Soft Matter

Cell plasma membranes exhibit heterogeneous lateral organization whose dynamic compartmentalization is critical for processes such as viral infection and fertilization. While membrane tension is known to influence crucial cell remodeling processes, its role in regulating membrane heterogeneous organization remains unclear. To reveal the effect of tension on lateral membrane organization, we used supported lipid bilayers on flexible substrates. These were prepared by rupturing ternary-composition giant unilamellar vesicles exhibiting liquid order-disorder phase coexistence. The phase coexistence is observed using a fluorescent probe that preferentially partitions to the disordered phase. Using a motorized equibiaxial stretching device, we observed domain morphology homogenization under membrane stretching. We define an order parameter based on the relative concentration of the dye in the two phases, which is a proxy for the membrane lateral organization. Order parameter analysis revealed power-law scaling near the critical strain with an exponent {beta} = 1.0 {+/-} 0.3, consistent with an elastic theoretical model predicting {beta} = 1. The progressive broadening of the interfacial region width near the critical strain, and continuous transition to a homogeneous phase, is consistent with a second-order phase transition. These findings indicate that membrane tension may serve as a physical regulator of lateral lipid organization, with implications for how cells use mechanical forces to regulate their structure and function.

The actin cytoskeleton is an inherently disordered active system. the actomyosin cortex and reconstituted actomyosin systems are globally disordered, yet undergo transitions between distinct disordered states as parameters like motor and crosslinker concentration and filament length and rigidity change. In cells these changes are related to genetic mutations or differences in cell state and dictate fundamental biological processes. However, we dont have well established methods to detect and classify differences in disordered polymer networks. Image-based morphology techniques provide a non-invasive, high-throughput method of extracting information about a system. In this work we simulate biopolymer networks under varying conditions and develop and use morphological descriptors to construct trajectories in morphospace. Using statistical analysis we find that morphological descriptors are able to distinguish between different trajectories of the system, including differences not apparent to the eye. However, no single descriptor alone is able to capture all the differences in the simulated trajectories. Nematic order parameters typically perform the worst for our simulations while curvature and texture descriptors can collectively distinguish between dynamic trajectories. This work helps develop quantification of cytoskeleton dynamics for classification and data-driven modeling.

The interactions of droplets and filaments can lead to mutual deformations and complex combined behavior. Such interactions also occur within the cell, where biomolecular condensates, distinct liquid phases often composed of proteins, have been observed to structure and affect the organization of the cytoskeleton. In particular, biomolecular condensates have been shown to undergo characteristic deformations when cytoskeletal filaments are fully embedded within them. However, a full understanding of the underlying physical mechanisms is still missing. Here, we combine experiments with coarse-grained molecular dynamics simulations and analytical models to uncover the physical mechanisms that define emerging shapes of droplets containing filaments. We find that the surface tension of the liquid phase and the bending energy of the filament(s) suffice to accurately capture emerging shapes if the length of the filament is small compared to the liquid volume. As the volume fraction of filament(s) increases, wetting effects become increasingly important, setting physical constraints within which surface and bending energies compete to define the droplet shapes. We find that mutual deformations of condensate and filament extend accessible shapes beyond classical stability considerations, leading to structuring and entrapment of contained filaments. Shape deformations may further affect ripening dynamics that favor certain geometries. Our findings provide a physical framework for a better understanding of the possible roles of biomolecular condensates in cytoskeletal organization.

Coacervate droplets and lipid vesicles are two classes of self-assembled compartments that have been proposed as protocell models. Hybrid protocells, in which a coacervate core is surrounded by a lipid membrane, can integrate the advantages of both protocell systems while overcoming their limitations. Although hybrid protocell membranes have been produced with a variety of diacyl phospholipids related to modern biology and some single-chain amphiphiles inspired by prebiotic scenarios, little is known about how mixtures of single-chain amphiphiles impact hybrid protocell membrane formation and properties. Given the plausible diversity of amphiphiles in the prebiotic milieu, the resulting membranes would have inherently incorporated multiple lipids of different types, potentially altering the properties and viability of hybrid protocells in their environment. Here, we systematically increased the compositional heterogeneity of hybrid protocell membranes by using different prebiotically relevant single-chain amphiphiles of varying head groups and alkyl chain lengths. These membranes were assembled around model coacervate droplets generated from polyallylamine hydrochloride and adenosine diphosphate, and the effect of heterogeneity on membrane properties and stability was evaluated. Compared to protocells with homogeneous membranes, those with heterogeneous amphiphile membranes exhibited higher yields, smaller sizes, and greater sub-compartment formation. Also, they showed increased membrane order, retained similar lateral lipid diffusion, and showed population-level variability in permeability to small anionic molecules. Notably, heterogeneous membranes showed enhanced structural stability under acidic conditions, retaining key properties like size and sub-compartment heterogeneity, thereby broadening the pH range over which hybrid protocells remain intact. These findings suggest that amphiphile diversity not only would have influenced the structural properties of hybrid protocells but also created diversity within the protocell population and enhanced their robustness, thereby playing a crucial role in protocell evolution on early Earth.

Despite receiving significant interest from the biological and engineering communities, several questions about the underlying reasons for the form of the deep-sea sponge Venus Flower Basket (Euplectela aspergillum) remain unanswered. In particular, the basis for the sequence of emergence of three distinct macroscopic geometric features, while speculated upon, has not been validated. These features are (i) an interwoven cross-grid in the juvenile stage, (ii) a diagonal weave atop this initial grid, and (iii) a helical ridge that emerges in the mature phase of the sponge. This work uses computational design and additive manufacturing to fabricate models of each of these phases in sequence and subjects the models to mechanical tests in compression, bending and torsion. The results show that each feature has a singular advantage, even after accounting for the increase in mass associated with their addition: increased compliance for interwoven cross-grid, increased bending stiffness for diagonal weaves, and improved torsional rigidity for the helical ridge. The work postulates that the prioritization of compliance in the juvenile phase and a transition to a stiffer structure in the mature phase is a strategy that enables the sponge to avoid high internal stresses to avoid failure in its inherently brittle, silica-derived architecture. Highlights1. The benefits of three macrostructural design elements of the Venus Flower Basket (E. aspergillum) that emerge sequentially in its development are examined: (i) the interweaving cross-grid, (ii) the diagonal weave that overlays this cross-grid, and (iii) the helical ridge reinforcement that forms over this diagonal weave. 2. For the first time, this work models each of these design features sequentially and studies their mechanical benefits through an experimental exploration of the behavior of idealized geometries in three test domains: compression, bending, and torsion. 3. Results show that each of these three structural elements has a unique functional advantage depending on the organisms growth stage, even after accounting for differences in mass: interweaving enables higher compliance under compression, the diagonal weave improves bending stiffness, and the helical ridge improves torsional stiffness.

Efficient drug delivery using nanoparticles (NPs) critically depends on their ability to diffuse through biological tissues to reach target cells at therapeutic concentrations. The extracellular matrix (ECM) poses a key barrier to such transport, which directly influences bio-distribution, cellular uptake, and overall therapeutic efficacy. A key regulator of this transport is hyaluronic acid/hyaluronan (HA), a major ECM polysaccharide that forms a hydrated, viscoelastic network. Increased/reduced hyaluronan concentration can elevate/decrease ECM bulk and effective viscosity. Increase in effective viscosity at the nanometer/micrometer length scales can hinder NP mobility through steric obstruction and hydrodynamic drag. There is a large variability in the HA molecular weights and concentrations, especially across age, tissue/organ, and pathological conditions. This work aims to study the diffusion of different NP types in the mixtures of HA polymers with variable molecular weights using the dynamic light scattering technique (DLS). Furthermore, we perform coarse-grained molecular dynamics (CG-MD) simulations for a model system to complement our findings from the dynamic light scattering experiments. We observe NP undergo anomalous diffusion, which is strongly dependent on the ratio of particle size/HA network mesh size, especially for higher molecular weight mixtures. This is strongly influenced by the effective viscosity, which is defined at the local environment experienced by the NPs. Our work highlights developing a simplified predictive framework coupled with simulations for a target-specific extracellular matrix environment.

Saturated fatty acids such as stearic acid (SA) can exhibit both antimicrobial and growth-promoting effects on bacteria, depending on their concentration and chemical structure. However, the physical properties of the bacterial cell envelope in response to such molecules remain under-explored compared to their biochemical pathways. In this study, a comprehensive investigation is presented on the interaction of SA with the Gram-positive bacterium, Staphylococcus epider-midis (S. epi). SA alters bacterial growth, reflected in a higher maximum specific growth rate, a shorter lag phase, and an extended exponential phase, consistent with a prebiotic effect. Using fluorescence correlation spectroscopy and fluorescence lifetime imaging microscopy, we show that SA incorporation leads to significant fluidization of the lipid membrane, characterized by enhanced lateral diffusion and reduced membrane viscosity. Coarse-grained molecular dynamics (CG-MD) simulations demonstrate spontaneous insertion of SA into the membrane and a significant increase in mean-square displacement after insertion, supporting our experimental observations. Importantly, atomic force microscopy measurements show an increase in cell-envelope stiffness, reflected by a higher Youngs modulus which can be attributed to modulations in the glycan-peptide linkage density based on earlier studies that correlate stiffness changes to peptidoglycan (PG) crosslinking in Gram-positive strains [1]. These results provide direct evidence linking membrane fluidization induced by SA and increased cell wall stiffness due to transport modifications in the membrane mediated PG synthesis pathways to enhance bacterial cell viability.

In multicellular organisms, various cellular structures exhibit cytoplasmic sharing, where cells remain interconnected. While essential for development and function in contexts such as germ cell formation and insect early embryos, the physical basis of cell volume regulation in these systems remains poorly defined. Germline cysts are formed by interconnected sister cells via intercellular bridges. In mice, germline cysts form during gametogenesis in fetal ovaries and testes. In mouse fetal female cysts, cells with numerous bridges preferentially differentiate into oocytes by selectively increasing their volume, a process that may be mediated through cytoplasmic flow. This volume bias may be influenced by hydrostatic pressure within the cytoplasm. Here, we theoretically investigate how the mechanical properties of cells affect cytoplasmic pressure and volume distribution within interconnected cells. Our soap-bubble model revealed that cells with more bridges exhibit increased volume when they have large cell-cell contact areas, as observed in fetal cysts. We found that incorporating cell cycle (including cell growth and cell division) significantly enhances the likelihood of volume bias in favor of cells with more bridges. These theoretical findings suggest that intrinsic mechanical properties, coupled with cell cycle, establish robust cyst development in fetal female germline cysts. Our findings also provide insights into the volume dynamics observed in adult male germline cysts, which are characterized by smaller cell-cell contact areas. Impact statementA theoretical model demonstrates how mechanical properties and cell cycle dynamics regulate volume distribution in germline cysts, providing a physical basis for oocyte differentiation.

The apparent pKa of ionizable lipids in lipid nanoparticles (LNPs) is a key determinant of RNA encapsulation during formulation and endosomal release after cellular uptake. However, it is difficult to predict the effective pKa of a given ionizable lipid solely from its solution pKa, because it is sensitive to the membranes composition, as well as solution conditions such as the salt concentration. We developed a simple continuum electrostatics model, based on Gouy-Chapman theory, to predict the shift in effective pKa for ionizable lipids in lipid bilayers as a function of salt concentration and membrane composition. We derive equations for the surface potential and fraction of lipids charged, which are solved self-consistently as a function of solution pH to extract the titration curve and effective pKa. The model shows that the shift in effective pKa is largest when the concentration of titratable lipid is high, and the effect is diminished by increasing salt concentration. We provide a python implementation of the model and an interactive notebook that will allow users to further easily explore the predicted pKa shifts as a function of formulation variables.

Embryonic development in multicellular organisms exhibits diverse morphogenetic patterns, which can generally be categorized into fundamental types such as monolayer and multilayer spheres, as well as cell masses. Furthermore, we identify two distinct processes for the formation of spherical structures. These basic patterns are thought to be governed by the microscopic properties of intercellular adhesion. However, the specific mechanisms linking the microscopic factors to the emergence of distinct macroscopic morphogenetic patterns remain poorly understood. In this study, we explore how different morphogenetic patterns arise by employing a computational model that incorporates intercellular adhesion and polarity. Our results demonstrate that all fundamental morphogenetic patterns can be generated through the interplay of two key parameters: the strength of cell polarity and the regulation of polarity via mechanical signals. Furthermore, analytical discussions reveal partial mechanisms underlying the formation of these patterns. These findings highlight the critical role of physical constraints in morphogenesis and suggest potential applications in the design principles for artificial tissues and organoids. Author summaryLiving organisms build their bodies through morphogenesis, during which cells autonomously arrange themselves into functional structures such as sheets, tubes, and spheres. From simple monolayered spheres to complex multilayered tissues organized by adhesion, it remains unclear how such diverse forms arise. Here, we mathematically modeled a population of proliferating cells governed only by two microscopic factors: the strength of polarity-dependent adhesion and the time scale at which polarity is regulated by cell-cell contact. Surprisingly, we found that this minimal model reproduces five basic morphological types observed in living embryos, including monolayer/multilayer structures and two distinct modes of cavity formation: by wrapping around or by inflating from the inside. Systematic simulations revealed that these macroscale outcomes are determined solely by two parameters controlling polarity strength and its regulation, suggesting that simple physical rules underlie diverse developmental architectures. Analysis of the model uncovers phase transitions between the five morphogenetic types and reveals how varying polarity and adhesion can recapitulate features of real embryogenesis. Our work proposes a unified framework that connects microscopic polarity mechanics to diverse developmental morphologies and provides a foundation for future applications in organoid design and tissue engineering.

A broad range of cellular functions involve transient or persistent changes in the morphology of lipid membranes, from the organellar to the molecular scale. By and large, the thermodynamics of these remodeling processes remain to be understood. Molecular Dynamics simulations enhanced by advanced sampling methods are uniquely suited to examine and quantitate these phenomena. Here, we focus on the cellular process known as mechanosensation and use the Multi-Map simulation method to quantify how applied lateral tension impacts the energetics of both global and localized membrane perturbations induced extrinsically. We also examine how tension impacts the dynamics of lipid molecules. We find that the conformational energetics of the membrane clearly differs when it is stretched, and that this difference increases with the magnitude of the applied tension. The reason is not that tension alters the mechanical properties of the lipid bilayer, such as its bending modulus, but rather that it opposes any reduction in the projected area of the membrane relative to that at rest, while the opposite is favored. It follows that tension may shift a conformational equilibrium of a protein that deforms the membrane differently in alternative functional states, if that difference also entails a change in the projected membrane area. Conversely, we find that stretch has little to no effect on the dynamics of lipids at the single-molecule level, implying it would also have no bearing on the lifetime of specific protein-lipid interactions. Finally, we show how changes in lipid composition that result in global membrane thinning can mimic the effect of lateral stretch without any applied tension. Statement of SignificanceCells have evolved the ability to sense mechanical forces, such as pressure or stretch, through specialized proteins embedded in their membranes. How exactly the membrane transduces these stimuli to the proteins therein has been unclear. Using state-of-the-art computer simulations, we show that stretching a membrane does not result in forces that pull or push on the individual lipid molecules that constitute the membrane. Instead, lateral tension alters the energetics of reshaping the membrane. This shift in plasticity explains why several well-known force-sensing proteins switch between active and inactive states at specific tension values observed experimentally. We also show that altering the lipid composition of the membrane can produce the same effect as lateral stretch, without any applied force.

This study uses a previously reported 3D-printed variable-height flow cell to investigate the viscoelastic properties of chondrocytes from 2D monolayer and 3D alginate cultures. It was hypothesized that chondrocytes could be distinguished by phenotype associated with their culture environment using viscoelastic recovery time, owing to variation in the pericellular matrix (PCM) produced by chondrocytes from different culture methods. The PCM surrounding the chondrocytes was imaged with confocal microscopy during applied deformation and subsequent recovery. The projected cell area was fitted with a Burgers mechanical model to extract the viscoelastic recovery time. No difference between bovine and primary OA cells from monolayer cultures was observed. However, a statistically significant difference in recovery time was observed between cells from monolayer and alginate cultures in both the bovine (31 s vs. 13 s) and primary OA (34 s vs. 13 s) groups. This work shows that viscoelastic recovery time is influenced by the culture method used for chondrocytes and further demonstrates the role of the PCM as a mechanical protector of chondrocytes.

Lipid nanoparticles (LNPs) are the most successful drug delivery carrier to date, but optimizing lipid formulations to improve membrane fusion capabilities for effective drug release has been challenging due to lack of a quantitative measure for fusogenicity. Here we introduce a new framework based on small angle X-ray scattering to experimentally measure [Formula] for lipids used in LNP formulations such as glycerol monooleate (GMO) and ionizable lipids (SM-102 and ALC-0315). Q intrinsically captures spontaneous curvature (J0), which is traditionally used to assess fusogenicity. The change of cubic lattice parameters with temperature was measured for GMO-containing lipid mixtures, and the Q extracted quantitatively correlated with LNP fusogenicity power validated by fluorescence-based fusion assays and cryogenic electron microscopy. Fusogenicity of SM-102 and ALC-0315 was quantified by adding them to host membranes and assessing change in Q. This framework provides researchers with the ability to optimize the fusogenicity of LNP formulations for potent drug release and enhances understanding of parameters governing fusion in all biomembranes.

-Synuclein (Syn) remodels cellular membranes through interactions that involve both its structured, membrane-binding N-terminal domain (NTD) and intrinsically disordered C-terminal domain (CTD). While the amphipathic NTD helix is known to insert into lipid bilayers and generate curvature, the contribution of the acidic CTD remains unclear. Here, we dissect the individual and cooperative roles of these domains using Supported Bilayers with Excess Membrane Reservoir (SUPER) templates to quantify membrane remodeling via membrane fission and membrane morphological deformations (i.e., membrane budding and tubulation). We show that both the NTD and CTD independently remodel membranes, while full-length Syn exhibits greater remodeling ability than either the NTD or CTD in isolation. This result demonstrates a synergistic amplification between helix insertion of the NTD and the tethered, disordered CTD. To further probe the mechanism of membrane remodeling by the CTD, we modulated the chain length of the protein, the bulk ionic strength of the solution (i.e., charge screening), and applied relevant polymer scaling laws for disordered proteins. Our results suggest that the membrane remodeling mechanism for the disordered CTD is electrostatic in nature, stemming from protein-protein repulsion at elevated binding densities. Together, our findings reveal a cooperative energetic mechanism in which N-terminal helix insertion biases membrane curvature and the disordered, C-terminal domain adds an additional electrostatic component that helps to overcome the free energy barrier for membrane bending.

Escherichia coli (E. coli) biofilms consist of bacteria, an extracellular matrix (ECM) mainly made of curli amyloid fibers, phosphoethanolamine-modified cellulose (pEtN-cellulose), and water. While curli amyloid fibers contribute to biofilm rigidity, pEtN-cellulose contributes to their cohesion. This work explores the interplay between these fibers, and how their interaction influence biofilm structure and mechanical properties. We performed a multiscale analysis on E. coli biofilms grown using strains producing curli and pEtN-cellulose, and only curli and only pEtN-cellulose in co-seeded ratios. Micro-indentation experiments, confocal microscopy, and cryo-FIBSEM 3D imaging revealed a composite-like behavior of the biofilm, where its mechanical properties depend on ECM composition and organization. Spectroscopic analysis of the extracted fibers showed that their biophysical properties are influenced by their pEtN-cellulose to curli ratio and assembly. We propose that pEtN-cellulose swelling is contrained by its interactions with rigid curli fibers. The reference E. coli strain maximizes this effect by assembling a curli/pEtN-cellulose hybrid material at the sub-micron scale, where its composition, interactions, and architecture can explain biofilm emergent properties. This knowledge on microbial ECM assembly opens new avenues for engineering living materials, especially for the use of bacterial biofilms as a source of bio-sourced materials.

Adhesion of spherical nanoparticles or virus-like particles to membranes can lead to membrane tubules in which linear chains of adhering particles are cooperatively wrapped by the membrane. This cooperative wrapping of spherical particles in tubules is energetically favourable compared to the individual wrapping of the particles because of a favourable interplay of bending and adhesion energies in the contact regions in which the membrane detaches from the particles, and because a particle in a tubule has two such contact regions in the membrane necks that connect the particle to the neighbouring particles, whereas an individually wrapped particle has only one contact region to the surrounding membrane. The energetic gain of cooperative wrapping strongly depends on the range of the particle-membrane adhesion potential, which determines the size of the contact regions. At sufficiently large adhesion energies for wrapping, the energy gain {Delta}E per particle is only weakly affected by the membrane tension{tau} as long as the characteristic length [Formula] of the membranes with bending rigidity{kappa} is clearly larger than the contact regions. For large particle adhesion energies at which the particles are fully wrapped, however, {Delta}E can be limited by the minimum possible radius of the membrane necks, depending on the adhesion potential range.

Cerebrospinal fluid (CSF) is a Newtonian fluid that bathes the brain and spinal cord and oscillates in response to the physiological periodic changes in brain volume, of which the cardiac cycle is a major driver. Understanding this motion is essential for clarifying its contribution to solute transport, waste clearance, and drug delivery. In this work, we study oscillatory and steady streaming flow in the cranial subarachnoid space using a lubrication-based theoretical framework. The model represents the cranial CSF compartment as a thin fluid layer bounded internally by the brain surface and externally by the dura, driven by time-dependent brain surface displacements. We first derive simplified governing equations for flow over an arbitrary smooth sphere-like brain surface and obtain analytical solutions for an idealised spherical geometry with uniform displacements. We then incorporate realistic displacement fields reconstructed from MRI measurements in healthy subjects and solve the reduced equations numerically. The results show that oscillatory forcing produces a steady streaming component that may enhance solute transport compared with diffusion alone. This work provides a mechanistic description of the flow generated by physiological brain motion and highlights the potential presence of steady streaming in cranial subarachnoid fluid dynamics.

Motile cells can sense and exert forces on the extracellular environment through dynamic actin networks. Increased stress against the polymerizing barbed ends of branched actin networks has been shown to lead to an increase in the density of these networks through a force feedback mechanism, though this phenomenon has not been explored through the examination of real-time responses of endogenous actin networks in cells. Here, we utilize mouse embryonic fibroblast CRISPR knock-in lines with labeled ARP2/3 complex to identify cellular and extracellular conditions that regulate branched actin density and enrichment at the leading edge of lamellipodial protrusions. A common theme shared among all branched actin density-increasing conditions is higher levels of interface stress between the plasma membrane and the barbed ends of the lamellipodial actin network. Among these conditions, we find that ARP2/3 is specifically required for robust spreading and protrusion in response to increased extracellular viscosity. Interestingly, time-lapse traction force microscopy of ARP2/3-dependent viscosity responses show significantly reduced changes in strain energy applied to the substrate when compared to spreading and motility through cell-matrix adhesion. In addition, we find that increased extracellular viscosity can bypass the need for extracellular matrix proteins to support lamellipodial protrusion driven by optogenetic Rac activation. Our studies provide strong support for in vitro models of branched actin force feedback responses and further characterize an essential role for branched actin in mediating dramatic cell shape changes in response to increased extracellular viscosity.

We develop a self-consistent free-energy framework in which membrane shape and osmotic pressure are determined simultaneously in a finite reservoir by minimizing bending elasticity and solute entropy. Solute conservation makes osmotic pressure a thermodynamic variable rather than an externally prescribed parameter, producing a nonlinear coupling between membrane mechanics and solvent entropy. This coupling modifies the classical stability condition for spherical vesicles: instability emerges from global free-energy competition rather than the linear Helfrich stability criterion. The resulting critical pressures differ by orders of magnitude from Helfrich predictions and agree with simulations for small and large unilamellar vesicles. The framework is relevant to cellular environments involving biomolecular condensate confinement as well as synthetic vesicles and the development of osmotic-pressure-driven encapsulation platforms.

Colorectal cancer (CRC) is the second most common cause of cancer-related mortality. At the molecular level, CRC is associated with genetic mutations and epigenetic modifications that dysregulate various signaling networks. From the biophysical viewpoint, invasive and metastatic cell migration need to be empowered by mechanical forces. In this study, we analyze the dynamic deformation of patient-derived CRC organoids in Fourier space and demonstrate how organoids with protooncogene BRAF mutation exhibit deformation phenotypes at an early stage. The organoids with BRAFmut have significantly lower elasticity and higher viscosity than those with BRAFWT, which mathematically indicated as the weakening of cell-cell adhesion. Immunohistochemical images, qRT-PCR, and TCGA data analysis confirm the downregulation of E-cadherin (CDH1) in BRAFmut organoids as well as in BRAFmut CRC, suggesting that the decrease in cell-cell adhesion in BRAFmut CRC facilitates invasive and metastatic migration. Notably, the recovery of CDH1 expression by pharmacological inhibition of DNA methylation can quantitatively be detected as the change in mechanical properties, suggesting that the complementary combination of dynamic phenotyping, mathematical modelling, and molecular-level analyses has a potential to unravel the mechanistic causality of the critical gene mutation and CRCs prognosis and the response to therapeutic interventions.