Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

The osteocyte network in bone is believed to play an important role for how bone tissues sense and respond to mechanical stimulation. Yet, bone adaptation to mechanical loads is often conceptualised as a simple response to mechanical stimuli, such as Wolffs law, which is based on mechanical variables only and takes no account of the cellular basis of mechanosensation. Wolffs law presumes the existence of a reference mechanical stimulus, the mechanical setpoint, above which bone is consolidated, and under which bone is removed. In this paper, we develop a theory of bone tissue sensing and adaptation based on osteocytes to provide new understanding of the role played by osteocyte signals in mechanical adaptation. In this theory, the mechanical setpoint of Frosts mechanostat is explicitly embodied as osteocyte properties involved in mechanotransduction. The mechanical setpoint is allowed to adapt due to the replacement of osteocytes during remodelling, making the setpoint space and time dependent. We propose a mathematical model to implement this new theory of bone adapation and present numerical simulations of this model to explore how mechanobiological response curves (effective Wolffs laws) are modulated by setpoint adaptation during remodelling. By accounting for varying osteocyte populations within bone tissue, we explore bone adaptation under osteocyte disruptions, which is particularly relevant to age-related bone loss. Our model suggests that biological disruptions of remodelling balance cannot always be compensated by mechanical feedback, and that setpoint adaptation during remodelling may have significant observable consequences, such as hysteresis in bone response signatures that resemble lazy zones.

Knee joint injury is a major risk factor for post-traumatic osteoarthritis (PTOA), often associated with early cartilage degeneration. Mechanical overloading and cytokine-driven inflammation are key drivers of this process, yet the underlying mechanisms and their distinct temporal and spatial contributions to cartilage degradation remain unclear. Here, we present a mechanobiological finite element framework that simulates cartilage degradation through cell-mediated proteolytic activity triggered by mechanoinflammation and cytokine-driven inflammation. The model reproduces experimentally observed depth-dependent loss of collagen and aggrecan, with mechanoinflammation inducing a transient response and cytokine-driven inflammation sustaining prolonged matrix degradation. Sensitivity analysis further shows that mechanoinflammation-driven degradation is governed mainly by protease production per cell, whereas cytokine-driven degradation is more sensitive to the rate of cellular stimulation. Together, this framework provides a mechanistic basis to study proteolytic cartilage degeneration and supports future in silico evaluation of therapeutic strategies aimed at mitigating cartilage degradation in PTOA.

Biomolecular condensates that form via liquid-liquid phase separation (LLPS) of, most prominently, intrinsically disordered proteins (IDPs) are ubiquitous in eukaryotic cells and responsible for regulating a plethora of biological functions. Amongst these, they contribute to regulating cell motility, either individually within an extracellular matrix or collectively within confluent epithelial tissue. In this computational study we focus on the latter with the aim of investigating whether the mutual exertion of mechanical forces during collective migration in an epithelium can principally trigger cytoplasmatic LLPS. Since present models for confluent epithelial motility have so far only considered cells that are devoid of phase separating (protein) solutes, we extend a common multiphase approach for 2D cell motility with a mixing contribution including any number of protein solutes. Our model considers the phase behavior in both intracellular and extracellular regions and determines to what extend the membrane is permeated by the solutes under the influence of mechanical and osmotic forces. Our initial calculations unlock a very rich behavior involving formation and dissolution of condensates during migration, as well as an impact of LLPS on the very nature of the motility itself, through feedback mechanisms which may bear biological relevance.

Diffuse gliomas are deadly because the individual tumor cells invade - they travel far from the imageable mass, so it is impossible to remove the tumor completely. On the cellular level, glioma cells seem to be in either a "go" state (in which they do not divide) or a "grow" state (in which they do not migrate). We investigate what this tiny choice has to say about the large-scale speed of the invasion front and whether the implication is sufficiently strong to rule out the classical description of the Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) type, in which a single phenotype migrates and proliferates. We derive a two-phenotype reaction-diffusion model with density-dependent switching, and we prove the cooperative (quasi-monotone) structure and the associated comparison principle and study travelling-wave solutions of the model. A leading-edge linearization gives minimal front speed as minimizer of an explicit dispersion relation, and direct simulation verifies the predicted speed. In the experimentally relevant fast switching limit, we find a closed-form expression for the speed, that is, we obtain an effective Fisher-KPP equation with rescaled diffusivity and growth rate, with the fractions of the phenotypes. The "go-or-grow" (GoG) front can move at a maximum speed of half the Fisher speed for the same single-cell motility $D$ and proliferation rate $r$, which occurs only when the cells divide their time equally between the two phenotypes. This bound is directly testable: measurement of the front speed, plus independent determination of $D$ and $r$, discriminates the two hypotheses, and in the GoG case, yields recovery of the phenotype balance. We then extend the result to anisotropic (DTI-informed) invasion along white-matter tracts and discuss implications for understanding clinical measurements of growth rate.

The Poisson-Nernst-Planck (PNP) system is an accurate model of electrodiffusion of ionic species. It is commonly used in situations where nanoscale resolution is required, for instance close to ion channels in the membranes of biological cells. The inherent stiffness of the equations has made them challenging to solve and has limited the applicability of the system. In particular, the time step required for stable solutions has typically needed to be very short (nanoseconds), which makes simulations on the time scale of an action potential (milliseconds) difficult. Recently, it has been observed that avoiding operator splitting and instead solving the concentration equations and the electrostatic equation in a coupled manner relaxes the time-step limitation considerably. However, no theoretical explanation of this observation has been provided. Here, we aim to explain why the coupled scheme allows much larger time steps. We illustrate the mechanism by considering special cases that define necessary, but not sufficient, conditions for stability. We also show that these conditions remain relevant for the fully coupled PNP model in 3D.

Microbes exhibit complex dynamic behavior as the result of a large number of biochemical processes, spatial and temporal interactions, environmental variations, and evolutionary pressure. Although significant progress has been achieved in understanding microbial ecological dynamics, multiple open questions remain, including the microscopic mechanisms of growth and the roles of nutrients and stochasticity. In this work, we present a minimal theoretical approach to clarify the link between consumption of resources by microbes and their growth. A stochastic model that accounts for a single microbial species consuming a single type of resource while growing via cell division is studied analytically and via Monte Carlo computer simulations. We identify three distinct dynamical regimes of microbial growth determined by the relative magnitudes of resource uptake and division rates and initial conditions. We also show that stochasticity influences the dynamic behavior when the amounts of microbes or resources are low. The model recovers Monod growth kinetics and provides a mechanistic interpretation of the Monod constant and maximal growth rate. The theoretical framework presented captures a wide spectrum of dynamic behaviors in microbial systems, providing a clearer microscopic picture to explain their underlying complex mechanisms.

Biomolecular condensates are thought to play a pivotal role in cellular organization by regulating biochemical reactants in space and time. Sustained molecular fluxes across condensate boundaries, together with the participation of phase-separating molecules in active chemical reactions such as ATP hydrolysis, call for a nonequilibrium description. Here, we propose a self-consistent framework in which diffusion-drift dynamics and chemical reactions are coupled through a conditional free energy, defined as the excess contribution to the chemical potential. Self-consistency is achieved by deriving this quantity from the same free-energy functional that governs molecular interactions and phase separation. We apply the framework to a minimal client-scaffold system and investigate how active chemical processes and phase separation interact at steady state. In doing so, our approach recovers the fundamental rules previously identified for the emergence of nonequilibrium steady-state fluxes. The model shows that active reactions involving the scaffold molecules can regulate the phase behavior of the condensate. Moreover, nonequilibrium steady-state fluxes are maximal near the boundary between the phase-separated and homogeneous regimes, suggesting that condensates sustaining molecular transport may operate close to their stability threshold. In the same region, client fluxes are also enhanced, revealing an indirect coupling between scaffold activity and client transport. These results provide a baseline for developing more detailed theories of chemically active condensates.

Mechanical properties of epithelial tissues play essential roles in morphogenesis and physiological function. In this study, we analytically derived the in-plane bulk modulus, shear modulus, and Poissons ratio of a three-dimensional cell vertex model of epithelial monolayers. We showed that the model can robustly reproduce a near-zero in-plane Poissons ratio, a mechanical feature reported in cultured epithelial tissues. Numerical simulations further confirmed that the theoretically predicted Poissons ratio accurately describes the response of the model under finite, biologically relevant strains. In addition, the model exhibits not only morphological bistability between squamous-like and columnar-like states, but also mechanical bistability characterized by distinct elastic responses. Together, these results provide a minimal three-dimensional framework that links cell-scale mechanical interactions and epithelial morphology to tissue-scale elastic properties.

Cetaceans reduce the net cost of sustained swimming through intermittent locomotion, alternating active fluking with unpowered gliding. The energy balance of this strategy is central to understanding survival rates, population sustainability, and the effects of anthropogenic and environmental pressures. While active-phase energetics have been characterized extensively, the glide phase remains largely unexplored. Here we derive the optimal glide duration (Topt) and the maximum glide duration beyond which energy savings vanish (Tzero) for three odontocetes spanning a 20-fold range in body mass, using high-fidelity CAD models and wall-modeled large eddy simulations. We show analytically that speed retention at Topt and mass-specific peak energy savings are both fully determined by the active-to-passive drag ratio, propulsive efficiency, and swimming speed, independently of body morphometry and drag coefficient, and are therefore invariant across species at any given speed. These passive-phase optima extend the known size-independent active-phase invariants to the glide phase, towards a scale-independent energetic framework for burst-and-glide locomotion in small cetaceans.

I.Bone fragility is a major ang growing public health concern for many with degenerative bone diseases. A better understanding of fracture propagation in bone can better inform treatment options for these individuals. Human bone is an anisotropic material, with directional microstructure that fractures can propagate around. In a healthy individual, the bone remodeling process repairs damaged tissue. Calcium sulfate dihydrate is a well established surrogate material for bone. This study will mechanically investigate damage repaired plaster samples using three point bending to characterize crack propagation around repaired damage.

Balancing cellular loss in tissues requires fine balance of cell proliferation and differentiation. In differentiated tissues consisting of a single cell type, a mechanical regulation of proliferation has been proposed to underlie growth-control and homeostatic steady-states. Yet, how tissues containing different cell types with distinct proliferation rates, mechanical interactions, and spatial self-organization retain robust homeostasis of cell proportions remains poorly understood. Here, we combine particle-based mechanical models of proliferative tissues with a classical hierarchy of stem, progenitor, and differentiated cells, undergoing stochastic fate choices, and show that mechanical feedback alone is sufficient to stabilize populations. We derive analytically and computationally a phase diagram of possible stable states, in particular those maintained either via slow and rare stem cells with short-lived progenitors or no stem cells and long-lived progenitors. Our simulations uncover that mechanical control of growth is sufficient, in the absence of any codes of adhesion or extrinsic niche signals, to cause stable spatial structures, with small stem cell clusters forming and maintaining dynamical renewal units. Our results demonstrate how complex spatial structures can emerge in minimal stochastic and mechanical simulations with impact to understand the homeostasis of multi-cellular systems.

Curvature evolution on a deforming surface is governed by the full change in the surface metric, but on biological surfaces captured by serial three-dimensional imaging, only the local area change is observable. The loss of the shear component leaves prediction of curvature evolution underdetermined from imaging alone. On the thoracic aorta, where curvature change marks disease progression, we derive a closed-form equation that predicts the change in integrated Gaussian curvature from the area dilation and initial geometry. The equation combines a conformal term in the area dilation with a leading anisotropy correction from the initial geometry. These two analytic levels, augmented by multi-scale spatial features at neighboring regions and a graph neural network trained on residuals, form a four-level nested predictor. On a synthetic aortic geometry under prescribed isotropic expansion, the equation recovers the analytic coefficient exactly. Across a continuum from pure expansion to pure shear, it holds R2 [≥] 0.71. On 236 paired thoracic aortic surfaces spanning dissection, aneurysm, traumatic injury, and non-pathologic controls, the equation recovers within-surface curvature change patterns with per-patient median Pearson [Formula] and pooled R2 = +0.238 [+0.225, +0.250], matching the graph neural network on the same inputs. The residual is a direct measurement of how far the observed growth field departs from conformality. HighlightsO_LIClosed-form equation predicts aortic curvature change from paired computed tomography scans. C_LIO_LIRecovers analytic predictions exactly on synthetic aortic geometries. C_LIO_LIAnisotropy proxy holds R2 [≥] 0.71 from pure expansion to pure shear. C_LIO_LICoefficients tie to geometric mechanisms ensuring interpretability. C_LIO_LIAnisotropy term, computable from one CT, is twice as large on diseased aortas. C_LI

Cell migration plays a central role in numerous physiological and pathological processes and emerges from the coordinated interplay between intracellular force generation, adhesion dynamics, and mechanical interactions with the environment. A minimal, mechanistically grounded understanding of these processes is required to disentangle the respective contributions of cell-intrinsic and environmental cues. Here, a two-dimensional in silico cell motility model is introduced to describe mesenchymal migration driven by intracellular traction forces generated within actin-rich protrusions anchored to a substrate. The model explicitly accounts for adhesion nucleation, maturation, force buildup and rupture, and relies on a small set of physically interpretable parameters. A systematic mechanical analysis identifies parameter regimes that permit effective cell translocation and delineates conditions leading to stalled or mobile cells. Within motile regimes, the model reproduces a broad spectrum of cell morphologies and migratory behaviours. In particular, cell trajectories exhibit the statistical features of a persistent random walk, with a crossover from ballistic to diffusive motion that arises solely from adhesion dynamics and force balance, without imposing polarization or directional bias. Cell morphology is shown to strongly regulate migration speed, persistence, and pausing behaviour. Altogether, this model provides a minimal reference framework for cell migration on non-deformable substrates and establishes a baseline for future studies of mechanically driven guidance. By construction, it is well suited for extension to deformable fibrous substrates, where cell-induced matrix remodeling and stiffness feedback are expected to bias migration and regulate cell encounters relevant to tissue morphogenesis and anastomosis.

Arterial thrombosis is initiated when mechanical forces in flowing blood exceed the activation thresholds of platelets and von Willebrand factor (vWF). Despite extensive experimental characterization of shear-induced platelet aggregation, a unified theoretical framework that maps hemodynamic forcing onto clot nucleation is lacking. Here we present Force-Gated Thrombosis (FGT), a non-equilibrium mechanical theory that treats thrombus formation as a continuous phase transition driven by an effective mechanical forcing {Sigma} ={sigma} + |{nabla}{sigma}| + {beta}{varepsilon}, which combines local wall shear stress{sigma} , shear gradient |{nabla}{sigma}|, and extensional strain rate{varepsilon} . We introduce a dimensionless Thrombosis Number {Theta} = ({Sigma}/{Sigma}c)(P/P0)m(C/C0)n, which incorporates platelet concentration P and coagulation factor concentration C, and governs the transition between stable flow ({Theta} < 1) and active clot growth ({Theta} > 1). The thrombus density is represented by a scalar order parameter{varphi} whose dynamics follow a Ginzburg- Landau free energy functional. For a simplified stenosed artery we derive an analytic closed-form thrombosis onset criterion and a critical flow rate [Formula], where{delta} is stenosis severity. Linear stability analysis shows that perturbations grow at rate{omega} (k) = {Lambda}({Theta}) - D{varphi}k2, becoming unstable when {Theta} > 1. Near threshold the clot volume fraction scales as{varphi} [~] ({Theta} - 1)1/2, a mean-field critical exponent consistent with Ginzburg- Landau theory. Systematic comparison with fifteen published experimental and computational datasets spanning shear rates from 100 to 15,000 s-1 confirms that FGT correctly predicts the existence, location, and approximate severity of pathological thrombus formation across diverse vascular geometries. The theory provides a quantitative bridge between single-molecule mechanobiology and macroscale clinical thrombosis, and yields experimentally testable predictions distinguishing FGT from purely biochemical models.

Background: Major soccer tournaments may temporarily change recreational soccer activity, community gatherings, and injury-prevention needs, but evidence for population-level emergency department (ED) injury patterns during these events is limited. Understanding whether ED-treated soccer injury burden changes during Men's FIFA World Cup periods may help inform surveillance readiness and prevention planning for future tournaments. Objective: To evaluate whether Men's FIFA World Cup tournament periods temporally coincided with changes in ED-treated soccer-coded injury burden in the United States and to assess the implications for public health surveillance and injury-prevention preparedness. Methods: We conducted a retrospective, repeated cross-sectional calendar-period analysis of publicly available national ED injury surveillance records from 1999 through 2025. Soccer-coded injuries were identified using product code 1267 in any available product field. The primary exposure was the set of official Men's FIFA World Cup tournament dates from 2002, 2006, 2010, 2014, 2018, and 2022. Tournament dates were compared with matched same-calendar dates in adjacent years, excluding dates that overlapped other FIFA World Cup tournament windows. The primary estimands were the mean daily difference and ratio in weighted national ED-treated soccer-coded injury estimates between tournament and matched-control periods. Results: The analytic cohort included 170,679 soccer-coded ED cases, corresponding to an estimated 5,366,681 ED-treated soccer-coded injuries nationally. Mean daily weighted estimates were 453.1 during Men's World Cup tournament dates and 384.1 during matched control dates. The absolute mean daily difference was 68.9 injuries per day (95% CI, -0.5 to 138.3), and the mean daily ratio was 1.18 (95% CI, 1.00 to 1.39). Tournament-specific estimates were heterogeneous, with a near-null estimate for the 2022 winter tournament and higher estimates for prior summer tournaments. Conclusions: Men's FIFA World Cup periods were associated with a modest, imprecise increase in mean daily ED-treated soccer-coded injury estimates, but the findings were heterogeneous and compatible with no difference to a moderate increase. These results should be interpreted as ecological and hypothesis-generating rather than causal. The primary implication is not that World Cup tournaments directly cause injuries, but that major soccer events provide a practical opportunity for real-time ED injury surveillance, targeted recreational soccer injury-prevention messaging, concussion awareness, and coordinated preparedness for community and fan-event injury patterns during future tournaments.

Experimental studies involving mechanical loading of the human head and brain in vivo are necessarily limited, making computational modeling essential for advancing our understanding of brain biomechanics. Demographic factors such as age and gender are known to influence brain anatomical structures, material properties, and potentially vulnerability to injurious loading. To address this, we construct six group-average brain models stratified by age and gender from a total of 135 subjects, and investigate the mechanical responses of these "group-average brains" using computational simulations. We use Pearson correlations to assess to what degree the group-average models represent individuals within each demographic category, showing strong correlations. Further, our p-value hypothesis test of the first principal strain across the six groups shows significant differences. This study demonstrates that age- and gender-stratified group-average models can effectively represent biomechanical responses of the individuals within the groups, and can reveal meaningful demographic differences that may influence susceptibility to traumatic brain injury. We show that the age-dependent change in material properties plays a greater role than anatomical changes in driving differences in the deformations. We hope to see increased utilization of these group-average models in both research and clinical applications.

Bacterial communities grow as dynamic populations that respond to their environments. A clinically relevant example is the inactivation of beta-lactam antibiotics by intracellular beta-lactamase in E. faecalis resistant strains. In these populations, resistant bacteria act as antibiotic sinks, detoxifying the environment and allowing sensitive bacteria to survive treatment through a cooperative interaction. In this work, we study strongly coupled planktonic and biofilm populations of mixed sensitive-resistant E. faecalis bacteria under antibiotic stress using fluorescent microscopy. The presence of resistant bacteria in the system benefits both resistant and sensitive cells, leading to mixed planktonic and biofilm populations at super-inhibitory drug concentrations. We show that a beta-lactam antibiotic with or without the addition of a beta-lactam inhibitor can lead to a population inversion effect, characterized by a non-monotonic relation between initial and final fractions of resistant bacteria. The effect is observed in both the planktonic and biofilm populations and is modulated by the total initial cell density. A well-mixed model with competition mediated by resource sharing and cooperation from global degradation of toxins predicts the experimentally observed behavior. These observations suggest underlying population-level mechanisms that are largely independent of biofilm spatial structure.

The emergence of amino acids (AAs) and nucleobases (NBs) across meteorites, interstellar ices, and laboratory shock experiments presents a paradox: why do these specific molecular motifs--a minuscule subset of organic chemistrys combinatorial space--appear repeatedly across diverse environments, in the absence of biological selection? We identify a physical mechanism, prebiotic selection, which biases driven chemical systems toward configurations with high stationary probability p*(x) under sustained entropy flux. The bias is quantified by an information quasi-potential {Phi}I (x) = - ln p*(x), entering the overdamped Langevin dynamics O_FD O_INLINEFIG[Formula 1]C_INLINEFIGM_FD(1)C_FD where {Sigma} is the local entropy production rate (Schnakenberg 1976). {Phi}I is defined self-consistently via the full non-equilibrium stationary density, avoiding the circularity of identifying it with a scalar potential. Two central theorems underlie the framework. Theorem 1 establishes that {nabla}{Sigma} and {nabla}{Phi}I are generically linearly independent off equilibrium, so the dynamics is genuinely two-field. Theorem 2 (structural constraints on single-field gradient dynamics) shows that single-field models on compact manifolds (i) produce yield curves that are at most unimodal under linear driving, and (ii) combine disjoint perturbations additively, giving superlinearity factor S = 1 + O(||{delta} V ||2). The observed superlinear synergy of Ferris et al. (1996) lies far outside this perturbative bound and therefore requires the two-field structure of EOM-IFF; the non-monotonic peak of Blank et al. (2001) is consistent with two-field dynamics and also with single-field dynamics in the unimodal-with-peak case of Theorem 2 part 1, so it does not by itself discriminate. From these results, we: (i) define a formal substrate-minimal criterion for prebiotic selection; (ii) show consistency with the non-monotonic shock-synthesis yield of Blank et al. (2001) (R2 = 0.885, peak at P* = 28.4 {+/-} 1.4 GPa); (iii) show consistency with the superlinear clay-catalysed RNA polymerisation of Ferris et al. (1996) (synergy factor S {approx} 5.75, robust under {+/-}1-nucleotide measurement uncertainty); and (iv) state two further falsifiable predictions awaiting dedicated experimental tests. Every lemma and theorem is accompanied by explicit assumptions, regime of validity, and regime of failure; the frameworks scope is what it claims, not more. Prebiotic selection is identified as a physical process distinct from and prior to biological selection, offering a unified account of chemical convergence in carbon-nitrogen chemistry under sustained entropy flux.

Take-off is a fast and energy-efficient strategy for bipedal animals, such as birds, to achieve rapid movement; however, how muscle physiology scales to govern this universal behavior remains unresolved. Research in other species physiologies is not readily applicable. As a result, important questions, whether theropod dinosaurs such as Tyrannosaurus rex were capable of jumping, remain unanswered. In this article, we coupled Lagrangian dynamics with Hills muscle equations and developed new experimental methods to quantify joint rotational stiffness and damping, thereby enabling a systematic description of lower-limb mechanics. The approach establishes a novel kinetic framework that links muscle contractile properties to lower-limb performance without invoking control optimization. Animal observations and tabletop mechanisms validate the framework. The mechanics model reveals that the take-off time of about 0.1 s across body masses of 0.003 to 90 kg is achievable, as heavier birds generate proportionally higher reaction forces. Additionally, Tyrannosaurus rex should be capable of jumping, based on the available physiology data. Beyond evolutionary insights, our framework provides a new methodology for analyzing the mechanical properties of biological joints and informing the design of scalable bio-inspired robots.

AO_SCPLOWBSTRACTC_SCPLOWOncolytic viruses provide cancer therapy using replication-competent viruses that selectively infect and lyse tumour cells. Their tumour-specific replication also enables the delivery of targeted, virus-encoded gene products, such as enzymes that activate prodrugs. This dual functionality offers the potential for synergistic effects by combining direct oncolysis with localised drug activation. The interplay between infection, replication, lysis, and gene product delivery remains poorly understood. Here, we introduce a spatially structured, multi-patch model of cancer cells infected by an oncolytic virus engineered to deliver a prodrug-activating enzyme. The spatial system is first represented as a microscopic model and subsequently reduced via spectral dimension reduction techniques. This reduction yields an ordinary differential equation model for a set of coarse-grained variables, which we analyze both without the transgene (OV model) and with the transgene (TOV model). For each case, we compute the basic reproduction number, R0, which determines the conditions for viral spread. Both models exhibit three regimes via transcritical bifurcations: (i) R0 < 0, extinction of both cancer and infected cells; (ii) 0 < R0 [&le;] 1, persistence of cancer cells only; and (iii) R0 > 1, coexistence as a stable node or as a focus. The TOV model, as a difference form the OV model, can undergo periodic oscillations arising from a Hopf-Andronov bifurcation. Notably, oscillation amplitudes can be controlled such that cancer cells largely decrease when drug-induced death is stronger in non-infected cells than in infected ones, enabling effective cancer cells killing while maintaining viral replication and prodrug activation. The qualitative behaviour of the coarse-grained model is shown to be preserved in both the microscopic and spatially explicit models.