Anomalous diffusion for neuronal growth on surfaces with controlled geometries

Geometrical cues are known to play a very important role in neuronal growth and the formation of neuronal networks. Here, we present a detailed analysis of axonal growth and dynamics for neuronal cells cultured on patterned polydimethylsiloxane surfaces. We use fluorescence microscopy to image neurons, quantify their dynamics, and demonstrate that the substrate geometrical patterns cause strong directional alignment of axons. We quantify axonal growth and report a general stochastic approach that quantitatively describes the motion of growth cones. The growth cone dynamics is described by Langevin and Fokker-Planck equations with both deterministic and stochastic contributions. We show that the deterministic terms contain both the angular and speed dependence of axonal growth, and that these two contributions can be separated. Growth alignment is determined by surface geometry, and it is quantified by the deterministic part of the Langevin equation. We combine experimental data with theoretical analysis to measure the key parameters of the growth cone motion: speed and angular distributions, correlation functions, diffusion coefficients, characteristics speeds and damping coefficients. We demonstrate that axonal dynamics displays a cross-over from Brownian motion (Ornstein-Uhlenbeck process) at earlier times to anomalous dynamics (superdiffusion) at later times. The superdiffusive regime is characterized by non-Gaussian speed distributions and power law dependence of the axonal mean square length and the velocity correlation functions. These results demonstrate the importance of geometrical cues in guiding axonal growth, and could lead to new methods for bioengineering novel substrates for controlling neuronal growth and regeneration.Comment: 27 pages, 13 figures. arXiv admin note: substantial text overlap with arXiv:1903.0133

Design, Analysis, And Optimization Of Diffractive Optical Elements Under High Numerical Aperture Focusing

The demand for high optical resolution has brought researchers to explore the use of beam shaping diffractive optical elements (DOEs) for improving performance of high numerical aperture (NA) optical systems. DOEs can be designed to modulate the amplitude, phase and/or polarization of a laser beam such that it focuses into a targeted irradiance distribution, or point spread function (PSF). The focused PSF can be reshaped in both the transverse focal plane and along the optical axis. Optical lithography, microscopy and direct laser writing are but a few of the many applications in which a properly designed DOE can significantly improve optical performance of the system. Designing DOEs for use in high-NA applications is complicated by electric field depolarization that occurs with tight focusing. The linear polarization of off-axis rays is tilted upon refraction towards the focal point, generating additional transverse and longitudinal polarization components. These additional field components contribute significantly to the shape of the PSF under tight focusing and cannot be neglected as in scalar diffraction theory. The PSF can be modeled more rigorously using the electromagnetic diffraction integrals derived by Wolf, which account for the full vector character of the field. In this work, optimization algorithms based on vector diffraction theory were developed for designing DOEs that reshape the PSF of a 1.4-NA objective lens. The optimization techniques include simple exhaustive search, iterative optimization (Method of Generalized Projections), and evolutionary computation (Particle Swarm Optimization). DOE designs were obtained that can reshape either the transverse PSF or the irradiance distribution along the optical axis. In one example of transverse beam shaping, all polarization components were simultaneously reshaped so their vector addition generates a focused flat-top square irradiance pattern. Other designs were obtained that can be used to narrow the axial irradiance distribution, giving a focused beam that is superresolved relative to the diffraction limit. In addition to theory, experimental studies were undertaken that include (1) fabricating an axially superresolving DOE, (2) incorporating the DOE into the optical setup, (3) imaging the focused PSF, and (4) measuring aberrations in the objective lens to study how these affect performance of the DOE

PhaseMax: Convex Phase Retrieval via Basis Pursuit

We consider the recovery of a (real- or complex-valued) signal from magnitude-only measurements, known as phase retrieval. We formulate phase retrieval as a convex optimization problem, which we call PhaseMax. Unlike other convex methods that use semidefinite relaxation and lift the phase retrieval problem to a higher dimension, PhaseMax is a "non-lifting" relaxation that operates in the original signal dimension. We show that the dual problem to PhaseMax is Basis Pursuit, which implies that phase retrieval can be performed using algorithms initially designed for sparse signal recovery. We develop sharp lower bounds on the success probability of PhaseMax for a broad range of random measurement ensembles, and we analyze the impact of measurement noise on the solution accuracy. We use numerical results to demonstrate the accuracy of our recovery guarantees, and we showcase the efficacy and limits of PhaseMax in practice

Quantitative description of metal center organization and interactions in single-atom catalysts

Ultra-high-density single-atom catalysts (UHD-SACs) present unique opportunities for harnessing cooperative effects between neighboring metal centers. However, the lack of tools to establish correlations between the density, type, and arrangement of the isolated metal atoms with the support surface properties hinders efforts to engineer advanced material architectures. Here, we precisely describe the metal center organization in various mono- and multimetallic UHD-SACs based on nitrogen-doped carbon (NC) supports by coupling transmission electron microscopy with tailored machine-learning methods (released as a user-friendly web app) and density functional theory simulations. Our approach quantifies the non-negligible presence of multimers with increasing atom density, characterizes the size and shape of these low-nuclearity clusters, and identifies surface atom density criteria to ensure isolation. Further, it provides previously inaccessible experimental insights into coordination site arrangements in the NC host, uncovering a repulsive interaction that influences the disordered distribution of metal centers in UHD-SACs. This observation holds in multimetallic systems, where chemically-specific analysis quantifies the degree of intermixing. These fundamental insights into the materials chemistry of single-atom catalysts are crucial for designing catalytic systems with superior reactivity.This publication was created as part of NCCR Catalysis (grant number 180544), a National Centre of Competence in Research funded by the Swiss National Science Foundation. A. R.-F. acknowledges funding from the Generalitat de Catalunya and the European Union under Grant 2023 FI-3 00027. N.L. acknowledges support from the Ministerio de Ciencia e Innovación, ref. no. RTI2018-101394-B-100, and the Severo Ochoa Grant, MCIN/AEI/10.13039/501100011033-CEX2019-000925-S. The authors thank BSC-RES for generously providing computational resources.Peer ReviewedPostprint (published version

Size-tunable nanoneedle arrays for influencing stem cell morphology, gene expression and nuclear membrane curvature

High-aspect-ratio nanostructures have emerged as versatile platforms for intracellular sensing and biomolecule delivery. Here, we present a microfabrication approach in which a combination of reactive ion etching protocols was used to produce high-aspect-ratio, nondegradable silicon nanoneedle arrays with tip diameters that can be finely tuned between 20 and 700 nm. We used these arrays to guide the long-term culture of human mesenchymal stem cells (hMSCs). Notably, we used the nanoneedle tip diameter to control the morphology, nuclear size and F-actin alignment of interfaced hMSCs, and to regulate the expression of nuclear lamina genes, Yes-associated protein (YAP) target genes and focal adhesion genes. These topography-driven changes were attributed to signaling by Rho-family GTPase pathways, differences in the effective stiffness of the nanoneedle arrays and the degree of nuclear membrane impingement, with the latter clearly visualized using focused-ion beam scanning electron microscopy (FIB-SEM). Our approach to design high-aspect-ratio nanostructures will be broadly applicable to design biomaterials and biomedical devices used for long-term cell stimulation and monitoring

Improvements in Digital Holographic Microscopy

The Ph.D. dissertation consists of developing a series of innovative computational methods for improving digital holographic microscopy (DHM). DHM systems are widely used in quantitative phase imaging for studying micrometer-size biological and non-biological samples. As any imaging technique, DHM systems have limitations that reduce their applicability. Current limitations in DHM systems are: i) the number of holograms (more than three holograms) required in slightly off-axis DHM systems to reconstruct the object phase information without applying complex computational algorithms; ii) the lack of an automatic and robust computation algorithm to compensate for the interference angle and reconstruct the object phase information without phase distortions in off-axis DHM systems operating in telecentric and image plane conditions; iii) the necessity of an automatic computational algorithm to simultaneously compensate for the interference angle and numerically focus out-of-focus holograms on reconstructing the object phase information without phase distortions in off-axis DHM systems operating in telecentric regime; iv) the deficiency of reconstructing phase images without phase distortions at video-rate speed in off-axis DHM operating in telecentric regime, and image plane conditions; v) the lack of an open-source library for any DHM optical configuration; and, finally, vi) the tradeoff between speckle contrast and spatial resolution existing in current computational strategies to reduce the speckle contrast. This Ph.D. dissertation is motivated to overcome or at least reduce the six limitations mentioned above. Each chapter of this dissertation presents and discusses a novel computational method from the theoretical and experimental point of view to address each of these limitations

Holistic improvement of image acquisition and reconstruction in fluorescence microscopy

Recent developments in microscopic imaging led to a better understanding of intra- and intercellular metabolic processes and, for example, to visualize structural properties of viral pathogens. In this thesis, the imaging process of widefield and confocal scanning microscopy techniques is treated holistically to highlight general strategies and maximise their information content. Poisson or shot noise is assumed to be the fundamental noise process for the given measurements. A stable focus position is a basic condition for e.g. long-term measurements in order to provide reliable information about potential changes inside the Field-of-view. While newer microscopy systems can be equipped with hardware autofocus, this is not yet the widespread standard. For image-based focus analysis, different metrics for ideal, noisy and aberrated, in case of spherical aberration and astigmatism, measurements are presented. A stable focus position is also relevant in the example of 2-photon confocal imaging and at the same time the situation is aggravated in the given example, the measurement of the retina in the living mouse. In addition to the natural drift of the focal position, which can be evaluated by means of previously introduced metrics, rhythmic heartbeat, respiration, unrhythmic muscle twitching and movement of the mouse kept in artificial sleep are added. A dejittering algorithm is presented for the measurement data obtained under these circumstances. Using the additional information about the sample distribution in ISM, a method for reconstructing 3D from 2D image data is presented in the form of thick slice unmixing. This method can further be used for suppression of light generated outside the focal layer of 3D data stacks and is compared to selective layer multi-view deconvolution. To reduce phototoxicity and save valuable measurement time for a 3D stack, the method of zLEAP is presented, by which omitted Z-planes are subsequently calculated and inserted

Modeling and applications of the focus cue in conventional digital cameras

El enfoque en cámaras digitales juega un papel fundamental tanto en la calidad de la imagen como en la percepción del entorno. Esta tesis estudia el enfoque en cámaras digitales convencionales, tales como cámaras de móviles, fotográficas, webcams y similares. Una revisión rigurosa de los conceptos teóricos detras del enfoque en cámaras convencionales muestra que, a pasar de su utilidad, el modelo clásico del thin lens presenta muchas limitaciones para aplicación en diferentes problemas relacionados con el foco. En esta tesis, el focus profile es propuesto como una alternativa a conceptos clásicos como la profundidad de campo. Los nuevos conceptos introducidos en esta tesis son aplicados a diferentes problemas relacionados con el foco, tales como la adquisición eficiente de imágenes, estimación de profundidad, integración de elementos perceptuales y fusión de imágenes. Los resultados experimentales muestran la aplicación exitosa de los modelos propuestos.The focus of digital cameras plays a fundamental role in both the quality of the acquired images and the perception of the imaged scene. This thesis studies the focus cue in conventional cameras with focus control, such as cellphone cameras, photography cameras, webcams and the like. A deep review of the theoretical concepts behind focus in conventional cameras reveals that, despite its usefulness, the widely known thin lens model has several limitations for solving different focus-related problems in computer vision. In order to overcome these limitations, the focus profile model is introduced as an alternative to classic concepts, such as the near and far limits of the depth-of-field. The new concepts introduced in this dissertation are exploited for solving diverse focus-related problems, such as efficient image capture, depth estimation, visual cue integration and image fusion. The results obtained through an exhaustive experimental validation demonstrate the applicability of the proposed models

The biophysics of bacterial collective motion: Measuring responses to mechanical and genetic cues

Mechanobiology is an emerging field investigating mechanical signals as a necessary component of cellular and developmental regulation. These mechanical signals play a well-established role in the differentiation of animal cells, whereby cells with identical genes specialize their function and create distinct tissues depending on the physical properties of their environment, such as shear stiffness. These differences arise from the cell’s ability to use those incoming signals to inform which genes it expresses and what molecular machinery it builds and activates. Understanding the various missing factors that cause cells with specific genes to express an emergent phenotype is termed the genotype-to-phenotype problem, and mechanical signaling pathways present themselves as a significant piece of this puzzle. Despite the strong evidence for mechanosensing in eukaryotes, the pathways by which prokaryotes respond to mechanical stimuli are still largely unknown. Bacteria are among the simplest and yet most abundant forms of life. Many of their survival strategies depend on multicellular development and the coordinated formation of a colony into functional structures that may also feature cellular differentiation. This dissertation employs bacteria as a model system to investigate multiple biophysical questions of collective motion through novel experimental and analytical techniques. This work addresses the understudied mechanical relationship between a bacterial colony and the substrate it colonizes by asking “what is the effect of substrate stiffness on colony growth?” This is done by measuring bacterial growth on hydrogel substrates that decouple the effects of substrate stiffness from other material properties of the substrate that vary with stiffness. We report a previously unobserved effect in which bacteria colonize stiffer substrates faster than softer substrates, in opposition to previous studies done on agar, where permeability, viscoelasticity, and other material properties vary with stiffness.A second theme of this work probes the genetic inputs to the genotype-to-phenotype problem in multicellular development. The bacterial species Myxococcus xanthus producing macroscopic aggregates called fruiting bodies is used as a model organism for these studies. It has long been conjectured that genes may stand in for each other functionally, allowing for development to be more consistent and stable, but the extent of this redundancy has resisted measurement. We approach the question “how does redundancy among related genes lead to robust collective behavior?” by quantifying developmental phenotype in a large dataset of time lapse microscopy videos that show development in many mutant strains. We observe that when knocking out multiple genes that have a common origin (i.e. homologous genes), the resulting phenotypes differ from wild-type in a similar way. These phenotype clusters also differ from knockouts from other homologous gene families. These distinct phenotypic clusters provide evidence for the existence of networks of redundant genes that are larger than could previously be tested directly. Because of this robustness, the effects of individual gene mutations can be hidden or damped. We thus develop our analytical techniques further to address the question “how can subtle changes in phenotype be measured?” This involves quantifying the breadth of variation observed in wild-type development and creating a statistical technique to distinguish probabilistic distributions of phenotypic outcomes. We present a coherent method of visualizing large phenotypic datasets that include multiple metrics that we use to distinguish small developmental differences from wild-type, giving each mutant strain a phenotypic fingerprint that can be used in future studies on gene annotation and environmental impacts on phenotype

Liquid phase blending of metal-organic frameworks.

The liquid and glass states of metal-organic frameworks (MOFs) have recently become of interest due to the potential for liquid-phase separations and ion transport, alongside the fundamental nature of the latter as a new, fourth category of melt-quenched glass. Here we show that the MOF liquid state can be blended with another MOF component, resulting in a domain structured MOF glass with a single, tailorable glass transition. Intra-domain connectivity and short range order is confirmed by nuclear magnetic resonance spectroscopy and pair distribution function measurements. The interfacial binding between MOF domains in the glass state is evidenced by electron tomography, and the relationship between domain size and Tg investigated. Nanoindentation experiments are also performed to place this new class of MOF materials into context with organic blends and inorganic alloys