Comparative Studies of Disordered Proteins with Similar Sequences: Application to Aβ40 and Aβ42

Quantitative comparisons of intrinsically disordered proteins (IDPs) with similar sequences, such as mutant forms of the same protein, may provide insights into IDP aggregation—a process that plays a role in several neurodegenerative disorders. Here we describe an approach for modeling IDPs with similar sequences that simplifies the comparison of the ensembles by utilizing a single library of structures. The relative population weights of the structures are estimated using a Bayesian formalism, which provides measures of uncertainty in the resulting ensembles. We applied this approach to the comparison of ensembles for Aβ40 and Aβ42. Bayesian hypothesis testing finds that although both Aβ species sample β-rich conformations in solution that may represent prefibrillar intermediates, the probability that Aβ42 samples these prefibrillar states is roughly an order of magnitude larger than the frequency in which Aβ40 samples such structures. Moreover, the structure of the soluble prefibrillar state in our ensembles is similar to the experimentally determined structure of Aβ that has been implicated as an intermediate in the aggregation pathway. Overall, our approach for comparative studies of IDPs with similar sequences provides a platform for future studies on the effect of mutations on the structure and function of disordered proteins

Learning to Evolve Structural Ensembles of Unfolded and Disordered Proteins Using Experimental Solution Data

We have developed a Generative Recurrent Neural Networks (GRNN) that learns the probability of the next residue torsions $X_{i+1}=\ [\phi_{i+1},\psi_{i+1},\omega _{i+1}, \chi_{i+1}]$from the previous residue in the sequence$X_i$ to generate new IDP conformations. In addition, we couple the GRNN with a Bayesian model, X-EISD, in a reinforcement learning step that biases the probability distributions of torsions to take advantage of experimental data types such as J-couplingss, NOEs and PREs. We show that updating the generative model parameters according to the reward feedback on the basis of the agreement between structures and data improves upon existing approaches that simply reweight static structural pools for disordered proteins. Instead the GRNN "DynamICE" model learns to physically change the conformations of the underlying pool to those that better agree with experiment

Intrinsically Disordered Proteins: Where Computation Meets Experiment

Proteins are heteropolymers that play important roles in virtually every biological reaction. While many proteins have well-defined three-dimensional structures that are inextricably coupled to their function, intrinsically disordered proteins (IDPs) do not have a well-defined structure, and it is this lack of structure that facilitates their function. As many IDPs are involved in essential cellular processes, various diseases have been linked to their malfunction, thereby making them important drug targets. In this review we discuss methods for studying IDPs and provide examples of how computational methods can improve our understanding of IDPs. We focus on two intensely studied IDPs that have been implicated in very different pathologic pathways. The first, p53, has been linked to over 50% of human cancers, and the second, Amyloid-β (Aβ), forms neurotoxic aggregates in the brains of patients with Alzheimer’s disease. We use these representative proteins to illustrate some of the challenges associated with studying IDPs and demonstrate how computational tools can be fruitfully applied to arrive at a more comprehensive understanding of these fascinating heteropolymers.National Science Foundation (U.S.). Directorate for Biological Sciences. Postdoctoral Research Fellowship (Grant 1309247

A scalable approach to the computation of invariant measures for high-dimensional Markovian systems

The Markovian invariant measure is a central concept in many disciplines. Conventional numerical techniques for data-driven computation of invariant measures rely on estimation and further numerical processing of a transition matrix. Here we show how the quality of data-driven estimation of a transition matrix crucially depends on the validity of the statistical independence assumption for transition probabilities. Moreover, the cost of the invariant measure computation in general scales cubically with the dimension - and is usually unfeasible for realistic highdimensional systems. We introduce a method relaxing the independence assumption of transition probabilities that scales quadratically in situations with latent variables. Applications of the method are illustrated on the Lorenz-63 system and for the molecular dynamics (MD) simulation data of the alpha-synuclein protein. We demonstrate how the conventional methodologies do not provide good estimates of the invariant measure based upon the available alpha-synuklein MD data. Applying the introduced approach to these MD data we detect two robust meta-stable states of alpha-synuclein and a linear transition between them, involving transient formation of secondary structure, qualitatively consistent with previous purely experimental reports

A novel regulatory unit in the N-terminal region of c-Src

[eng] c-Src is a central player in several cellular signaling pathways. It controls impor- tant cellular processes like cellular proliferation, survival or motility. Therefore, a number of tumoral diseases have been related to abnormal c-Src activity. Among them, colorectal cancer stands out, as c-Src deregulation correlates with tumor progression and clinical outcome. This tyrosine kinase is part of a larger group of functionally and structurally related proteins termed Src Family Kinases. These proteins share the same domain architecture: a cassette formed by a catalytic domain (SH1), two reg- ulatory domains, SH2 and SH3, and a variable intrinsically disordered region (the Unique domain) that ultimately anchors to the inner face of the cellular membrane via the N-terminal SH4 domain, also disordered. The sequence and structure of the cassette are highly conserved, and thus unsurprisingly Src Family Kinases perform closely related and often overlapping functions. However, the role of intrinsically disordered regions has remained unclear, although they are known to be functionally relevant. In this work, the structural and functional relationship between the intrinsically disordered SH4 and Unique domains with the neighboring folded SH3 domain in c-Src is explored. Interactions between disordered and ordered proteins are often characterized by the formation of complexes that are specific and functional but structurally heterogeneous. Moreover, conformational plasticity is a fundamental feature for function. These assemblies are known as fuzzy complexes. Here this theoretical framework, usually applied to isolated partners, is extended to the intramolecular interface between covalently bound domains instead of isolated pairs. The concept of fuzzy binding is also used in order to describe interactions based on sets of dynamic, transient, and promiscuous contacts between ill-defined sets of interactors. In order to characterize the system, an integrative strategy using short and long range Nuclear Magnetic Resonance techniques and Small Angle X-ray Scattering is applied to several constructs containing different combinations of bound or isolated domains. It is demonstrated that the folded SH3 domain acts as a scaffold for the disordered region, which interacts in a specific manner with its partner. Both disordered domains, SH4 and Unique, are involved in the process albeit they contribute differently. Additionally, it is shown that the Unique domain is not a random coil, but contains a significant degree of pre-arrangement that is independent of the scaffold. Sequence determinants are then searched by comparison of the sequences of different Src Family Kinases. Four conserved phenylalanine residues are found and their implication in Unique domain pre-organization and Unique:SH3 domain interaction tested. All these amino acids are found to favor compaction of the intrinsically disordered region, and at the same time to perturb close contact with the scaffold. In addition, mutations in the interacting zones of the SH3 domain are also studied to test reciprocity. In all, the fuzzy complex model is proven for the SH4:Unique:SH3 system. Then, the results are extrapolated to the full-length c-Src to test its biological relevance. A co evolutionary analysis suggests that the fuzzy model may be a general feature for the whole Src Family, so the closest member of the family, Yes, is also tested experimentally. The initial results on long-range contacts suggests a similar arrangement between the scaffold and the disordered region. In all, it is suggested that plastic, fuzzy interfaces between ordered and disordered domains may be a relevant mode for the transmission of functional information within multidomain proteins. Finally, a first approach for a structural study of the c-Src fuzzy complex in a native-like lipid environment, including natural co-translational modifications, is presented. A protocol for sample preparation is developed and Dynamic Nuclear Polarization solid state NMR is shown to be an adequate tool for further analysis.[spa] c-Src es una tirosina quinasa clave en múltiples rutas de señalización celulares. Su desregulación ha sido asociada a diversos procesos tumorales, entre los que destaca el cáncer de cólon. Una actividad anómala de c-Src se correlaciona con el desarrollo tumoral y pronóstico clínico desfavorable. c-Src forma parte de un grupo de proteínas relacionadas estructural y funcional- mente, la Familia de Quinasas Src. Todas ellas comparten la misma arquitectura modular, que incluye un dominio catalítico (SH1), dos dominios regulatorios, SH2 y SH3, y a continuación una región variable intrínsecamente desordenada que incluye los dominios Único y SH4. Mientras que el segmento ordenado está bien caracterizado, el papel de la región desordenada no está claro, aunque es funcionalmente relevante. En este trabajo se explora la relación estructural y funcional entre la región desordenada y el dominio ordenado adyacente SH3. Dado que este tipo de interacciones implican un grado significativo de heterogeneidad estructural, se ha aplicado el concepto de unión difusa para caracterizar este sistema. Este marco teórico permite modelar interacciones basadas en contactos dinámicos y transitorios entre múltiples interactores vagamente definidos, que sin embargo son específicos y funcionales. Para ello, se ha usado una estrategia que implica el uso combinado de técnicas de Resonancia Magnética Nuclear de largo y corto alcance, así como Dispersión de rayos X a Bajo Ángulo. Se demuestra así que el dominio plegado SH3 actúa como armazón para la región desordenada, que a su vez contiene un grado significativo de pre-organización estructural. Se han identificado cuatro fenilalaninas en el dominio Único responsables de esta pre-formación que también afectan a la interacción entre la región desordenada y el armazón. Los resultados demuestran que el conjunto de dominios SH4, Único y SH3 forman una unidad funcional que puede ser definida como un complejo difuso. Además, datos teóricos y experimentales de otros miembros de la familia sugieren que el modelo difuso es una característica común de todos ellos. Finalmente, se ha demostrado que la Resonancia Magnética de estado sólido con Polarización Dinámica Nuclear es una técnica adecuada para el estudio estructural de c-Src unida a una matriz lipídica similar a la natural

RNA Folding Pathways in Stop Motion

We introduce a method for predicting RNA folding pathways, with an application to the most important RNA tetraloops. The method is based on the idea that ensembles of three-dimensional fragments extracted from high-resolution crystal structures are heterogeneous enough to describe metastable as well as intermediate states. These ensembles are first validated by performing a quantitative comparison against available solution NMR data of a set of RNA tetranucleotides. Notably, the agreement is better with respect to the one obtained by comparing NMR with extensive all-atom molecular dynamics simulations. We then propose a procedure based on diffusion maps and Markov models that makes it possible to obtain reaction pathways and their relative probabilities from fragment ensembles. This approach is applied to study the helix-to-loop folding pathway of all the tetraloops from the GNRA and UNCG families. The results give detailed insights into the folding mechanism that are compatible with available experimental data and clarify the role of intermediate states observed in previous simulation studies. The method is computationally inexpensive and can be used to study arbitrary conformational transitions