arXiv subjects

Marcus Roper

Publications and source records attributed to Marcus Roper.

At least 19 recordsLinked to original sources

arXiv2026

PUNCH: Physics-informed Uncertainty-aware Network for Coronary Hemodynamics

More than 10 million coronary angiograms are performed globally each year, providing a gold standard for detecting obstructive coronary artery disease. Yet, no obstructive lesions are identified in 70% of patients evaluated for ischemic heart disease. Up to half of these patients have undiagnosed, life-limiting coronary microvascular dysfunction (CMD), which remains under-detected due to the limited availability of invasive tools required to measure coronary flow reserve (CFR). Here, we introduce PUNCH, a non-invasive, uncertainty-aware framework for estimating CFR directly from standard coronary angiography. PUNCH integrates physics-informed neural networks with variational inference to infer coronary blood flow from first-principles models of contrast transport, without requiring ground-truth flow measurements or population-level training. The pipeline runs in approximately three minutes per patient on a single GPU. Validated on synthetic angiograms with controlled noise and imaging artifacts, as well as on clinical bolus thermodilution data from 20 patients, PUNCH demonstrates accurate and uncertainty-calibrated CFR estimation. This approach establishes a new paradigm for CMD diagnosis and illustrates how physics-informed inference can substantially expand the diagnostic utility of available clinical imaging.

cs.LG↗

arXiv2025

mRNA-protein assembly reduces fluctuations in a system with bursty transcription

mRNA-protein assemblies play a fundamental role in forming membraneless compartments within cells, whose functions may include activating, inhibiting, and localizing reactions. Recruitment of proteins into droplets can diminish cell to cell variability in protein abundance. However, the extent to which mRNA-protein assemblies may also buffer noise arising from transcription is not understood. Complicating study of this question is that models of kinetics typically treat this as a phase separation process, when mRNA-protein assemblies can contain as few as 2 mRNA transcripts, far below the thermodynamic thresholds for phase separation. Here, through stochastic simulations and asymptotic analysis, we quantify noise suppression by mRNA-protein assemblies as a function of gene expression kinetic parameters, and show that assemblies formed from just a handful of mRNAs effectively regulate transcript abundances and suppress fluctuations. We place particular emphasis on how this mechanism can facilitate regulated transcription by reducing noise even in the context of infrequent bursts of transcription. We investigate two biologically relevant models in which mRNA assembly acts to either "buffer" noise by storing mRNA in inert droplets, or "filter" assembled mRNAs by accelerating their decay, and quantify expression noise as a function of kinetic parameters. In either case, the most controlled expression occurs when bursts produce mRNAs close to the assembly threshold, which we find to be broadly consistent with observations of an RNP-droplet forming cyclin in multinucleate \textit{Ashbya gossypii} cells.

q-bio.SC↗

arXiv2025

Thin gap approximations for microfluidic device design

Over 125 years ago, Henry Selby Hele-Shaw realized that the depth-averaged flow in thin gap geometries can be closely approximated by two-dimensional (2D) potential flow, in a surprising marriage between the theories of viscous-dominated and inviscid flows. Hele-Shaw approximation allows visualization of potential flows over 2D airfoils and also undergirds important discoveries in the dynamics of interfacial instabilities and convection, yet it has found little use in modeling flows in microfluidic devices, although these devices often have thin gap geometries. Here, we derive a Hele-Shaw approximation for the flow in the kinds of thin gap geometries created within microfluidic devices. Using the Method of Weighted Residuals (MWR), we reinterpret the Hele-Shaw approximation as the leading term of an orthogonal polynomial expansion that can be systematically extended to higher-order corrections. The resulting leading-order equation coincides with the previously derived 2D approximations, but our derivation is shorter and more direct. By extending the expansion beyond leading order, we obtain a new reduced model that captures non-parabolic gap-wise velocity profiles and out-of-plane flow effects. We provide substantial numerical evidence showing that approximate equations can successfully model real microfluidic and inertial-microfluidic device geometries. By reducing three-dimensional (3D) flows to 2D models, our validated model will allow for accelerated device modeling and design.

physics.flu-dyn↗

arXiv2025

Decision-making in light-trapped slime molds involves active mechanical processes

Decision-making is the process of selecting an action among alternatives, allowing biological and artificial systems to navigate complex environments and optimize behavior. While neural systems rely on neuron-based sensory processing and evaluation, decision-making also occurs in organisms without a centralized organizing unit, such as the unicellular slime mold \textit{Physarum polycephalum}. Unlike neural systems, P. polycephalum relies on rhythmic peristaltic contractions to drive internal flows and redistribute mass, allowing it to adapt to its environment. However, while previous studies have focused on the outcomes of these decisions, the underlying mechanical principles that govern this mass relocation remain unknown. Here, we investigate the exploration process of P. polycephalum confined by blue light into polygonal shapes up to its escape. While the escape occurs along the longest axis of the polygones, independent of confinement shape, the exploration process prior to escape extends protrusions almost everywhere around a shape boundary. We find protrusions to align with the direction of peristaltic contraction waves driving mass relocation. Mapping out contraction modes during exploration in detail we observe an ongoing switching between different dominant principle contraction modes. Only over the course of time does the organism ultimately settle on the contraction mode most efficient for transport, which coincides with the escape. Thus, we find that only harsh environmental confinement triggers optimal behaviour which is reached by long time re-organization of the flow patterns. Our findings provide insights into the mechanics of decision-making in non-neuronal organisms, shedding light on how decentralized systems process environmental constraints to drive adaptive behavior.

physics.bio-ph↗

arXiv2023

Inertial Migration in Micro-Centrifuge Devices

Within microcentrifuge devices, a microfluidic vortex separates larger particles from a heterogeneous suspension using inertial migration, a phenomenon that causes particles to migrate across streamlines. The ability to selectively capture particles based on size differences of a few microns makes microcentrifuges useful diagnostic tools for trapping rare cells within blood samples. However, rational design of microcentrifuges has been held back from its full potential by a lack of quantitative modeling of particle capture mechanics. Here we use an asymptotic method, in which particles are accurately modeled as singularities in a linearized flow field, to rapidly calculate particle trajectories within microcentrifuges. Our predictions for trapping thresholds and trajectories agree well with published experimental data. Our results clarify how capture reflects a balance between advection of particles within a background flow and their inertial focusing and shows why the close proximity of trapped and untrapped incoming streamlines makes it challenging to design microcentrifuges with sharp trapping thresholds.

physics.flu-dyn↗

arXiv2022

The Role of RNA Condensation in Reducing Gene Expression Noise

Biomolecular condensates have been shown to play a fundamental role in localizing biochemistry in a cell. RNA is a common constituent of condensates, and can determine their biophysical properties. Functions of biomolecular condensates are varied including activating, inhibiting, and localizing reactions. Recent theoretical work has shown that the phase separation of proteins into droplets can diminish cell to cell variability in protein abundance. However, the extent to which phase separation involving mRNAs may also buffer noise has yet to be explored. In this paper, we introduce a phenomenological model for the phase separation of mRNAs into RNP condensates, and quantify noise suppression as a function of gene expression kinetic parameters. Through stochastic simulations, we highlight the ability for condensates formed from just a handful of mRNAs to regulate the abundance and suppress the fluctuations of proteins. We place particular emphasis on how this mechanism can facilitate efficient transcription by reducing noise even in the situation of infrequent bursts of transcription by exploiting the physics of a concentration-dependent, deterministic phase separation threshold. We investigate two biologically relevant models in which phase separation acts to either "buffer" noise by storing mRNA in inert droplets, or "filter" phase separated mRNAs by accelerating their decay, and quantify expression noise as a function of kinetic parameters. In either case the most efficient expression occurs when bursts produce mRNAs close the phase separation threshold, which we find to be broadly consistent with observations of an RNP-droplet forming cyclinin multinucleate Ashbya gossypii cells. We finally consider the contribution of noise in the phase separation threshold, and show that protein copy number noise can be suppressed by phase separation threshold fluctuations in certain conditions.

q-bio.SC↗

arXiv2022

Modeling Insights from COVID-19 Incidence Data: Part I -- Comparing COVID-19 Cases Between Different-Sized Populations

Comparing how different populations have suffered under COVID-19 is a core part of ongoing investigations into how public policy and social inequalities influence the number of and severity of COVID-19 cases. But COVID-19 incidence can vary multifold from one subpopulation to another, including between neighborhoods of the same city, making comparisons of case rates deceptive. At the same time, although epidemiological heterogeneities are increasingly well-represented in mathematical models of disease spread, fitting these models to real data on case numbers presents a tremendous challenge, as does interpreting the models to answer questions such as: Which public health policies achieve the best outcomes? Which social sacrifices are most worth making? Here we compare COVID-19 case-curves between different US states, by clustering case surges between March 2020 and March 2021 into groups with similar dynamics. We advance the hypothesis that each surge is driven by a subpopulation of COVID-19 contacting individuals, and make detecting the size of that population a step within our clustering algorithm. Clustering reveals that case trajectories in each state conform to one of a small number (4-6) of archetypal dynamics. Our results suggest that while the spread of COVID-19 in different states is heterogeneous, there are underlying universalities in the spread of the disease that may yet be predictable by models with reduced mathematical complexity. These universalities also prove to be surprisingly robust to school closures, which we choose as a common, but high social cost, public health measure.

q-bio.PE↗

arXiv2022

Approximating pressure-driven Stokes flow using the principle of minimal excess dissipation

Stokes' equations model microscale fluid flows including the flows of nanoliter-sized fluid samples in lab-on-a-chip systems. Helmholtz's dissipation theorem guarantees that the solution of Stokes' equations in a given domain minimizes viscous dissipation among all incompressible vector fields that are compatible with the velocities imposed at the domain boundaries. Helmholtz's dissipation theorem directly guarantees the uniqueness of solutions of Stokes flow, and provides a practical method for calculating approximate solutions for flow around moving bodies. However, although generalization of the principle to domains with mixtures of velocity and stress boundary conditions is relatively straight-forward (Keller et al., 1967), it appears to be little known. Here we show that the principle of minimal excess dissipation can be used to derive accurate analytical approximations for the flows in microchannels with different cross-section shapes including when the channel walls are engineered to have different distributions of slip boundary conditions. In addition to providing a simple, rapid, method for approximating the conductances of micro-channels, analysis of excess dissipation allows for a comparison principle that can be used, for example, to show that the conductance of a channel is always increased by adding additional slip boundary conditions.

physics.flu-dyn↗

arXiv2021

Fast Asymptotic-Numerical Method For Coarse Mesh Particle Simulation In Channels Of Arbitrary Cross Section

Particles traveling through inertial microfluidic devices migrate to focusing streamlines. We present a numerical method that calculates migration velocities of particles in inertial microfluidic channels of arbitrary cross section by representing particles by singularities. Refinements to asymptotic analysis are given that improve the regularity of the singularity approximation, making finite element approximations of flow and pressure fields more effective. Sample results demonstrate that the method is computationally efficient and able to capture bifurcations in particle focusing positions due to changes in channel shape and Reynolds number.

physics.flu-dyn↗

arXiv2020

Modeling Insights from COVID-19 Incidence Data: Part II -- Why are compartment models so accurate?

The SIR-compartment model is among the simplest models that describe the spread of a disease through a population. The model makes the unrealistic assumption that the population through which the disease is spreading is well-mixed. Although real populations have heterogeneities in contacts not represented in the SIR model, it nevertheless well fits real U.S. state data at multiple points throughout the pandemic. Here we demonstrate mathematically how closely the simple continuous SIR model approximates a model which includes heterogeneous contacts, and provide insight onto how one can interpret parameters gleaned from regression in the context of heterogeneous dynamics.

q-bio.PE↗

arXiv2020

Optimal Mixing in Transport Networks: Numerical Optimization and Analysis

Many foraging microorganisms rely upon cellular transport networks to deliver nutrients, fluid and organelles between different parts of the organism. Networked organisms ranging from filamentous fungi to slime molds demonstrate a remarkable ability to mix or disperse molecules and organelles in their transport media. Here we introduce mathematical tools to analyze the structure of energy efficient transport networks that maximize mixing and sending signals originating from and arriving at each node. We define two types of entropies on flows to quantify mixing and develop numerical algorithms to optimize the combination of entropy and energy on networks, given constraints on the amount of available material. We present an in-depth exploration of optimal single source-sink networks on finite triangular grids, a fundamental setting for optimal transport networks in the plane. Using numerical simulations and rigorous proofs, we show that, if the constraint on conductances is strict, the optimal networks are paths of every possible length. If the constraint is relaxed, our algorithm produces loopy networks that fan out at the source and pour back into a single path that flows to the sink. Taken together, our results expand the class of optimal transportation networks that can be compared with real biological data, and highlight how real network morphologies may be shaped by tradeoffs between transport efficiency and the need to mix the transported matter.

nlin.AO↗

arXiv2017

A Gradient Descent Method for Optimization of Model Microvascular Networks

Within animals, oxygen exchange occurs within networks containing potentially billions of microvessels that are distributed throughout the animal's body. Innovative imaging methods now allow for mapping of the architecture and blood flows within real microvascular networks. However, these data streams have so far yielded little new understanding of the physical principles that underlie the organization of microvascular networks, which could allow healthy networks to be quantitatively compared with networks that have been damaged, e.g. due to diabetes. A natural mathematical starting point for understanding network organization is to construct networks that are optimized accordingly to specified functions. Here we present a method for deriving transport networks that optimize general functions involving the fluxes and conductances within the network. In our method Kirchoff's laws are imposed via Lagrange multipliers, creating a large, but sparse system of auxiliary equations. By treating network conductances as adiabatic variables, we derive a gradient descent method in which conductances are iteratively adjusted, and auxiliary variables are solved for by two inversions of O(N^2) sized sparse matrices. In particular our algorithm allows us to validate the hypothesis that microvascular networks are organized to uniformly partition the flow of red blood cells through vessels. The theoretical framework can also be used to consider more general sets of objective functions and constraints within transport networks, including incorporating the non-Newtonian rheology of blood (i.e. the Fahraeus-Lindqvist effect). More generally by forming linear combinations of objective functions, we can explore tradeoffs between different optimization functions, giving more insight into the diversity of biological transport networks seen in nature.

q-bio.QM↗

arXiv2017

Minimal transport networks with general boundary conditions

Vascular networks are used across the kingdoms of life to transport fluids, nutrients and cellular material. A popular unifying idea for understanding the diversity and constraints of these networks is that the conduits making up the network are organized to optimize dissipation or other functions within the network. However the general principles governing the optimal networks remain unknown. In particular Durand showed that under Neumann boundary conditions networks, that minimize dissipation should be trees. Yet many real transport networks, including capillary beds, are not simply connected. Previously multiconnectedness in a network has been assumed to provide evidence that the network is not simply minimizing dissipation. Here we show that if the boundary conditions on the flows within the network are enlarged to include physical reasonable Neumann and Dirichlet boundary conditions (i.e. constraints on either pressure or flow) then minimally dissipative networks need not be trees. To get to this result we show that two methods of producing optimal networks, namely enforcing constraints via Lagrange multipliers or via penalty methods, are equivalent for tree networks.

math.OC↗

arXiv2017

Pairwise interactions in inertially-driven one-dimensional microfluidic crystals

In microfluidic devices, inertia drives particles to focus on a finite number of inertial focusing streamlines. Particles on the same streamline interact to form one-dimensional microfluidic crystals (or "particle trains"). Here we develop an asymptotic theory to describe the pairwise interactions underlying the formation of a 1D crystal. Surprisingly, we show that particles assemble into stable equilibria, analogous to the motion of a damped spring. Although previously it has been assumed that particle spacings scale with particle diameters, we show that the equilibrium spacing of particles depends on the distance between the inertial focusing streamline and the nearest channel wall, and therefore can be controlled by tuning the particle radius.

physics.flu-dyn↗

arXiv2016

Anti-jamming in a fungal transport network

Congestion limits the efficiency of transport networks ranging from highways to the internet. Fungal hyphal networks are studied as an examples of optimal biological transport networks, but the scheduling and direction of traffic to avoid congestion has not been examined. We show here that the Neurospora crassa fungal network exhibits anticongestion: more densely packed nuclei flow faster along hyphal highways, and transported nuclei self-organize into fast flowing solitons. Concentrated transport by solitons may allow cells to cycle between growing and acting as transport conduits.

physics.bio-ph↗

arXiv2015

Mushroom spore dispersal by convectively-driven winds

Thousands of fungal species rely on mushroom spores to spread across landscapes. It has long been thought that spores depend on favorable airflows for dispersal -- that active control of spore dispersal by the parent fungus is limited to an impulse delivered to the spores to carry them clear of the gill surface. Here we show that evaporative cooling of the air surrounding the mushroom pileus creates convective airflows capable of carrying spores at speeds of centimeters per second. Convective cells can transport spores from gaps that may be only a centimeter high, and lift spores ten centimeters or more into the air. The work reveals how mushrooms tolerate and even benefit from crowding, and provides a new explanation for their high water needs.

physics.bio-ph↗

arXiv2015

Optimal occlusion uniformly partitions red blood cells fluxes within a microvascular network

In animals, gas exchange between blood and tissues occurs in narrow vessels, whose diameter is comparable to that of a red blood cell. Red blood cells must deform to squeeze through these narrow vessels, transiently blocking or occluding the vessels they pass through. Although the dynamics of vessel occlusion have been studied extensively, it remains an open question why microvessels need to be so narrow. We study occlusive dynamics within a model microvascular network: the embryonic zebrafish trunk. We show that pressure feedbacks created when red blood cells enter the finest vessels of the trunk act together to uniformly partition red blood cells through the microvasculature. Using mathematical models as well as direct observation, we show that these occlusive feedbacks are tuned throughout the trunk network to prevent the vessels closest to the heart from short-circuiting the network. Thus occlusion is linked with another open question of microvascular function: how are red blood cells delivered at the same rate to each micro-vessel? Our analysis shows that tuning of occlusive feedbacks increase the total dissipation within the network by a factor of 11, showing that uniformity of flows rather than minimization of transport costs may be prioritized by the microvascular network.

q-bio.TO↗

arXiv2015

Defining individual size in the model filamentous fungus $\textit{Neurospora crassa}$

It is challenging to apply the tenets of individuality to filamentous fungi: a fungal mycelium can contain millions of genetically diverse but totipotent nuclei, each capable of founding new mycelia. Moreover a single mycelium can potentially stretch over kilometers and it is unlikely that its distant parts share resources or have the same fitness. Here we directly measure how a single mycelium of the model ascomycete {\it Neurospora crassa} is patterned into Reproductive Units (RUs); subpopulations of nuclei that propagate together as spores, and function as reproductive individuals. The density of RUs is sensitive to the geometry of growth; we detect 50-fold smaller RUs when mycelia had expanding frontiers than when they were constrained to grow in one direction only. RUs fragmented further when the mycelial network was perturbed. In mycelia with expanding frontiers RU composition was strongly influenced by the distribution of genotypes early in development. Our results provide a concept of fungal individuality that is directly connected to reproductive potential, and therefore to theories of how fungal individuals adapt and evolve over time. Our data show that the size of reproductive individuals is a dynamic and environment-dependent property, even within apparently totally connected fungal mycelia.

q-bio.PE↗