Physical Review Letters

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.

Contact inhibition of proliferation (CIP) enables epithelial tissues to self-regulate growth and maintain tissue homeostasis. However, how cell-level mechanical contact, tissue-scale structural order, and proliferation kinetics interplay remains a fundamental open question in living matter physics. Here, we present a particle-based model of a confluent epithelial monolayer governed by overdamped dynamics, where individual cells interact via a two-dimensional hard core- soft shoulder potential. By comparing structural evolution during quasistatic densification with previously reported experimental division kinetics, we find that the dynamics of proliferation arrest mimics the onset of direct steric contacts between the hard cores of the shell. Identifying hard core contacts as the physical driver of CIP, we couple our mechanical model with a stochastic Monte Carlo division scheme in which the instantaneous division rate decreases to zero from an intrinsic value as the number of hard core contact increases to six from zero. We demonstrate that for high intrinsic division rates, the cellular densification outpaces mechanical relaxation. This kinetic mismatch drives premature hard-core contact formation, shifts the onset of jamming and contact inhibition to lower packing fractions, and induces increasingly disordered transient configurations before the tissue universally converges to a hexagonal close-packed limit. Our model's predicted division kinetics and structural order evolution are consistent with epithelial monolayer experiments, both reported and our own. This minimal physical framework links single-cell steric contact mechanics directly to tissue-scale growth regulation and structural evolution.

Enzymatic reactions in biomolecular condensates are often assumed to be regulated through local enrichment of reactants. However, condensates also reshape molecular transport and reaction kinetics, making it unclear how phase separation controls catalysis in living cells. Here, we develop a quantitative theory of biomolecular catalysis in phase-separated systems and find that liquid condensates can act as tunable catalytic switches, transitioning between regimes of enhanced and suppressed enzymatic activity, exhibiting optimal responses at biologically relevant condensate sizes. We show that condensate-mediated catalysis cannot be understood from reactant enrichment alone, but instead emerges from the coupled interplay of molecular partitioning, diffusive transport, and phase-dependent reaction kinetics. The strongest regulatory effects occur under rapid interphase exchange, where the spatially heterogeneous catalytic network admits a system-level Michaelis-Menten description governed by system-averaged concentrations and reaction kinetics. Our framework predicts that micron-sized condensates can either enhance or suppress enzymatic activity by up to two orders of magnitude, and that optimal catalytic regulation can emerge at condensate sizes comparable to many biomolecular condensates. These results provide experimentally testable predictions for condensate-mediated catalysis and establish quantitative principles for understanding and engineering enzyme-catalysed reactions in biomolecular condensates.

The collective spatial phenomenon of complement protein opsonization on nanoparticle surfaces is a key component of the immune response to viruses, engineered nanoparticles, and diseased cells. Recent work showed this opsonization follows a sharp, percolation-like transition versus the spacing d between surface-bound attachment sites, leaving two open questions: 1) whether the transition exhibits hallmarks of true criticality, such as diverging susceptibility, and 2) whether it can be distinguished from an alternative first-order cooperative (Hill-type) process producing an equally sharp threshold without true criticality. Here, we resolve both questions using a hierarchical statistical-mechanics treatment spanning stochastic, mean-field, and spatial reaction-diffusion models. The variance of two order parameters, peak complement activity and activation lifetime, diverges near threshold and sharpens systematically with system size, the defining signature of a critical point rather than a smooth cooperative response. Extending the analysis across site spacing and intrinsic kinetic rate constants traces a two-dimensional locus of critical points with consistent critical exponents throughout, establishing a single, robust universality class. The mean-field dynamic exponent for activation lifetime agrees quantitatively with the exact value predicted for the general epidemic process. Finally, a reaction-diffusion model of the nanoparticle surface shows the critical locus is set by a diffusion-limited length scale, establishing complement percolation as a fundamentally transport-limited surface reaction. These results place complement activation within the percolation universality class and identify the physical parameters, diffusion, catalysis, and decay, that govern its critical threshold, with direct implications for rational design of complement-evading nanomaterials, immunology, and evolutionary biology.

Recent experiments show that protein condensates sitting on opposite surfaces of a flat lipid membrane move together and prefer to overlap, even though they cannot touch each other. This points to an indirect, membrane-mediated interaction. Two mechanisms could be responsible: a curvature-induced interaction, which is energetic in origin, and a fluctuation-induced interaction, which is entropic. Here we study both with coarse-grained molecular dynamics simulations, using Cookes implicit-solvent lipid model together with a generic bead-spring polymer model for the condensate. We compute the potential of mean force between two condensates across the membrane. For condensates of the same size, full overlap is unfavorable, and the pair instead settles into a partially overlapping state that bends the membrane into an S-like shape. When the two condensates differ strongly in size, full overlap becomes favorable. We explain this with a simple geometric picture. The condensate wets the membrane as a thin film and imposes curvature only along its rim, while membrane tension flattens the membrane under its interior. The resulting ring of curvature can trap a smaller condensate on the opposite side. We also compare the bending undulations and the effective bending modulus of a bare membrane, a membrane with one condensate, and a membrane with condensates on both sides. A wetting condensate suppresses the undulation modes and stiffens the membrane, but whether this makes overlap entropically favorable remains inconclusive. Our results indicate that the coupling is driven mainly by curvature, and that it depends on the wetting mechanism and on the membrane tension.

A classical study found no excitation transfer when isolated cardiomyocytes were placed side by side, whereas a recent paper reported action potential transfer in carrdiomyocytes placed end to end. We use nanoscale numerical simulations based on the full Poisson-Nernst-Planck equations to investigate whether these apparently opposing observations can be explained by the different geometrical configurations. The computations show that in the end-to-end configuration, ephaptic coupling occurs when the intercellular cleft is sufficiently narrow and a sufficiently large fraction of the sodium channels is localized at the intercalated disc. Coupling is strengthened when the sodium channels are concentrated in fewer clusters and when ionic diffusion within the cleft is reduced. Under these conditions, excitation transfer occurs on a timescale consistent with rapid cell-to-cell activation. Conduction depends biphasically on cleft width and terminates abruptly beyond a critical width. Localization of potassium channels at the intercalated disc has only a moderate effect, whereas gap junctions substantially improve conduction and reduce the relative contribution of ephaptic coupling. In the side-by-side configuration, excitation transfer does not occur under physiological conditions and requires highly flattened cells, minimal separation, and unrealistically strong sodium-channel clustering. The different outcomes of the side-by-side and end-to-end experiments can therefore be explained by the fundamentally different geometrical conditions for ephaptic coupling.

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.

BackgroundPlatelet activation in flowing blood is a multiscale process in which vessel-scale hemodynamics, red blood cell (RBC) mechanics, adhesive receptor interactions, and intracellular signalling jointly determine thrombotic risk. Individual components are well studied, but a single reduced description that carries each explicitly from vessel-scale flow to mechanosensitive calcium entry, with dimensionally consistent couplings, remains uncommon. ObjectivesWe develop and analyse a reduced, six-module mechanobiological framework for platelet priming spanning the cascade from hemodynamic shear to mechanosensitive calcium entry, and we delineate which elements are supported by existing evidence and which are new, testable hypotheses. MethodsThe framework comprises six coupled modules: (I) hemodynamic forcing from the incompressible Navier-Stokes equations, with an objective principal-strain-rate measure for extensional flow; (II) RBC-mediated platelet margination and near-wall delivery, closed by a near-wall arrival flux; (III) von Willebrand factor (VWF) activation with a bounded kernel and glycoprotein Ib (GPIb) catch-slip capture, resolved through an explicit contact area and a bond-dependent mobility that progressively immobilises wall-interacting platelets; (IV) a single-load membrane-stimulus formulation; (V) mechanosensitive gating and a dimensionally consistent cytosol-store calcium model with extracellular influx; and (VI) a phenomenological mechanical-memory state. We formally derive that the single-platelet stochastic dynamics and the continuum population balance form a Fokker-Planck pair, with the spatially varying diffusivity handled by an explicit drift correction. ResultsThe framework yields a family of mechanochemical dimensionless groups delineating priming regimes. Its central prediction is reformulated as a falsifiable, history-sensitive signature: in a conditioning-test protocol, a low-tension conditioning block charges the memory state, and a fixed sub-threshold test pulse then reports a delay-dependent calcium facilitation that decays on the memory time{tau} m and is distinguishable from no-memory gating, channel adaptation, and residual-calcium priming. We show explicitly that the previously proposed pulsatile-versus-monotone contrast is a nonlinear convexity/thresholding effect of the gating nonlinearity--its difference-in-differences is approximately zero-- and is therefore not a valid test of memory; the conditioning-test signature is. A second prediction links RBC stiffening to reduced near-wall delivery and captured-platelet calcium response, upstream of intrinsic platelet signalling. ConclusionsThe framework provides a dimensionally consistent, mechanistically grounded and hypothesis-generating description linking hemodynamic forcing to mechanosensitive calcium entry. It demonstrates how history-dependent platelet priming may arise from a phenomenological sensitisation state and proposes a conditioning-test protocol for comparison against adhesive, channel and intracellular-store persistence. The framework is calibratable rather than validated, and the quantitative outputs shown use representative uncalibrated parameters.

In linear polysomes, excluded-volume interactions among ribosomes can induce dimensional reduction of mRNA. Yet linear architectures allow steric stress to relax at open ends-- limiting how strongly crowding can remodel the mRNA's structure and dynamics. Using coarse-grained molecular-dynamics simulations, we compare circular and linear polysomes over a range of ribosome densities. Circular closure selects a predominantly quasi-planar global conformational ensemble, as indicated by a shape dimensionality dshape {approx} 2 over a range of ribosome densities. Crucially, circular topology and ribosome crowding act cooperatively to suppress structural fluctuations. While closure alone or linear crowding reduces relative global size fluctuations ({Delta}Rg/Rg) only to {approx} 0.16, their combined effect drives this fluctuation down to {approx} 0.07. Within this stabilized architecture, increasing ribosome density drives a distinct in-plane reorganization: the ring becomes more isotropic, global size fluctuations are strongly suppressed, and the scaling exponent increases toward {nu} [~=] 0.74 - 0.77, consistent with two-dimensional self-avoiding walk-like value over the accessible finite-size window, 1000 [≤] N [≤] 4969. Closure shortens the radius-of-gyration decorrelation time of circular polysomes by 40-fold relative to matched linear systems, reflecting the topological elimination of free ends. Within this closureselected ensemble, ribosome crowding further reduces the decorrelation time by up to 20% at the highest density. A fluctuation-informed crossover model links the density dependence of the global scaling exponent to inter-ribosomal subchain statistics. These results distinguish the geometric role of circular closure from the density-dependent steric response that it enables, revealing a confined yet dynamically responsive conformational regime for circular polysomes.

Biological aging is accompanied by systematic changes in epigenetic modifications and chromatin organization. The reversal of the effects of aging, rejuvenation, is experimentally achieved by the transient induction of factors that modify these marks in cells and organisms. Here, we show that key features of rejuvenation experiments emerge from the biophysical interplay between dynamic epigenetic marks and the three-dimensional conformation of chromatin. Using a minimal field theory and molecular dynamics simulations, we show that the system responds in three distinct temporal regimes. The intermediary regime fulfills necessary conditions for successful rejuvenation. In this regime, the system spends time near a separatrix, allowing for high epigenetic plasticity, while memory retained in the chromatin conformation enables restoration of the original epigenetic correlations. Analysis of sequencing data further supports the predicted coupling between chromatin compaction and epigenetic correlations. Our results provide a physical explanation for how rejuvenation may remodel age-associated epigenetic states without irreversibly erasing cellular identity. We identify a general mechanism by which memory stored in a slow structural variable permits reversible remodeling of a faster internal state.

Radiation-induced DNA double-strand breaks (DSBs) drive cellular mortality, mutagenesis, and severe evolutionary bottlenecks. While classical phenomenological models, such as the Linear-Quadratic (LQ) framework, reliably predict macroscopic population survival, they obscure the intrinsic single-cell stochasticity that governs critical rare events like tumor recurrence or the emergence of radioresistant persisters. To bridge this divide, we develop a mathematically exact stochastic differential equation (SDE) framework that models continuous DSB induction and repair as a Feller square-root process. By deriving exact closed-form expressions for the foci moments, we establish a highly efficient Maximum Likelihood Estimation (MLE) pipeline that circumvents computationally exhaustive Monte Carlo simulations, allowing the direct extraction of deterministic repair velocities and intrinsic molecular noise from empirical single-cell $\gamma$-H2AX data. Integrating this kinetic model with a cumulative damage hazard via the Feynman-Kac formalism, our framework seamlessly recovers the classic macroscopic LQ survival topology from microscopic first principles. Furthermore, systematic sensitivity analysis uncovers a fundamental evolutionary duality: while initial physical damage operates additively, ultimate cellular fate is driven by a nonlinear survival response governed by the trade-off between the damage hazard rate and intrinsic molecular noise strength. Crucially, we demonstrate that this molecular noise inherently enhances population survival. Governed by Jensen's inequality, stochastic variance acts as a non-genetic bet-hedging mechanism that buffers the population by favoring cells with transiently low damage loads. Ultimately, this exact stochastic framework bridges microscopic biophysics and macroscopic demographics, offering deep mechanistic insights into the evolutionary roots of radioresistance.

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.

MotivationWith the rapid development of AI methods that predict protein structures from sequence, understanding the structure-function relation increasingly depends on quantitative structural descriptors that are both biologically meaningful and scalable to large datasets. Here, we introduce mathematical topology metrics that quantify the entanglement complexity of a tertiary protein structure while respecting uncrossability constraints. ResultsBy employing only three such metrics across all protein structures in the Protein Data Bank, we represent the proteome structural space in a continuous three-dimensional space. Distances within this space capture structural similarity and correlate with functional similarity. We find that the mathematical entanglement based landscape of protein structural space diversifies with the evolutionary expansion of protein function across species. Moreover, this continuous representation reproduces CATH classifications with high accuracy for major structural classes. These results indicate that these metrics efficiently encode structural features linked to protein function and provide a more informative description than conventional metrics. AvailabilityData used in this study are available in the Protein Data Bank. Details of the machine learning model used can be found in https://github.com/roshitac/CATH_Classification-. ContactBanu.Ozkan@asu.edu, Eleni.Panagiotou@asu.edu Supplementary informationSupplementary data are available at Journal Name online.

Cellular activity drives epithelial fluidization -- a widespread phenomenon observed during tissue development, remodeling, and repair both in vivo and in vitro. Yet the physical origins and spatial organization of active forces vary widely across biological systems and are often represented by a single generic mechanism in theoretical models. Here, using an active vertex model, we systematically compare four modes of epithelial activity spanning subcellular to tissue scales: apolar motility, polar motility, fluctuating contractility, and mechanochemical regulation. Although all four mechanisms drive the same global transition from a solid-like rectangular tissue to a fluid-like circular morphology, they reach this state through distinct pathways -- differing in the rates and topology of junctional rearrangements, cell elimination, and collective motion and leave distinguishable signatures in tissue architecture, cell dynamics, and mechanical relaxation. Among these observables, spatial velocity correlations directly capture the spatial organization of activity: their correlation length and functional form together resolve all four mechanisms. The robustness of these signatures across activity strengths suggests that spatial velocity correlations offer an experimentally accessible means of identifying the physical origin of epithelial activity from live-cell imaging alone.

Classical neurogeometric models describe the primary visual cortex as a fibered structure in which retinal position and local orientation are coupled through the geometry of the roto-translation group. We extend this approach to the visuomotor cortex by modeling it as an assemblage of visual and motor cortical geometries. The model combines orientation-selective representations, analogous to those of the primary visual cortex, with movement-direction-selective representations, analogous to those of the primary motor cortex, in order to describe the mixed visual and motor selectivity observed in the visuomotor cortex. We introduce a coupled visuomotor structure in which visual orientation and motor direction coexist over a common spatial plane and interact through a relative-orientation constraint. Neural responses are modeled by orientation- and direction-dependent profile functions, and preference maps are obtained from vectorized population responses. Numerical simulations generate visual, motor, and mixed visuomotor response maps. A competition rule between visual and motor responses produces incidence ratios close to experimental observations in macaque visuomotor cortex. This framework provides a first neurogeometric approximation of visuomotor functional architecture and a mathematical setting for studying visually guided action.

Fingertip friction plays a central role in tactile exploration and object manipulation. During sliding, tangential force depends jointly on the real contact area and the interfacial shear stress, both of which can be influenced by sliding conditions. However, changes in fingertip friction are often interpreted primarily through changes in real contact area, whereas the accompanying changes in interfacial shear stress remain less well characterized. This gap is especially relevant for electrostatic surface haptic displays, which modulate fingertip friction by applying a voltage between the finger and the touch surface. Here, we experimentally quantify the mean interfacial shear stress of a sliding fingertip on an electrostatically actuated touchscreen using simultaneous measurements of tangential force and optically resolved real contact area. Ten participants performed sliding trials across three speeds and three normal forces with and without electrostatic actuation. Interfacial shear stress increased with speed and decreased with normal force; in both cases, these trends arose because real contact area varied more strongly than tangential force. Electrostatic actuation further reduced interfacial shear stress, as increasing voltage produced a larger increase in real contact area than in tangential force. These findings show that interfacial shear stress varies systematically with sliding conditions and electrostatic actuation, clarifying how changes in real contact area and interfacial shear stress combine to shape fingertip-surface friction.

Electrostatic actuation is an emerging technology for generating tactile sensations on capacitive touchscreens through voltage-induced attractive forces between a fingertip and the surface. However, accurate control of electrostatic attraction during natural touchscreen interactions remains challenging because the applied normal force and sliding speed continuously vary, and their effects on the fingertip-screen contact and resulting actuation strength are not fully characterized. Here, we show how normal force and sliding speed systematically alter fingertip- screen contact area and electrical impedance, and use these measured changes to estimate electrostatic attraction during sliding. Contact area, interaction forces, and electrical impedance were measured simultaneously as participants slid their fingertips across an electrostatic surface under systematically varied normal forces and sliding speeds. These measurements revealed condition-dependent changes in fingertip contact, electrical interaction impedance, effective capacitance, derived effective gap thickness, and electrostatic attraction. We then incorporated these measured contact quantities into a physics-informed, data-driven model based on parallel-plate capacitor theory, in which effective capacitance, apparent contact area, and effective voltage determine the estimated electrostatic attraction. The resulting model links force- and speed-dependent changes in these quantities to electrostatic attraction while accounting for inter-participant variability through a participant-specific scaling factor. These findings provide experimentally grounded guidance for designing electrostatic surface-haptic feedback and future adaptive control strategies under realistic touch conditions.

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

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.