236 research outputs found
DNA nano-mechanics: how proteins deform the double helix
It is a standard exercise in mechanical engineering to infer the external
forces and torques on a body from its static shape and known elastic
properties. Here we apply this kind of analysis to distorted double-helical DNA
in complexes with proteins. We extract the local mean forces and torques acting
on each base-pair of bound DNA from high-resolution complex structures. Our
method relies on known elastic potentials and a careful choice of coordinates
of the well-established rigid base-pair model of DNA. The results are robust
with respect to parameter and conformation uncertainty. They reveal the complex
nano-mechanical patterns of interaction between proteins and DNA. Being
non-trivially and non-locally related to observed DNA conformations, base-pair
forces and torques provide a new view on DNA-protein binding that complements
structural analysis.Comment: accepted for publication in JCP; some minor changes in response to
review 18 pages, 5 figure + supplement: 4 pages, 3 figure
Single-molecule stretching experiments of flexible (wormlike) chain molecules in different ensembles: Theory and a potential application of finite chain length effects to nick-counting in DNA
We propose a formalism for deriving force\u2013elongation and elongation\u2013force relations for flexible chain molecules from analytical expressions for their radial distribution function, which provides insight into the factors controlling the asymptotic behavior and finite chain length corrections. In particular, we apply this formalism to our previously developed interpolation formula for the wormlike chain end-to-end distance distribution. The resulting expression for the asymptotic limit of infinite chain length is of similar quality to the numerical evaluation of Marko and Siggia\u2019s variational theory and considerably more precise than their interpolation formula. A comparison to numerical data suggests that our analytical finite chain length corrections achieve a comparable accuracy. As an application of our results, we discuss the possibility of inferring the time-dependent number of nicks in single-molecule stretching experiments on double-stranded DNA from the accompanying changes in the effective chain length
Sequence Dependent Elasticity of DNA
The DNA contained in every living cell not only stores the genetic information; it functions in a complex molecular network that can condense, transcribe, replicate and repair genes. The essential role played by the sequence dependent structure and deformability of DNA in these basic processes of life, has received increasing attention over the past years. The present work aims at better understanding sequence dependent elasticity of double stranded DNA elasticity, across biologically relevant length scales. A theoretical description is developed that makes is possible to relate structural, biochemical and biophysical experiments and simulation. It is based on the rigid baseâpair chain (rbc) model which captures all basic deformation modes on the scale of individual baseâpair (bp) steps. Existing microscopic parametrizations of the rbc model rely on indirect methods. A way to relate them to biochemical experiments is provided by the indirect readout mechanism, where DNA elasticity determines proteinâDNA complexation afïŹnities. By correlating theoretical afïŹnity predictions with in vitro measurements in a wellâstudied test case, different parameter sets were evaluated. As a result a new, hybrid parameter set is proposed which greatly reduces prediction errors. Indirect readout occurs mostly at particular binding subsites in a complex. A statistical marker is developed which localizes indirect readout subsites, by detecting elastically optimized sub-sequences. By a systematic coarseâgraining of the rbc to the wellâcharacterized wormâlike chain (wlc) model, a quantitative connection between microscopic and kbp scale elasticity is established. The general helical rbc geometry is mapped to an effective, linear âon-axisâ version, yielding the full set of wlc elastic parameters for any given sequence repeat. In the random sequence case, structural variability adds conformational ïŹuctuations which are correlated by sequence continuity. The sequence disorder correction to entropic elasticity in the rbc model is shown to coincide with the conformational correction. The results show remarkable overall agree- ment of the coarseâgrained with the mesoscale wlc parameters, lending support to the model and to the microscopic parameter sets. A continuum version of the rbc is formulated as Brownian motion on the rigid motion group. Analytic expressions for angular correlation functions and moments of the endâtoâend distance distribution are given. In an equivalent Lagrangian approach, conserved quantities along, and the linear response around, a general equilibrium shape are explored.Die in jeder lebenden Zelle enthaltene DNS speichert nicht nur die genetische Information; Sie funktioniert innerhalb eines komplexen molekularen Netzwerks, das in der Lage ist, Gene zu kondensieren, transkribieren, replizieren und reparieren. Die zentrale Rolle, welche der sequenzabhĂ€ngigen Struktur und Deformierbarkeit von DNS in diesen grundlegenden Lebensprozessen zukommt, erregte in den letzten Jahren zunehmendes Interesse. Die vorliegende Arbeit hat ein besseres VerstĂ€ndnis der sequenzabhĂ€ngigen elastischen Eigenschaften von DNS auf biologisch relevanten LĂ€ngenskalen zum Ziel. Es wird eine theoretische Beschreibung entwickelt, die es ermöglicht, strukturbiologische, biochemische und biophysikalische Experimente und Simulationen in Beziehung zu setzen. Diese baut auf dem Modell einer Kette aus starren Basenpaaren (rbc) auf, das alle wichtigen Deformationsmoden von DNS auf der Ebene von einzelnen Basenpaar (bp)âSchritten abbildet. Bestehende ParametersĂ€tze des rbc-Modells beruhen auf indirekten Methoden. Eine direkte Beziehung zu biochemischen Experimenten kann mithilfe des indirekten Auslese-Mechanismus hergestellt werden. Hierbei bestimmt die DNSâ ElastizitĂ€t KomplexierungsafïŹnitĂ€ten von ProteinâDNSâKomplexen. Durch eine Korrelation von theoretischen Vorhersagen mit in vitro Messungen in einem gut untersuchten Beispielfall werden verschiedene ParametersĂ€tze bewertet. Als Resultat wird ein neuer HybridâParametersatz vorgeschlagen, der die Vorhersagefehler stark reduziert. Indirektes Auslesen tritt meistens an speziellen Teilbindungsstellen innerhalb eines Komplexes auf. Es wird eine statistische KenngröĂe entwickelt, die indirektes Auslesen durch Detektion elastisch optimierter Subsequenzen erkennt. Durch ein systematisches CoarseâGraining des rbc-Modells auf das gut charakterisierte Modell der wurmartigen Kette (wlc) wird eine quantitative Beziehung zwischen der mikroskopischen und der ElastizitĂ€t auf einer kbp-Skala hergestellt. Die allgemeine helikale Geometrie wird auf eine effektive, lineare Version der Kette âauf der Achseâ abgebildet. Dies fĂŒhrt zur Berechnung des vollen Satzes von wlc-elastischen Parameters fĂŒr eine beliebig vorgegebene periodische Sequenz. Im Fall zufĂ€lliger Sequenz fĂŒhrt die StrukturvariabilitĂ€t zu zusĂ€tzlichen KonformationsïŹuktuationen, die durch die KontinuitĂ€t der Sequenz kurzreichweitig korreliert sind. Es wird gezeigt, daĂ die Sequenzunordnungs-Korrektur zur entropischen ElastizitĂ€t im rbc-Modell identisch ist zur Korrektur der Konformationsstatistik. Die Ergebnisse zeigen eine bemerkenswerte Ăbereinstimmung der hochskalierten mikroskopischen mit den mesoskopischen wlc-Parameter und bestĂ€tigen so die Wahl des Modells und seiner mikroskopischen Parametrisierung. Eine Kontinuumsversion des rbc-Modells wird formuliert als Brownsche Bewegung auf der Gruppe der Starrkörpertransformationen. Analytische AusdrĂŒcke fĂŒr Winkelkorrelationsfunktionen und Momente der Verteilung des End-zu-EndâVektors werden angegeben. In einem Ă€quivalenten Lagrange-Formalismus werden ErhaltungsgröĂen entlang von Gleichgewichtskonformationen und die lineare Antwort in ihrer Umgebung untersucht
DNA: From rigid base-pairs to semiflexible polymers
The sequence-dependent elasticity of double-helical DNA on a nm length scale
can be captured by the rigid base-pair model, whose strains are the relative
position and orientation of adjacent base-pairs. Corresponding elastic
potentials have been obtained from all-atom MD simulation and from
high-resolution structural data. On the scale of a hundred nm, DNA is
successfully described by a continuous worm-like chain model with homogeneous
elastic properties characterized by a set of four elastic constants, which have
been directly measured in single-molecule experiments. We present here a theory
that links these experiments on different scales, by systematically
coarse-graining the rigid base-pair model for random sequence DNA to an
effective worm-like chain description. The average helical geometry of the
molecule is exactly taken into account in our approach. We find that the
available microscopic parameters sets predict qualitatively similar mesoscopic
parameters. The thermal bending and twisting persistence lengths computed from
MD data are 42 and 48 nm, respectively. The static persistence lengths are
generally much higher, in agreement with cyclization experiments. All
microscopic parameter sets predict negative twist-stretch coupling. The
variability and anisotropy of bending stiffness in short random chains lead to
non-Gaussian bend angle distributions, but become unimportant after two helical
turns.Comment: 13 pages, 6 figures, 6 table
Strengthening Deterministic Policies for POMDPs
The synthesis problem for partially observable Markov decision processes
(POMDPs) is to compute a policy that satisfies a given specification. Such
policies have to take the full execution history of a POMDP into account,
rendering the problem undecidable in general. A common approach is to use a
limited amount of memory and randomize over potential choices. Yet, this
problem is still NP-hard and often computationally intractable in practice. A
restricted problem is to use neither history nor randomization, yielding
policies that are called stationary and deterministic. Previous approaches to
compute such policies employ mixed-integer linear programming (MILP). We
provide a novel MILP encoding that supports sophisticated specifications in the
form of temporal logic constraints. It is able to handle an arbitrary number of
such specifications. Yet, randomization and memory are often mandatory to
achieve satisfactory policies. First, we extend our encoding to deliver a
restricted class of randomized policies. Second, based on the results of the
original MILP, we employ a preprocessing of the POMDP to encompass memory-based
decisions. The advantages of our approach over state-of-the-art POMDP solvers
lie (1) in the flexibility to strengthen simple deterministic policies without
losing computational tractability and (2) in the ability to enforce the
provable satisfaction of arbitrarily many specifications. The latter point
allows taking trade-offs between performance and safety aspects of typical
POMDP examples into account. We show the effectiveness of our method on a broad
range of benchmarks
Stable developmental patterns of gene expression without morphogen gradients
Gene expression patterns are established by cross-regulating target genes
that interpret morphogen gradients. However, as development progresses,
morphogen activity is reduced, leaving the emergent pattern without stabilizing
positional cues. The pattern then can be deteriorated by the intrinsically
noisy biochemical processes acting at the cellular level. But remarkably, the
established gene expression patterns remain spatially and temporally stable in
many biological systems. Here we combine spatial-stochastic simulations with an
enhanced sampling method and a recently developed stability theory to address
how spatiotemporal integrity of a gene expression pattern is maintained in
developing tissue lacking morphogen gradients. Using a minimal embryo model
consisting of spatially coupled biochemical reactor volumes, we study a stripe
pattern in which weak cross-repression between nearest neighbor domians
alternates with strong repression between next-nearest neighbor domains,
inspired by the gap gene system in the Drosophila embryo. We find that
fine-tuning of the weak repressive interactions to an optimal level can
significantly increase temporal stability of the expression patterns, allowing
for stable patterns over developmentally relevant times in the absence of
morphogen gradients. The numerically determined optimal parameters closely
agree with the predictions of the stability theory. By analizing the dynamics
of factors characterizing pattern integrity, we trace back the stability
enhancement to the emergence of restoring forces, maintaining the pattern in a
meta-stable basin. Altogether our results demonstrate that metastable
attractors can emerge as a property of stochastic gene expression patterns even
without system-wide positional cues, provided that the gene regulatory
interactions shaping the pattern are optimally tuned
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