational resources. The simulation errors associated with a given choice of the quantum region are, however, rarely assessed in a systematic manner. Here we study the dependence of two relevant quantities on the QM region size: the force error at the center of the QM region and the free energy of a proton transfer reaction. Taking lysozyme as our model system, we find that in an apolar region the average force error rapidly decreases with increasing QM region size. In contrast, the average force error at the polar active site is considerably higher, exhibits large oscillations and decreases more slowly, and may not fall below acceptable limits even for a quantum region radius of 9.0 A. Although computation of free energies could only be afforded until 6.0 A, results were found to change considerably within these limits. These errors demonstrate that the results of QM/MM calculations are heavily affected by the definition of the QM region (not only its size), and a convergence test is proposed to be a part of setting up QM/MM simulations.

Statistics of natural movements are reflected in motor errors.

Humans use their arms to engage in a wide variety of motor tasks during everyday life. However, little is known about the statistics of these natural arm movements. Studies of the sensory system have shown that the statistics of sensory inputs are key to determining sensory processing. We hypothesized that the statistics of natural everyday movements may, in a similar way, influence motor performance as measured in laboratory-based tasks. We developed a portable motion-tracking system that could be worn by subjects as they went about their daily routine outside of a laboratory setting. We found that the well-documented symmetry bias is reflected in the relative incidence of movements made during everyday tasks. Specifically, symmetric and antisymmetric movements are predominant at low frequencies, whereas only symmetric movements are predominant at high frequencies. Moreover, the statistics of natural movements, that is, their relative incidence, correlated with subjects' performance on a laboratory-based phase-tracking task. These results provide a link between natural movement statistics and motor performance and confirm that the symmetry bias documented in laboratory studies is a natural feature of human movement.

Model-based influences on humans' choices and striatal prediction errors.

The mesostriatal dopamine system is prominently implicated in model-free reinforcement learning, with fMRI BOLD signals in ventral striatum notably covarying with model-free prediction errors. However, latent learning and devaluation studies show that behavior also shows hallmarks of model-based planning, and the interaction between model-based and model-free values, prediction errors, and preferences is underexplored. We designed a multistep decision task in which model-based and model-free influences on human choice behavior could be distinguished. By showing that choices reflected both influences we could then test the purity of the ventral striatal BOLD signal as a model-free report. Contrary to expectations, the signal reflected both model-free and model-based predictions in proportions matching those that best explained choice behavior. These results challenge the notion of a separate model-free learner and suggest a more integrated computational architecture for high-level human decision-making.

Dopamine-dependent prediction errors underpin reward-seeking behaviour in humans.

Theories of instrumental learning are centred on understanding how success and failure are used to improve future decisions. These theories highlight a central role for reward prediction errors in updating the values associated with available actions. In animals, substantial evidence indicates that the neurotransmitter dopamine might have a key function in this type of learning, through its ability to modulate cortico-striatal synaptic efficacy. However, no direct evidence links dopamine, striatal activity and behavioural choice in humans. Here we show that, during instrumental learning, the magnitude of reward prediction error expressed in the striatum is modulated by the administration of drugs enhancing (3,4-dihydroxy-L-phenylalanine; L-DOPA) or reducing (haloperidol) dopaminergic function. Accordingly, subjects treated with L-DOPA have a greater propensity to choose the most rewarding action relative to subjects treated with haloperidol. Furthermore, incorporating the magnitude of the prediction errors into a standard action-value learning algorithm accurately reproduced subjects' behavioural choices under the different drug conditions. We conclude that dopamine-dependent modulation of striatal activity can account for how the human brain uses reward prediction errors to improve future decisions.