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Intrinsically disordered proteins (IDPs) engage in various fundamental biological activities, and their behavior is of particular importance for a better understanding of the verbose but well-organized signal transduction in cells. IDPs exhibit uniquely paradoxical features with low affinity but simultaneously high specificity in recognizing their binding targets. The transcription factor p53 plays a crucial role in cancer suppression, carrying out some of its biological functions using its disordered regions, such as N-terminal transactivation domain 2 (TAD2). Exploration of the binding and unbinding processes between proteins is challenging, and the inherently disordered properties of these regions further complicate the issue. Computer simulations are a powerful tool to complement the experiments to fill gaps to explore the binding/unbinding processes between proteins. Here, we investigated the binding mechanism between p300 Taz2 and p53 TAD2 through extensive molecular dynamics (MD) simulations using the physics- based UNited RESidue (UNRES) force field with additional Go̅-like potentials. Distance restraints extracted from the NMR- resolved structures were imposed on intermolecular residue pairs to accelerate binding simulations, in which Taz2 was immobilized in a native-like conformation and disordered TAD2 was fully free. Starting from six structures with TAD2 placed at different positions around Taz2, we observed a metastable intermediate state in which the middle helical segment of TAD2 is anchored in the binding pocket, highlighting the significance of the TAD2 helix in directing protein recognition. Physics-based binding simulations show that successful binding is achieved after a series of stages, including (1) protein collisions to initiate the formation of encounter complexes, (2) partial attachment of TAD2, and finally (3) full attachment of TAD2 to the correct binding pocket of Taz2. Furthermore, machine-learning-based PathDetect-SOM was used to identify two binding pathways, the encounter complexes, and the intermediate states. 

Rooted in dynamic systems theory, convergent cross mapping (CCM) has attracted increased attention recently due to its capability in detecting linear and nonlinear causal coupling in both random and deterministic settings. One limitation with CCM is that it uses both past and future values to predict the current value, which is inconsistent with the widely accepted definition of causality, where it is assumed that the future values of one process cannot influence the past of another. To overcome this obstacle, in our previous research, we introduced the concept of causalized convergent cross mapping (cCCM), where future values are no longer used to predict the current value. In this paper, we focus on the implementation of cCCM in causality analysis. More specifically, we demonstrate the effectiveness of cCCM in identifying both linear and nonlinear causal coupling in various settings through a large number of examples, including Gaussian random variables with additive noise, sinusoidal waveforms, autoregressive models, stochastic processes with a dominant spectral component embedded in noise, deterministic chaotic maps, and systems with memory, as well as experimental fMRI data. In particular, we analyze the impact of shadow manifold construction on the performance of cCCM and provide detailed guidelines on how to configure the key parameters of cCCM in different applications. Overall, our analysis indicates that cCCM is a promising and easy-to-implement tool for causality analysis in a wide spectrum of applications.

 

The proteins of the Bin/Amphiphysin/Rvs167 (BAR) domain superfamily arebelieved to induce membrane curvature. PICK1 is a distinctive protein that consists of both a BAR anda PDZ domain, and it has been associated with numerous diseases. It is known to facilitate membranecurvature during receptor-mediated endocytosis. In addition to understanding how the BAR domainfacilitates membrane curvature, it's particularly interesting to unravel the hidden links between thestructural and mechanical properties of the PICK1 BAR domain.

This paper employs steered molecular dynamics (SMD) to investigate the mechanical propertiesassociated with structural changes in the PICK1 BAR domains.

Our findings suggest that not only do helix kinks assist in generating curvature of BAR domains,but they may also provide the additional flexibility required to initiate the binding betweenBAR domains and the membrane

We have observed a complex interaction network within the BAR monomer and at thebinding interface of the two BAR monomers. This network is crucial for maintaining the mechanicalproperties of the BAR dimer. Owing to this interaction network, the PICK1 BAR dimer exhibits differentresponses to external forces applied in opposite directions.

 

Convergent cross-mapping (CCM) has attracted increased attention recently due to its capability to detect causality in nonseparable systems under deterministic settings, which may not be covered by the traditional Granger causality. From an information-theoretic perspective, causality is often characterized as the directed information (DI) flowing from one side to the other. As information is essentially nondeterministic, a natural question is: does CCM measure DI flow? Here, we first causalize CCM so that it aligns with the presumption in causality analysis—the future values of one process cannot influence the past of the other, and then establish and validate the approximate equivalence of causalized CCM (cCCM) and DI under Gaussian variables through both theoretical derivations and fMRI-based brain network causality analysis. Our simulation result indicates that, in general, cCCM tends to be more robust than DI in causality detection. The underlying argument is that DI relies heavily on probability estimation, which is sensitive to data size as well as digitization procedures; cCCM, on the other hand, gets around this problem through geometric cross-mapping between the manifolds involved. Overall, our analysis demonstrates that cross-mapping provides an alternative way to evaluate DI and is potentially an effective technique for identifying both linear and nonlinear causal coupling in brain neural networks and other settings, either random or deterministic, or both.

 

Abstract We introduce and analyze a partially augmented fully mixed formulation and a mixed finite element method for the coupled problem arising in the interaction between a free fluid and a poroelastic medium. The flows in the free fluid and poroelastic regions are governed by the Navier–Stokes and Biot equations, respectively, and the transmission conditions are given by mass conservation, balance of fluid force, conservation of momentum and the Beavers–Joseph–Saffman condition. We apply dual-mixed formulations in both domains, where the symmetry of the Navier–Stokes and poroelastic stress tensors is imposed in an ultra-weak and weak sense. In turn, since the transmission conditions are essential in the fully mixed formulation, they are imposed weakly by introducing the traces of the structure velocity and the poroelastic medium pressure on the interface as the associated Lagrange multipliers. Furthermore, since the fluid convective term requires the velocity to live in a smaller space than usual, we augment the variational formulation with suitable Galerkin-type terms. Existence and uniqueness of a solution are established for the continuous weak formulation, as well as a semidiscrete continuous-in-time formulation with nonmatching grids, together with the corresponding stability bounds and error analysis with rates of convergence. Several numerical experiments are presented to verify the theoretical results and illustrate the performance of the method for applications to arterial flow and flow through a filter.