Insight into G-DNA Structural Polymorphism and Folding from Sequence and Loop Connectivity through Free Energy Analysis

The lengths of G-tracts and their connecting loop sequences determine G-quadruplex folding and stability. Complete understanding of the sequence–structure relationships remains elusive. Here, single-loop G-quadruplexes were investigated using explicit solvent molecular dynamics (MD) simulations to characterize the effect of loop length, loop sequence, and G-tract length on the folding topologies and stability of G-quadruplexes. Eight loop types, including different variants of lateral, diagonal, and propeller loops, and six different loop sequences [d0 (i.e., no intervening residues in the loop), dT, dT₂, dT₃, dTTA, and dT₄] were considered through MD simulation and free energy analysis. In most cases the free energetic estimates agree well with the experimental observations. The work also provides new insight into G-quadruplex folding and stability. This includes reporting the observed instability of the left propeller loop, which extends the rules for G-quadruplex folding. We also suggest a plausible explanation why human telomere sequences predominantly form hybrid-I and hybrid-II type structures in K⁺ solution. Overall, our calculation results indicate that short loops generally are less stable than longer loops, and we hypothesize that the extreme stability of sequences with very short loops could possibly derive from the formation of parallel multimers. The results suggest that free energy differences, estimated from MD and free energy analysis with current force fields and simulation protocols, are able to complement experiment and to help dissect and explain loop sequence, loop length, and G-tract length and orientation influences on G-quadruplex structure

Conceptions of the good, rivalry, and liberal neutrality

Liberal neutrality is assumed to pertain to rival conceptions of the good. The nature of the rivalry between conceptions of the good is pivotal to the coherence, scope and realisation of liberal neutrality. Yet, liberal theorists have said very little about rivalry. This paper attempts to fill this gap by reviewing three conceptions of rivalry: incompatibility rivalry, intra-domain rivalry and state power rivalry. I argue that state power rivalry is the morally relevant conception of rivalry, and that it has significant implications for the scope and realisation of liberal neutrality. I conclude that in the light of state power rivalry, the only feasible liberal neutral state is a very minimal one

Mapping the Functional Binding Sites of Cholesterol in β₂‑Adrenergic Receptor by Long-Time Molecular Dynamics Simulations

Cholesterol, an abundant membrane component in both lipid rafts and caveolae of cell membrane, plays a crucial role in regulating the function and organization of various G-protein coupled receptors (GPCRs). However, the underlying mechanism for cholesterol-GPCR interaction is still unclear. To this end, we performed a series of microsecond molecular dynamics (MD) simulations on β₂-adrenergic receptor (β₂AR) in the presence and absence of cholesterol molecules in the POPC bilayer. The unbiased MD simulation on the system with cholesterols reveals that cholesterol molecules can spontaneously diffuse to seven sites on the β₂AR surfaces, three in the extracellular leaflet (e1–e3) and four in the intracellular leaflet (i1, i2, i4, and i5). The MD simulation identifies three cholesterol-binding sites (i2, e2, and e3) that are also observed in the crystal structures of several GPCRs. Cholesterol binding to site e1 lock Trp313^7.40 into a certain conformation that may facilitate ligand–receptor binding, and cholesterol binding to site i2 provides a structural support for the reported cholesterol-mediate dimeric form of β₂AR (PDB code 2RH1). In addition, both competitive and cooperative effects between cholesterols and phospholipids in binding to β₂AR were observed in our MD simulations. Together, these results provide new insights into cholesterol–GPCR interactions

Binding Competition to the POPG Lipid Bilayer of Ca²⁺, Mg²⁺, Na⁺, and K⁺ in Different Ion Mixtures and Biological Implication

Ion mixtures are prevalent in both cytosol and the exterior of a plasma membrane with variable compositions and concentrations. Although abundant MD simulations have been performed to study the effects of single ion species on the structures of lipid bilayers, our understanding of the influence of the ion mixture on membranes is still limited; for example, the competition mechanism of different ions in binding with lipids is not clearly addressed yet. Here, microsecond MD simulations were carried out to study the effects of the mixtures of Ca²⁺, Mg²⁺, Na⁺, and K⁺ ions on a 1-palmitoyl-2-oleoyl-<i>sn</i>-glycero-3-phosphoglycerol (POPG) bilayer. It has been revealed that the binding efficiency of these ions with POPG lipids is in the following order, Ca²⁺ > Mg²⁺ > Na⁺ > K⁺. The binding free energy of Ca²⁺ to the lipid bilayer is ∼−4.0 kcal/mol, which is much lower than those of other ions. This result explains why the effects of the ion mixture on membranes are particularly sensitive to the concentration of calcium. The on-rates of different ions do not have a large difference, while the off-rate of Ca²⁺ is 2–3 orders of magnitude smaller than those of the others. Therefore, the strongest binding affinity of Ca²⁺ is mainly determined by its smallest off-rate. In addition, our study suggests that the structure of the lipid bilayer is influenced dominantly by the concentration of Ca²⁺ ions. The simulation results also provide a good explanation for a variety of biological processes relevant to Ca²⁺ and Mg²⁺ regulations, such as membrane fusion

Conformational Transition and Energy Landscape of ErbB4 Activated by Neuregulin1β: One Microsecond Molecular Dynamics Simulations

ErbB4, a receptor tyrosine kinase of the ErbB family, plays crucial roles in cell growth and differentiation, especially in the development of the heart and nervous system. Ligand binding to its extracellular region could modulate the activation process. To understand the mechanism of ErbB4 activation induced by ligand binding, we performed one microsecond molecular dynamics (MD) simulations on the ErbB4 extracellular region (ECR) with and without its endogenous ligand neuregulin1β (NRG1β). The conformational transition of the ECR-ErbB4/NRG1β complex from a tethered inactive conformation to an extended active-like form has been observed, while such large and function-related conformational change has not been seen in the simulation on the ECR-ErbB4, suggesting that ligand binding is indeed the active inducing force for the conformational transition and further dimerization. On the basis of MD simulations and principal component analysis, we constructed a rough energy landscape for the conformational transition of ECR-ErbB4/NRG1β complex, suggesting that the conformational change from the inactive state to active-like state involves a stable conformation. The energy barrier for the tether opening was estimated as ∼2.7 kcal/mol, which is very close to the experimental value (1–2 kcal/mol) reported for ErbB1. On the basis of the simulation results, an atomic mechanism for the ligand-induced activation of ErbB4 was postulated. The present MD simulations provide a new insight into the conformational changes underlying the activation of ErbB4