Identification of periodic attractors in Boolean networks using a priori information

Boolean networks (BNs) have been developed to describe various biological processes, which requires analysis of attractors, the long-term stable states. While many methods have been proposed to detection and enumeration of attractors, there are no methods which have been demonstrated to be theoretically better than the naive method and be practically used for large biological BNs. Here, we present a novel method to calculate attractors based on a priori information, which works much and verifiably faster than the naive method. We apply the method to two BNs which differ in size, modeling formalism, and biological scope. Despite these differences, the method presented here provides a powerful tool for the analysis of both networks. First, our analysis of a BN studying the effect of the microenvironment during angiogenesis shows that the previously defined microenvironments inducing the specialized phalanx behavior in endothelial cells (ECs) additionally induce stalk behavior. We obtain this result from an extended network version which was previously not analyzed. Second, we were able to heuristically detect attractors in a cell cycle control network formalized as a bipartite Boolean model (bBM) with 3158 nodes. These attractors are directly interpretable in terms of genotype-to-phenotype relationships, allowing network validation equivalent to an in silico mutagenesis screen. Our approach contributes to the development of scalable analysis methods required for whole-cell modeling efforts.

Microscopic Mechanism Angle of Repose in Friable Loess and Its Relationship With Slope Angle

The angle of repose in soil particles plays a key role in slope stability. There was a need for the investigation on the association between the angle of repose in loess particles and the angle of slopes. The fixed funnel methods with different particle sizes were carried out. The pressure of particle gravity weight was obtained based on the vibration stacking test. Four contact structures in loess particles were put forward including the triangular pyramid contact structure (TS), rectangular pyramid contact structure (RS), pentagonal pyramid contact structure (PS), and hexagon contact structure (HS). The particles transformed successively in four kinds of contact structures. The transformation of entropy value of the particles in different accumulation areas was discussed during the process of accumulation. The relationship between the natural angle of repose and the evolution of the contact structures was established. Combined with the existing experimental conclusion that loess particles transform in four stable states, in turn, the reason that the friction angle of uniform sand particles proposed by Shields in 1936 is 33° was explained. The formation theory of the loess angle of repose was well extended to speculate the formation process of the loess slope system. It is verified that loess slopes were mainly distributed under 30°.

Competing interactions give rise to two-state behavior and switch-like transitions in charge-rich intrinsically disordered proteins

The most commonly occurring intrinsically disordered proteins (IDPs) are polyampholytes, which are defined by the duality of low net charge per residue and high fractions of charged residues. Recent experiments have uncovered surprises regarding sequence-ensemble relationships of model polyampholytic IDPs. These include differences in conformational preferences for sequences with lysine vs. arginine, and the suggestion that well-mixed sequences either form globules or conformations with ensemble averages that are reminiscent of ideal chains wherein intra-chain and chain-solvent interactions are counterbalanced. Here, we explain these observations by analyzing results from atomistic simulations. We find that polyampholytic IDPs generally sample two distinct stable states, namely globules and self-avoiding walks. Globules are favored by electrostatic attractions between oppositely charged residues, whereas self-avoiding walks are favored by favorable free energies of hydration of charged residues. We find sequence-specific temperatures of bistability at which globules and self-avoiding walks can coexist. At these temperatures, ensemble averages over coexisting states give rise to statistics that resemble ideal chains without there being an actual counterbalancing of intra-chain and chain-solvent interactions. At equivalent temperatures, arginine-rich sequences tilt the preference toward globular conformations whereas lysine-rich sequences tilt the preference toward self-avoiding walks. This stems from intrinsic differences in free energies of hydration between arginine and lysine. We also identify differences between aspartate and glutamate containing sequences, whereby the shorter aspartate sidechain engenders preferences for metastable, necklace-like conformations. Finally, although segregation of oppositely charged residues within the linear sequence maintains the overall two-state behavior, compact states are highly favored by such systems.

Quantum Mechanical Study of Protonation of Oxygen Ligands in the Laccase Active Site Based on X-Ray Structures of Subatomic Resolution

Laccases are enzymes catalyzing oxidation of a wide range of organic and inorganic substrates accompanied by molecular oxygen reduction to water. Previously studies of oxygen reduction by laccases have recently been reported. They were based on single-crystal serial X-ray crystallography with increasing absorption doses at subatomic resolution, As a result, coordinates of all non-hydrogen atoms of the active site have been determined with high precision for both oxidized and reduced states of the enzyme. Those data can be used to clarify the mechanism of molecular oxygen reduction by laccases. However, the X-ray data lack information about protonation states of the oxygen ligands involved. Applying quantum mechanical calculations, in the present work protonation of oxygen ligands in the active site of laccase was determined for both reduced and oxidized states of the enzyme (the stable states observed in experiments at reduction of molecular oxygen in laccase). The high precision of X-ray-determined atom coordinates allowed us to simplify preliminary calculations of molecular mechanics for models used in the quantum mechanical calculations.

Conical Kresling origami and its applications to curvature and energy programming

Kresling origami has recently been widely used to design mechanical metamaterials, soft robots and smart devices, benefiting from its bistability and compression-twist coupling deformation. However, previous studies mostly focus on the traditional parallelogram Kresling patterns which can only be folded to cylindrical configurations. In this paper, we generalize the Kresling patterns by introducing free-form quadrilateral unit cells, leading to diverse conical folded configurations. The conical Kresling origami is modelled with a truss system, by which the stable states and energy landscapes are derived analytically. We find that the generalization preserves the bistable nature of parallelogram Kresling patterns, while enabling an enlarged design space of geometric parameters for structural and mechanical applications. To demonstrate this, we develop inverse design frameworks to employ conical Kresling origami to approximate arbitrary target surfaces of revolution and achieve prescribed energy landscapes. Various numerical examples obtained from our framework are presented, which agree well with the paper models and the finite-element simulations. We envision that the proposed conical Kresling pattern and inverse design framework can provide a new perspective for applications in deployable structures, shape-morphing devices, multi-modal robots and multistable metamaterials.

Water as a thermodynamic parameter of biosphere evolution

Water has a profound influence on the evolution of the biosphere and can be regarded as a thermodynamic parameter. The priorities and objectives in this research include determining the hydrological features of rivers and lakes in the region as indicators of the thermodynamic activity of water in the evolutionary processes; hydrology and ecology of the cryptobiosphere; the effects of water on the evolutionary adaptations and strategies in living organisms in biogeochemical systems of different origins; and the hydrology of possible alternative stable states of biogeochemical systems.

Thermodynamics of the evolution of the biosphere

The thermodynamic foundations of the evolution of the biosphere are considered: the variability of natural systems with different dispersion of their components, the alternative ways of development of such systems, the alternative of intermediate stable states of ecosystems depending on fluctuations of external factors, primarily climate. The necessity of developing a system of mutually agreed complex indicators of this process is postulated. The necessity of including the water content of ecosystems in the number of parameters of nonequilibrium thermodynamics is justified. A new section of land hydrology is formulated -the study of thermodynamic aspects of the dynamics of natural waters.

Paleovegetation dynamics in an alternative stable states landscape in the montane Western Ghats, India

Peat deposits (>50 ka) in the montane Nilgiris (Western Ghats, India), have been central to the reconstruction of late Quaternary paleoclimate using paleovegetation changes in the forest-grassland vegetation mosaic that coexist here. However, it is well-known that short-term disturbances can also cause vegetation switches when multiple stable vegetation states exist. We studied paleovegetation changes within the alternative stable states framework using stable carbon isotopes (relative abundance of C3-C4 vegetation) on the cellulose fraction from two high-resolution radiocarbon-dated peat cores ~170 m apart in the Sandynallah valley: Core 1 closer to the hillslope (32,000 years old) and Core 2 from the centre of the valley (45,000 years old). Core 1 is located in an ecotone showing shola-sedgeland dynamics with vegetation switching at c.22 ka from shola (possibly due to fire) to a prolonged unstable state until 13 ka sustained by low waterlogging. Following a hiatus c.13 ka, sedgeland dominates, with a shift into shola at 3.75 ka driven by increasing aridity. Core 2 shows a stable sedgeland mixed C3-C4 composition responding to temperature, enriched in C3-vegetation in the last glacial with C4-dominance beginning c.18.5 ka, indicative of deglacial warming. The distinctive vegetation states at corresponding times in Cores 1 and 2 within the same valley, responding independently to disturbances and climate, respectively, is the first paleo-record from an alternative stable states landscape in the montane tropics. Thus, short-term disturbances and site attributes need to be accounted for before ascribing vegetation change to changing climate in such vegetation mosaics.

Trajectories of Idea Emergence in Dialogic Collaborative Problem Solving: Toward a Complex Dynamic Systems Perspective

According to the complex dynamic systems (CDS) perspective, learning emerges at various system levels. This study built a coherent theoretical framework based on CDS and Bakhtinian dialogic theory and further employed the concept of attractor (i.e., certain stable states that recur over time) in CDS theory to investigate the trajectories of idea emergence and how they diversified group outcomes in dialogic collaborative problem solving (D-CPS). Two contrasting groups were compared using visual and qualitative analysis approaches. The analysis based on idea tree diagrams showed that new ideas emergent in group discussion tended to attract local utterances and performed features of attractors in CDS in both high-performing and low-performing groups. The analysis based on idea hierarchy diagrams revealed how ideas emerged at various system levels. It was also found that status problems were likely to affect the functioning of regulative feedback loops, which might give rise to different structures of idea evolution. This study proposed CDS theory as an alternative perspective, augmented by the ethical considerations of Bakhtinian dialogism, for examining the dynamics of D-CPS.

Catastrophic Hydraulic Failure and Tipping Points in Plants

Water inside plants forms a continuous chain from water in soils to the water evaporating from leaf surfaces. Failures in this chain result in reduced transpiration and photosynthesis and these failures are caused by soil drying and/or cavitation-induced xylem embolism. Xylem embolism and plant hydraulic failure share a number of analogies to “catastrophe theory” in dynamical systems. These catastrophes are often represented in the physiological and ecological literature as tipping points or alternative stable states when control variables exogenous (e.g. soil water potential) or endogenous (e.g. leaf water potential) to the plant are allowed to slowly vary. Here, plant hydraulics viewed from the perspective of catastrophes at multiple spatial scales is considered with attention to bubble expansion (i.e. cavitation), organ-scale vulnerability to embolism, and whole-plant biomass as a proxy for transpiration and hydraulic function. The hydraulic safety-efficiency tradeoff, hydraulic segmentation and maximum plant transpiration are examined using this framework. Underlying mechanisms for hydraulic failure at very fine scales such as pit membranes, intermediate scales such as xylem network properties and at larger scales such as soil-tree hydraulic pathways are discussed. Lacunarity areas in plant hydraulics are also flagged where progress is urgently needed.