Spherical Harmonics on constitutive equations for biological cells

Tese (doutorado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Civil e Ambiental, 2019.Desenvolvem-se e avaliam-se neste trabalho modelos constitutivos não-lineares incluindo o estudo de grandes deformações com o objetivo de modelar células biológicas representadas por elementos de cascas finas. É utilizada como ponto de partida a formulação clássica de elementos de cascas finas, considerando as hipóteses de Kirchhoff que apresentam como mais importante característica a redução dimensional. Esta é atingida derivando tensões 2D como médias das tensões 3D pela integração direta sob a espessura da casca. Para a definição da deformação do continuo é utilizada uma descrição Lagrangiana. As células biológicas não podem ser modeladas de forma correta utilizando modelos constitutivos lineares. Especificamente no estudo dos glóbulos vermelhos devem ser considerados: o comportamento elástico não linear e o aporte da viscosidade da parede da célula. Consequentemente, neste trabalho, modelos hiperelasticos são implementados junto ao modelo de Kelvin-Voigth para obter um modelo viscoelástico. Na implementação computacional Funções de Esféricos Harmônicos são utilizadas para sintetizar as principais variáveis, esforços e deslocamentos. Isto se deve a que a geometria dos glóbulos vermelhos pode ser descrita de forma simples utilizando coordenadas esféricas. Resultando numa implementação de baixo custo computacional que consegue lidar com altas não linearidades. Este trabalho apresenta uma formulação de um método indireto pois consiste no cálculo de coeficientes da expansão de Esféricos Harmônicos, sendo que estes coeficientes não têm sentido físico. É importante mencionar que o projeto se encontra num estágio inicial e não foi encontrado na literatura uma aplicação utilizando teoria de cascas, Harmônicos Esféricos junto com modelos constitutivos lidando com grandes deformações. Finalmente o método é validado e estudado suas possíveis aplicações.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) e Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).In this work, constitutive models are developed and evaluated with the aim of modeling biological cells represented by thin shell elements in a second-order analysis. The classical formulation of thin shell elements is used while considering dimensional reduction, which is the main feature of the Kirchhoff hypotheses. This reduction is achieved by deriving two-dimensional stresses as averages of the true three-dimensional stresses by means of direct integration through the shell thickness. A Lagrangian description is used to define the deformation of the continuum. Biological cells cannot be correctly modeled using linear constitutive relations. Specifically, in the study of red blood cells, one should consider both their nonlinear elastic behavior and the contribution of the cell wall viscosity. Consequently, hyperelastic constitutive equations are implemented using the Kelvin-Voigt approach to obtain a viscoelastic model. In the computational implementation, spherical harmonic functions are used to synthesize the main variables, resultant forces and displacements since the geometry of red blood cells can be simply described using spherical coordinates. As a result, a low-cost computational implementation for highly nonlinear analyses is obtained. This work presents a formulation of an indirect method since consists on the calculation of the expansion coefficients of a Spherical Harmonic Analysis, these coefficients have no physical meaning. It is important to mention that this work is part of a project that is at an early stage. In the literature no application was found using shell theory, Spherical Harmonics with constitutive models dealing with large deformations. Finally, the method is validated and its possible applications are discussed

Structure and Dynamics of Replication Domains in Single Chromosome Territories of Interphase Nuclei

Knowing the three-dimensional organization of chromatin sets the framework for understanding genome regulation. Our picture of higher order chromatin structure insitu however remains fragmentary at many scales, since it is not directly accessible by imaging technologies available today. The recently revealed domain organization of chromatin subunits into sub-megabasepair sized topologically associating domains (TADs), enabled by chromosome conformation capture based techniques, marks a significant advancement in understanding chromatin architecture. Similarly quantitative methods for the analysis of global structure and dynamics of chromatin in single living cells are currently lacking, leaving it unclear how TADs are manifested within a single nucleus and how dynamic topological chromatin interactions are in living cells. To start to address this gap in our knowledge, I set out to systematically probe the basic polymer features of chromatin at the level of replication domains (RDs) in single cells as a basis for a model of higher order chromatin organization. I have addressed both structural and dynamic aspects of RD organization during interphase. Using super-resolution microscopy, I was able to investigate RD organization at unprecedented resolution. I found that the median RD diameter is ~150 nm, significantly smaller than the ~270 nm distance to the nearest neighbor, which leaves sufficient physical space for extended linker regions between RDs. By quantifying correlated motion of neighboring RDs, I could reveal the typical elastic coupling range between RDs to be ~500 nm. Combining super-resolution microscopy with a perturbation experiment I could further obtain evidence for the model that chromatin compaction upon ATP depletion is predominantly mediated by preferential compaction of linker regions between RDs, rather than by compaction of RDs themselves. In addition to these structural parameters of RD organization, I also characterized the diffusional behavior of interphase RDs of single chromosome territories. Tracking 1,372 RDs of 141 chromosome territories allowed me to obtain a global and statistically robust view of interphase chromatin dynamics across the entire nucleus. My data confirms that heterochromatin chromatin is immobile within a few hundred nanometers of the nuclear membrane and nucleolar surface over the time scale of several minutes and that nucleoplasmic dynamics is characterized by anomalous diffusion. I did not observe reproducible directed motion of RDs on the timescale of seconds to a minute. I observed a systematic reduction in chromatin motion as the cell cycle progressed from G1 to late S-phase and an increase in mobility if I artificially increased nuclear volume by allowing cells to grow when DNA replication was inhibited. My observations on native and perturbed chromatin structure and dynamics in nuclei of living cells allow me to propose a comprehensive model of higher order chromatin organization in single cells, that consists of stable structuring units of RDs, which are connected by extended flexible linker domains, whose dynamics are limited by attachment to the nuclear periphery and nucleoli and the available free volume inside the nucleus

A multi–scale study of chromatin organisation and function: DNA topology, epigenetics and chromatin compaction

Understanding chromatin organisation at different length scales is still one of the most puzzling challenges in biophysics. Nowadays, it is clear that DNA or chromatin conformational changes can profoundly affect gene expression. Yet, the mechanisms underlying such conformational changes remain elusive. Several factors can intervene in gene regulation: supercoiling (SC), the extent of over– or under– twist of DNA double helix, can compact DNA in both bacteria and eukaryotes, yielding transcriptional over–expression or repression. Post-translational modifications of histone tails demarcate the “epigenetic” domains, which are therefore vital to establish the correct chromatin environment. Chromatin–binding proteins can form biological “condensates” via phase separation mechanisms. Recently, liquid–liquid phase separation (LLPS) has much been touted to motivate the formation of protein clusters in vivo, often referred to as ‘nuclear bodies’. In addition, the so-called bridging-induced phase separation (BIPS), explains how protein aggregation can be mediated by chromatin only, even in the absence of protein-protein interaction. By using a multi-technique approach, in this thesis’ work I investigate the structural and dynamical properties of DNA and chromatin at different length scales. Monte Carlo algorithms were implemented to simulate SC dynamics in a stochastic model for bacterial transcription. Similar techniques were used to show that an infection–like model can entail epigenetic bistability. Molecular dynamics simulations were employed to study the static and dynamical properties of model protein aggregates; the interplay between LLPS and BIPS was explored, showing properties which go far beyond the liquid state. Depending on the parameters, solid–like, glassy and fractal protein condensates can co–localise with chromatin

Biological Protein Patterning Systems across the Domains of Life: from Experiments to Modelling

Distinct localisation of macromolecular structures relative to cell shape is a common feature across the domains of life. One mechanism for achieving spatiotemporal intracellular organisation is the Turing reaction-diffusion system (e.g. Min system in the bacterium Escherichia coli controlling in cell division). In this thesis, I explore potential Turing systems in archaea and eukaryotes as well as the effects of subdiffusion. Recently, a MinD homologue, MinD4, in the archaeon Haloferax volcanii was found to form a dynamic spatiotemporal pattern that is distinct from E. coli in its localisation and function. I investigate all four archaeal Min paralogue systems in H. volcanii by identifying four putative MinD activator proteins based on their genomic location and show that they alter motility but do not control MinD4 patterning. Additionally, one of these proteins shows remarkably fast dynamic motion with speeds comparable to eukaryotic molecular motors, while its function appears to be to control motility via interaction with the archaellum. In metazoa, neurons are highly specialised cells whose functions rely on the proper segregation of proteins to the axonal and somatodendritic compartments. These compartments are bounded by a structure called the axon initial segment (AIS) which is precisely positioned in the proximal axonal region during early neuronal development. How neurons control these self-organised localisations is poorly understood. Using a top-down analysis of developing neurons in vitro, I show that the AIS lies at the nodal plane of the first non-homogeneous spatial harmonic of the neuron shape while a key axonal protein, Tau, is distributed with a concentration that matches the same harmonic. These results are consistent with an underlying Turing patterning system which remains to be identified. The complex intracellular environment often gives rise to the subdiffusive dynamics of molecules that may affect patterning. To simulate the subdiffusive transport of biopolymers, I develop a stochastic simulation algorithm based on the continuous time random walk framework, which is then applied to a model of a dimeric molecular motor. This provides insight into the effects of subdiffusion on motor dynamics, where subdiffusion reduces motor speed while increasing the stall force. Overall, this thesis makes progress towards understanding intracellular patterning systems in different organisms, across the domains of life

Filter-Based Probabilistic Markov Random Field Image Priors: Learning, Evaluation, and Image Analysis

Markov random fields (MRF) based on linear filter responses are one of the most popular forms for modeling image priors due to their rigorous probabilistic interpretations and versatility in various applications. In this dissertation, we propose an application-independent method to quantitatively evaluate MRF image priors using model samples. To this end, we developed an efficient auxiliary-variable Gibbs samplers for a general class of MRFs with flexible potentials. We found that the popular pairwise and high-order MRF priors capture image statistics quite roughly and exhibit poor generative properties. We further developed new learning strategies and obtained high-order MRFs that well capture the statistics of the inbuilt features, thus being real maximum-entropy models, and other important statistical properties of natural images, outlining the capabilities of MRFs. We suggest a multi-modal extension of MRF potentials which not only allows to train more expressive priors, but also helps to reveal more insights of MRF variants, based on which we are able to train compact, fully-convolutional restricted Boltzmann machines (RBM) that can model visual repetitive textures even better than more complex and deep models. The learned high-order MRFs allow us to develop new methods for various real-world image analysis problems. For denoising of natural images and deconvolution of microscopy images, the MRF priors are employed in a pure generative setting. We propose efficient sampling-based methods to infer Bayesian minimum mean squared error (MMSE) estimates, which substantially outperform maximum a-posteriori (MAP) estimates and can compete with state-of-the-art discriminative methods. For non-rigid registration of live cell nuclei in time-lapse microscopy images, we propose a global optical flow-based method. The statistics of noise in fluorescence microscopy images are studied to derive an adaptive weighting scheme for increasing model robustness. High-order MRFs are also employed to train image filters for extracting important features of cell nuclei and the deformation of nuclei are then estimated in the learned feature spaces. The developed method outperforms previous approaches in terms of both registration accuracy and computational efficiency

STED Nanoscopy to Illuminate New Avenues in Cancer Research – From Live Cell Staining and Direct Imaging to Decisive Preclinical Insights for Diagnosis and Therapy

Molecular imaging is established as an indispensable tool in various areas of cancer research, ranging from basic cancer biology and preclinical research to clinical trials and medical practice. In particular, the field of fluorescence imaging has experienced exceptional progress during the last three decades with the development of various in vivo technologies. Within this field, fluorescence microscopy is primarily of experimental use since it is especially qualified for addressing the fundamental questions of molecular oncology. As stimulated emission depletion (STED) nanoscopy combines the highest spatial and temporal resolutions with live specimen compatibility, it is best-suited for real-time investigations of the differences in the molecular machineries of malignant and normal cells to eventually translate the acquired knowledge into increased diagnostic and therapeutic efficacy. This thesis presents the application of STED nanoscopy to two acute topics in cancer research of direct or indirect clinical interest. The first project has investigated the structure of telomeres, the ends of the linear eukaryotic chromosomes, in intact human cells at the nanoscale. To protect genome integrity, a telomere can mask the chromosome end by folding back and sequestering its single-stranded 3’-overhang in an upstream part of the double-stranded DNA repeat region. The formed t-loop structure has so far only been visualized by electron microscopy and fluorescence nanoscopy with cross-linked mammalian telomeric DNA after disruption of cell nuclei and spreading. For the first time, this work demonstrates the existence of t-loops within their endogenous nuclear environment in intact human cells. The identification of further telomere conformations has laid the groundwork for distinguishing cancerous cells that use different telomere maintenance mechanisms based on their individual telomere populations by a combined STED nanoscopy and deep learning approach. The population difference was essentially attributed to the promyelocytic leukemia (PML) protein that significantly perturbs the organization of a subpopulation of telomeres towards an open conformation in cancer cells that employ a telomerase-independent, alternative telomere lengthening mechanism. Elucidating the nanoscale topology of telomeres and associated proteins within the nucleus has provided new insight into telomere structure-function relationships relevant for understanding the deregulation of telomere maintenance in cancer cells. After understanding the molecular foundations, this newly gained knowledge can be exploited to develop novel or refined diagnostic and treatment strategies. The second project has characterized the intracellular distribution of recently developed prostate cancer tracers. These novel prostate-specific membrane antigen (PSMA) inhibitors have revolutionized the treatment regimen of prostate cancer by enabling targeted imaging and therapy approaches. However, the exact internalization mechanism and the subcellular fate of these tracers have remained elusive. By combining STED nanoscopy with a newly developed non-standard live cell staining protocol, this work confirmed cell surface clustering of the targeted membrane antigen upon PSMA inhibitor binding, subsequent clathrin-dependent endocytosis and endosomal trafficking of the antigen-inhibitor complex. PSMA inhibitors accumulate in prostate cancer cells at clinically relevant time points, but strikingly and in contrast to the targeted antigen itself, they eventually distribute homogenously in the cytosol. This project has revealed the subcellular fate of PSMA/PSMA inhibitor complexes for the first time and provides crucial knowledge for the future application of these tracers including the development of new strategies in the field of prostate cancer diagnostics and therapeutics. Relying on the photostability and biocompatibility of the applied fluorophores, the performance of live cell STED nanoscopy in the field of cancer research is boosted by the development of improved fluorophores. The third project in this thesis introduces a biocompatible, small molecule near-infrared dye suitable for live cell STED imaging. By the application of a halogen dance rearrangement, a dihalogenated fluorinatable pyridinyl rhodamine could be synthesized at high yield. The option of subsequent radiolabeling combined with excellent optical properties and a non-toxic profile renders this dye an appropriate candidate for medical and bioimaging applications. Providing an intrinsic and highly specific mitochondrial targeting ability, the radiolabeled analogue is suggested as a vehicle for multimodal (positron emission tomography and optical imaging) medical imaging of mitochondria for cancer diagnosis and therapeutic approaches in patients and biopsy tissue. The absence of cytotoxicity is not only a crucial prerequisite for clinically used fluorophores. To guarantee the generation of meaningful data mirroring biological reality, the absence of cytotoxicity is likewise a decisive property of dyes applied in live cell STED nanoscopy. The fourth project in this thesis proposes a universal approach for cytotoxicity testing based on characterizing the influence of the compound of interest on the proliferation behavior of human cell lines using digital holographic cytometry. By applying this approach to recently developed live cell STED compatible dyes, pronounced cytotoxic effects could be excluded. Looking more closely, some of the tested dyes slightly altered cell proliferation, so this project provides guidance on the right choice of dye for the least invasive live cell STED experiments. Ultimately, live cell STED data should be exploited to extract as much biological information as possible. However, some information might be partially hidden by image degradation due the dynamics of living samples and the deliberate choice of rather conservative imaging parameters in order to preserve sample viability. The fifth project in this thesis presents a novel image restoration method in a Bayesian framework that simultaneously performs deconvolution, denoising as well as super-resolution, to restore images suffering from noise with mixed Poisson-Gaussian statistics. Established deconvolution or denoising methods that consider only one type of noise generally do not perform well on images degraded significantly by mixed noise. The newly introduced method was validated with live cell STED telomere data proving that the method can compete with state-of-the-art approaches. Taken together, this thesis demonstrates the value of an integrated approach for STED nanoscopy imaging studies. A coordinated workflow including sample preparation, image acquisition and data analysis provided a reliable platform for deriving meaningful conclusions for current questions in the field of cancer research. Moreover, this thesis emphasizes the strength of iteratively adapting the individual components in the operational chain and it particularly points towards those components that, if further improved, optimize the significance of the final results rendering live cell STED nanoscopy even more powerful

Live Cell Biomass Tracking for Basic, Translational, and Clinical Research

Single cell mass is tightly regulated throughout generations and the cell cycle, making it an important marker of cell health. Abnormal changes in cell size can be the first indication of dysfunction in response to environmental stimuli such as cytotoxic drugs. Described here is the further development of high-speed live cell interferometry (HSLCI) to concurrently measure the changes in single cell mass of thousands of cells over time. Critically, the high-throughput nature of HSLCI provides realistic pictures of tumor heterogeneity. This throughput enabled HSLCI to correctly predict in vivo carboplatin sensitivity of three triple negative breast cancer patient derived xenografts, while also characterizing the spectrum of drug response from apoptosis to senescence to drug resistance. HSLCI quantified previous qualitative observations of increases in cell size and losses in cell density in senescent cells, and importantly observed proliferative recovery in cells demonstrating thee senescent characteristics. Furthermore, the addition of a micropipette system has enabled the isolation of rare (~1%) drug resistant cells for further study with molecular biology methods. Together, this work highlights HSLCI’s versatility and potential for clinical, translational, and basic research

Dichotomic role of NAADP/two-pore channel 2/Ca2+ signaling in regulating neural differentiation of mouse embryonic stem cells

Poster Presentation - Stem Cells and Pluripotency: abstract no. 1866The mobilization of intracellular Ca2+stores is involved in diverse cellular functions, including cell proliferation and differentiation. At least three endogenous Ca2+mobilizing messengers have been identified, including inositol trisphosphate (IP3), cyclic adenosine diphosphoribose (cADPR), and nicotinic adenine acid dinucleotide phosphate (NAADP). Similar to IP3, NAADP can mobilize calcium release in a wide variety of cell types and species, from plants to animals. Moreover, it has been previously shown that NAADP but not IP3-mediated Ca2+increases can potently induce neuronal differentiation in PC12 cells. Recently, two pore channels (TPCs) have been identified as a novel family of NAADP-gated calcium release channels in endolysosome. Therefore, it is of great interest to examine the role of TPC2 in the neural differentiation of mouse ES cells. We found that the expression of TPC2 is markedly decreased during the initial ES cell entry into neural progenitors, and the levels of TPC2 gradually rebound during the late stages of neurogenesis. Correspondingly, perturbing the NAADP signaling by TPC2 knockdown accelerates mouse ES cell differentiation into neural progenitors but inhibits these neural progenitors from committing to the final neural lineage. Interestingly, TPC2 knockdown has no effect on the differentiation of astrocytes and oligodendrocytes of mouse ES cells. Overexpression of TPC2, on the other hand, inhibits mouse ES cell from entering the neural lineage. Taken together, our data indicate that the NAADP/TPC2-mediated Ca2+signaling pathway plays a temporal and dichotomic role in modulating the neural lineage entry of ES cells; in that NAADP signaling antagonizes ES cell entry to early neural progenitors, but promotes late neural differentiation.postprin

Spatiotemporal modelling in biology: from transcriptional regulation to plasmid positioning

Here I describe how cycles of mathematical modelling and experimenting have advanced our quantitative understanding of two different processes: transcriptional regulation of the floral repressor FLOWERING LOCUS C (FLC ) in Arabidopsis thaliana and spatial positioning of low copy number plasmids in Escherichia coli. Despite the diversity in biological subjects, my spatiotemporal modelling approach provides a common ground. FLC regulation involves an antisense-mediated chromatin silencing mechanism, where alternative polyadenylation of antisense transcripts is linked to changed histone modifications at the locus and altered expression. Mathematical model predictions of FLC transcriptional dynamics are validated by measurements of total and chromatinbound FLC intronic RNA. This demonstrates that FLC regulation involves a quantitative coordination between transcription initiation and elongation, potentially a general feature of gene regulation in a chromatin context. A quantitative analysis of cellular RNA levels indicates that FLC processing and degradation are well described by Poisson processes. FLC transcription correlates with cell volume, which underlies the large cellular variation in transcript levels. Low copy number plasmids in bacteria require segregation for stable inheritance through cell division. This is often achieved by a parABC locus, comprising an ATPase ParA, DNA-binding protein ParB and a parC region, encoding ParB-binding sites. These components space plasmids equally over the nucleoid, yet the underlying mechanism has not been understood. Here I show mathematically that differences between competing ParA concentrations on either side of a plasmid can specify regular plasmid positioning. This can be achieved regardless of the exact mechanism of plasmid movement. Experimentally, parABC from E. coli plasmid pB171 increases plasmid mobility, inconsistent with models based on plasmid diffusion and immobilization. Instead this observation favours a directed motion model. These results unify previously contradictory models for plasmid segregation and provide a mechanistic basis for selforganized plasmid spacing