Spatial-temporal order-disorder transition in angiogenic NOTCH signaling controls cell fate specification

Angiogenesis is a morphogenic process resulting in the formation of new blood vessels from pre-existing ones, usually in hypoxic micro-environments. The initial steps of angiogenesis depend on robust differentiation of oligopotent endothelial cells into the Tip and Stalk phenotypic cell fates, controlled by NOTCH-dependent cell-cell communication. The dynamics of spatial patterning of this cell fate specification are only partially understood. Here, by combining a controlled experimental angiogenesis model with mathematical and computational analyses, we find that the regular spatial Tip-Stalk cell patterning can undergo an order-disorder transition at a relatively high input level of a pro-angiogenic factor VEGF. The resulting differentiation is robust but temporally unstable for most cells, with only a subset of presumptive Tip cells leading sprout extensions. We further find that sprouts form in a manner maximizing their mutual distance, consistent with a Turing-like model that may depend on local enrichment and depletion of fibronectin. Together, our data suggest that NOTCH signaling mediates a robust way of cell differentiation enabling but not instructing subsequent steps in angiogenic morphogenesis, which may require additional cues and self-organization mechanisms. This analysis can assist in further understanding of cell plasticity underlying angiogenesis and other complex morphogenic processes.

Atomic Interactions and Order-Disorder Transition in FCC-Type FeCoNiAl1-xTix High-Entropy Alloys

Single-phase high-entropy alloys with compositionally disordered elemental arrangements have excellent strength, but show a serious embrittlement effect with increasing strength. Precipitation-hardened high-entropy alloys, such as those strengthened by L1₂-type ordered intermetallics, possess a superior synergy of strength and ductility. In this work, we employ first-principles calculations and thermodynamic simulations to explore the atomic interactions and order-disorder transitions in FeCoNiAl_1-xTi_x high-entropy alloys. Our calculated results indicate that the atomic interactions depend on the atomic size of the alloy components. The thermodynamic stability behaviors of L1₂ binary intermetallics are quite diverse, while their atomic arrangements are short-range in FeCoNiAl_1-xTi_x high-entropy alloys. Moreover, the order-disorder transition temperatures decrease with increasing Ti content in FeCoNiAl_1-xTi_x high-entropy alloys, the characteristics of order-disorder transition from first-principles calculations are in line with experimental observations and CALPHAD simulations. The results of this work provide a technique strategy for proper control of the order-disorder transitions that can be used for further optimizing the microstructure characteristics as well as the mechanical properties of FeCoNiAl_1-xTi_xhigh-entropy alloys.

Ultrahigh-pressure disordered eight-coordinated phase of Mg2GeO4: Analogue for super-Earth mantles

This work presents experimental evidence for the formation of a phase with eightfold coordination of germanium by oxygen in Mg₂GeO₄, a well-known analogue of Mg₂SiO₄ at extreme pressure and temperatures. Using both experiments and theoretical computations, we have determined the structure, equation of state, and phase stability of this phase at pressures above 200 GPa. The existence of this phase in the silicate counterpart may play an important role in the structure and dynamics of the deep interiors of large, rocky exoplanets.

Mg₂GeO₄ is important as an analog for the ultrahigh-pressure behavior of Mg₂SiO₄, a major component of planetary interiors. In this study, we have investigated magnesium germanate to 275 GPa and over 2,000 K using a laser-heated diamond anvil cell combined with in situ synchrotron X-ray diffraction and density functional theory (DFT) computations. The experimental results are consistent with the formation of a phase with disordered Mg and Ge, in which germanium adopts eightfold coordination with oxygen: the cubic, Th₃P₄-type structure. DFT computations suggest partial Mg-Ge order, resulting in a tetragonal I4¯2d structure indistinguishable from I4¯3d Th₃P₄ in our experiments. If applicable to silicates, the formation of this highly coordinated and intrinsically disordered phase may have important implications for the interior mineralogy of large, rocky extrasolar planets.

Interaction network effects on position- and velocity-based models of collective motion

We study how the structure of the interaction network affects self-organized collective motion in two minimal models of self-propelled agents: the Vicsek model and the Active-Elastic (AE) model. We perform simulations with topologies that interpolate between a nearest-neighbour network and random networks with different degree distributions to analyse the relationship between the interaction topology and the resilience to noise of the ordered state. For the Vicsek case, we find that a higher fraction of random connections with homogeneous or power-law degree distribution increases the critical noise, and thus the resilience to noise, as expected due to small-world effects. Surprisingly, for the AE model, a higher fraction of random links with power-law degree distribution can decrease this resilience, despite most links being long-range. We explain this effect through a simple mechanical analogy, arguing that the larger presence of agents with few connections contributes localized low-energy modes that are easily excited by noise, thus hindering the collective dynamics. These results demonstrate the strong effects of the interaction topology on self-organization. Our work suggests potential roles of the interaction network structure in biological collective behaviour and could also help improve decentralized swarm robotics control and other distributed consensus systems.

Structural and Dynamical Order of a Disordered Protein: Molecular Insights into Conformational Switching of PAGE4 at the Systems Level

Folded proteins show a high degree of structural order and undergo (fairly constrained) collective motions related to their functions. On the other hand, intrinsically disordered proteins (IDPs), while lacking a well-defined three-dimensional structure, do exhibit some structural and dynamical ordering, but are less constrained in their motions than folded proteins. The larger structural plasticity of IDPs emphasizes the importance of entropically driven motions. Many IDPs undergo function-related disorder-to-order transitions driven by their interaction with specific binding partners. As experimental techniques become more sensitive and become better integrated with computational simulations, we are beginning to see how the modest structural ordering and large amplitude collective motions of IDPs endow them with an ability to mediate multiple interactions with different partners in the cell. To illustrate these points, here, we use Prostate-associated gene 4 (PAGE4), an IDP implicated in prostate cancer (PCa) as an example. We first review our previous efforts using molecular dynamics simulations based on atomistic AWSEM to study the conformational dynamics of PAGE4 and how its motions change in its different physiologically relevant phosphorylated forms. Our simulations quantitatively reproduced experimental observations and revealed how structural and dynamical ordering are encoded in the sequence of PAGE4 and can be modulated by different extents of phosphorylation by the kinases HIPK1 and CLK2. This ordering is reflected in changing populations of certain secondary structural elements as well as in the regularity of its collective motions. These ordered features are directly correlated with the functional interactions of WT-PAGE4, HIPK1-PAGE4 and CLK2-PAGE4 with the AP-1 signaling axis. These interactions give rise to repeated transitions between (high HIPK1-PAGE4, low CLK2-PAGE4) and (low HIPK1-PAGE4, high CLK2-PAGE4) cell phenotypes, which possess differing sensitivities to the standard PCa therapies, such as androgen deprivation therapy (ADT). We argue that, although the structural plasticity of an IDP is important in promoting promiscuous interactions, the modulation of the structural ordering is important for sculpting its interactions so as to rewire with agility biomolecular interaction networks with significant functional consequences.

Structural consequences of hereditary spastic paraplegia disease-related mutations in kinesin

A wide range of mutations in the kinesin motor Kif5A have been linked to a neuronal disorder called hereditary spastic paraplegia (HSP). The position of these mutations can vary, and a range of different motile behaviors have been observed, indicating that the HSP mutants can alter distinct aspects of kinesin mechanochemistry. While focusing on four key HSP-associated mutants, this study examined the structural and dynamic perturbations that arise from these mutations using a series of different computational methods, ranging from bioinformatics analyses to all-atom simulations, that account for solvent effects explicitly. We show that two catalytic domain mutations (R280S and K253N) reduce the microtubule (MT) binding affinity of the kinesin head domains appreciably, while N256S has a much smaller impact. Bioinformatics analysis suggests that the stalk mutation A361V perturbs motor dimerization. Subsequent integration of these effects into a coarse-grained structure-based model of dimeric kinesin revealed that the order-disorder transition of the neck linker is substantially affected, indicating a hampered directionality and processivity of kinesin. The present analyses therefore suggest that, in addition to kinesin-MT binding and coiled-coil dimerization, HSP mutations affecting motor stepping transitions and processivity can lead to disease.

PAGE4 and Conformational Switching: Insights from Molecular Dynamics Simulations and Implications for Prostate Cancer

Prostate-associated gene 4 (PAGE4) is an intrinsically disordered protein implicated in prostate cancer. Thestress-response kinase homeodomain-interacting protein kinase 1 (HIPK1) phosphorylates two residues in PAGE4, serine 9 and threonine 51. Phosphorylation of these two residues facilitates the interaction of PAGE4 with activator protein-1 (AP-1) transcription factor complex to potentiate AP-1's activity. In contrast, hyperphosphorylation of PAGE4 by CDC-like kinase 2 (CLK2) attenuates this interaction with AP-1. Small-angleX-ray scattering and single-molecule fluorescence resonance energy transfer measurements have shown that PAGE4 expands upon hyperphosphorylation and that this expansion is localized to its N-terminal half. To understand the interactions underlying this structural transition, we performed molecular dynamics simulations using Atomistic AWSEM, a multi-scale molecular model that combines atomistic and coarse-grained simulation approaches. Our simulations show that electrostatic interactions drive transient formation of an N-terminal loop, the destabilization of which accounts for the dramatic change in size upon hyperphosphorylation. Phosphorylation also changes the preference of secondary structure formation of the PAGE4 ensemble, which leads to a transition between states that display different degrees of disorder. Finally, we construct a mechanism-based mathematical model that allows us to capture the interactions ofdifferent phosphoforms of PAGE4 with AP-1 and its downstream target, the androgen receptor (AR)-a key therapeutic target in prostate cancer. Our model predicts intracellular oscillatory dynamics of HIPK1-PAGE4, CLK2-PAGE4, and AR activity, indicating phenotypic heterogeneity in an isogenic cell population. Thus, conformational switching of PAGE4 may potentially affect the efficiency of therapeutically targeting AR activity.

Reconstructive phase transition in (NH4)3TiF7 accompanied by the ordering of TiF6 octahedra

An unusual phase transition P4/mnc → Pa\bar 3 has been detected after cooling the (NH4)3TiF7 compound. Some TiF6 octahedra, which are disordered in the room-temperature tetragonal structure, become ordered in the low-temperature cubic phase due to the disappearance of the fourfold axis. Other TiF6 octahedra undergo large rotations resulting in huge displacements of the F atoms by 1.5-1.8 Å that implies a reconstructive phase transition. It was supposed that phases P4/mbm and Pm\bar 3m could be a high-temperature phase and a parent phase, respectively, in (NH4)3TiF7. Therefore, the sequence of phase transitions can be written as Pm\bar 3m → P4/mbm → P4/mnc → Pa\bar 3. The interrelation between (NH4)3TiF7, (NH4)3GeF7 and (NH4)3PbF7 is found, which allows us to suppose phase transitions in relative compounds.