Objective:Diffusion-weighted MRI (dMRI) is a powerful tool for quantifying cellular microenvironment parameters. However, the inherently low signal-to-noise ratio (SNR) of dMRI can compromise the accuracy and reliability of parameter estimation. This study proposes a physics-assisted deep learning (DL)-based denoising framework designed to enhance dMRI signal quality and improve the robustness of subsequent biophysical model fitting, with potential relevance to low-SNR settings such as clinical 1.5 T MRI acquisitions. Approach:A dataset of paired noise-free and Rician-noise-corrupted dMRI signals was generated using the IMPULSED-dMRI signal model. Three denoising architectures were evaluated: Convolutional Neural Networks (CNN), Multilayer Perceptron (MLP), and Long Short-Term Memory (LSTM) networks. Denoised signals were then fitted to estimate cell diameter d , intracellular volume fraction V in , and extracellular apparent diffusion coefficient D e x . Performance was assessed using signal-domain Mean Absolute Error (MAE), fitted-parameter MAE, and fitting failure rate in synthetic IMPULSED-dMRI data with known ground-truth parameters and in in vitro evaluation using HeLa and MC38 cell lines. Main results:DL-based processing substantially improved dMRI signal denoising. The MLP and LSTM achieved similar performance, with the LSTM slightly better overall, and both outperformed the CNN. Averaged across all signals, the LSTM reduced denoising MAE from 5.97% to 1.58%. In the subsequent model fitting step, the LSTM produced modest reductions in parameter MAE, from 5.34 μm to 4.02 μm for d , from 15.00% to 11.96% for V i n , and from 0.77 to 0.63 μm2 /ms for D ex . The dominant benefit was fitting stabilization, with the overall fitting failure rate reduced from 57.6% to 17.7%. In in vitro experiments, relative to experimental references, the LSTM reduced MAE from 2.1 μm to 0.4 μm for d and from 7.8 to 5.4 percentage points for V i n , while reducing the mean overall fitting failure rate from 17.7% to 0%. Significance:The proposed framework improves dMRI signal quality and stabilizes subsequent IMPULSED-based microenvironmental parameter fitting. The primary value of this approach is improved fitting reliability under noisy dMRI conditions, with secondary gains in parameter accuracy, and it warrants further validation in heterogeneous tissues and in vivo datasets.
Ancient DNA and new inference methods have transformed the study of human origins, but consensus has not followed. Evidence increasingly indicates that hominin populations were pervasively structured and admixed, so complexity rather than simplicity is the appropriate prior. Here I highlight two blind spots that impede resolving that complexity. First, every inference passes through summaries of the data, and those summaries bound what can be recovered. Second, the space of candidate models is vast, yet competing model classes are rarely fit to common data, so a reported best model carries little evidence about untested model classes. This second blind spot reflects practice rather than data. It can be narrowed by testing competing models against withheld summaries and by reporting the models that were tried and rejected rather than only the winner.
We describe a systematic approach for spawning and aggregating multi-class cryo-EM reconstruction jobs. This approach formalizes standard ad hoc strategies of iterative classification and filtering typically used by practitioners to sort impure, heterogeneous samples. To our knowledge, this is the first method that can successfully perform ab initio reconstruction on datasets containing dozens of distinct species. We obtain 97% accuracy on ab initio reconstruction of a 45-class subset of Tomotwin-100, 75% accuracy on the full Tomotwin-100 dataset, and demonstrate recovery of ribosomal assembly states from an unfiltered experimental cryo-EM dataset. Our approach's capability scales with compute and lays the foundation for automated cryo-EM workflows in modern experimental settings.
Background:Establishing reliable reference dosimetry for ultra-high dose-rate (UHDR) beams (≥ 40 Gy/s) is challenging with conventional reference ionization chambers (IC) due to saturation effects arising from ion recombination. The Exradin A30 IC was introduced to overcome these challenges by utilizing an ultra-thin electrode spacing of 0.3 mm to enhance charge-collection efficiency (CCE). Purpose:The aim of this study is to investigate the commercial A30 IC as a reference dosimeter for UHDR electron beams. It explores the dosimetric properties of the A30 IC, including leakage current, CCE, polarity, and beam quality correction factors. Methods:Several measurements at the IntraOp® Mobetron® were acquired at a 1.5 cm distance from a medical UHDR electron accelerator head to achieve a maximum dose per pulse (DPP) of 9 Gy, and the instantaneous (or intra-pulse) dose rate (IDR) was 2.25 MGy/s using a 9 MeV electron beam. The measurements were obtained in a grounded water-equivalent plastic phantom, distilled water, and saline water. DPP values were adjusted by varying the SSD at a fixed pulse width (4 μs) while the pulse repetition frequency (PRF) was varied between 5 and 90 Hz. The CCE was calculated using EBT-XD radiochromic films under both UHDR and conventional beam conditions at identical dose and energy settings. Both CCE and Ppol were also measured as a function of DPP and PRF in distilled and saline water. Beam quality correction factors, k Q , were calculated using Monte Carlo and measured in electron beams from a TrueBeam linear accelerator. Results:The A30 IC exhibited a leakage current of less than 2 fA. Both Ppol and CCE decreased with increasing DPP, with CCE remaining in the 90-99% range across all three phantoms while polarity corrections decreased from 0.99 to 0.981 in both liquid and virtual water, respectively. Both CCE and Ppol were observed to be independent of the PRF, ranging from 5-90 Hz, in distilled and saline water. Measured k Q values agreed with calculation to within 0.8% for all energies except 9 MeV, which showed a 2% discrepancy. Conclusions:The commercial A30 ionization chamber exhibited 5% recombination with DPP of up to 5 Gy in both distilled and saline water. The IC signal in a solid phantom was found to be dependent on charge buildup effects, which can be mitigated by utilizing grounded phantoms. When appropriate CCE corrections are applied, the A30 IC is a suitable reference dosimeter for UHDR electron beams.
X-ray speckle-based dark-field imaging offers high sensitivity to sub-pixel structural features, yet its quantitative reliability in clinical and preclinical settings remains constrained by low photon flux and finite focal spot sizes. However, how hardware-induced noise and source blurring propagate through retrieval algorithms to degrade signal integrity is not fully understood. Here, we systematically evaluate algorithm robustness-quantified by signal linearity, sensitivity, and bias-under photon starvation and source blurring across two mathematically distinct frameworks: differential-based intrinsic tracking (Low-Coherence System, LCS) and patch-wise explicit tracking (X-ray Speckle-Tracking Speckle-Vector-Tracking, XST-XSVT). Our experimental results demonstrate that input speckle pattern distortions propagate through retrieval algorithms in fundamentally different ways depending on algorithm architecture. As an example, using our setup, under severe photon starvation (exposure reduced from 50 s to 1 s per mask step), derivative noise amplification in LCS causes its dark-field signal linearity and sensitivity to drop precipitously by 85.7% and 91.3%, respectively, while sharply elevating baseline bias. In contrast, XST-XSVT restricts these losses to 37.4% for linearity and 64.2% for sensitivity while maintaining a stable baseline, as its patch-wise variance calculation inherently suppresses stochastic noise. Similarly, under blur-limited conditions (expanding focal spot size from 7 μm to 50 μm), source blurring washes out the speckle pattern, directly reducing dark-field sensitivity for both LCS (by 47.8%) and XST-XSVT (by 42.6%). Beyond this shared sensitivity loss, the pattern smoothing causes the differential equations in LCS to become mathematically unstable, degrading its linearity by 5.3% and elevating baseline bias. Conversely, XST-XSVT robustly withstands the smoothed pattern, bypassing this instability to maintain linearity with a negligible 1.0% drop. This characterization establishes operational boundaries for low-power and low-coherence X-ray systems, guiding algorithm selection and framework optimization to realize quantitative dark-field imaging in preclinical and clinical applications.
Gaucher disease (GD), the most common lysosomal storage disorder, alters red blood cell (RBC) mechanics and circulation, contributing to vascular occlusions, bone infarcts, and splenomegaly. However, the individual roles of GD-RBC biophysical properties in these processes remain unclear. Here, we present a combined computational-experimental investigation to quantitatively characterize GD-RBC biophysical properties and determine how specific mechanical parameters drive abnormal RBC behavior. Informed by experimental data, we independently quantify key RBC properties, including shear modulus ( μ ) , surface-to-volume ratio ( S / V ) , and bending modulus k c . Based on these parameters, we construct three GD-RBC subtypes (GD-RBC1-3) to systematically isolate their individual contributions. At the single-cell level, optical tweezers simulations show up to ~27% reduction in axial diameter and ~42% reduction in transverse compression. Tank-treading dynamics exhibit non-monotonic behavior, with rotation frequencies increasing by up to ~70% or decreasing under elevated bending rigidity. In confined flow, traversal times through microchannel constrictions increase by more than a factor of two, while splenic slit passage times rise from ~250 ms (control) to > 1200 ms for the severe GD-RBC subtype, approaching a functional no-passage threshold. At the population level, viscosity simulations demonstrate that these alterations collectively elevate blood viscosity, with small fractions (~4.0%) of highly rigid cells disproportionately increasing flow resistance. Overall, this study provides a quantitative and mechanistic framework that disentangles the contributions of key RBC parameters to abnormal behavior in GD, linking cellular-scale biophysics to hematologic dysfunction and microvascular occlusion.
The speed of sound in tissue is a prerequisite for well-focused imaging and has diagnostic value, but recovering it from raw pulse-echo channel data is fundamentally a nonlinear inverse problem. Learned solvers are fast yet label hungry. Simulated sound-speed labels are expensive, while abundant real channel data is unlabeled. We propose IQ-JEPA to exploit both data types. An encoder is pretrained without labels to predict the latent representation of masked in-phase and quadrature (IQ) regions from visible context, then fine-tuned on simulated maps. Sound speed appears in the IQ signal as a phase difference, invariant to the constant phase offset. The encoder is a Hermitian vision transformer that operates on the complex signal directly. Its attention is equivariant to that phase and its conjugate-product feed-forward is invariant to it, so the encoder reads a quantity analogous to the one classical coherence methods use. On 79,293 Fullwave 2.5 simulations at 2.5 MHz, pretraining on the 63,435 unlabeled acquisitions reaches 15.60 m/s at 10,000 labels. This is a roughly threefold gain in label efficiency over supervised training, growing to over fourfold at 1,000 labels. It is about 2.2x below an InversionNet baseline, and 8.71 m/s at full labels. The gain still grows with more unlabeled pretraining data. Our comparisons point to self-supervision as the dominant factor. The same encoder transfers. Its frozen features expose sound speed and attenuation, and cross-distribution pretraining between layered and abdominal phantoms costs little accuracy. We see this as a first step toward a foundation model for quantitative ultrasound.
We present Loom, a spatial transcriptomics (ST) visual computing system to support the analysis of pseudo-temporal trajectories, comparative investigation across samples and regions of interest, and the examination of spatially structured processes within local microenvironments. ST is a molecular profiling technology that measures gene expression directly within a thin tissue section while preserving its spatial organization. For practical application-driven analyses, the ST local microenvironment data needs to be integrated with cell reference datasets and temporal simulations of cell behavior. This integration is challenging due to multi-modal registration issues and the complexity of the pseudo-temporal patterns, spatial enrichment data, and gene expression dynamics. Loom leverages a novel glyph coupled with a computational backbone to facilitate the detailed pseudo-temporal exploration of local microenvironments, cross-sample comparisons, and investigation of spatiotemporal biological mechanisms. We evaluate Loom through two case studies developed with experts in tissue pathology and oncologists and through an external usability study. The results demonstrate that Loom supports effectively the discovery of cellular transitions and spatiotemporal expression dynamics.
Biological information is often encoded in molecular variants that differ in just a few chemical traits, such as the number of phosphorylated sites or ubiquitin chain length, rather than in arbitrarily distinct species. These molecular distributions carry information about cellular state, yet reading them with conventional molecular circuits requires prohibitively many distinct sensors. In contrast, we show that collective physical instabilities can naturally integrate the information encoded in such distributions. Using an information-theoretic matching condition between an encoded distribution and a physical readout, we derive a geometric condition that any good decoder must satisfy, and establish that phase separation, percolation, and membrane curvature instabilities all approach it for biologically natural distributions while simple mass-action binding does not. Using mean-field theory and lattice Monte Carlo simulations, we find that phase separation reads the shape of a distribution beyond its mean, robustly capturing its variance and, more weakly, its skewness, whereas mass-action binding detects only the mean. Near phase boundaries the readout captures nearly all the information present in the molecular population. Finite valency, through the threshold for network formation, adds discriminatory power invisible to mean-field theory. These results suggest that cells can exploit collective physical instabilities as natural, compact, yet near-optimal sensors for decoding molecular distributional codes.
The shape of a planar curve is the geometric information that remains once translation, rotation, scale and reparametrisation are removed and is of interest in many health applications, e.g. in neuroimaging. We propose a deep shape regression model for open planar curves that admits multimodal and high-dimensional covariates. Representing curves as complex-valued functions, we show that the conditional full Procrustes mean is the leading eigenfunction of the conditional covariance. To estimate this covariance surface, we propose a novel deep conditional covariance smoother with modality-specific encoders - e.g. splines for scalar covariates and convolutional networks for images, which classical spline smoothers cannot accommodate. Our model is by construction invariant to translation, rotation and scaling of the input curves and handles sparsely and irregularly sampled curves. We further provide an algorithm for elastic mean estimation that also removes parametrisation by iterating covariance smoothing, rotational alignment and parametrisation alignment. We illustrate the method on simulated outlines with known conditional mean and multimodal covariates, and give a first application to hippocampal outlines from the ADNI cohort, recovering covariate effects consistent with the literature. Code is available at https://github.com/mpff/dnn-shapes.
Markov state models (MSMs) have become ubiquitous tools for analyzing molecular dynamics (MD) simulations because of their simple, powerful premise: although complete MD sampling may be impossible, the MSM can "stitch together" transition probabilities derived from local sampling to provide a global picture of kinetics and mechanisms. In the standard MSM framework, the available MD data is organized into a single transition matrix, which is then used to estimate all observables at a lag time chosen so the coarse-grained dynamics are approximately Markovian. This approach leads to avoidable model bias and motivates long lag times that obscure short-timescale processes of interest. In contrast, this paper shows how to obtain unbiased coarse-grained observables at any fixed lag time and for any fixed coarse-graining in the limit of infinite, properly weighted data. The central idea is to replace the single-matrix framework with two transition matrices -- one representing equilibrium dynamics and another representing source-sink recycling dynamics -- and use the correct matrix or matrices to estimate the matched dynamical observables.
Evaluating machine learning in scientific domains requires separating correct predictions from correct reasons under realistic distribution shifts. We introduce PertReason, a knowledge-grounded benchmark and framework suite for cell-state--conditioned reasoning about perturbation effects. At its core, PertReasonQA is a benchmark that tests whether models can generate mechanistically faithful explanations while remaining robust to complex shifts, such as new cells and unseen perturbations. PertReasonQA combines single-cell genetic and chemical perturbation data across multiple cellular contexts with knowledge graphs, and dynamically conditions pathways on cell-specific basal states to avoid generic memorization. Evaluations on state-of-the-art models reveal systematic gaps between predictive accuracy and mechanistic reasoning. Specifically, these models exhibit failure modes largely invisible to standard benchmarks, such as deriving correct answers through flawed logic, ignoring cellular context, and generating directionally inconsistent mechanisms. As a reference probe of the benchmark, we present PertReasonLM, a large language model trained to align outcome predictions with context-specific mechanistic reasoning. Our model targets the identified failure modes by grounding rationales in context-specific pathways and tightening agreement between outcomes and mechanisms. Together, we provide a diagnostic framework for exposing and mitigating failures in faithful reasoning in data-rich scientific systems.
Within topographic eccentricity maps in the primate visual system, center-preferring populations have higher spatial resolution and overlap face- and word-selective regions while periphery-preferring populations have lower spatial resolution and overlap scene-selective regions. Prior behavioral and neuroimaging evidence suggests that this "eccentricity bias" may reflect the relevance of visual field portions for different tasks: the central visual field may be more informative for fine-grained tasks like face recognition and reading, while the periphery may be more informative for large-scale scene understanding tasks. To examine whether such eccentricity-dependent coding can emerge from natural experience, we leveraged egocentric video and eye-tracking data from the Visual Experience Dataset (VEDB). We trained ResNet-18 models using contrastive learning (SimCLR) on video frames modified to isolate information available at different eccentricities (gaze-contingent fovea-only crops, periphery-only crops, and periphery-only crops with a NeuroFovea transform applied). We then evaluated downstream task performance and model alignment with human fMRI data (Natural Scenes Dataset; encoding model framework). When examining in-domain classification of VEDB frame categories, we observed systematic variability in the performance of fovea-only and periphery-only models across categories, suggesting differential informativeness of visual field eccentricities across tasks. On downstream classification without fine-tuning, VEDB-pretrained models generalized more strongly to scene recognition (Places365) than to face recognition (VGGFace2), with fovea-only models showing an advantage on both tasks. Across visual cortex, VEDB-pretrained models achieved similar neural predictivity to models trained on mid-sized non-egocentric datasets (ImageNet-100), suggesting experience-sampled egocentric data, despite its low diversity and constrained semantic content, supports emergence of cortically-aligned representations. In scene-selective sub-regions (PPA, RSC), periphery-only models held a small but consistent advantage in explained variance over fovea-only models, suggesting scene-selective cortex may be adapted to peripheral-field statistics. Together, these results suggest that naturalistic egocentric experience provides an organizing constraint on perception, leading to adaptive, task-aligned information processing.
Purpose:In advanced computational MRI techniques, acquisition and reconstruction techniques are jointly designed. For reproducibility, it is therefore important to provide an open implementation of both. At the same time, any use in a clinical environment usually requires a close integration with the MRI scanner. Ensuring long-time reproducibility and maintenance then poses additional challenges. In this work, we aim to provide a fully integrated open-source framework that can meet these demands. Methods:A software framework to develop pulse sequences is added to the BART toolbox. In addition, a vendor-specific driver sequence is developed that can be used to run the sequence on a clinical MRI scanner enabling online adjustment of all relevant sequence parameters. Using the Pulseq format, the exact same sequence can also be reproduced offline. As proof-of-concept, quantitative MRI methods for T 1 and joint water/fat R 2 ∗ mapping using radial FLASH and model-based reconstruction are implemented in the proposed framework. Consistency between online and offline acquisition is validated in phantom and in vivo experiments. Results:Quantitative MRI methods consisting of acquisition and reconstruction were successfully implemented in BART. Acquisition parameters and FOV can be adapted online on a clinical MRI system. Quantitative parameter maps from model-based reconstruction agree for online and offline regenerated Pulseq acquisitions. Conclusion:This work enables reproducibility of advanced computational MRI methods within a comprehensive end-to-end open-source framework.
This study presents the first mathematical model of pulsatile hemodynamics that encompasses the complete pulmonary circulation, explicitly linking the large arteries, arterioles, capillaries, venules, and large veins. To overcome the limitations of previous models that exclude explicit capillary dynamics, we incorporate a one-dimensional structured-tree model of the pulmonary arteries and veins with a dynamic capillary sheet model. This approach establishes a recursive method for coupling the capillary sheets to the structured trees, connecting arterioles and venules in a ladder-like architecture. To evaluate the impact of incorporating this capillary structure, we compare simulated hemodynamics in a healthy control subject and a pulmonary hypertension (PH) patient. Results illustrate that including capillaries in the model significantly alters hemodynamic predictions by introducing downstream damping. In the healthy control subject, the inclusion of the capillary network attenuates pulsatile energy, yielding the expected steady venous pressure and flow profiles, whereas omitting the capillaries results in an unphysiological high pulsatility transmitting into the venous system. The structural impact of the capillaries is even more pronounced in the PH patient, where explicitly modeling the capillary bed corrects an over-prediction in peak systolic pressure in the main pulmonary artery. Furthermore, unlike the healthy control subject, the remodeled PH microvasculature fails to completely isolate the venous system from arterial pulsations. Finally, we employ parametric sensitivity analysis to investigate how specific biomechanical factors drive vascular remodeling, demonstrating the framework's capability to quantify disease progression and severity.
Time-of-flight magnetic resonance angiography (TOF-MRA) is widely used for noninvasive visualization of arterial anatomy, but extracting hemodynamics like blood velocity typically requires supplementary phase-contrast scans, tagging or multi-TE images. This study proposes a novel, physics-informed computational framework to extract variable fluid velocity directly from standard TOF-MRA signal profiles. We analytically expand the approach-to-steady-state Bloch equations to include convective flow, establishing a mathematical relationship between the spatial decay of longitudinal magnetization and fluid velocity. The velocity derivation was further extended to pointwise estimation over a 1-D centerline, overcoming the limitations of constant-velocity assumptions. To validate and solve this problem, a MATLAB (R2025b) simulation framework was developed to model fluid flow in two variable-geometry flowing tube cases, i.e., continuous narrowing and focal stenosis, under synthetic scanner noise. A global inverse optimization approach utilizing Dual-Tikhonov regularization was applied to stably invert the ill-posed transit time integral, actively penalizing high-frequency numerical ringing while preserving structural curves. The computational simulations successfully recovered ground-truth point-wise velocities, tracking gradual hemodynamic accelerations and sharp stenotic jets. This theoretical framework and the example centerline TOF-MRA signal intensity provide a robust mathematical proof-of-concept that quantitative, localized functional hemodynamic metrics can be extracted from standard structural MRA imaging, establishing a foundation for advanced flow quantification without requiring additional scan time.
FLASH radiotherapy (FLASH-RT) is the phenomenon of relative sparing of normal tissue when ultra-high dose rates (UHDR) are used compared with conventional dose rates (CDR) as clinically used. Despite extensive investigation, the underlying mechanisms remain unexplained. Among the proposed hypotheses, tissue oxygen has consistently been a central theme because oxygen is the most dominant factor known to modulate radiation-induced damage. The factors implicated in FLASH sparing include the baseline partial pressure of oxygen (pO2), transient radiolytic oxygen consumption (ROC), and oxygen-dependent changes in the chemistry of reactive oxygen species (ROS) that vary with dose rate. This review synthesizes current evidence on in vivo oxygen measurement techniques, highlighting their capabilities and limitations in capturing the spatial and temporal heterogeneity of tissue oxygenation. Key experimental studies in skin are summarized and interpreted by modulating oxygen levels via changes in inspired oxygen gas and vascular clamping interventions, demonstrating that the FLASH effect occurs only at intermediate baseline pO2 (normoxic or slightly hypoxic) values, but not at hypoxia or hyperoxia. Direct measurement of oxygen consumption during UHDR irradiation is possible, providing one of the first in situ measurements of radiation chemistry in patients. In parallel, recent advances in fast in vitro radiation chemistry assays indicate that UHDR irradiation alters radical yields, favoring increased production of solvated electrons and reduced hydroxyl radical-mediated damage. Taken together, the available data suggest that the FLASH sparing effect arises from an interplay among the delivered dose and dose rate, local oxygen availability, and radiation chemistry, with tissue-specific variation in scavenging, leading to altered biological responses across the CDR-to-UHDR shift. This more complex interpretation seems more likely than the simpler interpretation of broad-area radiolytic oxygen depletion alone. However, it must be acknowledged that we have partial data on all aspects of this hypothesis, and further improvements in oxygen sampling are very likely to help in understanding ROS and scavenging effects in vivo. Key challenges in quantifying oxygen dynamics in vivo are highlighted, and the conclusions are used to identify critical areas for future research to enable mechanistic understanding and clinical translation of FLASH-RT.
Hamilton-Jacobi Reachability (HJR) is a central framework in safe control theory. While HJR has traditionally focused on a few fundamental tasks, there is increasing interest in scaling to more complex objectives. Recent works have studied the exact decomposition of the value functions for two fundamental dual-objective tasks in the adversary-free setting. However, not all value function decompositions in HJR remain valid with an adversary. In this work, we develop theoretical approaches to certify that for these two composite value functions, the proposed decompositions still hold with an adversary. Finally, we show how these results can solve issues that arise when applying HJR to optimal drug regimen design.
Understanding the dynamical properties of coupled phase oscillator systems with heterogeneous oscillator frequencies has been a long-standing challenge of complex systems theory. While the seminal work of Ott and Antonsen dramatically improved our theoretical understanding of coupled phase oscillators for a small family of oscillator frequency distributions, we here present a mean-field reduction method for arbitrary frequency distributions. Our method leverages the drastic dimensionality reduction obtained for Lorentzian frequency distributions, and combines it with a data-driven multi-ensemble approach. As such, the method renders the Ott-Antonsen equations directly applicable to empirical distributions of phase oscillator frequencies, often achieving a drastic dimensionality reduction and allowing to study real-world physical and biological systems by means of stability, sensitivity, and bifurcation analyses.
Ramkrishna, Kompala, and Tsao proposed the cybernetic model of microbial growth, in which cells allocate enzyme synthesis resources according to a matching rule that mimics rational decision-making. The matching rule was later shown to be optimal under general assumptions about the underlying return-on-investment structure, yet the specific objective the cell maximizes and the constraints bounding that choice were never written down as an explicit economic decision. Here we supply that missing decision, recasting cybernetic enzyme-synthesis control as a consumer choice problem from microeconomic theory: the cell allocates a limited proteome budget among competing catabolic enzymes as a linear program (LP), maximizing a linear growth utility subject to a linear proteome budget constraint. Because the utility is linear, the LP's solution is geometric: whenever the iso-utility line's slope differs from the budget constraint's, the optimum is a corner, and the entire proteome budget is allocated to the enzyme for the single most profitable substrate. Corner solutions correspond to diauxic growth, and sequential substrate consumption follows from the choice of corner rather than a distinct regulatory mechanism. Only when the two slopes coincide does the optimum spread across the entire budget line instead of concentrating at a single corner; this degenerate case is where simultaneous substrate use becomes admissible. Using kinetic parameters from single-substrate experiments together with a small set of model-level parameters set in this study, the LP-derived cybernetic variables reproduced the diauxic and triauxic batch growth of Klebsiella oxytoca on glucose-xylose and glucose-xylose-lactose mixtures, achieving a fit comparable to the classical matching law. Thus, sequential substrate use is the generic outcome of growth-maximizing specialization under perfect substitutability, and co-utilization is the degenerate case of equal profitability.
