Energy landscape

Résumé

An energy landscape is a mapping of possible states of a system. The concept is frequently used in physics, chemistry, and biochemistry, e.g. to describe all possible conformations of a molecular entity, or the spatial positions of interacting molecules in a system, or parameters and their corresponding energy levels, typically Gibbs free energy. Geometrically, the energy landscape is the graph of the energy function across the configuration space of the system. The term is also used more generally in geometric perspectives to mathematical optimization, when the domain of the loss function is the parameter space of some system. Applications The term is useful when examining protein folding; while a protein can theoretically exist in a nearly infinite number of conformations along its energy landscape, in reality proteins fold (or "relax") into secondary and tertiary structures that possess the lowest possible free energy. The key concept in the energy landscape approach t

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https://en.wikipedia.org/wiki/Energy_landscape

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Séances de cours associées (22)

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In order to compute the thermodynamic weights of the diﬀerent metastable conformations of a molecule, we want to approximate the molecule’s Boltzmann distribution π in a reasonable time. This is an essential issue in computational drug design. The energy landscape of active biomolecules is generally very rough with a lot of high barriers and low regions. Many of the algorithms that perform such samplings (e.g. the hybrid Monte Carlo method) have diﬃculties with such landscapes. They are trapped in low-energy regions for a very long time and cannot overcome high barriers. Moving from one low-energy region to another is a very rare event. For these reasons, the distribution of the generated sampling points converges very slowly against the thermodynamically correct distribution of the molecule. The idea of ConfJump is to use a priori knowledge of the localization of low-energy regions to enhance the sampling with artiﬁcial jumps between these low-energy regions. The artiﬁcial jumps are combined with the hybrid Monte Carlo method. This allows the computation of some dynamical properties of the molecule. In ConfJump, the detailed balance condition is satisﬁed and the mathematically correct molecular distribution is sampled.

2006

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The Role of Post-translational Modifications on the Energy Landscape of Huntingtin N-Terminus

Charlotte Julie Caroline Gehin, Hilal Lashuel

Huntington disease is a neurodegenerative disease characterized by a polymorphic tract of polyglutamine repeats in exon 1 of the huntingtin protein, which is thought to be responsible for protein aggregation and neuronal death. The polyglutamine tract is preceded by a 17-residue sequence that is intrinsically disordered. This region is subject to phosphorylation, acetylation and other post-translational modifications in vivo, which modulate its secondary structure, aggregation and, subcellular localization. We used Molecular Dynamics simulations with a novel Hamiltonian-replica-exchange-based enhanced sampling method, SWISH, and an optimal combination of water and protein force fields to study the effects of phosphorylation and acetylation as well as cross-talk between these modifications on the huntingtin N-terminus. The simulations, validated by circular dichroism, were used to formulate a mechanism by which the modifications influence helical conformations. Our findings have implications for understanding the structural basis underlying the effect of PTMs in the aggregation and cellular properties of huntingtin.

2019

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Jamming transition as a paradigm to understand the loss landscape of deep neural networks

Mario Geiger, Levent Dogus Sagun, Stefano Spigler, Matthieu Wyart

Deep learning has been immensely successful at a variety of tasks, ranging from classification to artificial intelligence. Learning corresponds to fitting training data, which is implemented by descending a very high-dimensional loss function. Understanding under which conditions neural networks do not get stuck in poor minima of the loss, and how the landscape of that loss evolves as depth is increased, remains a challenge. Here we predict, and test empirically, an analogy between this landscape and the energy landscape of repulsive ellipses. We argue that in fully connected deep networks a phase transition delimits the over- and underparametrized regimes where fitting can or cannot be achieved. In the vicinity of this transition, properties of the curvature of the minima of the loss (the spectrum of the Hessian) are critical. This transition shares direct similarities with the jamming transition by which particles form a disordered solid as the density is increased, which also occurs in certain classes of computational optimization and learning problems such as the perceptron. Our analysis gives a simple explanation as to why poor minima of the loss cannot be encountered in the overparametrized regime. Interestingly, we observe that the ability of fully connected networks to fit random data is independent of their depth, an independence that appears to also hold for real data. We also study a quantity Delta which characterizes how well (Delta < 0) or badly (Delta > 0) a datum is learned. At the critical point it is power-law distributed on several decades, P+(Delta) similar to Delta(theta) for Delta > 0 and P_(Delta) similar to (-Delta)(-gamma) for Delta < 0, with exponents that depend on the choice of activation function. This observation suggests that near the transition the loss landscape has a hierarchical structure and that the learning dynamics is prone to avalanche-like dynamics, with abrupt changes in the set of patterns that are learned.

AMER PHYSICAL SOC2019

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Jamming transition as a paradigm to understand the loss landscape of deep neural networks

Mario Geiger, Levent Dogus Sagun, Stefano Spigler, Matthieu Wyart

AMER PHYSICAL SOC2019