arXiv subjects

Ulrich Gerland

Publications and source records attributed to Ulrich Gerland.

At least 37 records · Page 2Linked to original sources

arXiv2010

Quantitative test of the barrier nucleosome model for statistical positioning of nucleosomes up- and downstream of transcription start sites

The positions of nucleosomes in eukaryotic genomes determine which parts of the DNA sequence are readily accessible for regulatory proteins and which are not. Genome-wide maps of nucleosome positions have revealed a salient pattern around transcription start sites, involving a nucleosome-free region (NFR) flanked by a pronounced periodic pattern in the average nucleosome density. While the periodic pattern clearly reflects well-positioned nucleosomes, the positioning mechanism is less clear. A recent experimental study by Mavrich et al. argued that the pattern observed in S. cerevisiae is qualitatively consistent with a `barrier nucleosome model', in which the oscillatory pattern is created by the statistical positioning mechanism of Kornberg and Stryer. On the other hand, there is clear evidence for intrinsic sequence preferences of nucleosomes, and it is unclear to what extent these sequence preferences affect the observed pattern. To test the barrier nucleosome model, we quantitatively analyze yeast nucleosome positioning data both up- and downstream from NFRs. Our analysis is based on the Tonks model of statistical physics which quantifies the interplay between the excluded-volume interaction of nucleosomes and their positional entropy. We find that although the typical patterns on the two sides of the NFR are different, they are both quantitatively described by the same physical model, with the same parameters, but different boundary conditions. The inferred boundary conditions suggest that the first nucleosome downstream from the NFR (the +1 nucleosome) is typically directly positioned while the first nucleosome upstream is statistically positioned via a nucleosome-repelling DNA region. These boundary conditions, which can be locally encoded into the genome sequence, significantly shape the statistical distribution of nucleosomes over a range of up to ~1000 bp to each side.

q-bio.QM↗

arXiv2009

Anomalous scaling in nanopore translocation of structured heteropolymers

Translocation through a nanopore is a new experimental technique to probe physical properties of biomolecules. A bulk of theoretical and computational work exists on the dependence of the time to translocate a single unstructured molecule on the length of the molecule. Here, we study the same problem but for RNA molecules for which the breaking of the secondary structure is the main barrier for translocation. To this end, we calculate the mean translocation time of single-stranded RNA through a nanopore of zero thickness and at zero voltage for many randomly chosen RNA sequences. We find the translocation time to depend on the length of the RNA molecule with a power law. The exponent changes as a function of temperature and exceeds the naively expected exponent of two for purely diffusive transport at all temperatures. We interpret the power law scaling in terms of diffusion in a one-dimensional energy landscape with a logarithmic barrier.

q-bio.BM↗

arXiv2008

Spontaneous Unknotting of a Polymer Confined in a Nanochannel

We study the dynamics of a knot in a semiflexible polymer confined to a narrow channel of width comparable to the polymers' persistence length. Using a combination of Brownian dynamics simulations and a coarse-grained stochastic model, we characterize the coupled dynamics of knot size variation and knot diffusion along the polymer, which ultimately leads to spontaneous unknotting. We find that the knot grows to macroscopic size before disappearing. Interestingly, an external force applied to the ends of the confined polymer speeds up spontaneous unknotting.

cond-mat.soft↗

arXiv2007

Kinetic Accessibility of Buried DNA Sites in Nucleosomes

Using a theoretical model for spontaneous partial DNA unwrapping from histones, we study the transient exposure of protein-binding DNA sites within nucleosomes. We focus on the functional dependence of the rates for site exposure and reburial on the site position, which is measurable experimentally and pertinent to gene regulation. We find the dependence to be roughly described by a random walker model. Close inspection reveals a surprising physical effect of flexibility-assisted barrier crossing, which we characterize within a toy model, the "semiflexible Brownian rotor."

q-bio.SC↗

arXiv2007

Optimal flexibility for conformational transitions in macromolecules

Conformational transitions in macromolecular complexes often involve the reorientation of lever-like structures. Using a simple theoretical model, we show that the rate of such transitions is drastically enhanced if the lever is bendable, e.g. at a localized "hinge''. Surprisingly, the transition is fastest with an intermediate flexibility of the hinge. In this intermediate regime, the transition rate is also least sensitive to the amount of "cargo'' attached to the lever arm, which could be exploited by molecular motors. To explain this effect, we generalize the Kramers-Langer theory for multi-dimensional barrier crossing to configuration dependent mobility matrices.

q-bio.BM↗

arXiv2005

Coupled dynamics of RNA folding and nanopore translocation

The translocation of structured RNA or DNA molecules through narrow pores necessitates the opening of all base pairs. Here, we study the interplay between the dynamics of translocation and base-pairing theoretically, using kinetic Monte Carlo simulations and analytical methods. We find that the transient formation of basepairs that do not occur in the ground state can significantly speed up translocation.

q-bio.BM↗

arXiv2005

DNA as a programmable viscoelastic nanoelement

The two strands of a DNA molecule with a repetitive sequence can pair into many different basepairing patterns. For perfectly periodic sequences, early bulk experiments of Poerschke indicate the existence of a sliding process, permitting the rapid transition between different relative strand positions [Biophys. Chem. 2 (1974) 83]. Here, we use a detailed theoretical model to study the basepairing dynamics of periodic and nearly periodic DNA. As suggested by Poerschke, DNA sliding is mediated by basepairing defects (bulge loops), which can diffuse along the DNA. Moreover, a shear force f on opposite ends of the two strands yields a characteristic dynamic response: An outward average sliding velocity v~1/N is induced in a double strand of length N, provided f is larger than a threshold f_c. Conversely, if the strands are initially misaligned, they realign even against an external force less than f_c. These dynamics effectively result in a viscoelastic behavior of DNA under shear forces, with properties that are programmable through the choice of the DNA sequence. We find that a small number of mutations in periodic sequences does not prevent DNA sliding, but introduces a time delay in the dynamic response. We clarify the mechanism for the time delay and describe it quantitatively within a phenomenological model. Based on our findings, we suggest new dynamical roles for DNA in artificial nanoscale devices. The basepairing dynamics described here is also relevant for the extension of repetitive sequences inside genomic DNA.

q-bio.BM↗

arXiv2005

An intermediate phase in DNA melting

We predict a novel temperature-driven phase transition of DNA below the melting transition. The additional, intermediate phase exists for repetitive sequences, when the two strands have different lengths. In this phase, the excess bases of the longer strand are completely absorbed as bulge loops inside the helical region. When the temperature is lowered, the excess bases desorb into overhanging ends, resulting in a contour length change. This continuous transition is in many aspects analogous to Bose Einstein condensation. Weak sequence disorder renders the transition discontinuous.

q-bio.BM↗

arXiv2005

Nonlinear Protein Degradation and the Function of Genetic Circuits

The functions of most genetic circuits require sufficient degrees of cooperativity in the circuit components. While mechanisms of cooperativity have been studied most extensively in the context of transcriptional initiation control, cooperativity from other processes involved in the operation of the circuits can also play important roles. In this study, we examine a simple kinetic source of cooperativity stemming from the nonlinear degradation of multimeric proteins. Ample experimental evidence suggests that protein subunits can degrade less rapidly when associated in multimeric complexes, an effect we refer to as cooperative stability. For dimeric transcription factors, this effect leads to a concentration-dependence in the degradation rate because monomers, which are predominant at low concentrations, will be more rapidly degraded. Thus cooperative stability can effectively widen the accessible range of protein levels in vivo. Through theoretical analysis of two exemplary genetic circuits in bacteria, we show that such an increased range is important for the robust operation of genetic circuits as well as their evolvability. Our calculations demonstrate that a few-fold difference between the degradation rate of monomers and dimers can already enhance the function of these circuits substantially. These results suggest that cooperative stability needs to be considered explicitly and characterized quantitatively in any systematic experimental or theoretical study of gene circuits.

q-bio.MN↗

arXiv2004

Transcriptional Regulation by the Numbers 1: Models

The study of gene regulation and expression is often discussed in quantitative terms. In particular, the expression of genes is regularly characterized with respect to how much, how fast, when and where. Whether discussing the level of gene expression in a bacterium or its precise location within a developing embryo, the natural language for these experiments is that of numbers. Such quantitative data demands quantitative models. We review a class of models ("thermodynamic models") which exploit statistical mechanics to compute the probability that RNA polymerase is at the appropriate promoter. This provides a mathematically precise elaboration of the idea that activators are agents of recruitment which increase the probability that RNA polymerase will be found at the promoter of interest. We discuss a framework which describes the interactions of repressors, activators, helper molecules and RNA polymerase using the concept of effective concentrations, expressed in terms of a function we call the "regulation factor". This analysis culminates in an expression for the probability of RNA polymerase binding at the promoter of interest as a function of the number of regulatory proteins in the cell. In a companion paper [1], these ideas are applied to several case studies which illustrate the use of the general formalism.

q-bio.MN↗

arXiv2004

Transcriptional Regulation by the Numbers 2: Applications

With the increasing amount of experimental data on gene expression and regulation, there is a growing need for quantitative models to describe the data and relate them to the different contexts. The thermodynamic models reviewed in the preceding paper provide a useful framework for the quantitative analysis of bacterial transcription regulation. We review a number of well-characterized bacterial promoters that are regulated by one or two species of transcription factors, and apply the thermodynamic framework to these promoters. We show that the framework allows one to quantify vastly different forms of gene expression using a few parameters. As such, it provides a compact description useful for higher-level studies, e.g., of genetic networks, without the need to invoke the biochemical details of every component. Moreover, it can be used to generate hypotheses on the likely mechanisms of transcriptional control.

q-bio.MN↗

arXiv2004

Dynamics of force-induced DNA slippage

We study the basepairing dynamics of DNA with repetitive sequences where local strand slippage can create, annihilate, and move bulge loops. Using an explicit theoretical model, we find a rich dynamical behavior as a function of an applied shear force f: reptation-like dynamics at f=f_c with a rupture time scaling as N^3 with its length N, drift-diffusion dynamics for f_c < f < f^*, and a dynamical transition to an unraveling mode of strand separation at f = f^*. We predict a viscoelastic behavior for periodic DNA with time and force scales that can be programmed into its sequence.

q-bio.BM↗

arXiv2004

Translocation of structured polynucleotides through nanopores

We investigate theoretically the translocation of structured RNA/DNA molecules through narrow pores which allow single but not double strands to pass. The unzipping of basepaired regions within the molecules presents significant kinetic barriers for the translocation process. We show that this circumstance may be exploited to determine the full basepairing pattern of polynucleotides, including RNA pseudoknots. The crucial requirement is that the translocation dynamics (i.e., the length of the translocated molecular segment) needs to be recorded as a function of time with a spatial resolution of a few nucleotides. This could be achieved, for instance, by applying a mechanical driving force for translocation and recording force-extension curves (FEC's) with a device such as an atomic force microscope or optical tweezers. Our analysis suggests that with this added spatial resolution, nanopores could be transformed into a powerful experimental tool to study the folding of nucleic acids.

cond-mat.soft↗

arXiv2003

The style of genetic computing

Cells receive a wide variety of cellular and environmental signals, which must be processed combinatorially to generate specific and timely genetic responses. We present here a theoretical study on the combinatorial control and integration of transcription signals, with the finding that cis-regulatory systems with specific protein-DNA interaction and glue-like protein-protein interactions, supplemented by distal activation or repression mechanisms, have the capability to execute a wide range of control functions encoded in the regulatory DNA sequences. Using a quantitative model based on the well-characterized bacterial transcription system, we show explicitly how various regulatory logic functions can be implemented, by selecting the strengths and relative positions of the relevant protein-binding DNA sequences in the cis-regulatory region. The architecture that emerges is naturally modular and highly evolvable. Our findings suggest that the transcription regulatory apparatus is a "programmable" computing machine, belonging formally to the class of Boltzmann machines. We also expose critical shortcomings of the bacterial transcription systems, which limit the genome-wide adoption of schemes for complex transcription control, and discuss how they may be overcome by the eukaryotic transcription systems.

cond-mat.soft↗

arXiv2003

Dynamics of Competitive Evolution on a Smooth Landscape

We study competitive DNA sequence evolution directed by {\it in vitro} protein binding. The steady-state dynamics of this process is well described by a shape-preserving pulse which decelerates and eventually reaches equilibrium. We explain this dynamical behavior within a continuum mean-field framework. Analytical results obtained on the motion of the pulse agree with simulations. Furthermore, finite population correction to the mean-field results are found to be insignificant.

cond-mat.stat-mech↗

arXiv2003

On the Selection and Evolution of Regulatory DNA Motifs

The mutation and selection of regulatory DNA sequences is presented as an ideal model system of molecular evolution where genotype, phenotype, and fitness can be explicitly and independently characterized. In this theoretical study, we construct an explicit model for the evolution of regulatory sequences, making use of the known biophysics of the binding of regulatory proteins to DNA sequences, under the assumption that fitness of a sequence depends only on its binding affinity to the regulatory protein. The model is confined to the mean field (i.e., infinite population size) limit. Using realistic values for all parameters, we determine the minimum fitness advantage needed to maintain a binding sequence, demonstrating explicitly the ``error threshold'' below which a binding sequence cannot survive the accumulated effect of mutation over long time. The commonly observed ``fuzziness'' in binding motifs arises naturally as a consequence of the balance between selection and mutation in our model. In addition, we devise a simple model for the evolution of multiple binding sequences in a given regulatory region. We find the number of evolutionarily stable binding sequences to increase in a step-like fashion with increasing fitness advantage, if multiple regulatory proteins can synergistically enhance gene transcription. We discuss possible experimental approaches to resolve open questions raised by our study.

physics.bio-ph↗

arXiv2003

Mechanically probing the folding pathway of single RNA molecules

We study theoretically the denaturation of single RNA molecules by mechanical stretching, focusing on signatures of the (un)folding pathway in molecular fluctuations. Our model describes the interactions between nucleotides by incorporating the experimentally determined free energy rules for RNA secondary structure, while exterior single stranded regions are modeled as freely jointed chains. For exemplary RNA sequences (hairpins and the Tetrahymena thermophila group I intron), we compute the quasi-equilibrium fluctuations in the end-to-end distance as the molecule is unfolded by pulling on opposite ends. Unlike the average quasi-equilibrium force-extension curves, these fluctuations reveal clear signatures from the unfolding of individual structural elements. We find that the resolution of these signatures depends on the spring constant of the force-measuring device, with an optimal value intermediate between very rigid and very soft. We compare and relate our results to recent experiments by Liphardt et al. [Science 292, 733-737 (2001)].

cond-mat.soft↗

arXiv2002

Physical Constraints and Functional Characteristics of Transcription Factor-DNA Interaction

We study theoretical ``design principles'' for transcription factor-DNA interaction in bacteria, focusing particularly on the statistical interaction of the transcription factors (TF's) with the genomic background (i.e., the genome without the target sites). We introduce and motivate the concept of `programmability', i.e. the ability to set the threshold concentration for TF binding over a wide range merely by mutating the binding sequence of a target site. This functional demand, together with physical constraints arising from the thermodynamics and kinetics of TF-DNA interaction, leads us to a narrow range of ``optimal'' interaction parameters. We find that this parameter set agrees well with experimental data for the interaction parameters of a few exemplary prokaryotic TF's. This indicates that TF-DNA interaction is indeed programmable. We suggest further experiments to test whether this is a general feature for a large class of TF's.

physics.bio-ph↗