Off-lattice Model Research Articles

Impact of ageing on structure of random sequential adsorption packings of discorectangles

The ageing processes in the systems of elongated particles (discorectangles) adsorbed on a plane was studied numerically. An off-lattice model with continuous positional and orientational degrees of freedom was tested. The initial jammed state was produced using the random sequential adsorption (RSA) model. The transition from the jammed to equilibrium states were performed via translational and rotational Brownian motions. An aspect ratio of the particles (length-to-width ratio) was varied within the range ε=1−12 . At ɛ < 10 the relaxation into the isotropic state was always observed. In the intermediate range, 10⩽ε⩽11 , the relaxation transition into the states with ordered domains was observed. Particularly, for ɛ = 10 this transition was related with significant finite size scaling effects. For particles with ɛ = 12 formation of the large scale quasi-nematic domains and unlimited domain growth was observed. The impact of the relaxation on the domain structure, porosity, percolation connectivity and tracer particle diffusion in such barrier systems was also discussed.

Bilinear optimization of protein structure prediction: An exact approach via AB off-lattice model

Protein structure prediction (PSP) remains a central challenge in computational biology due to its inherent complexity and high dimensionality. While numerous heuristic approaches have appeared in the literature, their success varies. The AB off-lattice model, which characterizes proteins as sequences of A (hydrophobic) and B (hydrophilic) beads, presents a simplified perspective on PSP. This work presents a mathematical optimization-based methodology capitalizing on the off-lattice AB model. Dissecting the inherent non-linearities of the energy landscape of protein folding allowed for formulating the PSP as a bilinear optimization problem. This formulation was achieved by introducing auxiliary variables and constraints that encapsulate the nuanced relationship between the protein’s conformational space and its energy landscape. The proposed bilinear model exhibited notable accuracy in pinpointing the global minimum energy conformations on a benchmark dataset presented by the Protein Data Bank (PDB). Compared to traditional heuristic-based methods, this bilinear approach yielded exact solutions, reducing the likelihood of local minima entrapment. This research highlights the potential of reframing the traditionally non-linear protein structure prediction problem into a bilinear optimization problem through the off-lattice AB model. Such a transformation offers a route toward methodologies that can determine the global solution, challenging current PSP paradigms. Exploration into hybrid models, merging bilinear optimization and heuristic components, might present an avenue for balancing accuracy with computational efficiency.

Consequence of anisotropy on flocking: the discretized Vicsek model

We numerically study a discretized Vicsek model (DVM) with particles orienting in q possible orientations in two dimensions. The study investigates the significance of anisotropic orientation and microscopic interaction on macroscopic behavior. The DVM is an off-lattice flocking model like the active clock model (ACM; Chatterjee et al 2022 Europhys. Lett. 138 41001) but the dynamical rules of particle alignment and movement are inspired by the prototypical Vicsek model (VM). The DVM shows qualitatively similar properties as the ACM for intermediate noise strength where a transition from macrophase to microphase separation of the coexistence region is observed as q is increased. But for small q and noise strength, the liquid phase appearing in the ACM at low temperatures is replaced in the DVM by a configuration of multiple clusters with different polarizations, which does not exhibit any long-range order. We find that the dynamical rules have a profound influence on the overarching features of the flocking phase. We further identify the metastability of the ordered liquid phase subjected to a perturbation.

Calibration of agent based models for monophasic and biphasic tumour growth using approximate Bayesian computation

Agent-based models (ABMs) are readily used to capture the stochasticity in tumour evolution; however, these models are often challenging to validate with experimental measurements due to model complexity. The Voronoi cell-based model (VCBM) is an off-lattice agent-based model that captures individual cell shapes using a Voronoi tessellation and mimics the evolution of cancer cell proliferation and movement. Evidence suggests tumours can exhibit biphasic growth in vivo. To account for this phenomena, we extend the VCBM to capture the existence of two distinct growth phases. Prior work primarily focused on point estimation for the parameters without consideration of estimating uncertainty. In this paper, approximate Bayesian computation is employed to calibrate the model to in vivo measurements of breast, ovarian and pancreatic cancer. Our approach involves estimating the distribution of parameters that govern cancer cell proliferation and recovering outputs that match the experimental data. Our results show that the VCBM, and its biphasic extension, provides insight into tumour growth and quantifies uncertainty in the switching time between the two phases of the biphasic growth model. We find this approach enables precise estimates for the time taken for a daughter cell to become a mature cell. This allows us to propose future refinements to the model to improve accuracy, whilst also making conclusions about the differences in cancer cell characteristics.

Abstract B024: A histological data-driven analysis of the hypoxic microenvironment of preclinical murine bladder tumors

Abstract Hypoxia is common in many solid tumors, including bladder cancer (BC). Preclinical murine models that mimic relevant molecular and phenotypical characteristics of clinical BC were used to analyze the immune cell composition within the hypoxic tumor microenvironment. The experimental protocols involve intravesical installations, adoptively transferred T cells, and chemotherapy and were designed to recreate therapeutic procedures used in a recently open feasibility clinical trial of intravesical adoptive cell therapy (ACT) for BC patients. We analyzed 18 murine BC tissues from a treatment protocol that included intravesical installment of MB49-OVA tumor cells on day 0, gemcitabine treatment on day 10, and/or intravesical transfer of OT-I transgenic T cells on day 14, in addition to untreated controls and normal bladder tissues. The OT-I cells mimic the T cells used in clinical ACT. The collected tissues were sliced, and consecutive sections were stained for vasculature, tumor, and immune cells: CD8+, CD4+, and myeloid-derived suppressor cells (MDSCs). Subsequently, these histology images were co-registered, segmented, and preprocessed to identify the tumor boundaries, select viable vasculature, resolve cell overlaps, and annotate bladder cavities. A multi-cell off-lattice hybrid agent-based model that combines discrete cells and vasculature with continuous oxygen kinetics was developed to recreate the differential oxygenation in the tumor microenvironment. In all tissues, the hypoxic microenvironment was more prevalent in the tumor regions than in the nontumor regions due to differences between the irregular tumor vasculature vs. normal vasculature. The T cell and MDSC infiltration was increased in the tumors treated with gemcitabine (as mono- or combination therapy). Despite the significant hypoxia level in these tumors, only small proportions of CD8+s and CD4+s were hypoxic, as the majority resided in the well-oxygenated portions of the tumor. High infiltration of CD8+ cells was observed in tumors treated with OT-I cells compared to the controls. However, only a small proportion were hypoxic, and most CD8+s and MDSCs were well-oxygenated. The CD8+s were located far from the intravesical source, with some cells near the vasculature. Hypoxic native CD8+s in untreated tissues were observed inside the tumors, and most well-oxygenated CD8+s were near the tumor borders. The CD8+s also resided in the well-oxygenated regions in the normal tissues. Our reconstructed tissue oxygenation based on histology images revealed that the hypoxic tumor microenvironment hinders T cell accumulation in treated and untreated tumors. Such quantitative analyses may encourage designing more effective hypoxia-mediated therapies. Citation Format: Awino Maureiq E. Ojwang, Anjun Hu, McKenzie Williams, Sarah Bazargan, Joseph O. Johnson, Shari Pilon-Thomas, Katarzyna A. Rejniak. A histological data-driven analysis of the hypoxic microenvironment of preclinical murine bladder tumors [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: Translating Cancer Evolution and Data Science: The Next Frontier; 2023 Dec 3-6; Boston, Massachusetts. Philadelphia (PA): AACR; Cancer Res 2024;84(3 Suppl_2):Abstract nr B024.

Abstract PR006: Evolution of evolvability

Abstract The purpose of this work is to better understand how the rate of phenotypic adaptation of cells in a tumor affects its ability to survive treatment. Drug resistance is an ongoing problem for maintaining a sustained response in treating advanced cancers. Regardless of their lineage, heritable phenotypic adaptions may be beneficial for the tumor to survive stepwise changes in the environment during tumor growth. There may be further benefit for cells to develop the trait of being adaptable - to respond to large shifts in the microenvironment, survive metastasis to a new organ, and thrive when treatments are applied. Genomic instability and phenotypic redundancy may aid in adaptations, but there may be limits. With too much mutation and deviation from the parental phenotype, cells lose important regulatory and maintenance functions necessary to survive. So is there an optimal rate of evolvability? We use an off-lattice agent-based model to investigate how the rate of change through phenotypic trait space affects tumor growth and response to treatment. We assign cells with different combinations of proliferation rates and migration speeds and test how the variance from the parental cell on division affects the selection of trait combinations over time. During growth, heterogeneity is gained quickly and space matters less if evolvability is forced to continually increase, but there is more selection for proliferative phenotypes and slower evolvability if its rate is allowed to drift freely. We found that tradeoffs generally imposed a greater selection force leading to faster recurrence and the coexistence of proliferation or migration specialists. We compared responses to continuous, intermittent, and adaptive treatment schedules of an anti-proliferative drug. At some point with treatment, there is an optimal evolvability, as larger increases in diversity allows for cells to fall back into a sensitive state and be killed by treatment. We aim to design better treatment strategies that work for tumors with different levels of evolvability by understanding how the rate of tumor evolution affects growth and treatment response. Citation Format: Jill A. Gallaher, Maximilian Strobl, Jeffrey West, Mark Roberston-Tessi, Alexander R. A. Anderson. Evolution of evolvability [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: Translating Cancer Evolution and Data Science: The Next Frontier; 2023 Dec 3-6; Boston, Massachusetts. Philadelphia (PA): AACR; Cancer Res 2024;84(3 Suppl_2):Abstract nr PR006.

An efficient discrete unified gas-kinetic scheme for compressible thermal flows

In this paper, an efficient discrete unified gas-kinetic scheme (DUGKS) is developed for compressible thermal flows based on the total energy kinetic model for natural convection with a large relative temperature difference. A double distribution function model is designed with the second distribution representing the total energy. This efficient DUGKS enables the simulation of compressible thermal flows, governed by the compressible Navier–Stokes–Fourier system, using only a seventh-order, off-lattice Gauss–Hermite quadrature (GHQ) D3V27A7 combined with a fifth-order GHQ D3V13A5. The external force is included by truncated Hermite expansions. Based on the Chapman–Enskog approximation and Hermite projection, we propose a systematic approach to derive the discrete kinetic boundary conditions for the density and total energy distribution functions. The discrete kinetic boundary treatments are provided for the no-slip boundary condition, Dirichlet boundary condition and Neumann boundary condition. To validate our scheme, we perform simulations of steady natural convection (Ra=103−106) in two- and three-dimensional cavities with differentially heated sidewalls and a large temperature difference (ε=0.6), where the Oberbeck–Boussinesq approximation is invalid. The results demonstrate that the current efficient DUGKS is robust and accurate for thermal compressible flow simulations. With the D3V27A7 and D3V13A5 off-lattice discrete particle velocity model, the computational efficiency of the DUGKS is improved by a factor of 3.09 when compared to the previous partial energy kinetic model requiring the ninth-order Gauss–Hermite quadrature.

Free and Interfacial Boundaries in Individual-Based Models of Multicellular Biological systems

Coordination of cell behaviour is key to a myriad of biological processes including tissue morphogenesis, wound healing, and tumour growth. As such, individual-based computational models, which explicitly describe inter-cellular interactions, are commonly used to model collective cell dynamics. However, when using individual-based models, it is unclear how descriptions of cell boundaries affect overall population dynamics. In order to investigate this we define three cell boundary descriptions of varying complexities for each of three widely used off-lattice individual-based models: overlapping spheres, Voronoi tessellation, and vertex models. We apply our models to multiple biological scenarios to investigate how cell boundary description can influence tissue-scale behaviour. We find that the Voronoi tessellation model is most sensitive to changes in the cell boundary description with basic models being inappropriate in many cases. The timescale of tissue evolution when using an overlapping spheres model is coupled to the boundary description. The vertex model is demonstrated to be the most stable to changes in boundary description, though still exhibits timescale sensitivity. When using individual-based computational models one should carefully consider how cell boundaries are defined. To inform future work, we provide an exploration of common individual-based models and cell boundary descriptions in frequently studied biological scenarios and discuss their benefits and disadvantages.

Effects of sequence-dependent non-native interactions in equilibrium and kinetic folding properties of knotted proteins.

Determining the role of non-native interactions in folding dynamics, kinetics, and mechanisms is a classic problem in protein folding. More recently, this question has witnessed a renewed interest in light of the hypothesis that knotted proteins require the assistance of non-native interactions to fold efficiently. Here, we conduct extensive equilibrium and kinetic Monte Carlo simulations of a simple off-lattice C-alpha model to explore the role of non-native interactions in the thermodynamics and kinetics of three proteins embedding a trefoil knot in their native structure. We find that equilibrium knotted conformations are stabilized by non-native interactions that are non-local, and proximal to native ones, thus enhancing them. Additionally, non-native interactions increase the knotting frequency at high temperatures, and in partially folded conformations below the transition temperatures. Although non-native interactions clearly enhance the efficiency of transition from an unfolded conformation to a partially folded knotted one, they are not required to efficiently fold a knotted protein. Indeed, a native-centric interaction potential drives the most efficient folding transition, provided that the simulation temperature is well below the transition temperature of the considered model system.

Off-Lattice Coarse-Grained Model of Surface-Confined Metal–Organic Architectures

An off-lattice model of self-assembling surface-confined metal–organic nanostructures (SMONs) comprising tripod molecules has been developed. The model considers the directionality and saturability of coordination bonding. To parametrize the model, density functional theory methods have been used. Self-assembly of the SMONs has been simulated with Metropolis Monte Carlo method in the canonical ensemble. In this paper, we investigate how the directionality of metal–linker bonding and the linker/metal ratio affect the self-assembly of SMONs containing metal centers with different coordination numbers: M(II), M(III), and M(IV). The directionality of coordination bonding is determined by the functional group of the linker molecule and is defined in the model as the angular diameter of the interaction shell. Regardless of the preferred coordination number of the metal center, even a small change in the angular diameter significantly affects the structure of the SMONs. Depending on the angular diameter and composition of the metal–organic layer, various structures can appear. Using our model, we have simulated the self-assembly of the random porous (or defected honeycomb) and triangular structures, the set of hexagonal phases, amorphous structures of different densities, and metal–organic chains. Relative thermal stabilities of clusters of the main structures have been studied. The model reproduces correctly the main SMONs observed by scanning tunneling microscopy.

Agent-Based Model for Studying the Effects of Solid Stress and Nutrient Supply on Tumor Growth

An off-lattice agent-based model of tumor growth is presented, which describes a tumor as a network of proliferating cells, whose dynamics depend on the stress generated by intercellular bonds. A numerical method is introduced that ensures the smooth dynamics of the cell network and allows for relative numerical cheapness while reproducing the effects typical of more complex approaches such as the elongation of cells toward low-pressure regions and their tendency to maximize the contact area. Simulations of free tumor growth, restricted only by the stress generated within the tumor, demonstrate the influence of the tissue hydraulic conductivity and strength of cell–cell interactions on tumor shape and growth rate. Simulations of compact tumor growth within normal tissue show that strong interaction between tumor cells is a major factor limiting tumor growth. Moreover, the effects of normal tissue size and strength of normal cell interactions on tumor growth are ambiguous and depend on the value of tissue hydraulic conductivity. Simulations of tumor growth in normal tissue with the account of nutrients yield different growth regimes, including growth without saturation for at least several years with the formation of large necrotic cores in cases of low tissue hydraulic conductivity and sufficiently high nutrient supply, which qualitatively correlates with known clinical data.

Structure of adsorbed linear and cyclic block copolymers: A computer simulation study

A study of the adsorption of linear and cyclic mutiblock copolymers on a planar surface was performed using extensive computer simulations. A coarse-grained off-lattice model was designed and polymer chains were modeled as sequences of beads forming solvophilic and solvophobic blocks. A Monte Carlo simulation algorithm employing the Replica Exchange technique was used to determine properties of the model chains. The structure of collapsed and adsorbed chains was determined. The increase of the surface attraction and the number of blocks shifted the transition towards lower temperatures. It was also shown that the influence of the macromolecular architecture and the number of blocks in chains on polymer size is weak.

The BKT transition and its dynamics in a spin fluid.

We study the effect of particle mobility on phase transitions in a spin fluid in two dimensions. The presence of a phase transition of the BKT universality class is shown in an off-lattice model of particles with purely repulsive interaction employing computer simulations. A critical spin wave region 0 < T < TBKT is found with a nonuniversal exponent η(T) that follows the shape suggested by BKT theory, including a critical value consistent with ηBKT = 1/4. One can observe a transition from power-law decay to exponential decay in the static correlation functions at the transition temperature TBKT, which is supported by finite-size scaling analysis. A critical temperature TBKT = 0.17(1) is suggested. Investigations into the dynamic aspects of the phase transition are carried out. The short-time behavior of the incoherent spin autocorrelation function agrees with the Nelson-Fisher prediction, whereas the long-time behavior differs from the finite-size scaling known for the static XY model. Analysis of coherent spin wave dynamics shows that the spin wave peak is a propagating mode that can be reasonably well fitted by hydrodynamic theory. The mobility of the particles strongly enhances damping of the spin waves, but the model still lies within the dynamic universality class of the standard XY model.

Elitist Animal Migration Optimization for Protein Structure Prediction based on 3D Off-Lattice Model

Predicting the structure of protein has been the center of attraction for the researchers. The aim is to make a reliable prediction of the protein structure by obtaining the minimum energy values among amino acids interactions. According to the generated shape of amino acids, the functionality of the proteins can be determined. However, it is known as one of the most challenging tasks in the field of bioinformatics considering its high computation complexity. Metaheuristic algorithms are mainly preferred by researchers from various fields, since their performances are quite satisfactory in solving such complex problems. Animal Migration Optimization (AMO) algorithm is a metaheuristic approach which mimics the behavior of animals during the migration process. However, in this research to reach a high solution quality, an elitist version of Animal Migration Optimization (ELAMO) algorithm is considered and in particular it is applied to Protein Structure Prediction (PSP) problem. The performance of ELAMO is tested on some well-studied artificial and real protein sequences, and then compared with powerful optimization algorithms which are specially designed for solving PSP problem. The results show that ELAMO is quite capable in solving this problem. Hence, it can be used as an efficient optimizer for solving complex problems that require better solution quality in the field of bioinformatics.

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.

Effects of Residual Composition and Distribution on the Structural Characteristics of the Protein.

The effect of ratio and consecutive number of hydrophobic residues in the repeating unit of protein chains was investigated by MD simulation. The modified off-lattice HNP model was applied in this study. The protein chains constituted by different HNP ratios or different numbers of consecutively hydrophobic residues with the same chain length were simulated under a broad temperature range. We concluded that the proteins with higher ratio or larger number of sequentially hydrophobic residues present more orientated and compact structure under a certain low temperature. It is attributed to the lower non-bonded potential energy between H-H residual pairs, especially more hydrophobic residues in a procession among the protein chain. Considering the microscopic structure of the protein, more residue contacts are achieved with the proteins with higher ratios and sequential H residues under the low temperature. Meanwhile, with the ratio and consecutive number of H residues increasing, the distribution of stem length showed a transition from exponential decline to unimodal and even multiple peaks, indicating the specific ordered structure formed. These results provide an insight into 3D structural properties of proteins from their residue sequences, which has a primary structure at molecular level and, ultimately, a practical possibility of applying in biotechnological applications.

An efficient discrete unified gas-kinetic scheme for compressible turbulence

In this paper, we develop an efficient Boltzmann-equation-based mesoscopic approach to simulate three-dimensional (3D) compressible turbulence, using reduced Gauss–Hermite quadrature (GHQ) orders by redefining the second distribution in terms of the total energy in the double distribution function approach. This allows the use of two sets of 3D off-lattice discrete particle velocity models, namely, a 27 discrete velocity model of the seventh-order GHQ accuracy (D3V27A7) combined with a 13 discrete velocity model of the fifth-order GHQ accuracy (D3V13A5), to achieve full consistency with the Navier–Stokes–Fourier system. The source terms in the Boltzmann–Bhatnagar–Gross–Krook system are designed to adjust both the Prandtl number and bulk-to-shear viscosity ratio. Compressible decaying homogeneous isotropic turbulence (DHIT) is simulated at low and moderate turbulent Mach numbers to validate our code. It is observed that the simulation results are in good agreement with those in the existing literatures. Furthermore, the terms in the transport equation of turbulent kinetic energy are analyzed in detail, to illustrate four different transient stages from the initial random flow field to the developed DHIT. It is shown that the transient pressure-dilatation transfer happens rapidly, while the small-scale vortical structures take a longer time to establish physically. Compared to the existing literatures, our approach represents the most efficient mesoscopic scheme for compressible turbulence under the double distribution function formulation.

Large-scale kinetic roughening behavior of coffee-ring fronts.

We have studied the kinetic roughening behavior of the fronts of coffee-ring aggregates via extensive numerical simulations of the off-lattice model considered for this context [Dias et al., Soft Matter 14, 1903 (2018)1744-683X10.1039/C7SM02136D]. This model describes ballistic aggregation of patchy colloids and depends on a parameter r_{AB} which controls the affinity of the two patches, A and B. Suitable boundary conditions allow us to elucidate a discontinuous pinning-depinning transition at r_{AB}=0, with the front displaying intrinsic anomalous scaling, but with unusual exponent values α≃1.2,α_{loc}≃0.5,β≃1, and z≃1.2. For 0<r_{AB}≤1, comparison with simulations of standard off-lattice ballistic deposition indicates the occurrence of a morphological instability induced by the patch structure. As a result, we find that the asymptotic morphological behavior is dominated by macroscopic shapes. The intermediate time regime exhibits one-dimensional KPZ exponents for r_{AB}>0.01 and the system suffers a strong crossover dominated by the r_{AB}=0 behavior for r_{AB}≤0.01. A detailed analysis of correlation functions shows that the aggregate fronts are always in the moving phase for 0<r_{AB}≤1 and that their kinetic roughening behavior is intrinsically anomalous for r_{AB}≤0.01.

Importance of feature construction in machine learning for phase transitions.

Machine learning is an important tool in the study of the phase behavior from molecular simulations. In this work, we use un-supervised machine learning methods to study the phase behavior of two off-lattice models, a binary Lennard-Jones (LJ) mixture and the Widom-Rowlinson (WR) non-additive hard-sphere mixture. The majority of previous work has focused on lattice models, such as the 2D Ising model, where the values of the spins are used as the feature vector that is input into the machine learning algorithm, with considerable success. For these two off-lattice models, we find that the choice of the feature vector is crucial to the ability of the algorithm to predict a phase transition, and this depends on the particular model system being studied. We consider two feature vectors, one where the elements are distances of the particles of a given species from a probe (distance-based feature) and one where the elements are +1 if there is an excess of particles of the same species within a cut-off distance and -1 otherwise (affinity-based feature). We use principal component analysis and t-distributed stochastic neighbor embedding to investigate the phase behavior at a critical composition. We find that the choice of the feature vector is the key to the success of the unsupervised machine learning algorithm in predicting the phase behavior, and the sophistication of the machine learning algorithm is of secondary importance. In the case of the LJ mixture, both feature vectors are adequate to accurately predict the critical point, but in the case of the WR mixture, the affinity-based feature vector provides accurate estimates of the critical point, but the distance-based feature vector does not provide a clear signature of the phase transition. The study suggests that physical insight into the choice of input features is an important aspect for implementing machine learning methods.

Polar flocks with discretized directions: The active clock model approaching the Vicsek model

We consider the off-lattice two-dimensional q-state active clock model (ACM) as a natural discretization of the Vicsek model (VM) describing flocking. The ACM consists of particles able to move in the plane in a discrete set of q equidistant angular directions, as in the active Potts model (APM), with an alignment interaction inspired by the ferromagnetic equilibrium clock model. We find that for a small number of directions, the flocking transition of the ACM has the same phenomenology as the APM, including macrophase separation and reorientation transition. For a larger number of directions, the flocking transition in the ACM becomes equivalent to the one of the VM and displays microphase separation and only transverse bands, i.e., no re-orientation transition. Concomitantly also the transition of the q → ∞ limit of the ACM, the active XY model (AXYM), is in the same universality class as the VM. We also construct a coarse-grained hydrodynamic description for the ACM and AXYM akin to the VM.