Lattice-based Model Research Articles

Liquid State Sintering enhances Consolidation in Basalt-rich Lunar Regolith

Constructing habitable load-bearing structures on lunar and martian surfaces presents unique challenges, such as the ability to sustain extreme thermal fluctuations and frequent dust storms. A promising paradigm for effecting construction is via in situ resource utilization (ISRU), combined with sintering, wherein locally available regolith is consolidated at high temperatures to make load-bearing structures. This work investigates one route for effecting sintering via intermediate melting of a constituent mineral, termed liquid state sintering, to enhance consolidation in lunar regolith simulants. We work primarily with lunar highland simulant (LHS-1), with supporting comparative investigations of lunar mare dust simulant (LMS-1) and martian global simulant (MGS-1). We first establish a liquid-state sintering protocol above the melting point of the constituent basalt using a combination of differential scanning calorimetry (DSC) and post-consolidation Scanning electron microscopy (SEM). A numerical lattice-based model is used to explain several of the experimental observations, including complex pore-crack interactions in the consolidated bricks, potential strength anisotropy due to shrinkage, resulting crack patterns, and derive an exponential relation between strength and porosity.

Discrete and continuous mathematical models of sharp-fronted collective cell migration and invasion.

Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion are routinely employed and known to capture key experimental observations, linear diffusion fails to predict well-defined sharp fronts that are often observed experimentally. This observation has motivated the use of nonlinear degenerate diffusion; however, these nonlinear models and the associated parameters lack a clear biological motivation and interpretation. Here, we take a different approach by developing a stochastic discrete lattice-based model incorporating biologically inspired mechanisms and then deriving the reaction-diffusion continuum limit. Inspired by experimental observations, agents in the simulation deposit extracellular material, which we call a substrate, locally onto the lattice, and the motility of agents is taken to be proportional to the substrate density. Discrete simulations that mimic a two-dimensional circular barrier assay illustrate how the discrete model supports both smooth and sharp-fronted density profiles depending on the rate of substrate deposition. Coarse-graining the discrete model leads to a novel partial differential equation (PDE) model whose solution accurately approximates averaged data from the discrete model. The new discrete model and PDE approximation provide a simple, biologically motivated framework for modelling the spreading, growth and invasion of cell populations with well-defined sharp fronts. Open-source Julia code to replicate all results in this work is available on GitHub.

Membrane Catalyzed Formation of Nucleotide Clusters and Their Role in the Origins of Life: Insights from Molecular Simulations and Lattice Modeling.

One of the mysteries in studying the molecular "Origin of Life" is the emergence of RNA and RNA-based life forms, where nonenzymatic polymerization of nucleotides is a crucial hypothesis in formation of large RNA chains. The nonenzymatic polymerization can be mediated by various environmental settings, such as cycles of hydration and dehydration, temperature variations, and proximity to a variety of organizing matrices, such as clay, salt, fatty acids, lipid membrane, and mineral surface. In this work, we explore the influence of different phases of the lipid membrane toward nucleotide organization and polymerization in a simulated prebiotic setting. Our molecular simulations quantify the localization propensity of a mononucleotide, uridine monophosphate (UMP), in distinct membrane settings. We perform all-atom molecular dynamics (MD) simulations to estimate the role of the monophasic and biphasic membranes in modifying the behavior of UMPs localization and their clustering mechanism. Based on the interaction energy of mononucleotides with the membrane and their diffusion profile from our MD calculations, we developed a lattice-based model to explore the thermodynamic limits of the observations made from the MD simulations. The mathematical model substantiates our hypothesis that the lipid layers can act as unique substrates for "catalyzing" polymerization of mononucleotides due to the inherent spatiotemporal heterogeneity and phase change behavior.

Anomalous intralayer growth of epitaxial Si on Ag(111)

The epitaxial growth of silicene has been the subject of many investigations, controversies and non-classical results. In particular, the initially promising deposition of Si on a metallic substrate such as Ag(111) has revealed unexpected growth modes where Si is inserted at the beginning of the growth in the first atomic plane of the substrate. In order to rationalize this anomalous growth mode, we develop an out-of-equilibrium description of a lattice-based epitaxial growth model, which growth dynamics are analyzed via kinetic Monte-Carlo simulations. This model incorporates several effects revealed by the experiments such as the intermixing between Si and Ag, and surface effects. It is parametrized thanks to an approach in which we show that relatively precise estimates of energy barriers can be deduced by meticulous analysis of atomic microscopy images. This analysis enables us to reproduce both qualitatively and quantitatively the anomalous growth patterns of Si on Ag(111). We show that the dynamics results in two modes, a classical sub-monolayer growth mode at low temperature, and an inserted growth mode at higher temperatures, where the deposited Si atoms insert in the first layer of the substrate by replacing Ag atoms. Furthermore, we reproduce the non-standard Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} shape of the experimental plot of the island density as a function of temperature, with a shift in island density variation during the transition between the submonoloyer and inserted growth modes.

Residual cells and nutrient availability guide wound healing in bacterial biofilms.

Biofilms are multicellular heterogeneous bacterial communities characterized by social-like division of labor, and remarkable robustness with respect to external stresses. Increasingly often an analogy between biofilms and arguably more complex eukaryotic tissues is being drawn. One illustrative example of where this analogy can be practically useful is the process of wound healing. While it has been extensively studied in eukaryotic tissues, the mechanism of wound healing in biofilms is virtually unexplored. Combining experiments in Bacillus subtilis bacteria, a model organism for biofilm formation, and a lattice-based theoretical model of biofilm growth, we studied how biofilms recover after macroscopic damage. We suggest that nutrient gradients and the abundance of proliferating cells are key factors augmenting wound closure. Accordingly, in the model, cell quiescence, nutrient fluxes, and biomass represented by cells and self-secreted extracellular matrix are necessary to qualitatively recapitulate the experimental results for damage repair. One of the surprising experimental findings is that residual cells, persisting in a damaged area after removal of a part of the biofilm, prominently affect the healing process. Taken together, our results outline the important roles of nutrient gradients and residual cells on biomass regrowth on macroscopic scales of the whole biofilm. The proposed combined experiment-simulation framework opens the way to further investigate the possible relation between wound healing, cell signaling and cell phenotype alternation in the local microenvironment of the wound.

Membrane-Mediated Cooperative Interactions of CD47 and SIRPα.

The specific binding of the ubiquitous 'marker of self' protein CD47 to the SIRPα protein anchored in the macrophage plasma membrane results in the inhibition of the engulfment of 'self' cells by macrophages and thus constitutes a key checkpoint of our innate immune system. Consequently, the CD47-SIRPα protein complex has been recognized as a potential therapeutic target in cancer and inflammation. Here, we introduce a lattice-based mesoscale model for the biomimetic system studied recently in fluorescence microscopy experiments where GFP-tagged CD47 proteins on giant plasma membrane vesicles bind to SIRPα proteins immobilized on a surface. Computer simulations of the lattice-based mesoscale model allow us to study the biomimetic system on multiple length scales, ranging from single nanometers to several micrometers and simultaneously keep track of single CD47-SIRPα binding and unbinding events. Our simulations not only reproduce data from the fluorescence microscopy experiments but also are consistent with results of several other experiments, which validates our numerical approach. In addition, our simulations yield quantitative predictions on the magnitude and range of effective, membrane-mediated attraction between CD47-SIRPα complexes. Such detailed information on CD47-SIRPα interactions cannot be obtained currently from experiments alone. Our simulation results thus extend the present understanding of cooperative effects in CD47-SIRPα interactions and may have an influence on the advancement of new cancer treatments.

Kyber, Saber, and SK-MLWR Lattice-Based Key Encapsulation Mechanisms Model Checking with Maude

Facing the potential threat raised by quantum computing, a great deal of research from many groups and industrial giants has gone into building public-key post-quantum cryptographic primitives that are resistant to the quantum attackers. Among them, there is a large number of post-quantum key encapsulation mechanisms (KEMs), whose purpose is to provide a secure key exchange, which is a very crucial component in public-key cryptography. This paper presents a formal security analysis of three lattice-based KEMs including Kyber, Saber, and SK-MLWR. We use Maude, a specification language supporting equational and rewriting logic and a high-performance tool equipped with many advanced features, such as a reachability analyzer that can be used as a model checker for invariant properties, to model the three KEMs as state machines. Because they all belong to the class of lattice-based KEMs, they share many common parts in their designs, such as polynomials, vectors, and message exchange patterns. We first model these common parts and combine them into a specification, called base specification. After that, for each of the three KEMs, by extending the base specification, we just need to model some additional parts and the mechanism execution. Once completing the three specifications, we conduct invariant model checkings with the Maude search command, pointing out a similar man-in-the-middle attack. The occurrence of this attack is due to the fact that authentication is not part of the KEMs, and therefore an active attacker can modify all communication between two honest parties.

Tumour Growth Mechanisms Determine Effectiveness of Adaptive Therapy in Glandular Tumours.

In cancer treatment, adaptive therapy holds promise for delaying the onset of recurrence through regulating the competition between drug-sensitive and drug-resistant cells. Adaptive therapy has been studied in well-mixed models assuming free mixing of all cells and spatial models considering the interactions of single cells with their immediate adjacent cells. Both models do not reflect the spatial structure in glandular tumours where intra-gland cellular interaction is high, while inter-gland interaction is limited. Here, we use mathematical modelling to study the effects of adaptive therapy on glandular tumours that expand using either glandular fission or invasive growth. A two-dimensional, lattice-based model of sites containing sensitive and resistant cells within individual glands is developed to study the evolution of glandular tumour cells under continuous and adaptive therapies. We found that although both growth models benefit from adaptive therapy's ability to prevent recurrence, invasive growth benefits more from it than fission growth. This difference is due to the migration of daughter cells into neighboring glands that is absent in fission but present in invasive growth. The migration resulted in greater mixing of cells, enhancing competition induced by adaptive therapy. By varying the initial spatial spread and location of the resistant cells within the tumour, we found that modifying the conditions within the resistant cells containing glands affect both fission and invasive growth. However, modifying the conditions surrounding these glands affect invasive growth only. Our work reveals the interplay between growth mechanism and tumour topology in modulating the effectiveness of cancer therapy.

Numerical explorations of solvent borne adhesives: a lattice-based approach to morphology formation

The internal structure of adhesive tapes determines the effective mechanical properties. This holds true especially for blended systems, here consisting of acrylate and rubber phases. In this note, we propose a lattice-based model to study numerically the formation of internal morphologies within a four-component mixture (of discrete particles) where the solvent components evaporate. Mimicking numerically the interaction between rubber, acrylate, and two different types of solvents, relevant for the technology of adhesive tapes, we aim to obtain realistic distributions of rubber ball-shaped morphologies—they play a key role in the overall functionality of those special adhesives. Our model incorporates the evaporation of both solvents and allows for tuning the strength of two essentially different solvent–solute interactions and of the temperature of the system.

Matrix obstructions cause multiscale disruption in collective epithelial migration by suppressing leader cell function.

During disease and development, physical changes in extracellular matrix cause jamming, unjamming, and scattering in epithelial migration. However, whether disruptions in matrix topology alter collective cell migration speed and cell-cell coordination remains unclear. We microfabricated substrates with stumps of defined geometry, density, and orientation, which create obstructions for migrating epithelial cells. Here, we show that cells lose their speed and directionality when moving through densely spaced obstructions. Although leader cells are stiffer than follower cells on flat substrates, dense obstructions cause overall cell softening. Through a lattice-based model, we identify cellular protrusions, cell-cell adhesions, and leader-follower communication as key mechanisms for obstruction-sensitive collective cell migration. Our modeling predictions and experimental validations show that cells' obstruction sensitivity requires an optimal balance of cell-cell adhesions and protrusions. Both MDCK (more cohesive) and α-catenin-depleted MCF10A cells were less obstruction sensitive than wild-type MCF10A cells. Together, microscale softening, mesoscale disorder, and macroscale multicellular communication enable epithelial cell populations to sense topological obstructions encountered in challenging environments. Thus, obstruction-sensitivity could define "mechanotype" of cells that collectively migrate yet maintain intercellular communication.

Stiff bioinspired architectured beams bend Saint-Venant’s principle and generate large shape morphing

Large shape change from localized mechanical actuation is an attractive prospect for morphing materials and structures, but it is limited by Saint-Venant’s principle: In typical solids the effects of self-equilibrated loads applied over a small region of the solid rapidly decay away from that region, resulting in highly localized deformations and no shape change. Materials and structures with unusual and/or heterogenous combinations of properties can however overcome this limitation. Fish fins, for example, can undergo large changes in curvature distributed over long distances by simple push–pull forces applied at their base. While this type of morphing actuation is attractive, pathways to similar engineering structures are still not well established. Here we present a relatively simple lattice-based mechanical model for fish fin-like morphing. We show that the first moment of curvature is an accurate and robust measure for morphing. Morphing from push-pull forces requires unusual combinations of axial, shear and bending stiffness which cannot be achieved in traditional lattice structures. We then propose “meta-elements” composed of struts in parallel to achieve these combinations of elastic properties. We finally 3D print and test several of these designs to validate the models and to verify these new design guidelines for morphing structures.

Abstract 6621: Simulating the distortion of clonal fractions in ctDNA due to spatially heterogenous selection

Abstract Time-series circulating tumor DNA (ctDNA) sequencing has the potential to reveal emerging variants in the tissue in real time, and there is now substantial evidence that it can detect tumor growth and treatment-resistant mutations long before growth is visible. However, the reliability of ctDNA for profiling the primary tumor may be compromised by spatial heterogeneity in the tumor genetics, for example due to selective effects of differential drug penetration, immune infiltration, and oxygenation. We explore the influence of spatial factors on tumor genetics through a lattice-based branching process model of solid tumor evolution and ctDNA shedding with the goal of understanding where spatially variable selection pressure could lead to a significant difference between the clonal fractions in the blood and the tissue. The lattice model divides space into regions with different growth rates which result in different rates of driver mutation accumulation. The effects of regional differences in selection cause different apoptosis rates to correlate with the location of expanding driver clones. Using these rates to simulate ctDNA shedding, our model found that clones fit enough to invade a hostile region are temporarily amplified in the blood compared to their tissue frequency by as much as 300% for a limited window of time before the population expands further and the clonal fraction in the blood returns to close agreement with tissue. The results suggest evolutionary contexts in which liquid biopsy might provide highly biased estimates of tumor state, but also shows how this effect might be exploited to provide more sensitive detection of clonal expansion with implications for blood-based detection of recurrence and metastasis. Citation Format: Thomas W. Rachman, Oana Carja, Russell Schwartz. Simulating the distortion of clonal fractions in ctDNA due to spatially heterogenous selection [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 6621.

Bio-inspired design, modeling, and 3D printing of lattice-based scale model scooter decks

This research aims at enhancing the performance of scale-model scooter decks by investigating various architected cellular metamaterial and bio-inspired core structure designs, such as honeycomb, tetrachiral, re-entrant, arrowhead, and star-shaped arrangements. An initial effort is made toward the design and rapid prototyping of small-scale deck with a uniform honeycomb core structure. More specifically, polylactic acid is utilized to fabricate complex structures via fused filament fabrication technique. Investigation is then focused on its mechanical performance, such as its bending properties obtained through a three-point bending test. Simulations are also conducted with different core configurations using a geometrically non-linear finite element method which is implemented. Experiments are carried out to verify the numerical results. After validation, various patterns are modeled, and eventually, it is observed that the functionally graded arrowhead structure has the best bending resistance, compared to other bio-inspired and mechanical metamaterial structures. At a constant force of 845 N, the functionally graded arrowhead design lowers the deflection in the middle of the scale model of scooter deck by up to 14.7%, compared to the uniform arrowhead structure. Furthermore, comparing the tetrachiral and functionally graded arrowhead configurations at a constant force, a 30% reduction in central deflection was observed. Due to the lack of similar results and designs in the specialized literature, this work could potentially advance the state-of-the-art scooter core designs and provide designers with architectures that could enhance the performance and safety of scooters.

Mechanically primed cells transfer memory to fibrous matrices for invasion across environments of distinct stiffness and dimensionality.

Cells sense and migrate across mechanically dissimilar environments throughout development and disease progression. However, it remains unclear whether mechanical memory of past environments empowers cells to navigate new, three-dimensional extracellular matrices. Here, we show that cells previously primed on stiff, compared with soft, matrices generate a higher level of forces to remodel collagen fibers and promote invasion. This priming advantage persists in dense or stiffened collagen. We explain this memory-dependent, cross-environment cell invasion through a lattice-based model wherein stiff-primed cellular forces remodel collagen and minimize energy required for future cell invasion. According to our model, cells transfer their mechanical memory to the matrix via collagen alignment and tension, and this remodeled matrix informs future cell invasion. Thus, memory-laden cells overcome mechanosensing of softer or challenging future environments via a cell-matrix transfer of memory. Consistent with model predictions, depletion of yes-associated protein destabilizes the cellular memory required for collagen remodeling before invasion. We release tension in collagen fibers via laser ablation and disable fiber remodeling by lysyl-oxidase inhibition, both of which disrupt cell-to-matrix transfer of memory and hamper cross-environment invasion. These results have implications for cancer, fibrosis, and aging, where a potential cell-to-matrix transfer of mechanical memory of cells may generate a prolonged cellular response.

Modelling network formation in folded protein hydrogels by cluster aggregation kinetics.

Globular folded protein-based hydrogels are becoming increasingly attractive due to their specific biological functionality, as well as their responsiveness to stimuli. By modelling folded proteins as colloids, there are rich opportunities to explore network formation mechanisms in protein hydrogels that negate the need for computationally expensive simulations which capture the full complexity of proteins. Here we present a kinetic lattice-based model which simulates the formation of irreversibly chemically crosslinked, folded protein-based hydrogels. We identify the critical point of gel percolation, explore the range of network regimes covering diffusion-limited to reaction-limited cluster aggregation (DLCA and RLCA, respectively) network formation mechanisms and predict the final network structure, fractal dimensions and final gel porosity. We reveal a crossover between DLCA and RLCA mechanisms as a function of protein volume fraction and show how the final network structure is governed by the structure at the percolation point, regardless of the broad variation of non-percolating cluster masses observed across all systems. An analysis of the pore size distribution in the final network structures reveals that, approaching RLCA, gels have larger maximal pores than the DLCA counterparts for both volume fractions studied. This general kinetic model and the analysis tools generate predictions of network structure and concurrent porosity over a broad range of experimentally controllable parameters that are consistent with current expectations and understanding of experimental results.

Lattice-based model for pricing contingent claims under mixed fractional Brownian motion

We propose a lattice-based model to approximate the dynamics of an asset with diffusion driven by a mixed fractional Brownian motion. Being it defined as the sum of a fractional Brownian motion and an independent Brownian motion, the method starts by discretizing separately the two processes. For the first process, we develop a binomial approach that is able to replicate the process variance at each discrete epoch, while a recombining binomial lattice is used to discretize the Brownian motion. Given the fractional Brownian motion path-dependency, the binomial approach is not recombining. Hence, to reduce the computational complexity, we establish a grid of representative values whose elements cover the range of possible asset values at each time slice. For each value of the grid, the algorithm identifies four successors in a bivariate environment. The successors may not appear among the generated asset values at the next epoch. In such cases, interpolation techniques are needed when solving backward to compute the initial value of the contingent claim. The proposed discretization allows to evaluate both European and American derivatives and numerical experiments confirm its accuracy and efficiency.

Entropy production and its large deviations in an active lattice gas

Active systems are characterized by a continuous production of entropy at steady state. We study the statistics of entropy production within a lattice-based model of interacting active particles that is capable of motility-induced phase separation. Exploiting a recent formulation of the exact fluctuating hydrodynamics for this model, we provide analytical results for its entropy production statistics in both typical and atypical (biased) regimes. This complements previous studies of the large deviation statistics of entropy production in off-lattice active particle models that could only be addressed numerically. Our analysis uncovers an unexpectedly intricate phase diagram, with five different phases arising (under bias) within the parameter regime where the unbiased system is in its homogeneous state. Notably, we find the concurrence of first order and second order nonequilibrium phase transition curves at a bias-induced tricritical point, a feature not yet reported in previous studies of active systems.

Quantifying the coupled monovalent and divalent ions sorption in dense ion-exchange membranes

As a universal phenomenon in solution-membrane systems, the coupled competitive monovalent and divalent ions sorption significantly impacts the transport process in ion-exchange membranes. Often, the quantitative and qualitative relationships between them are unclear. Here, we present a lattice-based molecular model to capture the interplay effect of ion-pairing and electrostatic interaction on the competitive partitioning process. In particular, we utilize statistical mechanics to formulate how the monovalent and divalent counterions competitively pair with the fixed charge group in the membranes. To this end, the model can quantify (a) the counterions sorption and (b) the coion repulsion within the membranes, which, collectively, allow us to quantify the ion partitioning and the pairing site saturation. To showcase the capability of our model, we compare our results with published experiment data, where we achieve a relatively good agreement between them. We demonstrate that the competitive ion partitioning depends highly upon (i) the entropy change generated by the counterions pairing with the fixed charge group, (ii) the binding energy, and (iii) the osmotic pressure, and (iv) the electrostatic interaction. These different factors can explain the favorable sorption of divalent counterions in the cation-exchange membranes but monovalent counterions in the anion ones, as previously reported. Altogether, our theoretical approach provides an insight into the fundamental understanding of coupled competitive monovalent and divalent ions sorption within the dense ion-exchange membranes, further enhancing the knowledge of the competitive ion partitioning process.

Folding lattice proteins with quantum annealing

Quantum annealing is a promising approach for obtaining good approximate solutions to difficult optimization problems. Folding a protein sequence into its minimum-energy structure represents such a problem. For testing new algorithms and technologies for this task, the minimal lattice-based HP model is well suited, as it represents a considerable challenge despite its simplicity. The HP model has favorable interactions between adjacent, not directly bound hydrophobic residues. Here, we develop a novel spin representation for lattice protein folding tailored for quantum annealing. With a distributed encoding onto the lattice, it differs from earlier attempts to fold lattice proteins on quantum annealers, which were based upon chain growth techniques. With our encoding, the Hamiltonian by design has the quadratic structure required for calculations on an Ising-type annealer, without having to introduce any auxiliary spin variables. This property greatly facilitates the study of long chains. The approach is robust to changes in the parameters required to constrain the spin system to chain-like configurations, and performs very well in terms of solution quality. The results are evaluated against existing exact results for HP chains with up to $N=30$ beads with 100% hit rate, thereby also outperforming classical simulated annealing. In addition, the method allows us to recover the lowest known energies for $N=48$ and $N=64$ HP chains, with similar hit rates. These results are obtained by the commonly used hybrid quantum-classical approach. For pure quantum annealing, our method successfully folds an $N=14$ HP chain. The calculations were performed on a D-Wave Advantage quantum annealer.

A Lattice-Based Predictive Model for Interaction Mode of Hydraulic Fracture with Natural Fractures

A Lattice-Based Predictive Model for Interaction Mode of Hydraulic Fracture with Natural Fractures