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Background: In recent years, a relationship between the tumor microenvironment (TME) and patient response to targeted cancer immunotherapy has been suggested. We applied machine-learning algorithms on H&E stained tissue to study the TME in metastatic non-small cell lung cancer (NSCLC) patients. Our goal was to identify digital pathology (DP) features associated with outcome under combination treatment or monotherapy with atezolizumab (atezo), an anti-PD-L1 therapy, and relate those features to other data modalities. We analyzed patient data from two phase 3 clinical trials, OAK (docetaxel versus atezo in 2L+ NSCLC) and IMpower150 (bevacizumab, carboplatin, and paclitaxel (BCP) versus BCP+atezo (ABCP) in advanced 1L non-squamous NSCLC). Methods: As part of our effort to build a DP-based tumor-immune microenvironment atlas, digitized H&E images were registered onto the PathAI research platform. Over 200K annotations from 90 pathologists were used to train convolutional neural networks (CNNs) that classify slide-level human-interpretable features (HIFs) of cells and tissue structures from images and deployed on images from OAK and IMpower150. HIFs and PD-L1 status were associated with outcome in all samples in each arm in OAK and results were validated in IMpower150, using Cox proportional hazard models. Bulk RNAseq was run using samples extracted from the same area as the H&E slide. Results: We identified a composite feature capturing the ratio of immune cells to fibroblasts in the stroma predictive of both overall survival (OS) (HR=0.74 p=0.0046) and progression-free survival (PFS) (HR=0.87 p=0.14). While patients primarily benefit from atezo if they are PD-L1 high, we found that even PD-L1 negative patients benefited from atezo when enriched for this feature (22C3 PD-L1 assay: OS HR=0.59 p=0.015, PFS HR=0.8 p=0.25; SP142 PD-L1 assay: OS HR=0.74 p=0.12, PFS HR=0.88 p=0.45). We thus recognized a DP feature that was predictive for positive outcome with atezo treatment, independent of PD-L1 levels. This association was then validated in IMpower150 comparing ABCP to BCP, both overall (OS HR=0.69 p=0.012) and in PD-L1 negative patients (SP263 assay OS HR=0.56 p=0.034). Integrating with RNAseq, patients enriched for this DP feature showed similar enrichment for B and T gene signatures and depletion in CAF-related gene signatures, thus showing the harmonization of TME between different data modalities. Conclusions: Using a deep learning-based assay for quantifying pathology features of the TME from H&E images in two NSCLC trials, we identified a novel biomarker predictive of outcome to PD-L1 targeting therapy, even in PD-L1 low & negative patients. Importantly, our work shows how different data modalities (DP, gene expression) can be integrated to further our understanding of the TME. Citation Format: Aditi Qamra, Minu K. Srivastava, Eloisa Fuentes, Ben Trotter, Raymond Biju, Guillaume Chhor, James Cowan, Steven Gendreau, Webster Lincoln, Lisa McGinnis, Luciana Molinero, Namrata S. Patil, Amber Schedlbauer, Katja Schulze, Adam Stanford-Moore, Laura Chambre, Ilan Wapinski, David S. Shames, Hartmut Koeppen, Stephanie Hennek, Jane Fridlyand, Jennifer M. Giltnane, Assaf Amitai. Digital pathology based prognostic & predictive biomarkers in metastatic non-small cell lung cancer. [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 5705.

© 2020 Elsevier Inc. Nucleosomes package genomic DNA into chromatin. By regulating DNA access for transcription, replication, DNA repair, and epigenetic modification, chromatin forms the nexus of most nuclear processes. In addition, dynamic organization of chromatin underlies both regulation of gene expression and evolution of chromosomes into individualized sister objects, which can segregate cleanly to different daughter cells at anaphase. This collaborative review shines a spotlight on technologies that will be crucial to interrogate key questions in chromatin and chromosome biology including state-of-the-art microscopy techniques, tools to physically manipulate chromatin, single-cell methods to measure chromatin accessibility, computational imaging with neural networks and analytical tools to interpret chromatin structure and dynamics. In addition, this review provides perspectives on how these tools can be applied to specific research fields such as genome stability and developmental biology and to test concepts such as phase separation of chromatin.

Mammalian genomes are enormous. For a DNA-binding protein, this means that the number of non-specific, off-target sites vastly exceeds the number of specific, cognate sites. How mammalian DNA-binding proteins overcome this challenge to efficiently locate their target sites is not known. Here through live-cell single-molecule tracking, we show that CCCTC-binding factor, CTCF, is repeatedly trapped in small zones in the nucleus in a manner that is largely dependent on its RNA-binding region (RBR). Integrating theory, we devise a new model, Anisotropic Diffusion through transient Trapping in Zones (ADTZ), to explain this. Functionally, transient RBR-mediated trapping increases the efficiency of CTCF target search by ∼2.5 fold. Since the RBR-domain also mediates CTCF clustering, our results suggest a “guided” mechanism where CTCF clusters concentrate diffusing CTCF proteins near cognate binding sites, thus increasing the local ON-rate. We suggest that local “guiding” may represent a general target search mechanism in mammalian cells.

We describe a physics-based learning model for predicting the immunogenicity of Cytotoxic-T-Lymphocyte (CTL) epitopes derived from diverse pathogens including SARS-CoV-2. The model was trained and optimized on the relative immunodominance of CTL epitopes in Human Immunodeficiency Virus infection. Its accuracy was tested against experimental data from COVID-19 patients. Our model predicts that only some SARS-CoV-2 epitopes predicted to bind to HLA molecules are immunogenic. The immunogenic CTL epitopes across all SARS-CoV-2 proteins are predicted to provide broad population coverage, but those from the SARS-CoV-2 spike protein alone are unlikely to do so. Our model also predicts that several immunogenic SARS-CoV-2 CTL epitopes are identical to seasonal coronaviruses circulating in the population and such cross-reactive CD8+ T cells can indeed be detected in prepandemic blood donors, suggesting that some level of CTL immunity against COVID-19 may be present in some individuals prior to SARS-CoV-2 infection., National Science Foundation (U.S.) (Grant PHY-2026995), Frederick National Laboratory for Cancer Research (Contract HHSN261200800001E), National Institutes of Health (U.S.) (Grant AI138790)

The evolution of circulating viruses is shaped by their need to evade antibody response, which mainly targets the viral spike. Because of the high density of spikes on the viral surface, not all antigenic sites are targeted equally by antibodies. We offer here a geometry-based approach to predict and rank the probability of surface residues of SARS spike (S protein) and influenza H1N1 spike (hemagglutinin) to acquire antibody-escaping mutations utilizing in-silico models of viral structure. We used coarse-grained MD simulations to estimate the on-rate (targeting) of an antibody model to surface residues of the spike protein. Analyzing publicly available sequences, we found that spike surface sequence diversity of the pre-pandemic seasonal influenza H1N1 and the sarbecovirus subgenus highly correlates with our model prediction of antibody targeting. In particular, we identified an antibody-targeting gradient, which matches a mutability gradient along the main axis of the spike. This identifies the role of viral surface geometry in shaping the evolution of circulating viruses. For the 2009 H1N1 and SARS-CoV-2 pandemics, a mutability gradient along the main axis of the spike was not observed. Our model further allowed us to identify key residues of the SARS-CoV-2 spike at which antibody escape mutations have now occurred. Therefore, it can inform of the likely functional role of observed mutations and predict at which residues antibody-escaping mutation might arise., Author summary The immune system responds to viruses by making neutralizing antibodies to regions of the viral spike protein, which mutates to escape. To inform vaccine design and understand how the fitness landscape of the viral spike changes over time, it is necessary to identify and quantify the factors directing its evolution. Based on the 3D structure of the viral surface and spike as captured with Cryo-EM and crystallography, we aimed to create a coarse-grained model for the effect of antibodies in forcing surface residues of the spike to mutate. We found that for pre-pandemic influenza (hemagglutinin) and the corona sarbecovirus subgenus (S protein), the location of a residue on the spike protein, which modulates its accessibility to antibodies, highly correlates with its propensity to mutate. Hence, a mechanistic approach can be used to identify aspects of viral spike sequence diversity related to antibody escape.

Eukaryotic cells package their genomes around histone octamers. In response to DNA damage, checkpoint activation in yeast induces core histone degradation resulting in 20%-40% reduction in nucleosome occupancy. To gain insight into this process, we developed a new approach to analyze the chromatin-associated proteome comprehensively before and after damage. This revealed extensive changes in protein composition after Zeocin-induced damage. First, core histones and the H1 homolog Hho1 were partially lost from chromatin along with replication, transcription, and chromatin remodeling machineries, while ubiquitin ligases and the proteasome were recruited. We found that the checkpoint- and INO80C-dependent recruitment of five ubiquitin-conjugating factors (Rad6, Bre1, Pep5, Ufd4, and Rsp5) contributes to core and linker histone depletion, reducing chromatin compaction and enhancing DNA locus mobility. Importantly, loss of Rad6/Bre1, Ufd4/TRIP12, and Pep5/VPS11 compromise DNA strand invasion kinetics during homology-driven repair. Thus we provide a comprehensive overview of a functionally relevant genome-wide chromatin response to DNA damage.

To determine whether double-strand break (DSB) mobility enhances the physical search for an ectopic template during homology-directed repair (HDR), we tested the effects of factors that control chromatin dynamics, including cohesin loading and kinetochore anchoring. The former but not the latter is altered in response to DSBs. Loss of the nonhistone high-mobility group protein Nhp6 reduces histone occupancy and increases chromatin movement, decompaction, and ectopic HDR. The loss of nucleosome remodeler INO80-C did the opposite. To see whether enhanced HDR depends on DSB mobility or the global chromatin response, we tested the ubiquitin ligase mutant uls1Δ, which selectively impairs local but not global movement in response to a DSB. Strand invasion occurs in uls1Δ cells with wild-type kinetics, arguing that global histone depletion rather than DSB movement is rate limiting for HDR. Impaired break movement in uls1Δ correlates with elevated MRX and cohesin loading, despite normal resection and checkpoint activation.

Chromatin moves with subdiffusive and spatially constrained dynamics within the cell nucleus. Here, we use single-locus tracking by time-lapse fluorescence microscopy to uncover information regarding the forces that influence chromatin movement following the induction of a persistent DNA double-strand break (DSB). Using improved time-lapse imaging regimens, we monitor trajectories of tagged DNA loci at a high temporal resolution, which allows us to extract biophysical parameters through robust statistical analysis. Polymer modeling based on these parameters predicts chromatin domain expansion near a DSB and damage extrusion from the domain. Both phenomena are confirmed by live imaging in budding yeast. Calculation of the anomalous exponent of locus movement allows us to differentiate forces imposed on the nucleus through the actin cytoskeleton from those that arise from INO80 remodeler-dependent changes in nucleosome organization. Our analytical approach can be applied to high-density single-locus trajectories obtained in any cell type.

Chromosome organization and dynamics are critical for DNA transactions, including gene expression, replication, and DNA repair. In yeast, the chromosomes are anchored through their centromeres to the spindle pole body, and their telomeres are grouped into clusters at the nuclear periphery, constraining chromosome mobility. Here, we have used experimental and computational approaches to study the effects of chromosome-nuclear envelope (NE) attachments on the dynamics ofS. cerevisiaechromosomes. We found that although centromere proximal loci were, as predicted, more dynamically constrained than distal loci, telomeres were highly mobile, even when positioned at the nuclear periphery. Polymer modeling indicated that polymer ends are intrinsically more mobile than internal sites. We tested this model by measuring the mobility of a double strand break (DSB) end within a chromosome arm. Upon separation of the DSB ends, their mobility significantly increased. Altogether, our results reveal that telomeres behave as highly mobile polymer ends, despite interactions with the nuclear membrane.

Chromatin organization remains complex and far from understood. We discuss here recent statistical methods to extract biophysical parameters from in vivo single particle trajectories of loci to reconstruct chromatin reorganization in response to cellular stress such as DNA damages. We look at the methods to analyze both single loci as well as multiple loci tracked simultaneously and explain how to quantify and describe chromatin motion using a combination of extractable parameters. These parameters can be converted into information about chromatin dynamics and function. Furthermore, we discuss how the time scale of recurrent motion of a locus can be extracted and converted into local chromatin dynamics. We also discuss the effect of various sampling rates on the estimated parameters. Finally, we discuss polymer methods based on cross-linkers that account for minimal loop constraints hidden in tracked loci, that reveal chromatin organization at the 250nmspatial scale. We list and refer to some algorithm packages that are now publicly available. To conclude, chromatin organization and dynamics at hundreds of nanometers can be reconstructed from locus trajectories and predicted based on polymer models.

This chapter describes chromatin dynamics using stochastic modeling and polymer physics. It summarizes briefly modeling and analysis approaches that goes beyond classical Brownian motion and reviews how the cell imposes biological constraints on molecular motion. The chapter shows how single-particle trajectory data can be used to recover the chromatin organization and the ensemble of interactions it experiences. Trajectories of an individual particle inside a fluid, on the chromatin or a membrane, are usually described and analyzed in the physical literature using the Smoluchowski’s limit of the Langevin equation. To extract biophysical parameters from Single-Particle Trajectory of a chromatin locus, a physical model for the locus motion is needed. The dynamics of the locus reflects the local chromatin organization and the ensemble of interactions it experiences. The relation between chromatin structure/organization can be described using the dynamics of a tagged monomer when the chromatin is described as a static fractal globule.

Double-strand break (DSB) repair by homologous recombination (HR) requires an efficient and timely search for a homologous template. Here we first study global chromatin re-organization following a single DSB: due to the potential release of cross-linkers such as cohesin and CTCF molecules near the DSB site, loops are released and chromatin is decondensed, explaining the change of chromatin locus motion at larger genomic distances. This mechanism provides an elementary explanation for the increase of the anomalous exponent at sites located far away from the DSB, after break induction. Second, we explore the consequences of chromatin reorganization for the homology search during DNA repair: using polymer models, we estimate the mean first encounter time (MFET) between two loci on the chromatin in a confined nucleus. Reducing tethering forces, as reported experimentally on chromatin, is associated with a local decondensation near the break followed by the extrusion of the breaks. Consequently, we report here that the mean first encounter time between homologous sites is decreased by two orders of magnitude even when the homologue sequence is located on the nuclear boundary. To conclude, our results suggest that local changes in inter-nucleosomal contacts near DSBs, by cohesin removal, remodel the chromatin and drastically shorten the time required to complete a long-range search for a homologous template.

The antibody repertoire possesses near limitless diversity, enabling the adaptive immune system to accommodate essentially any antigen. However, this diversity explores the antigenic space unequally, allowing some pathogens like influenza virus to impose complex immunodominance hierarchies that distract antibody responses away from key sites of virus vulnerability. We developed a computational model of affinity maturation to map the patterns of immunodominance that evolve upon immunization with natural and engineered displays of hemagglutinin (HA), the influenza vaccine antigen. Based on this knowledge, we designed immunization protocols that subvert immune distraction and focus serum antibody responses upon a functionally conserved, but normally immunologically recessive, target of human broadly neutralizing antibodies. We tested in silico predictions by vaccinating transgenic mice in which antibody diversity was humanized to mirror clinically relevant humoral output. Collectively, our results demonstrate that complex patterns in antibody immunogenicity can be rationally defined and then manipulated to elicit engineered immunity.

The time for a DNA sequence to find its homologous counterpart depends on a long random search inside the cell nucleus. Using polymer models, we compute here the mean first encounter time (MFET) between two sites located on two different polymer chains and confined locally by potential wells. We find that reducing tethering forces acting on the polymers results in local decondensation, and numerical simulations of the polymer model show that these changes are associated with a reduction of the MFET by several orders of magnitude. We derive here new asymptotic formula for the MFET, confirmed by Brownian simulations. We conclude from the present modeling approach that the fast search for homology is mediated by a local chromatin decondensation due to the release of multiple chromatin tethering forces. The present scenario could explain how the homologous recombination pathway for double-stranded DNA repair is controlled by its random search step.

We present a theoretical study of the interaction between a protein (diffusing particle) with chromatin (polymer chain). Each monomer is a trap where a particle can transiently bind. We derive novel formulas for the transition rate between monomer sites, given a specific polymer configuration, and find that a particle is likely to rapidly rebind many times to its release site, before moving to another. The reattachment probability is larger when the local density around the release site is smaller. Interestingly, for an equilibrated polymer, the transition probability decays as a power-law for close monomer-to-monomer distances and reaches an asymptotic value for faraway ones. By computing the transition rate between monomers, we show that the problem of facilitated search by a protein can be mapped to a continuous time Markov chain, which we solve. Our findings suggest that proteins may be locally trapped for a time much longer than their dissociation time, while their overall motion is ergodic. Our results are corroborated by Brownian simulations.

We study the mean first time that two monomers, located on the same polymer, encounter in a confined microdomain. Approximating the confined geometry by a harmonic potential well, we obtain an asymptotic expression for the mean first encounter time (MFETC) as a function of the radius e around one monomer. By studying the end-to-end distance of the polymer in a ball using the Edwards’ formalism, we derive an other estimation of the MFETC. We validate the asymptotic formulas using Brownian simulations and derive their range of validity in terms of the polymer length. We apply the present models to compute the mean time for a gene located far away from a promoter site to be activated during looping in confined genomic territories.

We review here recent progress to link the nuclear organization to its function, based on elementary physical processes such as diffusion, polymer dynamics of DNA, chromatin and the search mechanism for a small target by double-stranded DNA (dsDNA) break. These physical models and their analysis make it possible to compute critical rates involved in cell reorganization timing, which depends on many parameters. In the framework of polymer models, various empirical observations are interpreted as anomalous diffusion of chromatin at various time scales. The reviewed theoretical approaches offer a framework for extracting features, biophysical parameters, predictions, and so on, based on a large variety of experimental data, such as chromosomal capture data, single particle trajectories, and more. Combining theoretical approaches with live cell microscopy data should unveil some of the still unexplained behavior of the nucleus in carrying out some of its key function involved in survival, DNA repair or gene activation.

Nucleosomes are essential for proper chromatin organization and the maintenance of genome integrity. Histones are post-translationally modified and often evicted at sites of DNA breaks, facilitating the recruitment of repair factors. Whether such chromatin changes are localized or genome-wide is debated. Here we show that cellular levels of histones drop 20-40% in response to DNA damage. This histone loss occurs from chromatin, is proteasome-mediated and requires both the DNA damage checkpoint and the INO80 nucleosome remodeler. We confirmed reductions in histone levels by stable isotope labeling of amino acids in cell culture (SILAC)-based mass spectrometry, genome-wide nucleosome mapping and fluorescence microscopy. Chromatin decompaction and increased fiber flexibility accompanied histone degradation, both in response to DNA damage and after artificial reduction of histone levels. As a result, recombination rates and DNA-repair focus turnover were enhanced. Thus, we propose that a generalized reduction in nucleosome occupancy is an integral part of the DNA damage response in yeast that provides mechanisms for enhanced chromatin mobility and homology search.

Experiments based on chromosome conformation capture have shown that mammalian genomes are partitioned into topologically associating domains (TADs), within which the chromatin fiber preferentially interacts. TADs may provide three-dimensional scaffolds allowing genes to contact their appropriate distal regulatory DNA sequences (e.g., enhancers) and thus to be properly regulated. Understanding the cell-to-cell and temporal variability of the chromatin fiber within TADs, and what determines them, is thus of great importance to better understand transcriptional regulation. We recently described an equilibrium polymer model that can accurately predict cell-to-cell variation of chromosome conformation within single TADs, from chromosome conformation capture-based data. Here we further analyze the conformational and energetic properties of our model. We show that the chromatin fiber within TADs can easily fluctuate between several conformational states, which are hierarchically organized and are not separated by important free energy barriers, and that this is facilitated by the fact that the chromatin fiber within TADs is close to the onset of the coil-globule transition. We further show that in this dynamic state the properties of the chromatin fiber, and its contact probabilities in particular, are determined in a nontrivial manner not only by site-specific interactions between strongly interacting loci along the fiber, but also by nonlocal correlations between pairs of contacts. Finally, we use live-cell experiments to measure the dynamics of the chromatin fiber in mouse embryonic stem cells, in combination with dynamical simulations, and predict that conformational changes within one TAD are likely to occur on timescales that are much shorter than the duration of one cell cycle. This suggests that genes and their regulatory elements may come together and disassociate several times during a cell cycle. These results have important implications for transcriptional regulation as they support the concept of highly dynamic interactions driven by a complex interplay between site-specific interactions and the intrinsic biophysical properties of the chromatin fiber.

Chromatin inside the cell nucleus consists of the DNA and its hierarchy of interacting molecules, which can be modeled as a complex polymer. To describe the chromatin dynamic, we develop and analyze here a polymer model that accounts for long-range interactions and not just those between the closest neighbors as in the Rouse polymer model. Our construction of the polymer model allows us to recover the local interaction between monomers from the anomalous diffusion exponent, which can be directly measured experimentally. We compute asymptotically for this polymer model the cross-correlation function for a given monomer and the mean time for a loop to be formed. Finally, we discuss some possible applications for interpretation of chromosome capture data.

Is it possible to extract the size and structure of chromosomal territories (confined domain) from the encounter frequencies of chromosomal loci? To answer this question, we estimate the mean time for two monomers located on the same polymer to encounter, which we call the mean first encounter time in a confined microdomain (MFETC). We approximate the confined domain geometry by a harmonic potential well and obtain an asymptotic expression that agrees with Brownian simulations for the MFETC as a function of the polymer length, the radius of the confined domain, and the activation distance radius e at which the two searching monomers meet. We illustrate the present approach using chromosome capture data for the encounter rate distribution of two loci depending on their distances along the DNA. We estimate the domain size that restricts the motion of one of these loci for chromosome II in yeast.

We study the first passage time for a polymer, that we call the narrow encounter time (NETP), to reach a small target located on the surface of a microdomain. The polymer is modeled as a Freely Joint Chain (beads connected by springs with a resting non zero length) and we use Brownian simulations to study two cases: when (i) any of the monomer or (ii) only one can be absorbed at the target window. Interestingly, we find that {in the first case} the NETP is an increasing function of the polymer length until a critical length, after which it decreases. Moreover, in the long polymer regime, we identified an exponential scaling law for the NETP as a function of the polymer length. {In the second case, the position of the absorbed monomer along the polymer chain strongly influences the NETP}. Our analysis can be applied to estimate the mean first time of a DNA fragment to a small target in the chromatin structure or for mRNA to find a small target., Comment: LaTeX, 25 pages, 6 eps figures

Using a novel theoretical approach, we study the mean first-encounter time (MFET) between the two ends of a polymer. Previous approaches used various simplifications that reduced the complexity of the problem, leading, however, to incompatible results. We construct here for the first time a general theory that allows us to compute the MFET. The method is based on estimating the mean time for a Brownian particle to reach a narrow domain in the polymer configuration space. In dimension two and three, we find that the MFET depends mainly on the first eigenvalue of the associated Fokker-Planck operator and provide precise estimates that are confirmed by Brownian simulations. Interestingly, although many time scales are involved in the encounter process, its distribution can be well approximated by a single exponential, which has several consequences for modeling chromosome dynamics in the nucleus. Another application of our result is computing the mean time for a DNA molecule to form a closed loop (when its two ends meet for the first time).

We consider a model system in which anomalous diffusion is generated by superposition of underlying linear modes with a broad range of relaxation times. In the language of Gaussian polymers, our model corresponds to Rouse (Fourier) modes whose friction coefficients scale as wavenumber to the power $2-z$. A single (tagged) monomer then executes subdiffusion over a broad range of time scales, and its mean square displacement increases as $t^\alpha$ with $\alpha=1/z$. To demonstrate non-trivial aspects of the model, we numerically study the absorption of the tagged particle in one dimension near an absorbing boundary or in the interval between two such boundaries. We obtain absorption probability densities as a function of time, as well as the position-dependent distribution for unabsorbed particles, at several values of $\alpha$. Each of these properties has features characterized by exponents that depend on $\alpha$. Characteristic distributions found for different values of $\alpha$ have similar qualitative features, but are not simply related quantitatively. Comparison of the motion of translocation coordinate of a polymer moving through a pore in a membrane with the diffusing tagged monomer with identical $\alpha$ also reveals quantitative differences., Comment: LaTeX, 10 pages, 8 eps figures

Is it possible to extract tethering forces applied on chromatin from the statistics of a single locus trajectories imaged in vivo? Chromatin fragments interact with many partners such as the nuclear membrane, other chromosomes or nuclear bodies, but the resulting forces cannot be directly measured in vivo. However, they impact chromatin dynamics and should be reflected in particular in the motion of a single locus. We present here a method based on polymer models and statistics of single trajectories to extract the force characteristics and in particular when they are generated by the gradient of a quadratic potential well. Using numerical simulations of a Rouse polymer and live cell imaging of the MAT-locus located on the yeast Saccharomyces cerevisiae chromosome III, we recover the amplitude and the distance between the observed and the interacting monomer. To conclude, the confined trajectories we observed in vivo reflect local interaction on chromatin., Author Summary Is it possible to recover the local environment, the external and internal forces acting on a polymer from a single locus trajectories? To study this question, we resolve this reverse cell biology problem by developing a method that uses in vivo live single locus trajectories to extract physical forces applied on chromatin. We applied the method to the statistics of the S. cerevisiae MAT-locus motion and recover tethering forces acting on the chromatin. The local confinement of a chromatin locus can either be due to crowding or to local interactions with partners such as the surface of the nuclear membrane, other chromosomes or nuclear bodies that cannot be directly measured. We conclude here that confined trajectories of a single chromatin locus can be generated by local tethering interactions. This approach is applicable to cells under various conditions, such as during double-stranded DNA break repair.

In many gene expression systems, a protein located on the DNA can affect the expression of a gene far along the chain. It has been recognized that the DNA can form transient loops, bringing a specific region of the gene close to another. Thus, transcription can be activated when a transcription factor is positioned far away from its site. The frequency of bending is a characteristic time scale of the activation process.The mean time for a DNA molecule to loop, bringing together two sites, is a fundamental factor that we studied. Various approximations have been used to model polymers. Interestingly, dsDNA has been found to be well described by the standard Rouse model, in which the polymer is described as a collection of bead monomers connected by harmonic springs. The Rouse model is relevant when the sites are at a distance considerably bigger than the DNA persistence length. When the distance between the sites is of several persistence lengths, the semi-flexible chain model is better suited to model the DNA dynamics. The polymer chain is subjected to random independent motion (Brownian motion). When the two monomers come closer than a certain distance, interaction takes place and the monomers connect. We assumed that the interaction rate is much faster than the encounter time, thus the process ends with the first encounter of the monomers. This allowed us to compute the asymptotic formula for the mean encounter time in the two models. We obtained precise estimates for this mean first encounter time in two and three dimensions. Brownian simulations confirm our formulas and we discuss consequences of our results for random gene activation in the nucleus.