On-lattice Model Research Articles

Migration and proliferation drive the emergence of patterns in co-cultures of differentiating vascular progenitor cells.

Vascular cells self-organize into unique structures guided by cell proliferation, migration, and/or differentiation from neighboring cells, mechanical factors, and/or soluble signals. However, the relative contribution of each of these factors remains unclear. Our objective was to develop a computational model to explore the different factors affecting the emerging micropatterns in 2D. This was accomplished by developing a stochastic on-lattice population-based model starting with vascular progenitor cells with the potential to proliferate, migrate, and/or differentiate into either endothelial cells or smooth muscle cells. The simulation results yielded patterns that were qualitatively and quantitatively consistent with experimental observations. Our results suggested that post-differentiation cell migration and proliferation when balanced could generate between 30-70% of each cell type enabling the formation of vascular patterns. Moreover, the cell-to-cell sensing could enhance the robustness of this patterning. These findings computationally supported that 2D patterning is mechanistically similar to current microfluidic platforms that take advantage of the migration-directed self-assembly of mature endothelial and mural cells to generate perfusable 3D vasculature in permissible hydrogel environments and suggest that stem or progenitor cells may not be fully necessary components in many tissue formations like those formed by vasculogenesis.

Debugging collective digging in Drosophila melanogaster using an agent-based model

Being a member of a group entails a range of possible costs and benefits; observing when and with whom groups form can help identify how these are weighted. Clustering behaviour in fruit fly (Drosophila melanogaster) third-instar larvae has been shown to provide individuals that cluster with improved foraging opportunities on otherwise inaccessible food. To isolate how environmental and genetic factors affect who clusters and when, we created an on-lattice agent-based model and systematically explored the effects of several variables, such as population density, resource distribution, and the phenotypic composition of the group. Our simple model reproduces most of the key features of larval clustering and demonstrates drastic differences in collective behaviour and fitness in response to changes in environmental variables, in ways that align with the limited empirical data available. This model can improve our understanding of this complex social behaviour and make testable predictions about the behavioural and ecological mechanisms of larval clustering.

Code for the cluster dichotomy model

The stability of colloid is closely related to the aggregation of colloidal particles and the dispersion of clusters in the system. Because aggregation changes the original state of the sol, previous studies have paid more attention to the aggregation process of the colloid. In fact, aggregation process and dispersion process coexist. The Cluster-Cluster Aggregation model has been widely used to simulate the process of colloidal agglomeration. In the aspect of cluster dispersion, people pay more attention to the simulation of cluster dispersion caused by external forces (such as shear force). In the actual system, the sudden decrease of electrolyte concentration leads to the increase of electrostatic repulsion between colloidal particles, resulting in the disintegration of the clusters. Inspired by the dimerization process of the traditional Cluster-Cluster Aggregation model, we previously proposed a dichotomy model to simulate the dispersion process of colloidal clusters. Here, we provide Java code for the dichotomy model, which can simulate dispersion caused by external forces and internal forces. This paper further elaborates the key points of the dichotomy model, mainly including: the definitions of the relevant probabilities involved in the dichotomy model, the data structures of particle, cluster and cube, and the functions of the relevant parameters related to the dichotomy model. Furthermore, the cluster's characteristics of erosion dispersion and collapse dispersion are studied respectively. Program summaryProgram Title: Dichotomy modelCPC Library link to program files:https://doi.org/10.17632/my9xzpm8xg.1Licensing provisions: Apache-2.0Programming language: JavaNature of problem: Many scholars focus on the research of cluster aggregation, but ignore the cluster dispersion, and there are few programs for the simulation of cluster dispersion. The program provided in this paper can well simulate the dynamic process of cluster dispersion.Solution method: Inspiring by the idea of dimerization in the classical CCA model, the process of dispersing a larger cluster into multiple smaller clusters is transformed into the superposition of several times of one-to-two processes. The three-dimensional on-lattice model is used to simulate the process of cluster dispersion. We use the Java language to write programs, and dynamically display the simulation results through the Java3D technology.

Atomistic kinetic Monte Carlo simulation on atomic layer deposition of TiN thin film

The atomic layer deposition (ALD) process of TiN thin films is widely used in microelectronics, but the detailed growth mechanism is still elusive at the atomistic level. In the present computational study, we carry out kinetic Monte Carlo (kMC) simulations on the ALD process using TiCl4 and NH3 precursors. Based on the on-lattice model, we sort out key reactions relevant for the ALD process such as adsorption/desorption of precursors, generation of surface Cl atoms, and evolution of free HCl and Cl2 molecules. The reaction energies considering local environments are calculated at the level of density functional theory (DFT) while the activation barriers are linearly fitted to sampled cases among distinct reaction families. The resulting kMC model produces the temperature-dependent growth rates and the amounts of Cl residues in reasonable agreement with experiments. The detailed growth pathway is discussed based on the simulation results, which underscores the critical role of surface Cl atoms in the ALD process by generating HCl gas molecules. By revealing the atomistic mechanisms in the TiN-ALD process, the present work would help optimize material properties of TiN thin films.

The impact of the spatial heterogeneity of resistant cells and fibroblasts on treatment response.

A long-standing practice in the treatment of cancer is that of hitting hard with the maximum tolerated dose to eradicate tumors. This continuous therapy, however, selects for resistant cells, leading to the failure of the treatment. A different type of treatment strategy, adaptive therapy, has recently been shown to have a degree of success in both preclinical xenograft experiments and clinical trials. Adaptive therapy is used to maintain a tumor’s volume by exploiting the competition between drug-sensitive and drug-resistant cells with minimum effective drug doses or timed drug holidays. To further understand the role of competition in the outcomes of adaptive therapy, we developed a 2D on-lattice agent-based model. Our simulations show that the superiority of the adaptive strategy over continuous therapy depends on the local competition shaped by the spatial distribution of resistant cells. Intratumor competition can also be affected by fibroblasts, which produce microenvironmental factors that promote cancer cell growth. To this end, we simulated the impact of different fibroblast distributions on treatment outcomes. As a proof of principle, we focused on five types of distribution of fibroblasts characterized by different locations, shapes, and orientations of the fibroblast region with respect to the resistant cells. Our simulation shows that the spatial architecture of fibroblasts modulates tumor progression in both continuous and adaptive therapy. Finally, as a proof of concept, we simulated the outcomes of adaptive therapy of a virtual patient with four metastatic sites composed of different spatial distributions of fibroblasts and drug-resistant cell populations. Our simulation highlights the importance of undetected metastatic lesions on adaptive therapy outcomes.

An on-lattice agent-based Monte Carlo model simulating the growth kinetics of multicellular tumor spheroids.

To develop an on-lattice agent-based model describing the growth of multicellular tumor spheroids using simple Monte Carlo tools. Cells are situated on the vertices of a cubic grid. Different cell states (proliferative, hypoxic or dead) and cell evolution rules, driven by 10 parameters, and the effects of the culture medium are included. About twenty spheroids of MCF-7 human breast cancer were cultivated and the experimental data were used for tuning the model parameters. Simulated spheroids showed adequate sizes of the necrotic nuclei and of the hypoxic and proliferative cell phases as a function of the growth time, mimicking the overall characteristics of the experimental spheroids. The relation between the radii of the necrotic nucleus and the whole spheroid obtained in the simulations was similar to the experimental one and the number of cells, as a function of the spheroid volume, was well reproduced. The statistical variability of the Monte Carlo model described the whole volume range observed for the experimental spheroids. Assuming that the model parameters vary within Gaussian distributions it was obtained a sample of spheroids that reproduced much better the experimental findings. The model developed allows describing the growth of in vitro multicellular spheroids and the experimental variability can be well reproduced. Its flexibility permits to vary both the agents involved and the rules that govern the spheroid growth. More general situations, such as, e. g., tumor vascularization, radiotherapy effects on solid tumors, or the validity of the tumor growth mathematical models can be studied.

Comparison of solitary and collective foraging strategies of Caenorhabditis elegans in patchy food distributions.

Collective foraging has been shown to benefit organisms in environments where food is patchily distributed, but whether this is true in the case where organisms do not rely on long-range communications to coordinate their collective behaviour has been understudied. To address this question, we use the tractable laboratory model organism Caenorhabditis elegans, where a social strain (npr-1 mutant) and a solitary strain (N2) are available for direct comparison of foraging strategies. We first developed an on-lattice minimal model for comparing collective and solitary foraging strategies, finding that social agents benefit from feeding faster and more efficiently simply owing to group formation. Our laboratory foraging experiments with npr-1 and N2 worm populations, however, show an advantage for solitary N2 in all food distribution environments that we tested. We incorporated additional strain-specific behavioural parameters of npr-1 and N2 worms into our model and computationally identified N2's higher feeding rate to be the key factor underlying its advantage, without which it is possible to recapitulate the advantage of collective foraging in patchy environments. Our work highlights the theoretical advantage of collective foraging owing to group formation alone without long-range interactions and the valuable role of modelling to guide experiments. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Global Existence Analysis of Cross-Diffusion Population Systems for Multiple Species

The existence of global-in-time weak solutions to reaction-cross-diffusion systems for an arbitrary number of competing population species is proved. The equations can be derived from an on-lattice random-walk model with general transition rates. In the case of linear transition rates, it extends the two-species population model of Shigesada, Kawasaki, and Teramoto. The equations are considered in a bounded domain with homogeneous Neumann boundary conditions. The existence proof is based on a refined entropy method and a new approximation scheme. Global existence follows under a detailed balance or weak cross-diffusion condition. The detailed balance condition is related to the symmetry of the mobility matrix, which mirrors Onsager’s principle in thermodynamics. Under detailed balance (and without reaction) the entropy is nonincreasing in time, but counter-examples show that the entropy may increase initially if detailed balance does not hold.

An Enhanced Genetic Algorithm for <italic>Ab Initio</italic> Protein Structure Prediction

In-vitro methods for protein structure determination are time-consuming, cost-intensive, and failure-prone. Because of these expenses, alternative computer-based predictive methods have emerged. Predicting a protein’s 3-D structure from only its amino acid sequence—also known as ab initio protein structure prediction (PSP)—is computationally demanding because the search space is astronomically large and energy models are extremely complex. Some successes have been achieved in predictive methods but these are limited to small sized proteins (around 100 amino acids); thus, developing efficient algorithms, reducing the search space, and designing effective search guidance heuristics are necessary to study large sized proteins. An on-lattice model can be a better ground for rapidly developing and measuring the performance of a new algorithm, and hence we consider this model for larger proteins (>150 amino acids) to enhance the genetic algorithms (GAs) framework. In this paper, we formulate PSP as a combinatorial optimization problem that uses 3-D face-centered-cubic lattice coordinates to reduce the search space and hydrophobic-polar energy model to guide the search. The whole optimization process is controlled by an enhanced GA framework with four enhanced features: 1) an exhaustive generation approach to diversify the search; 2) a novel hydrophobic core-directed macro-mutation operator to intensify the search; 3) a per-generation duplication elimination strategy to prevent early convergence; and 4) a random-walk technique to recover from stagnation. On a set of standard benchmark proteins, our algorithm significantly outperforms state-of-the-art algorithms. We also experimentally show that our algorithm is robust enough to produce very similar results regardless of different parameter settings.

Lattice model for amyloid peptides: OPEP force field parametrization and applications to the nucleus size of Alzheimer's peptides.

Coarse-grained protein lattice models approximate atomistic details and keep the essential interactions. They are, therefore, suitable for capturing generic features of protein folding and amyloid formation at low computational cost. As our aim is to study the critical nucleus sizes of two experimentally well-characterized peptide fragments Aβ16-22 and Aβ37-42 of the full length Aβ1-42 Alzheimer's peptide, it is important that simulations with the lattice model reproduce all-atom simulations. In this study, we present a comprehensive force field parameterization based on the OPEP (Optimized Potential for Efficient protein structure Prediction) force field for an on-lattice protein model, which incorporates explicitly the formation of hydrogen bonds and directions of side-chains. Our bottom-up approach starts with the determination of the best lattice force parameters for the Aβ16-22 dimer by fitting its equilibrium parallel and anti-parallel β-sheet populations to all-atom simulation results. Surprisingly, the calibrated force field is transferable to the trimer of Aβ16-22 and the dimer and trimer of Aβ37-42. Encouraged by this finding, we characterized the free energy landscapes of the two decamers. The dominant structure of the Aβ16-22 decamer matches the microcrystal structure. Pushing the simulations for aggregates between 4-mer and 12-mer suggests a nucleus size for fibril formation of 10 chains. In contrast, the Aβ37-42 decamer is largely disordered with mixed by parallel and antiparallel chains, suggesting that the nucleus size is >10 peptides. Our refined force field coupled to this on-lattice model should provide useful insights into the critical nucleation number associated with neurodegenerative diseases.

A Competitive Lattice Model Monte Carlo Method for Simulation of Competitive Growth of Different Polytypes in SiC Single Crystal

A competitive lattice model was developed for the Kinetic Monte Carlo (KMC) simulation of the competition of 4H and 6H polytypes in SiC crystal growth based on the on-lattice model. In the competitive lattice model, site positions are fixed at the perfect crystal lattice positions without any adjustment of the site positions. The effect of surface steps was investigated, and behavior similar to step-controlled homoepitaxy was observed in KMC simulation of PVT grown SiC. Maintaining the step growth mode is an important factor to maintain a stable single polytype during SiC growth.

Guided macro-mutation in a graded energy based genetic algorithm for protein structure prediction

Protein structure prediction is considered as one of the most challenging and computationally intractable combinatorial problem. Thus, the efficient modeling of convoluted search space, the clever use of energy functions, and more importantly, the use of effective sampling algorithms become crucial to address this problem. For protein structure modeling, an off-lattice model provides limited scopes to exercise and evaluate the algorithmic developments due to its astronomically large set of data-points. In contrast, an on-lattice model widens the scopes and permits studying the relatively larger proteins because of its finite set of data-points. In this work, we took the full advantage of an on-lattice model by using a face-centered-cube lattice that has the highest packing density with the maximum degree of freedom. We proposed a graded energy—strategically mixes the Miyazawa–Jernigan (MJ) energy with the hydrophobic-polar (HP) energy—based genetic algorithm (GA) for conformational search. In our application, we introduced a 2×2 HP energy guided macro-mutation operator within the GA to explore the best possible local changes exhaustively. Conversely, the 20×20 MJ energy model—the ultimate objective function of our GA that needs to be minimized—considers the impacts amongst the 20 different amino acids and allow searching the globally acceptable conformations. On a set of benchmark proteins, our proposed approach outperformed state-of-the-art approaches in terms of the free energy levels and the root-mean-square deviations.

Multiscale reaction-diffusion simulations with Smoldyn.

Summary: Smoldyn is a software package for stochastic modelling of spatial biochemical networks and intracellular systems. It was originally developed with an accurate off-lattice particle-based model at its core. This has recently been enhanced with the addition of a computationally efficient on-lattice model, which can be run stand-alone or coupled together for multiscale simulations using both models in regions where they are most required, increasing the applicability of Smoldyn to larger molecule numbers and spatial domains. Simulations can switch between models with only small additions to their configuration file, enabling users with existing Smoldyn configuration files to run the new on-lattice model with any reaction, species or surface descriptions they might already have.Availability and Implementation: Source code and binaries freely available for download at www.smoldyn.org, implemented in C/C++ and supported on Linux, Mac OSX and MS Windows.Contact: martin.robinson@maths.ox.ac.ukSupplementary Information: Supplementary data are available at Bioinformatics online and include additional details on model specification and modelling of surfaces, as well as the Smoldyn configuration file used to generate Figure 1.

Higher-order Galilean-invariant lattice Boltzmann model for microflows: Single-component gas

We introduce a scheme which gives rise to additional degree of freedom for the same number of discrete velocities in the context of the lattice Boltzmann model. We show that an off-lattice D3Q27 model exists with correct equilibrium to recover Galilean-invariant form of Navier-Stokes equation (without any cubic error). In the first part of this work, we show that the present model can capture two important features of the microflow in a single component gas: Knudsen boundary layer and Knudsen Paradox. Finally, we present numerical results corresponding to Couette flow for two representative Knudsen numbers. We show that the off-lattice D3Q27 model exhibits better accuracy as compared to more widely used on-lattice D3Q19 or D3Q27 model. Finally, our construction of discrete velocity model shows that there is no contradiction between entropic construction and quadrature-based procedure for the construction of the lattice Boltzmann model.

Stochastic modelling of reaction–diffusion processes: algorithms for bimolecular reactions

Several stochastic simulation algorithms (SSAs) have recently been proposed for modelling reaction–diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice model described by the reaction–diffusion master equation. The second SSA is an off-lattice model based on the simulation of Brownian motion of individual molecules and their reactive collisions. In both cases, it is shown that the commonly used implementation of bimolecular reactions (i.e. the reactions of the form A + B → C or A + A → C) might lead to incorrect results. Improvements of both SSAs are suggested which overcome the difficulties highlighted. In particular, a formula is presented for the smallest possible compartment size (lattice spacing) which can be correctly implemented in the first model. This implementation uses a new formula for the rate of bimolecular reactions per compartment (lattice site).

In Silico Protein Fragmentation Reveals the Importance of Critical Nuclei on Domain Reassembly

Protein complementation assays (PCAs) based on split protein fragments have become powerful tools that facilitate the study and engineering of intracellular protein-protein interactions. These assays are based on the observation that a given protein can be split into two inactive fragments and these fragments can reassemble into the original properly folded and functional structure. However, one experimentally observed limitation of PCA systems is that the folding of a protein from its fragments is dramatically slower relative to that of the unsplit parent protein. This is due in part to a poor understanding of how PCA design parameters such as split site position in the primary sequence and size of the resulting fragments contribute to the efficiency of protein reassembly. We used a minimalist on-lattice model to analyze how the dynamics of the reassembly process for two model proteins was affected by the location of the split site. Our results demonstrate that the balanced distribution of the “folding nucleus,” a subset of residues that are critical to the formation of the transition state leading to productive folding, between protein fragments is key to their reassembly.

On the disordered SAW model for DNA denaturation

We investigate numerically the transition properties for models of DNA denaturation, which can be relevant for certain classes of disordered systems. The investigation follows two, complementary, numerical approaches: on-lattice Monte Carlo like simulations or off-lattice statistical mechanics calculations, which can extend very significantly the affordable lengths for the sequences. The on-lattice model consists of two interacting self-avoiding walks with the same origin on a three-dimensional cubic lattice. We introduce two different contact energies, for the adenine–thymine coupling and the guanine–cytosine one, respectively, distributed according to a bimodal law. Whereas the transition is recognized to be of first order in the pure (homopolymer) case, the behaviour of quantities averaged over disorder suggests that the random system undergoes a second-order transition.

Protein translocation through a tunnel induces changes in folding kinetics: A lattice model study

Compaction of a nascent polypeptide chain inside the ribosomal exit tunnel, before it leaves the ribosome, has been proposed to accelerate the folding of newly synthesized proteins following their release from the ribosome. Thus, we used Kinetic Monte Carlo simulations of a minimalist on-lattice model to explore the effect that polypeptide translocation through a variety of channels has on protein folding kinetics. Our results demonstrate that tunnel confinement promotes faster folding of a well-designed protein relative to its folding in free space by displacing the unfolded state towards more compact structures that are closer to the transition state. Since the tunnel only forbids rarely visited, extended configurations, it has little effect on a "poorly designed" protein whose unfolded state is largely composed of low-energy, compact, misfolded configurations. The beneficial effect of the tunnel depends on its width; for example, a too-narrow tunnel enforces unfolded states with limited or no access to the transition state, while a too-wide tunnel has no effect on the unfolded state entropy. We speculate that such effects are likely to play an important role in the folding of some proteins or protein domains in the cellular environment and might dictate whether a protein folds co-translationally or post-translationally.

Effects of the screening breakdown in the diffusion-limited aggregation model

Several models based on the diffusion-limited aggregation (DLA) model were proposed and their scaling properties explored by computational and theoretical approaches. In this paper, we consider a new extension of the on-lattice DLA model in which the unitary random steps are replaced by random flights of fixed length. This procedure reduces the screening for particle penetration present in the original DLA model and, consequently, generates new pattern classes. The patterns have DLA-like scaling properties at small length of the random flights. However, as the flight size increases, the patterns are initially round and compact but become fractal for sufficiently large clusters. Their radius of gyration and number of particles at the cluster surface scale asymptotically as in the original DLA model. The transition between compact and fractal patterns is characterized by wavelength selection, and $1/k$ noise was observed far from the transition.

Minimum Coating Thickness in Pore Size Reduction of Inorganic Substrates through Particle Deposition

The determination of minimum coating thickness for covering substrate holes through particle deposition is achieved with a combined, three-dimensional, on-lattice model, in which both deterministic and non-deterministic driving forces are taken into account. The relative importance of deterministic forces to non-deterministic forces is quantified by a dimensionless parameter, Peclet number. The minimum covering thickness normalized with the characteristic hole size (hc/Hw) is investigated subject to variation in Peclet number (Pe) and normalized size (Dp/L) of the depositing particle, normalized hole size (Hw/L), and degree of post-contact restructuring allowed (Nr). It is found that there exists a scaling relationship between the normalized minimum covering thickness and the normalized hole size as hc/Hw∼(Hw/L)E with E=0.53, 0.54, 0.96, and 1.42 for Pe of 1000, 10, 0.5, and 0.1, respectively. The magnitude of the scaling exponent implies that the hole covering ability of diffusive particle movement varies more than that of ballistic particle movement over variation in hole size. It is also found that hc/Hw increases with increasing Hw/L and Dp/L. At low Pe (<1), hc/Hw increases with increasing Pe for smaller holes, but decreases with increasing Pe for larger holes. For larger Pe, hc/Hw decreases with increasing Pe, implying that ballistic particle movement is more efficient in covering holes. Post-contact surface restructuring deteriorates the hole covering efficiency of particle deposition for ballistic movement dominated situations (large Pe). But for low Pe situations, there exists an optimal surface restructuring extent, at which hc/Hw is a minimum.