Physica A: Statistical Mechanics and its Applications

A fundamental biological process of transcription occurs in the cell nucleus, which is a complex medium that also contains multiple heterogeneous structures known as biomolecular condensates. Interestingly, some of these condensates contain mRNA molecules in addition to proteins, suggesting an important cellular role in transcription that is not yet well understood. In this work, we develop a minimal theoretical framework for quantitative investigation of the role of reversible mRNA condensation in transcription. Our discrete-state stochastic approach accounts for the most relevant processes, allowing us to explicitly evaluate the properties of the system and clarify the effects of condensation. Analytical calculations supported by computer simulations suggest that reversible mRNA condensation influences the transcription processes by maintaining a constant level of free mRNA in the nucleoplasm while lowering the degree of stochastic noise and increasing the robustness against external perturbations. Physicochemical arguments are presented to explain these observations. The proposed theoretical framework elucidates important microscopic aspects of transcription, providing a convenient quantitative tool for investigating complex biological phenomena.

Interleukin-13 (IL-13) is an immunomodulatory cell signaling cytokine that has been implicated in neurodegenerative disease and chronic inflammation. IL-13 binds to its low and high affinity receptors, IL-13 receptor 1 (IL-13R1) and IL-13 receptor 2 (IL-13R2), respectively, with residence times that vary accordingly. As the binding kinetics of the cytokine-receptor complexes influence cellular responses, we employed the molecular dynamics (MD) simulation-based{tau} -random acceleration molecular dynamics method ({tau}RAMD) to compute relative residence times for wild-type (WT) IL-13 and 19 IL-13 mutants to the two receptors. Comparison with experimental kinetic data shows that the{tau} RAMD computations capture the trends in residence times. Analysis of simulated dissociation trajectories of the cytokine-receptor complexes reveals two distinct dissociation pathways of IL-13 from each of the receptors. This study thus pinpoints key determinants of the interaction of IL-13 with its receptors which could be targeted for therapeutic design. Statement of SignificanceCytokines are regulatory proteins that bind to cell surface receptors and thereby send signals to the cellular interior. Interleukin-13 (IL-13) is a cytokine that has a low and a high affinity receptor. It has important physiological roles, and its deregulation is involved in diseases such as atopic dermatitis and asthma. We employed a molecular dynamics simulation-based method to compute the effects of changes in the sequence of IL-13 on the lifetimes of complexes of IL-13 and its receptors. Comparison with experiments supports the validity of the computational approach and analysis of the simulations reveals two distinct ways in which IL-13 dissociates from each receptor. These results thus provide a map for targeting IL-13 - receptor interactions for the design of therapeutics.

We present a quantum-enhanced version of the classic k-Nearest Neighbors (kNN) classification algorithm, applied to the prediction of arterial hypertension. The traditional Euclidean distance metric of the kNN algorithm is replaced with a Fidelity-derived quantum dissimilarity measure to evaluate the similarity between data samples. We map classical real-world clinical and ECG-derived data features into quantum states via the Dense-Angle Encoding, which efficiently utilizes parameterized rotation gates to pack multiple features into minimal qubits while maintaining pure states. We evaluate the performance of the dissimilarity measure using both the noiseless state vector Simulator and the IBM Qiskit Estimator primitives. The quantum circuit demonstrates robust predictive capabilities comparable to the classical model. While it does not claim computational supremacy over the classical baseline, the framework proves that fidelity-based similarity is a physically meaningful and efficient approach for hybrid quantum classical classification.

Within the studies of stochastic gene expression, apart from the variability of copy number of gene products, the problems of threshold crossing of those products are biologically important as they often lead to terminal cellular events. Here, we study the threshold crossing problem of the messenger ribonucleic acid (mRNA) and present an exact probability distribution of first passage times in Laplace space. The function furnishes moments of any order and also predicts the characteristic time of the exponential tail of the distribution, which we match against Gillespie simulations. We find that all the measures of relative fluctuations of the threshold crossing times show U-shapes within this simple model of mRNA, as was found earlier in more mathematically involved models of threshold crossing time statistics of proteins. Furthermore, we extend the exact formula to include the phenomenon of DNA duplication and the corresponding doubling of transcription rate. As expected, the distribution varies considerably depending on the onset of the duplication stage within the cell cycle.

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.

Structural network representations of metastatic dissemination typically focus on static topology without resolving transport dynamics, relaxation timescales, or steady-state behaviour. Here, we formulate a discrete Markovian transport model on a directed higher-order network with transition rates derived from qualitative clinical affinity classes. By constructing a non-Hermitian row-stochastic transfer operator, we characterise the relaxation dynamics through its spectral decomposition. The system exhibits a fast-mixing regime characterised by a spectral gap of {gamma} {approx} 0.67, corresponding to a characteristic relaxation timescale of {tau} {approx} 1.49 discrete steps, with the influence of the primary tumour origin progressively attenuated during dissemination. Convergence towards a non-equilibrium steady state (NESS) is accompanied by a reduction in Shannon entropy, concentrating probability mass within specific topological sinks. This spectral relaxation delineates two distinct dynamical regimes: early transient dissemination (n < {tau}), dominated by local organ-specific transition probabilities (organotropism), and the asymptotic regime (n > {tau}), determined increasingly by the global transport architecture of the network. Comparison with independent clinical and autopsy observations across 21 primary tumours and 23 target organs indicates that the predicted stationary distribution is consistent with the observed hierarchy of metastatic organ involvement.

The study of tissue dynamics has been stimulated during the last decades thanks to the use of quantitative descriptions, with the development of several theoretical and computational frameworks, many of them revolving around the notion of reaction-diffusion systems, eventually with additional structure variables beyond time and space. The use of structure variables can accommodate phenotypic traits. In this work, we study a family of competition models, where a given population depends on a resource (e.g. oxygen) and several populations are competing for it. Our quantitative description incorporates phenotypic traits and heterogeneity at the level of cell cycle variations, which influence replication rates via oxygen consumption. This enables us to replicate the fitness of specific subpopulations to environmental conditions (e.g. oxygen shortage or external influences). Using numerical simulations, we show that such models display dynamical pattern formation in the form of coupled travelling wave profiles that expand or retreat at the same wave speed. The full theoretical analysis of such dynamics is quite involved; to circumvent this difficulty, we introduce a quasi-stationary approximation for the resource dynamics. We find that this approximation can reproduce the overall behaviour very accurately, with the additional benefit of allowing theoretical treatment of the reduced model. In this way, we provide estimates on the wave speed which are numerically shown to be robust across a wide range of macroscopic parameters of the full model. The wave speeds are thus found to depend strongly on the proliferation rate of the fittest population, resembling a winner-takes-all dynamics.

Time compaction theory is a general framework explaining how a brain can efficiently deal with dynamic situations occurring in, e.g., sports games. It involves a geometric representation of the time dimension, which enables effective learning and strategic action planning. The theory has recently received experimental support in humans. However, its current computational model has an important limitation: it does not account for deliberate waiting and speed modulation, behaviors ubiquitous in natural environments. This work substantially extends the original model formulation by a dimensional lifting of an n-D workspace into (n + 1)-D mental space, where time remains geometrically embedded. The proposed biologically inspired computational model can generate adaptive behavior across increasingly complex situations, from navigation in everyday social environments to competitive sports. Furthermore, by actively conditioning the expected responses of other agents and stabilizing future predictions, we introduce the concept of uncertainty points in sequences of generalized cognitive maps to support the generation of adaptive strategies in interactive environments, where future prediction has a limited time horizon. Thus, we provide a mechanism for chaining short-term solutions into long-term strategies, which is illustrated by simulating the behavior of a player in a real football game. Author summaryHumans often anticipate future interactions in dynamic environments. Many behaviors, such as avoiding other pedestrians, letting someone pass through a narrow corridor, or reproducing the kind of dribbling maneuvers performed by elite football players, require deciding not only where to move but also when to move. Existing theories suggest that the brain simplifies such situations by representing future interactions as static spatial maps, making them easier to learn and recall. However, current computational models cannot naturally account for common behaviors such as waiting, slowing down, or modulating speed. Here we show that these behaviors readily emerge if the model space is extended by an additional virtual coordinate that encodes accumulated waiting rather than physical time. The proposed model simultaneously admits a wide variety of behaviors, including speed modulation, multigoal decisions, and compound actions, while preserving the principles of time compaction. We illustrate the model in everyday situations and by reproducing two real football plays, comparing the observed behaviors with model simulations. Our results suggest computational principles through which the human brain may efficiently represent, memorize, and exploit dynamic situations.

This paper presents and critically reviews the results of original and some literature based experimental studies conducted by the authors last years on the structural organization of DNA in dormant (starvation stress), anabiotic dormant (4 HR treatment) E. coli cells, as well as the K12 {Delta}dps strain, which lacks the Dps protein (Dps null E. coli). The experimental data includes small-angle synchrotron radiation diffraction (SAXS) and transmission electron microscopy (TEM) data. Synchrotron radiation diffraction experiments on K12{Delta}dps cells allowed us to conclude that peaks at 44.3, 22.1, and 14.8 angstrom resolutions are associated exclusively with ordered DNA organization. Peaks at 44.3, 22.1, and 14.8 angstrom resolutions are also observed for samples of dormant (starvation stress) cells and anabiotically dormant cells. Therefore, this ordered DNA organization also applies to samples of dormant and anabiotically dormant cells. A model is proposed that considers the ordered DNA organization in the cell as a cholesteric liquid crystal. The powder diffraction pattern calculated based on this model is compared with experimental small angle X ray scattering (SAXS) data obtained on Dps-null cell samples. The model completely reproduces the key features of the experimental diffraction pattern from Dps-null cell samples. Accordingly, the cholesteric liquid crystal model corresponds to DNA packaging in dormant and anabiotically dormant cells. Cholesteric liquid crystal ordering should be further considered in all models of cellular DNA packaging. To address the question of which structural organization of DNA predominates in the cell: the cholesteric liquid crystal or nanocrystalline or whether they coexist and fully manifest themselves under different external conditions, it is necessary to utilize the latest methodological advances in structural analysis.

Based on our experimental observation of activation state oscillations of different frequencies used to communicate information by the master human stress response regulator protein p38 MAPK 1, we develop a simple graphical approach for understanding and predicting the behavior of complex biological networks acting upon signals carrying information as different frequency waves of chemicals. This approach uses the same techniques used for analyzing and understanding information transmission using waves of electrical currents and fields used in electrical alternating current (AC) circuits. We show how biological components can be organized to behave as standard components found in electronic telecommunications circuits. Finally, we demonstrate how such components can be organized into complex biological signaling cascades whose behavior can be qualitatively and quantitatively understood, and whose output resembles that experimentally observed in p38.

The process of drug unbinding is of immense importance in the field of biophysics and therapeutics. The behavior of these systems is greatly influenced by their thermodynamic and kinetic properties. Therefore, it is crucial to accurately estimate the ligand binding free energies and rate of ligand dissociation, yet these processes are often governed by rare event transitions that lie beyond the reach of standard brute-force molecular dynamics simulations. While enhanced sampling simulations offer a solution, their efficacy is strictly contingent upon the selection of appropriate collective variables (CVs) which is non-trivial for complex systems like protein-ligand complexes. In this study, we present a method to derive optimized CV from transition state region (TS) via an interpretable machine learning (ML) model, Elastic Net. By employing some physically intuitive order parameters, the derived optimized CV from the TS-region greatly accelerate ligand binding-unbinding transitions and achieves rapid free energy surface (FES) convergence across diverse systems including buried and solvent exposed active sites such as Trpsin-benzamidine complex, host-guest systems and sodium epoxidase etc. Intriguingly significant contribution of the ligand hydration is found in the optimized CV which depicts crucial role of solvent in driving ligand binding-unbinding transitions. The estimated binding free energies for different protein-ligand complexes match quite well with experiments, while maintaining a low computational cost. The derived optimized CV is also used to calculate the ligand residence times across different systems and calculated residence times are within the experimental range for all systems, again with very little computational costs. Moreover, we show that the optimized CV constructed from TS region via an interpretable ML model is transferable across diverse systems, offering a robust and scalable framework for drug discovery and investigation of complex biomolecular recognition.

With 302 neurons and a rigorously characterized connectome, the nematode Caenorhabditis elegans represents a powerful model organism to study the fundamental roles of neuronal circuits in behavior. However, despite the breadth of research, many questions remain unanswered regarding how these organisms are able to successfully navigate their environment. Here, we present a biologically grounded dynamical circuit model for the investigation of sensory-guided behavior during C. elegans chemotaxis. Our mathematical model consists of the chemosensory neuron AWA, interneurons RIM and RIA, motor neurons, including SMDs and RMDs, and body wall muscles that provide proprioceptive feedback through stretch receptors. After optimization with an evolutionary algorithm, the model locomotes effectively toward a chemical attractant, realistically capturing nematode chemotactic behavior. Chemotaxis is ensured by sharp turns, which resemble the omega turns of living nematodes, as a key emergent property of the model. The sharp turning behavior is triggered by decreases in the concentration of the attractant. These result in reduced AWA activity, which in turn triggers disinhibition of RIM and subsequent changes in RIA oscillations. The ensuing coordinated changes in downstream motor neurons activity patterns produce sharp turns, which correct the nematodes path, so that the model worm heads toward the attractant, and remains at its proximity, after it reaches the gradient peak. The proposed framework, along with its emergent dynamics, provides new insights into the minimum requirements for C. elegans circuitry to display major features of its chemotactic behavior, including omega turns. In parallel, it generates experimentally testable hypotheses with respect to the participating neuronal elements.

Equivalent numbers represent biodiversity as the effective number of equally distinct units, typically species, and can be partitioned across scales. In practice, they summarize each unit of biodiversity by a single value and compare units pairwise, misrepresenting units that are better described as distributions and the relationships between several units that share the same space. We introduce an equivalent-number index for assemblages of units represented as probability density functions (PDFs) over a continuous space, estimated as the integral of the pointwise maximum across abundance-weighted PDFs. Resulting equivalent PDF numbers fulfil elementary properties of classical equivalent numbers, and support additive partitioning across any number of nested scales. We illustrate the framework with case studies across three domains: (1) measuring trait diversity considering intraspecific variability in grasslands, (2) partitioning realized bioclimatic niches among clades of Carnivora, and (3) understanding seasonal changes in the partitioning of fish home ranges in geographic space.

Mechanical properties of biological tissues, driven by passive and active forces, play a vital role in several processes ranging from development to cancer metastasis. However, the dynamical responses of cells in tissues, subject to mechanical deformations such as shear and the associated rheological properties, are not well characterized. Here, we use three-dimensional agent-based models for normal and cancer tissues to investigate their responses to simple shear as a function of cell stiffness and stochastic active forces. In the normal epithelium, with uniform strength of active force, the yield stress as a function of shear rate follows the Herschel-Bulkley form over a range of cell volume fraction. Strikingly, the shear rate dependence and the elasticity-dependent changes in the yield stress fall on master curves upon suitable scaling. To model cancer-like behavior, a certain fraction (Np) of cells was chosen to have enhanced activity and decreased stiffness. As Np increases, the extent of collective cell movement decreases, transitioning from affine (collective) to non-affine (individualistic) movement, a finding that is in accord with imaging experiments. Simulations of a model of a stiff solid tumor, with radius Rs embedded in normal tissue, show that as Rs increases, the yield stress increases. Interestingly, the cells migrate collectively as Rs increases. A Gaussian Mixture Model (GMM) and a mean field theory quantitatively account for the simulation as well as experimental results on cancerous, non-cancerous, and a mixture of these two types. The combined theoretical and experimental study establishes that heterogeneity in stiffness and activity determines non-affine movements in normal and cancer tissues.

Wound repair is an important mechanism to preserve tissue integrity in organisms after injury. However, why different tissues exhibit different mechanisms to repair wounds is a long-standing question that remains unanswered. In this work, we theoretically explore the role of the purse string, an actomyosin contractile cable used by tissues to close small wounds. Does the tissue 3D geometry influence the efficiency of the purse string in driving wound closure? Using a 3D biophysical model, we study in silico tissues with the same cell volumes but different aspect ratios, ranging from squamous to thick and tall tissues. The model predicts that taller cells are easily deformed by the purse string. In contrast, very squamous cells require a very strong purse string that might demand additional cellular mechanisms to close the gap. These findings establish a theoretical framework to predict the optimal biophysical mechanisms of wound healing in different tissues. Graphical abstractCells of different aspect ratios can be observed in a range of organisms with different function and mechanics. The wound healing efficiency of the purse string increases with the cell aspect ratio in our theoretical exploration. O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=135 SRC="FIGDIR/small/743165v1_ufig1.gif" ALT="Figure 1"> View larger version (23K): org.highwire.dtl.DTLVardef@d44ab0org.highwire.dtl.DTLVardef@1737cbaorg.highwire.dtl.DTLVardef@101b5d4org.highwire.dtl.DTLVardef@1487f26_HPS_FORMAT_FIGEXP M_FIG C_FIG

Numerous advances in quantum and computational chemistry over the last decades, well as the development of computer science, allowed utilisation of more precise and complex models, which can be now applied to much bigger systems than in the past. The authors used Gaussian, coupled with theoretical methods, to predict a new way of peptide bond formation, which could have taken place in prebiotic conditions. To better tackle this difficult task, the properties of substrates (glycine-derived radicals) were extensively analysed, using the aforementioned tool - Gaussian, paired with taking resonance and hybridisation into account, to better understand the stereochemistry and the very nature of processes taking place. The result is a series of reactions, which without any sophisticated catalysts and with relatively low energy thresholds ({inverted exclamation}20 kcal/mol) can lead to formation of dipeptides (and further, oligopeptides). The authors also hope, the other predicted properties of the investigated molecules can be of use to any researcher, who would like to utilise them in their experiments. Author summaryOur goal was to investigate a way first peptide bonds in prebiotic conditions could have been formed. This is an extremely important step in research into the beginning of life on Earth. We found a very promising series of reactions, which uses atomic hydrogen as its only catalyst and confirmed our expectations with theoretical calculations, using Gaussian. There are two radicals derived from glycine, which perform major roles in the process, so we investigated their properties with Gaussian and verified that the results are in agreement with our own theoretical considerations. This involved checking for possible geometric isomers and conformers and creating models which could explain their properties. We are well aware that such calculations have limitations and there is no model, which is 100% accurate, so our results should be further confirmed by empirical data in the future. However, we still to be as thorough as possible in how we approached the subject.

In the active loop extrusion model, the cohesin protein complex creates chromatin loops in eukaryotic cells. Extrusion maintains topologically associated domains (TADs), which are contiguous segments of chromatin that preferentially colocalize in space and are typically bounded by CTCF proteins that pause cohesin translocation. Here, we model active loop extrusion with hybrid molecular dynamics - Monte Carlo simulations in entangled flexible linear polymer melts. Intra-chain contact probabilities of polymers with active loop extrusion are enhanced compared to their equilibrium, passive counterparts. Extrusion causes the size of chain segments to be much smaller than in passive melts. While the overlap parameter in passive melts without extrusion monotonically increases with segment length, it is nonmonotonic in active melts and on the order of unity within the parameters of this study. Active loop extrusion suppresses contacts between TADs in favor of intra-TAD contacts. Reduction of overlaps between chain segments dilutes entanglements in active melts. Depending on parameters, active extrusion without TADs may induce more compact conformations than with TADs, due in part to fractal loopy globule-like dynamics. This work suggests that active loop extrusion reduces overlaps between TADs, contributing to effective gene regulation by cis-regulatory elements.

This study aimed to (1) develop an elasticity framework for the sprint force-velocity (F-V) relationship and (2) examine how maximal force (F_{0}), maximal velocity (v_{0}), and sprint distance modulate the four derived elasticity metrics, and (3) explore these elasticity metrics' interrelation. After modelling the F-V relationship differential equation, four elasticity metrics were defined as force elasticity (F_{e}), the elasticity of sprint time to F_{0}; velocity elasticity (v_{e}), the elasticity of sprint time to v_{0}; the force-velocity elasticity norm {(\mathrm{F}-\mathrm{V}}_{\mathrm{EN}}=\sqrt{F_{e}^{2}+v_{e}^{2}}), capturing the combined sprint time sensitivity to proportional changes in F_{0} and v_{0}; and the force-velocity elasticity ratio {(\mathrm{F}-\mathrm{V}}_{\mathrm{ER}}=F_{e}{\div v}_{e}), indicating which variable dominates the sprint time response. Model simulations showed that F_{e} decreased with rising F_{0} and increased with rising v_{0}, while v_{e} showed the opposite pattern. With increasing sprint distance, F_{e} decreased and v_{e} increased. Given its negligible effect on sprint time, ignoring air resistance yields a conservation law (2F_{e}+v_{e}\equiv 1), indicating that a gain in one elasticity metric necessarily diminishes the other in a fixed proportion. This framework also identifies a valley distance (d_{valley}) at {\mathrm{F}-\mathrm{V}}_{\mathrm{ER}}=2, where {\mathrm{F}-\mathrm{V}}_{\mathrm{EN}} is minimized (\sqrt{0.2}) and sprint time is least responsive to changes in F-V relationship variables. Empirical data confirmed that the two theoretical laws still hold approximately when air resistance is considered. By linking changes in F_{0} and v_{0} to sprint time across different distances, the elasticity framework provides a quantitative basis for estimating the theoretical sprint time response to documented changes in F-V relationship variables.

Background: Tuberculosis remains a persistent infectious disease whose control is complicated by latent infection, delayed treatment, incomplete recovery, reinfection, and continuing transmission from infectious individuals. Although treatment is central to tuberculosis management, it is frequently represented only as a transition parameter in mathematical models rather than as a separate epidemiological state. In this study, treatment was therefore incorporated explicitly as an independent compartment so that its influence on transmission, recovery, disease-induced mortality, and long-term disease persistence could be evaluated. Methods: A deterministic nonlinear compartmental model was formulated by dividing the total population into susceptible, exposed, actively infected, treated, and recovered classes. Reinfection of recovered individuals, progression from latent infection to active disease, movement of infectious individuals into treatment, treatment-associated recovery, natural mortality, and disease-induced mortality were included. Positivity and boundedness of the solutions were examined to establish biological validity. The basic reproduction number, R0, was derived through the next-generation matrix approach. Disease-free and endemic equilibria were determined, and their local and conditional global stability properties were investigated using Jacobian analysis, the Routh-Hurwitz criterion, center manifold theory, Lyapunov functions, and LaSalles invariance principle. Normalized sensitivity indices, Latin hypercube sampling, partial rank correlation coefficients, and numerical simulations were also applied. Results: The disease-free equilibrium was shown to be locally asymptotically stable when ,R0<1 whereas sustained transmission and a unique endemic equilibrium were associated with R0>1. Under the stated reduced-model assumptions, stability of the endemic equilibrium was established. Transmission-related parameters were identified as the strongest positive contributors to disease persistence. In contrast, treatment and recovery parameters were found to reduce the reproduction number and infectious burden. Numerical simulations indicated that stronger treatment implementation and reduced transmission opportunities produced substantial reductions in active tuberculosis cases. Conclusion: Treatment was shown to function as both a clinical pathway and an epidemiological control mechanism. The proposed framework may support the design of treatment-centered strategies for reducing tuberculosis prevalence and preventing long-term endemic persistence.

Tumors consist of heterogeneous phenotypic cells, such as normoxic cells, which are highly proliferative, and hypoxic cells, which are less proliferative. Their phenotypic switching depends on tumor microenvironmental factors, such as oxygen and nutrient concentrations supplied by local blood vessels. However, during ongoing angiogenesis, the process of sprouting new blood vessels at the tumor site from pre-existing blood vessels, and how this phenotypic switching affects and impacts tumor growth, remains poorly understood. In this article, we formulate a mathematical model to elucidate the crosstalk between vasculature and tumor cellular heterogeneity during tumor progression. The model results show a strong agreement with the experimental data. Our simulation results demonstrate that ongoing angiogenesis increases tumor growth rate. In addition, we observe that the influence of hypoxic cells on phenotypic switching from normoxic to hypoxic is more pronounced than their influence on the transition from hypoxic to normoxic. Furthermore, we perform a global sensitivity analysis using the Sobol's method to assess the importance of the model's parameters. It highlights that the volume at which blood vessels attain half-maximal rate has the maximum effect on the model.