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On the Analytic Origin of Two Species of Cochlear Eigenmodes
Authors:
Asheesh S. Momi,
Isabella R. Graf,
Michael C. Abbott,
Benjamin B. Machta
Abstract:
After entering the ear, sound waves propagate as surface waves along the cochlea's basilar membrane. In recent work, we showed numerically that the system supports two types of modes: localized resonant modes, which underpin the modern understanding of cochlear mechanics, and a novel class of spatially extended modes. Here, we develop an analytic framework that explains the emergence of this mode…
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After entering the ear, sound waves propagate as surface waves along the cochlea's basilar membrane. In recent work, we showed numerically that the system supports two types of modes: localized resonant modes, which underpin the modern understanding of cochlear mechanics, and a novel class of spatially extended modes. Here, we develop an analytic framework that explains the emergence of this mode structure. We show that extended modes arise from globally continuous standing-wave solutions, whereas localized modes result from internal resonance requiring matching across a singular point. These results clarify the generic structure of cochlear wave equations.
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Submitted 16 March, 2026;
originally announced March 2026.
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Precision magnetometry at cryogenic temperatures with gaseous 3He NMR probes
Authors:
P. Blümler,
M. Fertl,
H. -J. Grafe,
R. Graf,
W. Heil
Abstract:
We report on compact, gaseous 3He NMR probes for precision magnetometry of magnetic fields B > 0.1 T in the temperature range from ambient temperatures down to 4 Kelvin. The gas is polarized at thermal equilibrium under pressures up to 100 bar to provide a high nuclear spin density. In order to achieve sensor readout rates of order (Hz), paramagnetic substances and/or silica gel with high specific…
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We report on compact, gaseous 3He NMR probes for precision magnetometry of magnetic fields B > 0.1 T in the temperature range from ambient temperatures down to 4 Kelvin. The gas is polarized at thermal equilibrium under pressures up to 100 bar to provide a high nuclear spin density. In order to achieve sensor readout rates of order (Hz), paramagnetic substances and/or silica gel with high specific surface area were added to reduce the otherwise long T1 relaxation time of pure 3He gas to reach thermal polarization equilibrium. Sensitivity limits, which cover the range from 10-11 < dB/B < 10-7, are accessible in a single-pulse NMR measurement and can be further improved through signal averaging in accumulated NMR scans.
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Submitted 23 May, 2025; v1 submitted 15 January, 2025;
originally announced January 2025.
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Towards detection of molecular parity violation via chiral co-sensing: the $^1$H/$^{31}$P model system
Authors:
Erik Van Dyke,
James Eills,
Kirill Sheberstov,
John Blanchard,
Manfred Wagner,
Robert Graf,
Andrés Emilio Wedenig,
Konstantin Gaul,
Robert Berger,
Rudolf Pietschnig,
Denis Kargin,
Danila A. Barskiy,
Dmitry Budker
Abstract:
Fundamental weak interactions have been shown to violate parity in both nuclear and atomic systems. However, observation of parity violation in a molecular system has proven an elusive target. Nuclear spin dependent contributions of the weak interaction are expected to result in energetic differences between enantiomers manifesting in nuclear magnetic resonance (NMR) spectra as chemical shift diff…
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Fundamental weak interactions have been shown to violate parity in both nuclear and atomic systems. However, observation of parity violation in a molecular system has proven an elusive target. Nuclear spin dependent contributions of the weak interaction are expected to result in energetic differences between enantiomers manifesting in nuclear magnetic resonance (NMR) spectra as chemical shift differences on the order of $10^{-6}$ Hz to $10^{-3}$ Hz for high-$Z$ nuclei. By employing simultaneous measurements of the diastereomeric splittings for a light and a heavy nucleus in solution-state NMR, residual chemical shift differences persisting in non-chiral environment between enantiomers of chiral compounds smaller than the typical linewidth of high-field NMR may be resolved. Sources of error must be identified and minimized to verify that the observed effect is, in fact, due to parity violation and not systematic effects. This paper presents a detailed analysis of a system incorporating \textsuperscript{31}P and \textsuperscript{1}H NMR to elucidate the systematic effects and to guide experiments with higher-$Z$ nuclei where molecular parity violation may be resolved.
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Submitted 30 December, 2024;
originally announced December 2024.
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Hair cells in the cochlea must tune resonant modes to the edge of instability without destabilizing collective modes
Authors:
Asheesh S. Momi,
Michael C. Abbott,
Julian Rubinfien,
Benjamin B. Machta,
Isabella R. Graf
Abstract:
Sound produces surface waves along the cochlea's basilar membrane. To achieve the ear's astonishing frequency resolution and sensitivity to faint sounds, dissipation in the cochlea must be canceled via active processes in hair cells, effectively bringing the cochlea to the edge of instability. But how can the cochlea be globally tuned to the edge of instability with only local feedback? To address…
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Sound produces surface waves along the cochlea's basilar membrane. To achieve the ear's astonishing frequency resolution and sensitivity to faint sounds, dissipation in the cochlea must be canceled via active processes in hair cells, effectively bringing the cochlea to the edge of instability. But how can the cochlea be globally tuned to the edge of instability with only local feedback? To address this question, we use a discretized version of a standard model of basilar membrane dynamics, but with an explicit contribution from active processes in hair cells. Surprisingly, we find the basilar membrane supports two qualitatively distinct sets of modes: a continuum of localized modes and a small number of collective extended modes. Localized modes sharply peak at their resonant position and are largely uncoupled. As a result, they can be amplified almost independently from each other by local hair cells via feedback reminiscent of self-organized criticality. However, this amplification can destabilize the collective extended modes; avoiding such instabilities places limits on possible molecular mechanisms for active feedback in hair cells. Our work illuminates how and under what conditions individual hair cells can collectively create a critical cochlea.
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Submitted 18 December, 2024; v1 submitted 19 July, 2024;
originally announced July 2024.
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Lattice ultrasensitivity amplifies signals in E. coli without fine-tuning
Authors:
Derek M. Sherry,
Isabella R. Graf,
Samuel J. Bryant,
Thierry Emonet,
Benjamin B. Machta
Abstract:
The E. coli chemosensory lattice, consisting of receptors, kinases, and adaptor proteins, is an important test case for biochemical signal processing. Kinase output is characterized by precise adaptation to a wide range of background ligand levels and large gain in response to small relative changes in concentration. Existing models of this lattice achieve their gain through allosteric interaction…
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The E. coli chemosensory lattice, consisting of receptors, kinases, and adaptor proteins, is an important test case for biochemical signal processing. Kinase output is characterized by precise adaptation to a wide range of background ligand levels and large gain in response to small relative changes in concentration. Existing models of this lattice achieve their gain through allosteric interactions between either receptors or core units of receptors and kinases. Here we introduce a model which operates through an entirely different mechanism in which receptors gate inherently far from equilibrium enzymatic reactions between neighboring kinases. Our lattice model achieves gain through a mechanism more closely related to zero-order ultrasensitivity than to allostery. Thus, we call it lattice ultrasensitivity (LU). Unlike other lattice critical models, the LU model can achieve arbitrarily high gain through time-scale separation, rather than through fine-tuning. The model also captures qualitative experimental results which are difficult to reconcile with existing models. We discuss possible implementations in the lattice's baseplate where long flexible linkers could potentially mediate interactions between neighboring core units.
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Submitted 15 February, 2025; v1 submitted 28 May, 2024;
originally announced May 2024.
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Preserved Edge Convolutional Neural Network for Sensitivity Enhancement of Deuterium Metabolic Imaging (DMI)
Authors:
Siyuan Dong,
Henk M. De Feyter,
Monique A. Thomas,
Robin A. de Graaf,
James S. Duncan
Abstract:
Purpose: Common to most MRSI techniques, the spatial resolution and the minimal scan duration of Deuterium Metabolic Imaging (DMI) are limited by the achievable SNR. This work presents a deep learning method for sensitivity enhancement of DMI.
Methods: A convolutional neural network (CNN) was designed to estimate the 2H-labeled metabolite concentrations from low SNR and distorted DMI FIDs. The C…
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Purpose: Common to most MRSI techniques, the spatial resolution and the minimal scan duration of Deuterium Metabolic Imaging (DMI) are limited by the achievable SNR. This work presents a deep learning method for sensitivity enhancement of DMI.
Methods: A convolutional neural network (CNN) was designed to estimate the 2H-labeled metabolite concentrations from low SNR and distorted DMI FIDs. The CNN was trained with synthetic data that represent a range of SNR levels typically encountered in vivo. The estimation precision was further improved by fine-tuning the CNN with MRI-based edge-preserving regularization for each DMI dataset. The proposed processing method, PReserved Edge ConvolutIonal neural network for Sensitivity Enhanced DMI (PRECISE-DMI), was applied to simulation studies and in vivo experiments to evaluate the anticipated improvements in SNR and investigate the potential for inaccuracies.
Results: PRECISE-DMI visually improved the metabolic maps of low SNR datasets, and quantitatively provided higher precision than the standard Fourier reconstruction. Processing of DMI data acquired in rat brain tumor models resulted in more precise determination of 2H-labeled lactate and glutamate + glutamine levels, at increased spatial resolution (from >8 to 2 $μ$L) or shortened scan time (from 32 to 4 min) compared to standard acquisitions. However, rigorous SD-bias analyses showed that overuse of the edge-preserving regularization can compromise the accuracy of the results.
Conclusion: PRECISE-DMI allows a flexible trade-off between enhancing the sensitivity of DMI and minimizing the inaccuracies. With typical settings, the DMI sensitivity can be improved by 3-fold while retaining the capability to detect local signal variations.
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Submitted 13 September, 2023; v1 submitted 7 September, 2023;
originally announced September 2023.
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A bifurcation integrates information from many noisy ion channels
Authors:
Isabella R. Graf,
Benjamin B. Machta
Abstract:
In various biological systems information from many noisy molecular receptors must be integrated into a collective response. A striking example is the thermal imaging organ of pit vipers. Single nerve fibers in the organ reliably respond to mK temperature increases, a thousand times more sensitive than their molecular sensors, thermo-TRP ion channels. Here, we propose a mechanism for the integrati…
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In various biological systems information from many noisy molecular receptors must be integrated into a collective response. A striking example is the thermal imaging organ of pit vipers. Single nerve fibers in the organ reliably respond to mK temperature increases, a thousand times more sensitive than their molecular sensors, thermo-TRP ion channels. Here, we propose a mechanism for the integration of this molecular information. In our model, amplification arises due to proximity to a dynamical bifurcation, separating a regime with frequent and regular action potentials (APs), from a regime where APs are irregular and infrequent. Near the transition, AP frequency can have an extremely sharp dependence on temperature, naturally accounting for the thousand-fold amplification. Furthermore, close to the bifurcation, most of the information about temperature available in the TRP channels' kinetics can be read out from the timing of APs even in the presence of readout noise. While proximity to such bifurcation points typically requires fine-tuning of parameters, we propose that having feedback act from the order parameter (AP frequency) onto the control parameter robustly maintains the system in the vicinity of the bifurcation. This robustness suggests that similar feedback mechanisms might be found in other sensory systems which also need to detect tiny signals in a varying environment.
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Submitted 9 May, 2023;
originally announced May 2023.
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Thermodynamic stability and critical points in multicomponent mixtures with structured interactions
Authors:
Isabella R. Graf,
Benjamin B. Machta
Abstract:
Theoretical work has shed light on the phase behavior of idealized mixtures of many components with random interactions. But typical mixtures interact through particular physical features, leading to a structured, non-random interaction matrix of lower rank. Here we develop a theoretical framework for such mixtures and derive mean-field conditions for thermodynamic stability and critical behavior.…
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Theoretical work has shed light on the phase behavior of idealized mixtures of many components with random interactions. But typical mixtures interact through particular physical features, leading to a structured, non-random interaction matrix of lower rank. Here we develop a theoretical framework for such mixtures and derive mean-field conditions for thermodynamic stability and critical behavior. Irrespective of the number of components and features, this framework allows for a generally lower-dimensional representation in the space of features and proposes a principled way to coarse-grain multicomponent mixtures as binary mixtures. Moreover, it suggests a way to systematically characterize different series of critical points and their codimensions in mean-field. Since every pairwise interaction matrix can be expressed in terms of features, our work is applicable to a broad class of mean-field models.
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Submitted 1 September, 2022; v1 submitted 21 October, 2021;
originally announced October 2021.
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Stochastic Yield Catastrophes and Robustness in Self-Assembly
Authors:
Florian M. Gartner,
Isabella R. Graf,
Patrick Wilke,
Philipp M. Geiger,
Erwin Frey
Abstract:
A guiding principle in self-assembly is that, for high production yield, nucleation of structures must be significantly slower than their growth. However, details of the mechanism that impedes nucleation are broadly considered irrelevant. Here, we analyze self-assembly into finite-sized target structures employing mathematical modeling. We investigate two key scenarios to delay nucleation: (i) by…
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A guiding principle in self-assembly is that, for high production yield, nucleation of structures must be significantly slower than their growth. However, details of the mechanism that impedes nucleation are broadly considered irrelevant. Here, we analyze self-assembly into finite-sized target structures employing mathematical modeling. We investigate two key scenarios to delay nucleation: (i) by introducing a slow activation step for the assembling constituents and, (ii) by decreasing the dimerization rate. These scenarios have widely different characteristics. While the dimerization scenario exhibits robust behavior, the activation scenario is highly sensitive to demographic fluctuations. These demographic fluctuations ultimately disfavor growth compared to nucleation and can suppress yield completely. The occurrence of this stochastic yield catastrophe does not depend on model details but is generic as soon as number fluctuations between constituents are taken into account. On a broader perspective, our results reveal that stochasticity is an important limiting factor for self-assembly and that the specific implementation of the nucleation process plays a significant role in determining the yield.
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Submitted 18 March, 2020; v1 submitted 23 May, 2019;
originally announced May 2019.
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Self-organized system-size oscillation of a stochastic lattice-gas model
Authors:
Mareike Bojer,
Isabella R. Graf,
Erwin Frey
Abstract:
The totally asymmetric simple exclusion process (TASEP) is a paradigmatic stochastic model for non-equilibrium physics, and has been successfully applied to describe active transport of molecular motors along cytoskeletal filaments. Building on this simple model, we consider a two-lane lattice-gas model that couples directed transport (TASEP) to diffusive motion in a semi-closed geometry, and simu…
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The totally asymmetric simple exclusion process (TASEP) is a paradigmatic stochastic model for non-equilibrium physics, and has been successfully applied to describe active transport of molecular motors along cytoskeletal filaments. Building on this simple model, we consider a two-lane lattice-gas model that couples directed transport (TASEP) to diffusive motion in a semi-closed geometry, and simultaneously accounts for spontaneous growth and particle-induced shrinkage of the system's size. This particular extension of the TASEP is motivated by the question of how active transport and diffusion might influence length regulation in confined systems. Surprisingly, we find that the size of our intrinsically stochastic system exhibits robust temporal patterns over a broad range of growth rates. More specifically, when particle diffusion is slow relative to the shrinkage dynamics, we observe quasi-periodic changes in length. We provide an intuitive explanation for the occurrence of these self-organized temporal patterns, which is based on the imbalance between the diffusion and shrinkage speed in the confined geometry. Finally, we formulate an effective theory for the oscillatory regime, which explains the origin of the oscillations and correctly predicts the dependence of key quantities, as for instance the oscillation frequency, on the growth rate.
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Submitted 20 June, 2018; v1 submitted 11 March, 2018;
originally announced March 2018.
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Exploiting ecology in drug pulse sequences in favour of population reduction
Authors:
Marianne Bauer,
Isabella R. Graf,
Vudtiwat Ngampruetikorn,
Greg J. Stephens,
Erwin Frey
Abstract:
A deterministic population dynamics model involving birth and death for a two-species system, comprising a wild-type and more resistant species competing via logistic growth, is subjected to two distinct stress environments designed to mimic those that would typically be induced by temporal variation in the concentration of a drug (antibiotic or chemotherapeutic) as it permeates through the popula…
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A deterministic population dynamics model involving birth and death for a two-species system, comprising a wild-type and more resistant species competing via logistic growth, is subjected to two distinct stress environments designed to mimic those that would typically be induced by temporal variation in the concentration of a drug (antibiotic or chemotherapeutic) as it permeates through the population and is progressively degraded. Different treatment regimes, involving single or periodical doses, are evaluated in terms of the minimal population size (a measure of the extinction probability), and the population composition (a measure of the selection pressure for resistance or tolerance during the treatment). We show that there exist timescales over which the low-stress regime is as effective as the high-stress regime, due to the competition between the two species. For multiple periodic treatments, competition can ensure that the minimal population size is attained during the first pulse when the high-stress regime is short, which implies that a single short pulse can be more effective than a more protracted regime. Our results suggest that when the duration of the high-stress environment is restricted, a treatment with one or multiple shorter pulses can produce better outcomes than a single long treatment. If ecological competition is to be exploited for treatments, it is crucial to determine these timescales, and estimate for the minimal population threshold that suffices for extinction. These parameters can be quantified by experiment.
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Submitted 7 February, 2018;
originally announced February 2018.
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Generic transport mechanisms for molecular traffic in cellular protrusions
Authors:
Isabella R. Graf,
Erwin Frey
Abstract:
Transport of molecular motors along protein filaments in a half-closed geometry is a common feature of biologically relevant processes in cellular protrusions. Using a lattice gas model we study how the interplay between active and diffusive transport and mass conservation leads to localised domain walls and tip localisation of the motors. We identify a mechanism for task sharing between the activ…
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Transport of molecular motors along protein filaments in a half-closed geometry is a common feature of biologically relevant processes in cellular protrusions. Using a lattice gas model we study how the interplay between active and diffusive transport and mass conservation leads to localised domain walls and tip localisation of the motors. We identify a mechanism for task sharing between the active motors (maintaining a gradient) and the diffusive motion (transport to the tip), which ensures that energy consumption is low and motor exchange mostly happens at the tip. These features are attributed to strong nearest-neighbour correlations that lead to a strong reduction of active currents, which we calculate analytically using an exact moment-identity, and might prove useful for the understanding of correlations and active transport also in more elaborate systems.
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Submitted 7 March, 2017;
originally announced March 2017.
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Proton radiography to improve proton radiotherapy: Simulation study at different proton beam energies
Authors:
A. K. Biegun,
Jun Takatsu,
M-J. van Goethem,
E. R. van der Graaf,
M. van Beuzekom,
J. Visser,
S. Brandenburg
Abstract:
To improve the quality of cancer treatment with protons, a translation of X-ray Computed Tomography (CT) images into a map of the proton stopping powers needs to be more accurate. Proton stopping powers determined from CT images have systematic uncertainties in the calculated proton range in a patient of typically 3-4\% and even up to 10\% in region containing bone~\cite{USchneider1995,USchneider1…
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To improve the quality of cancer treatment with protons, a translation of X-ray Computed Tomography (CT) images into a map of the proton stopping powers needs to be more accurate. Proton stopping powers determined from CT images have systematic uncertainties in the calculated proton range in a patient of typically 3-4\% and even up to 10\% in region containing bone~\cite{USchneider1995,USchneider1996,WSchneider2000,GCirrone2007,HPaganetti2012,TPlautz2014,GLandry2013,JSchuemann2014}. As a consequence, part of a tumor may receive no dose, or a very high dose can be delivered in healthy ti\-ssues and organs at risks~(e.g. brain stem)~\cite{ACKnopf2013}. A transmission radiograph of high-energy protons measuring proton stopping powers directly will allow to reduce these uncertainties, and thus improve the quality of treatment.
The best way to obtain a sufficiently accurate radiograph is by tracking individual protons traversing the phantom (patient)~\cite{GCirrone2007,TPlautz2014,VSipala2013}. In our simulations we have used an ideal position sensitive detectors measuring a single proton before and after a phantom, while the residual energy of a proton was detected by a BaF$_{2}$ crystal. To obtain transmission radiographs, diffe\-rent phantom materials have been irradiated with a 3x3~cm$^{2}$ scattered proton beam, with various beam energies. The simulations were done using the Geant4 simulation package~\cite{SAgostinelli2003}.
In this study we focus on the simulations of the energy loss radiographs for various proton beam energies that are clinically available in proton radiotherapy.
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Submitted 29 January, 2016;
originally announced January 2016.
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Quest for the Nuclear Georeactor
Authors:
R. J. de Meijer,
E. R. van der Graaf,
K. P. Jungmann
Abstract:
The paper focuses on a proposal for an underground antineutrino antenna to further develop the dectection of these particles as a tool to map the distribution of radiogenic heat sources, such as the natural radionuclides and a hypothetical nuclear georeactor.
The paper focuses on a proposal for an underground antineutrino antenna to further develop the dectection of these particles as a tool to map the distribution of radiogenic heat sources, such as the natural radionuclides and a hypothetical nuclear georeactor.
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Submitted 8 April, 2004;
originally announced April 2004.