Publications

Mathematical models are indispensable for disentangling the interactions through which biological components work together to generate the forces and flows that position, mix, and distribute proteins, nutrients, and organelles within the cell. To illuminate the ever more specific questions studied at the edge of biological inquiry, such models inevitably become more complex. Solving, simulating, and learning from these more realistic models requires the development of new analytic techniques, numerical methods, and scalable software. In this review, we discuss some recent developments in tools for understanding how large numbers of cytoskeletal filaments, driven by molecular motors and interacting with the cytoplasm and other structures in their environment, generate fluid flows, instabilities, and material deformations which help drive crucial cellular processes.

Genetic diagnosis promises to guide treatment and manage expectations for patients and physicians. Yet even when a variant in a disease gene is identified, the assignment of pathogenic impact is not always possible.1 Of the 215 million possible substitutions in approximately 19,900 genes, 71 million are missense mutations that result in an amino acid substitution rather than a stop codon or a frameshift.2 Only 4 million missense variants have been observed, of which approximately 2% have been clinically classified as pathogenic or benign by testing companies and collected in the public ClinVar repository. The rest are classified as variants of uncertain significance (VUS) due to the dearth of information on the functional impact or pathogenic consequences of the mutation.
A key challenge is to understand how changes in protein sequence affect function and contribute to disease. While the development of mutational scanning assays enables scientists to test thousands of substitutions at a time in cell lines, it is not possible to experimentally test all mutations, let alone assess fitness in humans. To meet this challenge, computational approaches that integrate many types of information and can predict functional impacts are becoming increasingly more sophisticated in their ability to accurately classify variants.
The early and powerful strategy for modeling the pathogenic impacts of variants involved employing evolutionary sequence information through the use of multiple sequence alignments (MSA). This approach examines sequence conservation across species and within humans, as demonstrated in models like PolyPhen and SIFT.3 The integration of functional insights related to protein domains and functions further enhances these models, coupled with artificial intelligence.3 Prediction of a correct 3-dimensional protein structure has long been a grail in research. Marks et al.4 suggested a global statistical model to massively reduce the search space of protein conformations by linking the pairwise correlations from MSA to fold a protein into a correct 3-dimensional structure (directly from Marks et al.4). AlphaFold5 marked a significant advancement in the field by using a large language model (LLM) to associate protein structure with MSA with unprecedented accuracy, effectively solving the “protein folding problem.” The ability of protein LLMs to learn not just amino acid relationships in linear sequences but also extremely rich relationships in any number of dimensions and contexts powers such models.

The visual world is richly adorned with texture, which can serve to delineate important elements of natural scenes. In anesthetized macaque monkeys, selectivity for the statistical features of natural texture is weak in V1, but substantial in V2, suggesting that neuronal activity in V2 might directly support texture perception. To test this, we investigated the relation between single cell activity in macaque V1 and V2 and simultaneously measured behavioral judgments of texture. We generated stimuli along a continuum between naturalistic texture and phase-randomized noise and trained two macaque monkeys to judge whether a sample texture more closely resembled one or the other extreme. Analysis of responses revealed that individual V1 and V2 neurons carried much less information about texture naturalness than behavioral reports. However, the sensitivity of V2 neurons, especially those preferring naturalistic textures, was significantly closer to that of behavior compared with V1. The firing of both V1 and V2 neurons predicted perceptual choices in response to repeated presentations of the same ambiguous stimulus in one monkey, despite low individual neural sensitivity. However, neither population predicted choice in the second monkey. We conclude that neural responses supporting texture perception likely continue to develop downstream of V2. Further, combined with neural data recorded while the same two monkeys performed an orientation discrimination task, our results demonstrate that choice-correlated neural activity in early sensory cortex is unstable across observers and tasks, untethered from neuronal sensitivity, and therefore unlikely to directly reflect the formation of perceptual decisions.

Including the effect of lattice anharmonicity on electron-phonon interactions has recently garnered attention due to its role as a necessary and significant component in explaining various phenomena, including superconductivity, optical response, and temperature dependence of mobility. This study focuses on analytically treating the effects of anharmonic electron-phonon coupling on the polaron self-energy, combined with numerical Diagrammatic Monte Carlo data. Specifically, we incorporate a quadratic interaction into the method of squeezed phonon states, which has proven effective for analytically calculating the polaron parameters. Additionally, we extend this method to nonparabolic finite-width conduction bands while maintaining the periodic translation symmetry of the system. Our results are compared with those obtained from Diagrammatic Monte Carlo, partially reported in a recent study [S. Ragni et al., Phys. Rev. B 107, L121109(2023)], covering a wide range of coupling strengths for the nonlinear interaction. Remarkably, our analytic method predicts the same features as the Diagrammatic Monte Carlo simulation.

The Anderson overlap catastrophe (AOC) is a many-body effect arising as a result of a shakeup of a Fermi sea due to an abrupt change of a local potential, leading to a power-law dependence of the density of states on energy. Here we demonstrate that a standard quantum-dot detector can be employed as a highly tuneable probe of the AOC, where the power law can be continuously modified by a gate voltage. We show that signatures of the AOC have already appeared in previous experiments, and give explicit predictions allowing to tune and pinpoint their non-perturbative aspects.

Many of the important phases observed in twisted transition metal dichalcogenide homobilayers are driven by short-range interactions, which should be captured by a local tight binding description since no Wannier obstruction exists for these systems. Yet, published theoretical descriptions have been mutually inconsistent, with honeycomb lattice tight binding models adopted for some twist angles, triangular lattice models adopted for others, and with tight binding models forsaken in favor of band projected continuum models in many numerical simulations. Here, we derive and study a minimal model containing both honeycomb orbitals and a triangular site that represents the band physics across a wide range of twist angles. The model provides a natural basis to study the interplay of interaction and topology in these heterostructures. It elucidates from generic features of the bilayer the sequence of Chern numbers occurring as twist angle is varied, and the microscopic origin of the magic angle at which flat-band physics occurs. At integer filling, the model successfully captures the Chern ferromagnetic and van-Hove driven antiferromagnetic insulators experimentally observed for small and large angles, respectively, and allows a straightforward calculation of the magneto-electric properties of the system.

Many of the important phases observed in twisted transition metal dichalcogenide homobilayers are driven by short-range interactions, which should be captured by a local tight binding description since no Wannier obstruction exists for these systems. Yet, published theoretical descriptions have been mutually inconsistent, with honeycomb lattice tight binding models adopted for some twist angles, triangular lattice models adopted for others, and with tight binding models forsaken in favor of band projected continuum models in many numerical simulations. Here, we derive and study a minimal model containing both honeycomb orbitals and a triangular site that represents the band physics across a wide range of twist angles. The model provides a natural basis to study the interplay of interaction and topology in these heterostructures. It elucidates from generic features of the bilayer the sequence of Chern numbers occurring as twist angle is varied, and the microscopic origin of the magic angle at which flat-band physics occurs. At integer filling, the model successfully captures the Chern ferromagnetic and van-Hove driven antiferromagnetic insulators experimentally observed for small and large angles, respectively, and allows a straightforward calculation of the magneto-electric properties of the system.

The Anderson overlap catastrophe (AOC) is a many-body effect arising as a result of a shakeup of a Fermi sea due to an abrupt change of a local potential, leading to a power-law dependence of the density of states on energy. Here we demonstrate that a standard quantum-dot detector can be employed as a highly tuneable probe of the AOC, where the power law can be continuously modified by a gate voltage. We show that signatures of the AOC have already appeared in previous experiments, and give explicit predictions allowing to tune and pinpoint their non-perturbative aspects.

Including the effect of lattice anharmonicity on electron-phonon interactions has recently garnered attention due to its role as a necessary and significant component in explaining various phenomena, including superconductivity, optical response, and temperature dependence of mobility. This study focuses on analytically treating the effects of anharmonic electron-phonon coupling on the polaron self-energy, combined with numerical Diagrammatic Monte Carlo data. Specifically, we incorporate a quadratic interaction into the method of squeezed phonon states, which has proven effective for analytically calculating the polaron parameters. Additionally, we extend this method to nonparabolic finite-width conduction bands while maintaining the periodic translation symmetry of the system. Our results are compared with those obtained from Diagrammatic Monte Carlo, partially reported in a recent study [S. Ragni et al., Phys. Rev. B 107, L121109(2023)], covering a wide range of coupling strengths for the nonlinear interaction. Remarkably, our analytic method predicts the same features as the Diagrammatic Monte Carlo simulation.

We provide a detailed exposition of our computational framework designed for the accurate calculation of real-frequency dynamical correlation functions of the single-impurity Anderson model in the regime of weak to intermediate coupling. Using quantum field theory within the Keldysh formalism to directly access the self-energy and dynamical susceptibilities in real frequencies, as detailed in our recent publication [Ge et al., Phys. Rev. B 109, 115128 (2024)], the primary computational challenge is the full three-dimensional real-frequency dependence of the four-point vertex. Our codebase provides a fully MPI+OpenMP parallelized implementation of the functional renormalization group (fRG) and the self-consistent parquet equations within the parquet approximation. It leverages vectorization to handle the additional complexity imposed by the Keldysh formalism, using optimized data structures and highly performant integration routines. Going beyond the results shown in the previous publication, the code includes functionality to perform fRG calculations in the multiloop framework, up to arbitrary loop order, including self-consistent self-energy iterations. Moreover, implementations of various regulators, such as hybridization, interaction, frequency, and temperature, are supplied.