Pairwise Interactions Research Articles

Improved Selection of Pairwise Interaction Effects via Automated Calibration of Hierarchical Group-LASSO Regularization in a Stability Selection Framework.

Improved Selection of Pairwise Interaction Effects via Automated Calibration of Hierarchical Group-LASSO Regularization in a Stability Selection Framework.

Evolutionary dynamics of cooperation coupled with ecological feedback compensation

A simple theoretical model (or a demonstrative example) was developed to illustrate how the evolution of cooperation can be affected by the density-dependent survival competition, in which we assume that the fertility of an individual depends only on the pairwise interaction between him and other individuals based on Prisoner’s Dilemma game, while its viability is only related to the density-dependent survival competitiveness. Our results show that not only cooperation could be evolutionarily stable if the advantage of cooperators in viability can compensate for the cost they pay for their fertility, but also the long-term stable coexistence of cooperation and defection is possible if none of cooperation and defection is evolutionarily stable. Moreover, for the stochastic evolutionary dynamics in a finite population, our analysis shows that the increase (or decrease) of the survival competitiveness of cooperators (or defectors) should be conductive to the evolutionary emergence of cooperation.

A “bond-focused” local atomic environment representation for a high throughput solute interaction spectrum analysis

Local atomic environment (LAE) representations have enabled a deeper understanding of complex alloy configurations, by enabling machine learning and data science approaches to previously inaccessible tasks. For example, recent developments have used site-centered descriptors to interpret the structurally complex LAEs present in polycrystalline grain boundary (GB) networks and learn the spectrum of grain boundary segregation energies available across many binary alloys. One limitation of many LAE representations is their “site-focus”, which limits their ability to capture chemical complexity at the atomic scale. This paper introduces a modified “bond-focused” LAE representation, which is used to assess pair-wise solute interactions in the topologically complex environments of grain boundaries. This approach opens the pathway to learning models, which we develop here to construct a large-scale database of spectral parameters describing grain boundaries in binary alloys.

Oncogenic transcription factors instruct promoter-enhancer hubs in individual triple negative breast cancer cells.

Sequencing-based mapping of ensemble pairwise interactions among regulatory elements support the existence of topological assemblies known as promoter-enhancer hubs or cliques in cancer. Yet, prevalence, regulators, and functions of promoter-enhancer hubs in individual cancer cells remain unclear. Here, we systematically integrated functional genomics, transcription factor screening, and optical mapping of promoter-enhancer interactions to identify key promoter-enhancer hubs, examine heterogeneity of their assembly, determine their regulators, and elucidate their role in gene expression control in individual triple negative breast cancer (TNBC) cells. Optical mapping of individual SOX9 and MYC alleles revealed the existence of frequent multiway interactions among promoters and enhancers within spatial hubs. Our single-allele studies further demonstrated that lineage-determining SOX9 and signaling-dependent NOTCH1 transcription factors compact MYC and SOX9 hubs. Together, our findings suggest that promoter-enhancer hubs are dynamic and heterogeneous topological assemblies, which are controlled by oncogenic transcription factors and facilitate subtype-restricted gene expression in cancer.

Convolutional neural networks can identify brain interactions involved in decoding spatial auditory attention.

Human listeners have the ability to direct their attention to a single speaker in a multi-talker environment. The neural correlates of selective attention can be decoded from a single trial of electroencephalography (EEG) data. In this study, leveraging the source-reconstructed and anatomically-resolved EEG data as inputs, we sought to employ CNN as an interpretable model to uncover task-specific interactions between brain regions, rather than simply to utilize it as a black box decoder. To this end, our CNN model was specifically designed to learn pairwise interaction representations for 10 cortical regions from five-second inputs. By exclusively utilizing these features for decoding, our model was able to attain a median accuracy of 77.56% for within-participant and 65.14% for cross-participant classification. Through ablation analysis together with dissecting the features of the models and applying cluster analysis, we were able to discern the presence of alpha-band-dominated inter-hemisphere interactions, as well as alpha- and beta-band dominant interactions that were either hemisphere-specific or were characterized by a contrasting pattern between the right and left hemispheres. These interactions were more pronounced in parietal and central regions for within-participant decoding, but in parietal, central, and partly frontal regions for cross-participant decoding. These findings demonstrate that our CNN model can effectively utilize features known to be important in auditory attention tasks and suggest that the application of domain knowledge inspired CNNs on source-reconstructed EEG data can offer a novel computational framework for studying task-relevant brain interactions.

Virtual walks and phase transitions in the two-dimensional Biswas-Chatterjee-Sen model with extreme switches.

In kinetic exchange models of opinion formation, one considers pairwise interactions to update the states of the agents. We have studied a kinetic exchange model with three opinion states 0,±1, by considering a walk in a one-dimensional virtual space which evolves according to the dynamical states of the agents. The model involves two noise parameters p and q; p represents the fraction of negative interactions and q corresponds to the probability of a stronger interaction with the other agent, which may result in extreme switches (change of state from +1 to -1 or vice versa). The nature of the walks can indicate where the phase transitions occur in the p-q plane; these results are corroborated with those obtained using finite-size scaling method. The criticality is found to be Ising-like, even when extreme switches are allowed. A new critical exponent associated with the probability distribution of the displacements in the virtual space is also obtained independent of the values of the critical parameters. The nature of the walks is compared to similar virtual walks studied earlier.

Effect of individual activity level heterogeneity on disease spreading in higher-order networks.

The active state of individuals has a significant impact on disease spread dynamics. In addition, pairwise interactions and higher-order interactions coexist in complex systems, and the pairwise networks proved insufficient for capturing the essence of complex systems. Here, we propose a higher-order network model to study the effect of individual activity level heterogeneity on disease-spreading dynamics. Activity level heterogeneity radically alters the dynamics of disease spread in higher-order networks. First, the evolution equations for infected individuals are derived using the mean field method. Second, numerical simulations of artificial networks reveal that higher-order interactions give rise to a discontinuous phase transition zone where the coexistence of health and disease occurs. Furthermore, the system becomes more unstable as individual activity levels rise, leading to a higher likelihood of disease outbreaks. Finally, we simulate the proposed model on two real higher-order networks, and the results are consistent with the artificial networks and validate the inferences from theoretical analysis. Our results explain the underlying reasons why groups with higher activity levels are more likely to initiate social changes. Simultaneously, the reduction in group activity, characterized by measures such as "isolation," emerges as a potent strategy for disease control.

Robustness of higher-order interdependent networks with reinforced nodes.

In reality, pairwise interactions are no longer sufficient to describe the higher-order interactions between nodes, such as brain networks, social networks, etc., which often contain groups of three or more nodes. Since the failure of one node in a high-order network can lead to the failure of all simplices in which it is located and quickly propagates to the whole system through the interdependencies between networks, multilayered high-order interdependent networks are challenged with high vulnerability risks. To increase the robustness of higher-order networks, in this paper, we proposed a theoretical model of a two-layer partial high-order interdependent network, where a proportion of reinforced nodes are introduced that can function and support their simplices and components, even losing connection with the giant component. We study the order parameter of the proposed model, including the giant component and functional components containing at least one reinforced node, via theoretical analysis and simulations. Rich phase transition phenomena can be observed by varying the density of 2-simplices and the proportion of the network's reinforced nodes. Increasing the density of 2-simplices makes a double transition appear in the network. The proportion of reinforced nodes can alter the type of second transition of the network from discontinuous to continuous or transition-free, which is verified on the double random simplicial complex, double scale-free simplicial complex, and real-world datasets, indicating that reinforced nodes can significantly enhance the robustness of the network and can prevent networks from abrupt collapse. Therefore, the proposed model provides insights for designing robust interdependent infrastructure networks.

Motility and pairwise interactions of chemically active droplets in one-dimensional confinement.

Self-propelled droplets serve as ideal model systems to delve deeper into understanding the motion of biological microswimmers by simulating their motility. Biological microorganisms are renowned for showcasing a diverse array of dynamic swimming behaviors when confronted with physical constraints. This study aims to elucidate the impact of physical constraints on swimming characteristics of biological microorganisms. To achieve this, we present observations on the individual and pairwise behavior of micellar solubilized self-propelled 4-cyano-4'-pentyl-biphenyl (5CB) oil droplets in a square capillary channel filled with a surfactant trimethyl ammonium bromide aqueous solution. To explore the effect of the underlying Péclet number of the swimming droplets, the study is also performed in the presence of additives such as high molecular weight polymer polyethylene oxide and molecular solute glycerol. The capillary confinement restricts droplet to predominantly one-dimensional motion, albeit with noticeable differences in their motion across the three scenarios. Through a characterization of the chemical and hydrodynamic flow fields surrounding the droplets, we illustrate that the modification of the droplets' chemical field due to confinement varies significantly based on the underlying differences in the Péclet number in these cases. This alteration in the chemical field distribution notably affects the individual droplets' motion. Moreover, these distinct chemical field interactions between the droplets also lead to variations in their pairwise motion, ranging from behaviors like chasing to scattering.

A generalized Dean–Kawasaki equation for an interacting Brownian gas in a partially absorbing medium

The Dean–Kawasaki (DK) equation is a stochastic partial differential equation (SPDE) for the global density ρ = N − 1 ∑ j = 1 N δ ( x − X j ( t ) ) of a gas of N over-damped Brownian particles, where X j ( t ) is the position of the j th particle. In the thermodynamic limit N → ∞ with weak pairwise interactions, the expectation ⟨ ρ ⟩ with respect to the white noise processes converges in distribution to the solution of a McKean–Vlasov (MV) equation. In this article, we use an encounter-based approach to derive a generalized DK equation for an interacting Brownian gas on the half-line with a partially absorbing boundary at x = 0 . Each particle is independently absorbed when its local time L j ( t ) at x = 0 exceeds a random threshold ℓ ^ j . The global density is now summed over the set of particles that have not yet been absorbed, and expectations are taken with respect to the Gaussian noise and the random thresholds ℓ ^ j . Assuming the DK equation has a well-defined mean-field limit, we derive the corresponding MV equation on the half-line. We illustrate the theory by (i) analysing stationary solutions for a Curie–Weiss (quadratic) interaction potential and a totally reflecting boundary; and (ii) calculating the effective rate of particle loss in the weak absorption limit. Extensions to finite intervals and partially absorbing traps are also considered.

Temporal interaction and its role in the evolution of cooperation.

This research investigates the impact of dynamic, time-varying interactions on cooperative behavior in social dilemmas. Traditional research has focused on deterministic rules governing pairwise interactions, yet the impact of interaction frequency and synchronization in groups on cooperation remains underexplored. Addressing this gap, our work introduces two temporal interaction mechanisms to model the stochastic or periodic participation of individuals in public goods games, acknowledging real-life variances due to exogenous temporal factors and geographical time differences. We consider that the interaction state significantly influences both game payoff calculations and the strategy updating process, offering new insights into the emergence and sustainability of cooperation. Our results indicate that maximum game participation frequency is suboptimal under a stochastic interaction mechanism. Instead, an intermediate activation probability maximizes cooperation, suggesting a vital balance between interaction frequency and inactivity security. Furthermore, local synchronization of interactions within specific areas is shown to be beneficial, as time differences hinder the spread of cross-structures but promote the formation of dense cooperative clusters with smoother boundaries. We also note that stronger clustering in networks, larger group sizes, and lower noise increase cooperation. This research contributes to understanding the role of node-based temporality and probabilistic interactions in social dilemmas, offering insights into fostering cooperation.

A simplex path integral and a simplex renormalization group for high-order interactions *

Modern theories of phase transitions and scale invariance are rooted in path integral formulation and renormalization groups (RGs). Despite the applicability of these approaches in simple systems with only pairwise interactions, they are less effective in complex systems with undecomposable high-order interactions (i.e. interactions among arbitrary sets of units). To precisely characterize the universality of high-order interacting systems, we propose a simplex path integral and a simplex RG (SRG) as the generalizations of classic approaches to arbitrary high-order and heterogeneous interactions. We first formalize the trajectories of units governed by high-order interactions to define path integrals on corresponding simplices based on a high-order propagator. Then, we develop a method to integrate out short-range high-order interactions in the momentum space, accompanied by a coarse graining procedure functioning on the simplex structure generated by high-order interactions. The proposed SRG, equipped with a divide-and-conquer framework, can deal with the absence of ergodicity arising from the sparse distribution of high-order interactions and can renormalize a system with intertwined high-order interactions at the p-order according to its properties at the q-order ( p⩽q ). The associated scaling relation and its corollaries provide support to differentiate among scale-invariant, weakly scale-invariant, and scale-dependent systems across different orders. We validate our theory in multi-order scale-invariance verification, topological invariance discovery, organizational structure identification, and information bottleneck analysis. These experiments demonstrate the capability of our theory to identify intrinsic statistical and topological properties of high-order interacting systems during system reduction.

Divergent folding-mediated epistasis among unstable membrane protein variants.

Many membrane proteins are prone to misfolding, which compromises their functional expression at the plasma membrane. This is particularly true for the mammalian gonadotropin-releasing hormone receptor GPCRs (GnRHR). We recently demonstrated that evolutionary GnRHR modifications appear to have coincided with adaptive changes in cotranslational folding efficiency. Though protein stability is known to shape evolution, it is unclear how cotranslational folding constraints modulate the synergistic, epistatic interactions between mutations. We therefore compared the pairwise interactions formed by mutations that disrupt the membrane topology (V276T) or tertiary structure (W107A) of GnRHR. Using deep mutational scanning, we evaluated how the plasma membrane expression of these variants is modified by hundreds of secondary mutations. An analysis of 251 mutants in three genetic backgrounds reveals that V276T and W107A form distinct epistatic interactions that depend on both the severity and the mechanism of destabilization. V276T forms predominantly negative epistatic interactions with destabilizing mutations in soluble loops. In contrast, W107A forms positive interactions with mutations in both loops and transmembrane domains that reflect the diminishing impacts of the destabilizing mutations in variants that are already unstable. These findings reveal how epistasis is remodeled by conformational defects in membrane proteins and in unstable proteins more generally.

Divergent folding-mediated epistasis among unstable membrane protein variants

Many membrane proteins are prone to misfolding, which compromises their functional expression at the plasma membrane. This is particularly true for the mammalian gonadotropin-releasing hormone receptor GPCRs (GnRHR). We recently demonstrated that evolutionary GnRHR modifications appear to have coincided with adaptive changes in cotranslational folding efficiency. Though protein stability is known to shape evolution, it is unclear how cotranslational folding constraints modulate the synergistic, epistatic interactions between mutations. We therefore compared the pairwise interactions formed by mutations that disrupt the membrane topology (V276T) or tertiary structure (W107A) of GnRHR. Using deep mutational scanning, we evaluated how the plasma membrane expression of these variants is modified by hundreds of secondary mutations. An analysis of 251 mutants in three genetic backgrounds reveals that V276T and W107A form distinct epistatic interactions that depend on both the severity and the mechanism of destabilization. V276T forms predominantly negative epistatic interactions with destabilizing mutations in soluble loops. In contrast, W107A forms positive interactions with mutations in both loops and transmembrane domains that reflect the diminishing impacts of the destabilizing mutations in variants that are already unstable. These findings reveal how epistasis is remodeled by conformational defects in membrane proteins and in unstable proteins more generally.

Response theory identifies reaction coordinates and explains critical phenomena in noisy interacting systems

We consider a class of nonequilibrium systems of interacting agents with pairwise interactions and quenched disorder in the dynamics featuring, in the thermodynamic limit, phase transitions. We identify mathematical conditions on the microscopic interaction structure, namely the separability of the interaction kernel, that lead to a dimension reduction of the system in terms of a finite number of reaction coordinates (RCs). Such RCs prove to be proper nonequilibrium thermodynamic variables as they carry information on correlation, memory and resilience properties of the system. Phase transitions can be identified and quantitatively characterised as singularities of the complex valued susceptibility functions associated to the RCs. We provide analytical and numerical evidence of how the singularities affect the physical properties of finite size systems.

Synthesis of organotin(IV) heterocycles containing a xanthenyl group by a Barbier approach via ultrasound activation: synthesis, crystal structure and Hirshfeld surface analysis.

A series of organotin heterocycles of general formula [{Me2C(C6H3CH2)2O}SnR2] [R= methyl (Me, 4), n-butyl (n-Bu, 5), benzyl (Bn, 6) and phenyl (Ph, 7)] was easily synthesized by a Barbier-type reaction assisted by the sonochemical activation of metallic magnesium. The 119Sn{1H} NMR data for all four compounds confirm the presence of a central Sn atom in a four-coordinated environment in solution. Single-crystal X-ray diffraction studies for 17,17-dimethyl-7,7-diphenyl-15-oxa-7-stannatetracyclo[11.3.1.05,16.09,14]heptadeca-1,3,5(16),9(14),10,12-hexaene, [Sn(C6H5)2(C17H16O)], 7, at 100 and 295 K confirmed the formation of a mononuclear eight-membered heterocycle, with a conformation depicted as boat-chair, resulting in a weak Sn...O interaction. The Sn and O atoms are surrounded by hydrophobic C-H bonds. A Hirshfeld surface analysis of 7 showed that the eight-membered heterocycles are linked by weak C-H...π, π-π and H...H noncovalent interactions. The pairwise interaction energies showed that the cohesion between the heterocycles are mainly due to dispersion forces.

Cascading failures on interdependent hypergraph

Scientists are aware of the importance of studying interdependent networks, as they represent real-world scenarios better than isolated networks, such as the interdependent communication and power networks. However, in real scenarios, higher-order interactions exist in these networks. Recent research has shown that higher-order interactions that cannot be reflected in simple networks (i.e., a network only has pairwise interaction) can be reflected through hypergraph. This paper proposes an interdependent hypergraph model that considers the dependencies of interlayer nodes. We studied the cascading failures in the hypergraph with different interlayer dependencies. Through theoretical analysis, we have determined the maximum attack intensity the network can withstand and how its robustness changes under different attack intensities. In completely interdependent hypergraph, the network becomes increasingly fragile as the attack intensity increases, and the final network size suddenly jumps to zero, indicating a first-order phase transition in the network. We conducted experiments on multiple artificially synthesized hypergraph. The experimental results indicate that our analytical solution is consistent with the simulated solution. These findings will help us better understand the impact of different topologies on network robustness in interdependent hypergraph, enabling us to take more effective measures to address potential network failures and attacks.

Optimization-Based Pairwise Interaction Point Process (O-PIPP): A Precise and Universal Retinal Mosaic Modeling Approach.

A retinal mosaic, the spatial organization of a population of homotypic neurons, is thought to sample a specific visual feature into the feedforward visual pathway. The purpose of this study was to propose a universal modeling approach for precisely generating retinal mosaics and overcoming the limitations of previous models, especially in modeling abnormal mosaic patterns under disease conditions. Here, we developed the optimization-based pairwise interaction point process (O-PIPP). It incorporates optimization techniques into previous simulation approaches, enabling directional control of the simulation process according to the user-designed optimization target. For the convenience of the community, we implemented the O-PIPP approach into a Python package and a website application. We showed that the O-PIPP can generate more precise neural spatial patterns of healthy and diseased mosaics compared to previous phenomenological approaches. Notably, through modeling the retinal neural circuitry with O-PIPP-simulated retinitis pigmentosa cone mosaics, we elucidated how the cone mosaic rearrangement impacted the information processing of ganglion cells. The O-PIPP provides a precise and universal tool to simulate realistic mosaics, which could help to investigate the function of retinal mosaics in vision.

Effective mechanical potential of cell-cell interaction in tissues harboring cavity and in cell sheet toward morphogenesis.

Measuring mechanical forces of cell-cell interactions is important for studying morphogenesis in multicellular organisms. We previously reported an image-based statistical method for inferring effective mechanical potentials of pairwise cell-cell interactions by fitting cell tracking data with a theoretical model. However, whether this method is applicable to tissues with non-cellular components such as cavities remains elusive. Here we evaluated the applicability of the method to cavity-harboring tissues. Using synthetic data generated by simulations, we found that the effect of expanding cavities was added to the pregiven potentials used in the simulations, resulting in the inferred effective potentials having an additional repulsive component derived from the expanding cavities. Interestingly, simulations by using the effective potentials reproduced the cavity-harboring structures. Then, we applied our method to the mouse blastocysts, and found that the inferred effective potentials can reproduce the cavity-harboring structures. Pairwise potentials with additional repulsive components were also detected in two-dimensional cell sheets, by which curved sheets including tubes and cups were simulated. We conclude that our inference method is applicable to tissues harboring cavities and cell sheets, and the resultant effective potentials are useful to simulate the morphologies.

Histidine in Proteins: pH-Dependent Interplay between π-π, Cation-π, and CH-π Interactions.

Histidine (His) stands out as the most versatile natural amino acid due to its side chain's facile propensity to protonate at physiological pH, leading to a transition from aromatic to cationic characteristics and thereby enabling diverse biomolecular interactions. In this study, our objective was to quantify the energetics and geometries of pairwise interactions involving His at varying pH levels. Through quantum chemical calculations, we discovered that His exhibits robust participation in both π-π and cation-π interactions, underscoring its ability to adopt a π or cationic nature, akin to other common residues. Of particular note, we found that the affinity of protonated His for aromatic residues (via cation-π interactions) is greater than the affinity of neutral His for either cationic residues (also via cation-π interactions) or aromatic residues (via π-π interactions). Furthermore, His frequently engages in CH-π interactions, and notably, depending on its protonation state, we found that some instances of hydrogen bonding by His exhibit greater stability than is typical for interamino acid hydrogen bonds. The strength of the pH-dependent pairwise energies of His with aromatic residues is supported by the abundance of pairwise interactions with His of low and high predicted pKa values. Overall, our findings illustrate the contribution of His interactions to protein stability and its potential involvement in conformational changes despite its relatively low abundance in proteins.