A minimalist model for simulation of structure and dynamics of helical polypeptides

Proteins are molecular machines, building block and arms of a living cell. They are finely structured biomolecules highly specialized for functional roles. A protein is organized in hierarchical levels. The primary structure is a chain formed by amino acids (of 20 different types) linked together by peptide bonds in a specific sequence forming the polypeptide. The secondary structure describes local recurrent structural motifs adopted by the polypeptide. The tertiary structure is the organization of secondary structures, through the interactions between residues often widely apart in the primary sequence. A quaternary structure can sometimes be recognized in how the tertiary structures of different polypeptide chains organize. The biological function of a protein depends on its overall 3D fold. The chain folds through a stepwise process, generally mirroring the hierarchical structural organization. Thus, to understand the final shape of a protein, the deep comprehension of the secondary structures and of their sequential determinants is mandatory, as the first step of this hierarchy. Given the rigid geometry of the peptide bond, two internal variables (for each amino- acid) are sufficient to describe the conformation of the backbone of the polypeptide. These are the dihedral angles Φ and Ψ describing the rotation around the two single bonds connecting the central amino-acid Carbon (Cα) with its neighboring amino- and carbossilic- groups along the chain. The distribution of the (Φ,Ψ) couples represented in a plane is called the Ramachandran plot (RP). The two main classes of secondary structures namely helices and sheets, occupy well distinct areas of the RP. More difficult is the separation of the different sub-classes of helices (α-helix, 310-helix and π-helix), located in near and partially superposing areas of the RP. While the sheets are stabilized by hydrogen bonds connecting amino-acids belonging to different strands, often sequentially far, helices are stabilized by periodic and local intra-strand patterns of hydrogen bonds. Considering the relatively low number of internal variables capable of describing the backbone conformation, several attempts exist in the literature of building a ”minimalist” model for proteins, i.e. the simplest and coarser possible less-than-atomic-resolution model having the following characteristics: (i) possibility of back-mapping to the full atomistic representation, (ii) capability of describing all the different kinds of secondary structures and their dynamics/thermodynamics and (iii) in general, capability of predicting accurately structure and dynamics of the global fold of the protein. A linear chain of interacting center (“beads”) located on the Cαs is a possibility often considered in the literature. In this class of models, condition (i) is satisfied at least concerning the backbone conformation. The investigation of condition (ii) is one of the focus of this thesis. Condition (iii) is not completely satisfied by any of the existing models belonging to this class, which are either accurate but with low generality and predictive power, or rather general but poorly accurate. This thesis work pursues the goal of building an accurate and predictive minimalist model, and takes some important steps in the road for reaching it. The first part of this work focuses on analyzing the situations in which (ii) is satisfied. This proceeds from the mapping of the atomistic structures of a protein onto the minimalist representation. In previous models, this mapping was based either on single or groups of structural data (from X-ray crystallography or NMR) or from data sets from atomistic simulations of a given protein of interest. In this work, and in view of giving more generality to the model, it was decided to extend the analysis, virtually to the whole set of existing experimental data. A software was build capable of downloading from the RCSB Protein Data Bank (the world-wide data set of freely available proteins structures) a data set with user-defined properties (e.g., maximum-minimum size of a protein, prevalence (or not) of a given secondary structure, given sequential/structural diversity among proteins, and many other). At will, the software can then “coarse grain” the structures at different levels included of course the one of the minimalist model, and analyze the distributions of internal variables, and their 2D and 3D correlations. The software, called SecStAnT, is made freely available to the scientific community. A paper describing it is currently under revision. A first important results come from the comparison of the RP build with the atomistic representation with its counterpart for the minimalist model, involving the two conformational internal variables of the Cα chain (i.e. the pseudo-bond angle θ and the pseudo dihedral φ). It was observed that even in the minimalist representation, the secondary structures occupy separated areas in the (θ,φ) plane, indicating that the minimalist model can represent the secondary structures, and that back-mapping to the atomistic RP is possible. The second part of this work focused on parameterizing the model in such a way that it is capable of reproducing the secondary structures with a high level of accuracy. In this part SecStAnT was used to produce distributions of internal variables θ, φ and other involved in the description of the secondary structures (e.g. the distances between the third, fourth and fifth neighboring Cαs along the chain, related to the hydrogen bonds stabilizing the helices) and their correlations. These data were then used as targets, and the parameterization optimized to reproduce them in the simulations of their minimalist model. The simulations were produced by means of general purpose molecular dynamics package DL POLY, in which the minimalist model was implemented, by means of in- house programmed software tools. The parameters optimization then proceeds by means of a physically driven trial-and-error procedure. The general goal is to produce a general model capable of describing all the secondary structures. The force field (Hamiltonian) of the model contains a set of conformational terms directly related to the internal variables θ and φ, aimed at describing the general conformational flexibility of the backbone even in the case of weakly structured or de- structured proteins; terms mimicking the hydrogen bonds will then stabilize the different secondary structures. In the final model the relative weight of these terms will be chosen primary-structure dependent. This is clearly a long time scale project, of which a part was concluded in this work, precisely the one regarding the helices. A model was produced capable of describing with a high degree of accuracy the three main different types of helices. Specifically, the structure, dynamics and distributions and correlations of internal variables of α– and 3–10 helices, from simulations compare well with available experimental data. For π–type helix the experimental data are very a few and elusive, thus our simulations can be considered a prediction in view of comparison with forthcoming experimental data, whose reliability is tested on the other two kinds of helices. These results are achieved with a minimal number of terms in the Hamiltonian, whose meaning can be directly understood in terms of physical interactions (e.g. hydrogen bonds). This, together with the high accuracy, can be considered the main innovation of this model: a physically based parameterization allow to straightforwardly extend the model to include other secondary structures, giving to it generality and predictive power. This extension is, in fact, the most immediate possible development of this thesis work, which can proceed by including hydrogen bonding patterns typical of the different kinds of sheets. Other more subtle secondary and super-secondary structures can be included with the same procedures. The subsequent determination of their relative weight based on the sequence and the inclusion of accurate long range interactions, can endow the model with the capability of predicting the folding, besides correctly reproducing the internal dynamics and thermodynamics

SecStAnT: Secondary Structure Analysis Tool for data selection, statistics and models building

Abstract Motivation: Atomistic or coarse grained (CG) potentials derived from statistical distributions of internal variables have recently become popular due to the need of simplified interactions for reaching larger scales in simulations or more efficient conformational space sampling. However, the process of parameterization of accurate and predictive statistics-based force fields requires a huge amount of work and is prone to the introduction of bias and errors. Results: This article introduces SecStAnT, a software for the creation and analysis of protein structural datasets with user-defined primary/secondary structure composition, with a particular focus on the CG representation. In addition, the possibility of managing different resolutions and the primary/secondary structure selectivity allow addressing the mapping-backmapping of atomistic to CG representation and study the secondary to primary structure relations. Sample datasets and distributions are reported, including interpretation of structural features. Availability and implementation: SecStAnT is available free of charge at secstant.sourceforge.net/. Source code is freely available on request, implemented in Java and supported on Linux, MS Windows and OSX. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online

25th annual computational neuroscience meeting: CNS-2016

The same neuron may play different functional roles in the neural circuits to which it belongs. For example, neurons in the Tritonia pedal ganglia may participate in variable phases of the swim motor rhythms [1]. While such neuronal functional variability is likely to play a major role the delivery of the functionality of neural systems, it is difficult to study it in most nervous systems. We work on the pyloric rhythm network of the crustacean stomatogastric ganglion (STG) [2]. Typically network models of the STG treat neurons of the same functional type as a single model neuron (e.g. PD neurons), assuming the same conductance parameters for these neurons and implying their synchronous firing [3, 4]. However, simultaneous recording of PD neurons shows differences between the timings of spikes of these neurons. This may indicate functional variability of these neurons. Here we modelled separately the two PD neurons of the STG in a multi-neuron model of the pyloric network. Our neuron models comply with known correlations between conductance parameters of ionic currents. Our results reproduce the experimental finding of increasing spike time distance between spikes originating from the two model PD neurons during their synchronised burst phase. The PD neuron with the larger calcium conductance generates its spikes before the other PD neuron. Larger potassium conductance values in the follower neuron imply longer delays between spikes, see Fig. 17.Neuromodulators change the conductance parameters of neurons and maintain the ratios of these parameters [5]. Our results show that such changes may shift the individual contribution of two PD neurons to the PD-phase of the pyloric rhythm altering their functionality within this rhythm. Our work paves the way towards an accessible experimental and computational framework for the analysis of the mechanisms and impact of functional variability of neurons within the neural circuits to which they belong

Décomposition des circuits de la rétine : comprendre le rôle des cellules bipolaires à bâtonnets avec une manipulation optique

In the retina, photoreceptors transduce light into electrical currents that are transmitted to bipolar cells before reaching ganglion cells, which send their spike trains to the brain. Each ganglion cell is sensitive to the stimulation of specific location of the visual field, its receptive field. Different types of ganglion cells (RGC) encode different features of the visual scene. In this work we aim at understanding the role of a specific type of bipolar cells: rod bipolar cells (RBC). We study their role in the computation of complex features by RGCs. We focus on two populations of RGCs: OFF Direction Selective RGCs, encoding visual motion, and OFF alpha RGCs, which have an OFF center ON surround organization of the receptive field. I present a new method to dissect the retinal circuit, which combines a highly precise optical activation of RBCs with an efficient recording of the RGCs. In order to manipulate RBCs, I express an optogenetic actuator specifically in these cells. I was able to selectively stimulate a specific type of bipolar cells while recording the impact of this stimulation on ganglion cells. I found that OFF direction selective RGCs receive an asymmetric input from RBCs, biased towards the preferred side, and that RBCs activate distant responses in OFF alpha RGCs, probably because they are involved in the ON surround computation. These results suggest that rod bipolar cells are a key element of two canonical computations performed in the retina. More generally, it shows that a precise dissection neural circuits is crucial to understand their function.Dans la rétine, les photorécepteurs convertissent la lumière en courants électriques qui sont transmis aux cellules bipolaires avant d'atteindre les cellules ganglionnaires (RGC), qui envoient leurs potentiels d’action au cerveau. Chaque RGC est sensible à la stimulation d’un emplacement spécifique du champ visuel, son champ récepteur. Différents types de RGCs codent différentes caractéristiques de la scène visuelle. Dans ce travail, nous cherchons à comprendre le rôle d’un type spécifique de cellules bipolaires: les cellules bipolaires à bâtonnets (RBC). Nous étudions leur rôle dans les calculs effectués par les RGCs. Nous nous concentrons sur deux populations de RGCs: les cellules sélectives à la direction, qui codent le mouvement visuel, et les RGC s OFF alpha, qui ont un champ récepteur antagoniste en centre-pourtour. Je présente une nouvelle méthode pour disséquer le circuit rétinien, qui combine une activation optique très précise des RBCs avec un enregistrement efficace des RGCs. Afin de manipuler les RBCs, j'exprime une protéine optogénétique sélectivement dans ces cellules. J'ai pu stimuler sélectivement les RBCs tout en enregistrant l'impact de cette stimulation sur les RGCs. J'ai trouvé que les RGC sélectives à la direction recevaient une entrée asymétrique des RBCs, et que les RBCs activent les réponses lointaines dans les RGCs OFF alpha, probablement parce qu’elles sont impliquées dans la formation du pourtour du champ récepteur. Ces résultats suggèrent que les RBCs sont un élément clé de deux calculs canoniques de la rétine. Plus généralement, il montre qu’une dissection précise des circuits neuronaux est cruciale pour comprendre leur fonction

Minimalist Model for the Dynamics of Helical Polypeptides: A Statistic-Based Parametrization

Low-resolution models are often used to address macroscopic time and size scales in molecular dynamics simulations of biomolecular systems. Coarse graining is often coupled to knowledge-based parametrization to obtain empirical potentials able to reproduce the system thermodynamic behavior. Here, a minimalist coarse grained (GC) model for the helical structures of proteins is reported. A knowledge-based parametrization strategy is coupled to the explicit inclusion of hydrogen-bonding-related terms, resulting in an accurate reproduction of the structure and dynamics of each single helical type, as well as the internal conformational variables correlation. The proposed strategy of basing the force field terms on real physicochemical interactions is transferable to different secondary structures. Thus, this work, though conclusive for helices, is to be considered the first of a series devoted to the application of the knowledge-based, physicochemical model to extended secondary structures and unstructured proteins

Optimization of Analytical Potentials for Coarse-Grained Biopolymer Models

The increasing trend in the recent literature on coarse grained (CG) models testifies their impact in the study of complex systems. However, the CG model landscape is variegated: even considering a given resolution level, the force fields are very heterogeneous and optimized with very different parametrization procedures. Along the road for standardization of CG models for biopolymers, here we describe a strategy to aid building and optimization of statistics based analytical force fields and its implementation in the software package AsParaGS (Assisted Parameterization platform for coarse Grained modelS). Our method is based on the use and optimization of analytical potentials, optimized by targeting internal variables statistical distributions by means of the combination of different algorithms (i.e., relative entropy driven stochastic exploration of the parameter space and iterative Boltzmann inversion). This allows designing a custom model that endows the force field terms with a physically sound meaning. Furthermore, the level of transferability and accuracy can be tuned through the choice of statistical data set composition. The methodillustrated by means of applications to helical polypeptidesalso involves the analysis of two and three variable distributions, and allows handling issues related to the FF term correlations. AsParaGS is interfaced with general-purpose molecular dynamics codes and currently implements the “minimalist” subclass of CG models (i.e., one bead per amino acid, Cα based). Extensions to nucleic acids and different levels of coarse graining are in the course