Ductal carcinoma in situ develops within clonal fields of mutant cells in morphologically normal ducts

Mutations are abundantly present in tissues of healthy individuals, including the breast epithelium. Yet it remains unknown whether mutant cells directly induce lesion formation or first spread, leading to a field of mutant cells that is predisposed towards lesion formation. To study the clonal and spatial relationships between morphologically normal breast epithelium adjacent to pre-cancerous lesions, we developed a three-dimensional (3D) imaging pipeline combined with spatially resolved genomics on archival, formalin-fixed breast tissue with the non-obligate breast cancer precursor ductal carcinoma in situ (DCIS). Using this 3D image-guided characterization method, we built high-resolution spatial maps of DNA copy number aberration (CNA) profiles within the DCIS lesion and the surrounding normal mammary ducts. We show that the local heterogeneity within a DCIS lesion is limited. However, by mapping the CNA profiles back onto the 3D reconstructed ductal subtree, we find that in eight out of 16 cases the healthy epithelium adjacent to the DCIS lesions has overlapping structural variations with the CNA profile of the DCIS. Together, our study indicates that pre-malignant breast transformations frequently develop within mutant clonal fields of morphologically normal-looking ducts. © 2024 The Authors. The Journal of Pathology published by John Wiley & Sons Ltd on behalf of The Pathological Society of Great Britain and Ireland.

Modeling the mosaic structure of bacterial genomes to infer their evolutionary history

The chronology and phylogeny of bacterial evolution are difficult to reconstruct due to a scarce fossil record. The analysis of bacterial genomes remains challenging because of large sequence divergence, the plasticity of bacterial genomes due to frequent gene loss, horizontal gene transfer, and differences in selective pressure from one locus to another. Therefore, taking advantage of the rich and rapidly accumulating genomic data requires accurate modeling of genome evolution. An important technical consideration is that loci with high effective mutation rates may diverge beyond the detection limit of the alignment algorithms used, biasing the genome-wide divergence estimates toward smaller divergences. In this article, we propose a novel method to gain insight into bacterial evolution based on statistical properties of genome comparisons. We find that the length distribution of sequence matches is shaped by the effective mutation rates of different loci, by the horizontal transfers, and by the aligner sensitivity. Based on these inputs, we build a model and show that it accounts for the empirically observed distributions, taking the Enterobacteriaceae family as an example. Our method allows to distinguish segments of vertical and horizontal origins and to estimate the time divergence and exchange rate between any pair of taxa from genome-wide alignments. Based on the estimated time divergences, we construct a time-calibrated phylogenetic tree to demonstrate the accuracy of the method.

A living biobank of patient-derived ductal carcinoma in situ mouse-intraductal xenografts identifies risk factors for invasive progression

Ductal carcinoma in situ (DCIS) is a non-obligate precursor of invasive breast cancer (IBC). Due to a lack of biomarkers able to distinguish high- from low-risk cases, DCIS is treated similar to early IBC even though the minority of untreated cases eventually become invasive. Here, we characterized 115 patient-derived mouse-intraductal (MIND) DCIS models reflecting the full spectrum of DCIS observed in patients. Utilizing the possibility to follow the natural progression of DCIS combined with omics and imaging data, we reveal multiple prognostic factors for high-risk DCIS including high grade, HER2 amplification, expansive 3D growth, and high burden of copy number aberrations. In addition, sequential transplantation of xenografts showed minimal phenotypic and genotypic changes over time, indicating that invasive behavior is an intrinsic phenotype of DCIS and supporting a multiclonal evolution model. Moreover, this study provides a collection of 19 distributable DCIS-MIND models spanning all molecular subtypes.

Abstract PR002: Genomic predictor can discriminate between high- and low-risk DCIS

Introduction: Ductal carcinoma in situ (DCIS) is considered a non-obligate precursor of invasive ductal carcinoma. With the aim of preventing a subsequent invasive cancer, all DCIS lesions are currently treated with surgical excision often supplemented with radiotherapy (RT). To prevent DCIS over- or undertreatment, a reliable marker of DCIS invasiveness risk is urgently needed. Methods: We studied two large DCIS cohorts: the Sloane cohort, a prospective breast screening cohort from the UK (median follow-up of 11 years), and a Dutch population-based cohort (NKI, median follow-up of 13 years). FFPE tissue specimens from patients with pure primary DCIS after breast-conserving surgery (BCS) +/- RT that did develop a subsequent ipsilateral event (DCIS or invasive) were considered as cases, whereas patients that did not develop any form of recurrence up to the last follow-up or death were considered as controls. We performed copy number analysis (CNA) and RNAseq analysis on 229 cases (80 DCIS only recurrences) and 344 controls. Results: DCIS was classified into the PAM50 subtypes using RNAseq data which revealed an enrichment of luminal A phenotype in DCIS that did not recur (P = 0.01, Fisher Exact test). No single copy number aberration was more common in cases compared to controls. RNAseq data did not reveal any genes significantly over/under-expressed in cases versus controls after FDR correction. However, by limiting the analysis to samples that had not had RT and excluding pure DCIS recurrences, we could develop a penalized Cox model from RNAseq data. The model was trained on weighted samples (to correct for the biased sampling of the case-control dataset) from the NKI series with double loop cross-validation. The genes were selected using the Elastic net framework of penalization. Using this predicted hazard ratio, the samples were split into high, medium, and low-risk quantiles, with a recurrence risk of 23%, 7% and 2%, respectively at 5 years (p = 10-10, Wald test). The NKI-trained predictor was independently validated in the Sloane No RT no DCIS recurrence cohort (p = 0.02, Wald test). GSEA analysis revealed proliferation hallmarks enriched in the recurrence predictor (FDR = 0.058). The RNAseq predictor was more predictive of recurrence than PAM50, clinical features (Grade, Her2 and ER) and the 12-gene Oncotype DCIS score (p < 0.001, permutation test using the Wald statistic) in both the NKI and Sloane series. Conclusion: Genomic profiling of two independent series of DCIS with outcome data did not reveal any clear associations with recurrence until analysis was limited to a set of samples who had not had radiotherapy and DCIS recurrences were excluded. We then identified an RNAseq-based classifier that could differentiate primary DCIS in low-, medium-, and high-risk groups, and validated it in an independent cohort. This classifier, if validated in other datasets, will allow us to identify women who do not need intensive treatment for their DCIS.

Citation Format: Maria Roman Escorza, Michael Sheinman, Tycho Bismeijer, Ahmed A. Ahmed, Vandna Shah, Jeffrey R. Marks, Lorraine M. King, Anargyros Megalios, Lindy L. Visser, Marlous Hoogstrat, Helen R. Davies, Tapsi Kumar, Deborah Collyar, Hilary Stobart, Sarah Pinder, Nicholas N. Navin, Andrew Futreal, Serena Nik-Zainal, E. Shelley Hwang, Esther H. Lips, Alastair Thompson, Lodewyk F.A. Wessels, Jelle Wesseling, Elinor J. Sawyer. Genomic predictor can discriminate between high- and low-risk DCIS [abstract]. In: Proceedings of the AACR Special Conference on Rethinking DCIS: An Opportunity for Prevention?; 2022 Sep 8-11; Philadelphia, PA. Philadelphia (PA): AACR; Can Prev Res 2022;15(12 Suppl_1): Abstract nr PR002.

Abstract 5108: Copy number analysis of pure DCIS and association with recurrence

With the widespread adoption of breast cancer screening the incidence of pure ductal carcinoma in situ (DCIS) has increased. As DCIS is considered a non-obligate precursor of invasive ductal carcinoma most women with pure DCIS are treated with breast conserving surgery (BCS) +/- radiotherapy. However, for many this is likely to be overtreatment as only a minority will develop a subsequent ipsilateral recurrence. Studies also show that only ~60% of these ipsilateral recurrences are invasive disease with the remainder being pure DCIS. To predict which women are most likely to benefit from interventions, there is a need to identify biomarkers that are associated with invasive recurrence. Our aim was to assess whether copy number aberrations (CNAs) could be used to identify DCIS that was likely to recur as invasive disease or remain recurrence-free during long-time follow up.

We performed somatic copy number profiling on 309 pure DCIS samples that had not developed an ipsilateral event (controls), 198 that had developed subsequent ipsilateral invasive disease (INV-cases) and 58 that had developed subsequent ipsilateral pure DCIS (DCIS-cases). The samples were obtained from two large nation-wide cohorts: the Sloane cohort, a prospective breast screening cohort from the UK with a median follow up of 12.5 years and a Dutch population based cohort, with a median follow up of 13 years. CNAs were assessed using the CytoSNP array or low pass whole genome sequencing and analyzed using GISTIC.

Integrative cluster (IntClust) subtyping revealed that only 5 subtypes were well represented in DCIS compared to 10 in invasive disease and the distribution of clusters between INV-cases and controls was similar with the exception of IntClust 4, which was significantly more common in controls (P= 0.025, Fishers exact test). IntClust 4 is characterized to have low levels of genomic instability and a CNA-devoid. INV-cases were globally more aberrant than controls (P = 0.006, Wilcoxon test) as assessed by the chromosomal instability index (CIN) score. GISTIC identified 17 recurrent amplifications, 21 recurrent gains and 22 recurrent losses in the whole cohort. Six of these regions were more common in INV-cases compared to controls: amplifications at 17q24.1 and 8p11.23, losses at 1p36.13 and 11q23.2 ​and gains at 17q21.33​ and 16p (Nominal P < 0.05 and FDR < 0.1, Fishers exact test). Subgroup analysis of ER+, Her2- INV-cases versus controls revealed an additional differential CNA, amplification at 11q13.3 more common in cases.

DCIS-cases had similar CNAs to INV-cases and were more aberrant than controls in terms of CIN score (P < 0.037, Wilcoxon test) but not as aberrant as INV-cases.

In conclusion, we have identified potential CNAs that are associated with invasive recurrence. Further analysis will integrate gene expression with copy number data to identify which genes are being targeted by these CNAs in order to identify pathways important in progression of DCIS.

Citation Format: Ahmed A. Ahmed, Maria Roman-Escorza, Tycho Bismeijer, Michael Sheinman, Vandna Shah, Rana Shami, Jeffrey R. Marks, Lorraine M. King, Anargyros Megalios, Lindy L. Visser, Marlous Hoogstraat, Helen R. Davies, Tapsi Kumar, Deborah Collyar, Hilary Stobart, Sarah Pinder, Nicholas N. Navin, Andrew Futreal, Serena Nik-Zainal, E. Shelley Hwang, Lodewyk F. Wessels, Esther H. Lips, Alastair Thompson, Jelle Wesseling, Elinor J. Sawyer. Copy number analysis of pure DCIS and association with recurrence [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 5108.

Genomic analysis defines clonal relationships of ductal carcinoma in situ and recurrent invasive breast cancer

Ductal carcinoma in situ (DCIS) is the most common form of preinvasive breast cancer and, despite treatment, a small fraction (5-10%) of DCIS patients develop subsequent invasive disease. A fundamental biologic question is whether the invasive disease arises from tumor cells in the initial DCIS or represents new unrelated disease. To address this question, we performed genomic analyses on the initial DCIS lesion and paired invasive recurrent tumors in 95 patients together with single-cell DNA sequencing in a subset of cases. Our data show that in 75% of cases the invasive recurrence was clonally related to the initial DCIS, suggesting that tumor cells were not eliminated during the initial treatment. Surprisingly, however, 18% were clonally unrelated to the DCIS, representing new independent lineages and 7% of cases were ambiguous. This knowledge is essential for accurate risk evaluation of DCIS, treatment de-escalation strategies and the identification of predictive biomarkers.

Abstract P1-22-05: Identifying predictors of invasive recurrence based on molecular profiles of DCIS lesions

Introduction Ductal carcinoma in situ (DCIS) is a non-obligate precursor of invasive breast cancer. Patients with DCIS are routinely treated by breast-conserving surgery often supplemented by radiotherapy, although many will never develop invasive disease. To date, no robust predictors of invasive breast cancer recurrence following DCIS have been identified. In our efforts to find such predictors, we performed gene expression, copy number and mutation analysis on two large DCIS cohorts with long-term follow-up. Methods Two nested case control series were analyzed, where cases are defined as DCIS with a subsequent invasive breast cancer and controls remained disease free during follow up. Cases and controls were matched on age and on follow up duration and were derived from two nation-wide cohort studies. The Sloane cohort is a prospective breast screening cohort from the UK, median follow up is 6 years (range 1-10). The Dutch cohort is population-based and had a median follow up of 13 years (range 2-23). We performed copy number analysis using CytoSNP array or low pass whole genome sequencing (lpWGS) on 310 controls and 196 cases, and RNA-seq on 295 controls and 206 cases. Results First analyses on the copy number data suggest that cases are genetically more aberrant with multiple regions of amplification compared to controls (p < 0.05). RNA-seq was used to classify DCIS into the PAM50 subtypes which did not appear to be predictive of recurrence. Initial RNA-seq analysis did not show consistent gene expression differences between cases and controls in the Sloane or Dutch cohorts, possibly explained by differences in clinical characteristics of the cohorts. A new computational method has been developed accounting for the differences in follow-up times, results will be presented at SABCS. Targeted sequencing revealed that the most common mutations were in PIK3CA and TP53, but there was no association with recurrence. Conclusion Only small molecular differences were identified between DCIS that recurs as invasive breast cancer and DCIS that remains disease-free. Currently, we are seeking to identify reproducible differences by a combined analysis of two population-based cohorts in a time dependent fashion. These will be presented at the SABCS. This work was supported by Cancer Research UK and by KWF Dutch Cancer Society (ref.C38317/A24043)

Citation Format: Tycho Bismeijer, Ahmed A Ahmed, Michael Sheinman, Maria Roman-Escorza, Vandna Shah, Jeffrey R Marks, Lorraine M King, Anargyros Megalios, Lindy L Visser, Marlous Hoogstraat, Helen R Davies, Tapsi Kumar, Deborah Collyar, Hilary Stobart, Nicholas N Navin, Andrew Futreal, Serena Nik-Zainal, Shelley Hwang, Esther H Lips, Alastair Thompson, Lodewyk FA Wessels, Elinor J Sawyer, Jelle Wesseling, Grand Challenge PRECISION Consortium. Identifying predictors of invasive recurrence based on molecular profiles of DCIS lesions [abstract]. In: Proceedings of the 2021 San Antonio Breast Cancer Symposium; 2021 Dec 7-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2022;82(4 Suppl):Abstract nr P1-22-05.

Identical sequences found in distant genomes reveal frequent horizontal transfer across the bacterial domain

Horizontal gene transfer (HGT) is an essential force in microbial evolution. Despite detailed studies on a variety of systems, a global picture of HGT in the microbial world is still missing. Here, we exploit that HGT creates long identical DNA sequences in the genomes of distant species, which can be found efficiently using alignment-free methods. Our pairwise analysis of 93,481 bacterial genomes identified 138,273 HGT events. We developed a model to explain their statistical properties as well as estimate the transfer rate between pairs of taxa. This reveals that long-distance HGT is frequent: our results indicate that HGT between species from different phyla has occurred in at least 8% of the species. Finally, our results confirm that the function of sequences strongly impacts their transfer rate, which varies by more than three orders of magnitude between different functional categories. Overall, we provide a comprehensive view of HGT, illuminating a fundamental process driving bacterial evolution.

Force percolation of contractile active gels

Living systems provide a paradigmatic example of active soft matter. Cells and tissues comprise viscoelastic materials that exert forces and can actively change shape. This strikingly autonomous behavior is powered by the cytoskeleton, an active gel of semiflexible filaments, crosslinks, and molecular motors inside cells. Although individual motors are only a few nm in size and exert minute forces of a few pN, cells spatially integrate the activity of an ensemble of motors to produce larger contractile forces (∼nN and greater) on cellular, tissue, and organismal length scales. Here we review experimental and theoretical studies on contractile active gels composed of actin filaments and myosin motors. Unlike other active soft matter systems, which tend to form ordered patterns, actin-myosin systems exhibit a generic tendency to contract. Experimental studies of reconstituted actin-myosin model systems have long suggested that a mechanical interplay between motor activity and the network's connectivity governs this contractile behavior. Recent theoretical models indicate that this interplay can be understood in terms of percolation models, extended to include effects of motor activity on the network connectivity. Based on concepts from percolation theory, we propose a state diagram that unites a large body of experimental observations. This framework provides valuable insights into the mechanisms that drive cellular shape changes and also provides design principles for synthetic active materials.

Conditions for positioning of nucleosomes on DNA

Positioning of nucleosomes along a eukaryotic genome plays an important role in its organization and regulation. There are many different factors affecting the location of nucleosomes. Some can be viewed as preferential binding of a single nucleosome to different locations along the DNA and some as interactions between neighboring nucleosomes. In this study, we analyze positioning of nucleosomes and derive conditions for their good positioning. Using analytic and numerical approaches we find that, if the binding preferences are very weak, an interplay between the interactions and the binding preferences is essential for a good positioning of nucleosomes, especially on correlated energy landscapes. Analyzing the empirical energy landscape, we conclude that good positioning of nucleosomes in vivo is possible only if they strongly interact. In this case, our model, predicting long-length-scale fluctuations of nucleosomes' occupancy along the DNA, accounts well for the empirical observations.

Inherently unstable networks collapse to a critical point

Nonequilibrium systems that are driven or drive themselves towards a critical point have been studied for almost three decades. Here we present a minimalist example of such a system, motivated by experiments on collapsing active elastic networks. Our model of an unstable elastic network exhibits a collapse towards a critical point from any macroscopically connected initial configuration. Taking into account steric interactions within the network, the model qualitatively and quantitatively reproduces results of the experiments on collapsing active gels.

Statistical properties of pairwise distances between leaves on a random Yule tree

A Yule tree is the result of a branching process with constant birth and death rates. Such a process serves as an instructive null model of many empirical systems, for instance, the evolution of species leading to a phylogenetic tree. However, often in phylogeny the only available information is the pairwise distances between a small fraction of extant species representing the leaves of the tree. In this article we study statistical properties of the pairwise distances in a Yule tree. Using a method based on a recursion, we derive an exact, analytic and compact formula for the expected number of pairs separated by a certain time distance. This number turns out to follow a increasing exponential function. This property of a Yule tree can serve as a simple test for empirical data to be well described by a Yule process. We further use this recursive method to calculate the expected number of the n-most closely related pairs of leaves and the number of cherries separated by a certain time distance. To make our results more useful for realistic scenarios, we explicitly take into account that the leaves of a tree may be incompletely sampled and derive a criterion for poorly sampled phylogenies. We show that our result can account for empirical data, using two families of birds species.

Anomalous discontinuity at the percolation critical point of active gels

We develop a percolation model motivated by recent experimental studies of gels with active network remodeling by molecular motors. This remodeling was found to lead to a critical state reminiscent of random percolation (RP), but with a cluster distribution inconsistent with RP. Our model not only can account for these experiments, but also exhibits an unusual type of mixed phase transition: We find that the transition is characterized by signatures of criticality, but with a discontinuity in the order parameter.

How evolution of genomes is reflected in exact DNA sequence match statistics

Genome evolution is shaped by a multitude of mutational processes, including point mutations, insertions, and deletions of DNA sequences, as well as segmental duplications. These mutational processes can leave distinctive qualitative marks in the statistical features of genomic DNA sequences. One such feature is the match length distribution (MLD) of exactly matching sequence segments within an individual genome or between the genomes of related species. These have been observed to exhibit characteristic power law decays in many species. Here, we show that simple dynamical models consisting solely of duplication and mutation processes can already explain the characteristic features of MLDs observed in genomic sequences. Surprisingly, we find that these features are largely insensitive to details of the underlying mutational processes and do not necessarily rely on the action of natural selection. Our results demonstrate how analyzing statistical features of DNA sequences can help us reveal and quantify the different mutational processes that underlie genome evolution.

Efficient fold-change detection based on protein-protein interactions

Various biological sensory systems exhibit a response to a relative change of the stimulus, often referred to as fold-change detection. In the past few years, fold-change detecting mechanisms, based on transcriptional networks, have been proposed. Here we present a fold-change detecting mechanism, based on protein-protein interactions, consisting of two interacting proteins. This mechanism does not consume chemical energy and is not subject to transcriptional and translational noise, in contrast to previously proposed mechanisms. We show by analytical and numerical calculations that the mechanism is robust and can have a fast, precise, and efficient response for parameters that are relevant to eukaryotic cells.

Elastic response of filamentous networks with compliant crosslinks

Experiments have shown that elasticity of disordered filamentous networks with compliant crosslinks is very different from networks with rigid crosslinks. Here, we model and analyze filamentous networks as a collection of randomly oriented rigid filaments connected to each other by flexible crosslinks that are modeled as wormlike chains. For relatively large extensions we allow for enthalpic stretching of crosslink backbones. We show that for sufficiently high crosslink density, the network linear elastic response is affine on the scale of the filaments' length. The nonlinear regime can become highly nonaffine and is characterized by a divergence of the elastic modulus at finite strain. In contrast to the prior predictions, we do not find an asymptotic regime in which the differential elastic modulus scales linearly with the stress, although an approximate linear dependence can be seen in a transition from entropic to enthalpic regimes. We discuss our results in light of recent experiments.

Fluctuation-stabilized marginal networks and anomalous entropic elasticity

We study the elastic properties of thermal networks of Hookean springs. In the purely mechanical limit, such systems are known to have a vanishing rigidity when their connectivity falls below a critical, isostatic value. In this work, we show that thermal networks exhibit a nonzero shear modulus G well below the isostatic point and that this modulus exhibits an anomalous, sublinear dependence on temperature T. At the isostatic point, G increases as the square root of T, while we find G∝Tα below the isostatic point, where α≃0.8. We show that this anomalous T dependence is entropic in origin.

Actively stressed marginal networks

We study the effects of motor-generated stresses in disordered three-dimensional fiber networks using a combination of a mean-field theory, scaling analysis, and a computational model. We find that motor activity controls the elasticity in an anomalous fashion close to the point of marginal stability by coupling to critical network fluctuations. We also show that motor stresses can stabilize initially floppy networks, extending the range of critical behavior to a broad regime of network connectivities below the marginal point. Away from this regime, or at high stress, motors give rise to a linear increase in stiffness with stress. Finally, we demonstrate that our results are captured by a simple, constitutive scaling relation highlighting the important role of nonaffine strain fluctuations as a susceptibility to motor stress.

Filament-length-controlled elasticity in 3D fiber networks

We present a model for disordered 3D fiber networks to study their linear and nonlinear elasticity. In contrast to previous 2D models, these 3D networks with binary crosslinks are underconstrained with respect to fiber stretching elasticity, suggesting that bending may dominate their response. We find that such networks exhibit a bending-dominated elastic regime controlled by fiber length, as well as a crossover to a stretch-dominated regime for long fibers. Finally, by extending the model to the nonlinear regime, we show that these networks become intrinsically nonlinear with a vanishing linear response regime in the limit of flexible or long filaments.

Nonlinear effective-medium theory of disordered spring networks

Disordered soft materials, such as fibrous networks in biological contexts, exhibit a nonlinear elastic response. We study such nonlinear behavior with a minimal model for networks on lattice geometries with simple Hookian elements with disordered spring constant. By developing a mean-field approach to calculate the differential elastic bulk modulus for the macroscopic network response of such networks under large isotropic deformations, we provide insight into the origins of the strain stiffening and softening behavior of these systems. We find that the nonlinear mechanics depends only weakly on the lattice geometry and is governed by the average network connectivity. In particular, the nonlinear response is controlled by the isostatic connectivity, which depends strongly on the applied strain. Our predictions for the strain dependence of the isostatic point as well as the strain-dependent differential bulk modulus agree well with numerical results in both two and three dimensions. In addition, by using a mapping between the disordered network and a regular network with random forces, we calculate the nonaffine fluctuations of the deformation field and compare them to the numerical results. Finally, we discuss the limitations and implications of the developed theory.

Classes of fast and specific search mechanisms for proteins on DNA

Problems of search and recognition appear over different scales in biological systems. In this review we focus on the challenges posed by interactions between proteins, in particular transcription factors, and DNA and possible mechanisms which allow for fast and selective target location. Initially we argue that DNA-binding proteins can be classified, broadly, into three distinct classes which we illustrate using experimental data. Each class calls for a different search process and we discuss the possible application of different search mechanisms proposed over the years to each class. The main thrust of this review is a new mechanism which is based on barrier discrimination. We introduce the model and analyze in detail its consequences. It is shown that this mechanism applies to all classes of transcription factors and can lead to a fast and specific search. Moreover, it is shown that the mechanism has interesting transient features which allow for stability at the target despite rapid binding and unbinding of the transcription factor from the target.

Searching fast for a target on DNA without falling to traps

Genomic expression depends critically on both the ability of regulatory proteins to locate specific target sites on DNA within seconds and on the formation of long-lived (many minutes) complexes between these proteins and the DNA. Equilibrium experiments show that indeed regulatory proteins bind tightly to their target site. However, they also find strong binding to other nonspecific sites which act as traps that can dramatically increase the time needed to locate the target. This gives rise to a conflict between the speed and stability requirements. Here we suggest a simple mechanism which can resolve this long-standing paradox.

The effects of intersegmental transfers on target location by proteins

We study a model of protein searching for a target, using facilitated diffusion, on a DNA molecule confined in a finite volume. The model includes three distinct pathways for facilitated diffusion: (a) sliding--in which the protein diffuses along the contour of the DNA, (b) jumping--where the protein travels between two sites along the DNA by three-dimensional diffusion and finally (c) intersegmental transfer--which allows the protein to move from one site to another by transiently binding both at the same time. The typical search time is calculated using scaling arguments which are verified numerically. Our results suggest that the inclusion of intersegmental transfer (i) decreases the search time considerably, (ii) makes the search time much more robust to variations in the parameters of the model and (iii) that the optimal search time occurs in a regime very different than that found for models which ignore intersegmental transfers. The behavior we find is rich and shows surprising dependences, for example on the DNA length.