Abstract Optimal branching in transport networks has been analysed mechanism by mechanism since Murray's law (branching exponent x=3), but no combining rule exists when several dissipation mechanisms coexist. We prove that the optimal exponent is the weighted harmonic mean of the single-mechanism exponents, weighted by each mechanism's share of the dissipation budget. The result holds for any smooth dissipation function and any smooth convex structural cost. A bounding consequence establishes a strict floor x>5/2 for any Poiseuille-plus-pulsatility combination at every finite Womersley number, providing a parameter-free test that distinguishes dissipation-based from impedance-based optimization of biological networks. The predictions are robust to wall compliance and physiological flow variability; the latter preferentially amplifies entrance losses, yielding a testable prediction that vascular beds with high flow variability should exhibit systematically lower branching exponents. Read inversely, the theorem predicts that roughly half of coronary pumping power is dissipated by entrance effects. An order-by-order analysis of the human pulmonary arterial tree predicts the observed transition from x≈2.1 to x≈3, in quantitative agreement with cross-species morphometric data. The same entrance-driven mechanism reproduces the two-regime architecture of allometric scaling theory as asymptotic limits of a single cost function.
Abstract In the early stages of wound healing, fibrin polymerization plays an essential role in clot formation and subsequent healing. Sialic acid is known to impact fibrin polymerization kinetics, but the exact mechanisms are not well understood. We build upon existing studies using a reaction system-based mathematical model for fibrin matrix formation by introducing randomization to local sensitivity-based parameter identifiability analysis, with biochemical reaction rates serving as the model parameters. The application of randomization to initial parameter values facilitates greater exploration throughout parameter space. Our approach generates several model realizations that are screened for the quality of curve fits to data for fibrin matrix concentration and then used to determine consistently unidentifiable parameters as candidates for removal. Among these candidate reduced models, the most accurate one is selected and then used to estimate and compare influential parameter values from data corresponding to three experimental designs with different levels of sialic acid. Using statistical significance tests on the estimated values of influential parameters, results are interpreted to inform the potential mechanisms that may be altered by sialic acid concentration on fibrinogen.
Abstract OpenGRF is a new OpenSim-based tool that estimates ground reaction forces and moments (GRF&Ms) and centre of pressure (CoP) directly from joint kinematics, addressing an existing limitation of current OpenSim workflows. The approach combines calibrated foot–ground contact probes with an optimization framework derived from static optimization, and computes CoP by accounting for both kinematic and dynamic contributions. Its performance was validated against force-plate measurements. Validation involved 126 marker-based trials from seven healthy adults, each performing six trials of level walking, stair ascent and stair descent. Results showed the highest accuracy for vertical GRF, with normalized root mean square error (nRMSE) ≤ 1.5% and Pearson's correlation coefficient (ρ) ≥ 0.94, particularly during level walking. Anterior–posterior GRF was also satisfactorily predicted (nRMSE 4.4%–6.1%, ρ = 0.81–0.91). By contrast, medial–lateral GRF was less reliable, especially in stair tasks, with errors up to 11.2% and correlations as low as 0.48. Free moments were the hardest variable to estimate (nRMSE up to 28%), whereas ankle moments showed excellent agreement with force-plate data (nRMSE ≈ 1.7%, ρ ≈ 0.98). Median CoP error was 21–23 mm, with the largest discrepancies during double support. Overall, OpenGRF enables physics-consistent estimation of GRF-related variables, particularly the vertical component, from kinematics alone, although generalizability is limited by the tested sample.
Abstract The equations of complex dynamical systems may not be identified by expert knowledge, especially if the underlying mechanisms are unknown. Data-driven discovery methods address this challenge by inferring governing equations from time-series data using a library of functions constructed from the measured variables. However, these methods typically assume time-invariant coefficients, which limits their ability to capture evolving system dynamics. To overcome this limitation, we allow some of the parameters to vary over time, learn their temporal evolution directly from data and infer a system of equations that incorporates both constant and time-varying parameters. We then transform this framework into a forecasting model by predicting the time-varying parameters and substituting these predictions into the learned equations. The model is validated on simulated susceptible–infected–recovered and consumer–resource systems, as well as on real-world greenhouse gas concentration and cyanobacteria cell count datasets. By dynamically adapting to temporal shifts, our proposed model achieved a mean absolute error below 3% for learning a time series and below 6% for forecasting up to a month ahead. We additionally compare forecasting performance against convolutional neural network–long short-term memory and gradient boosting machine, and show that our model outperforms these methods across most datasets. Our findings demonstrate that integrating time-varying parameters into data-driven discovery of differential equations improves both modelling accuracy and forecasting performance.
Abstract The dynamical effects of intrinsic noise in gene regulatory networks (GRNs) can be significant when the number of molecules is low. In previous work, we proposed a new conceptual model, comprising a network of three transcription factors (TFs) that mutually inhibit each other (i.e. a ‘cross-repressilator’, also referred to as a ‘toggle triad’), that offers a route to reconcile the direct fate restriction (DFR) and progressive fate restriction (PFR) hypotheses for stem cell fate choice. In the deterministic case, the cross-repressilator model generically displays three kinds of dynamics. Between the multipotent and fate-specified regimes there exists a third, initially unanticipated, intermediate oscillatory regime that provides a mechanism for environmental signals to influence fate choice. Here, we analyse in detail a stochastic version of the cross-repressilator model. Our findings reveal that, as the system size reduces, intrinsic noise systematically lowers the characteristic frequencies associated with fluctuations both in the multipotent state and in the oscillatory regime. Hence, while the cross-repressilator conceptual model points to a possible resolution of the DFR/PFR dichotomy, the effect of noise is to reduce the number of oscillatory cycles that would be present and thus to accelerate movement of the cell state towards differentiation during the fate specification process.
