The response of single DNA molecules to externally applied forces and torques was directly measured using an angular optical trap. Upon overwinding, DNA buckled abruptly as revealed by a sharp extension drop followed by a torque plateau. When the DNA was held at the buckling transition, its extension hopped rapidly between two distinct states. Furthermore, the initial plectonemic loop absorbed approximately twice as much extension as was absorbed into the plectoneme upon each additional turn. The observed extension change after buckling and the postbuckling torque support a recent DNA elasticity model.The bending and torsional properties of DNA influence numerous cellular processes, notably DNA compaction, replication, transcription, and protein-DNA binding. DNA elasticity regulates how proteins bend and twist DNA upon binding and how translocating molecular motors exert torque and force on their DNA substrates. Single molecule techniques have proven to be powerful approaches for the investigation of the response of DNA to mechanical stress; individual DNA molecules can be stretched and twisted under physiologically relevant conditions. To date the stretching and bending elasticities of DNA have been well characterized through measurements of the force-extension relation of DNA [1,2]. However, somewhat less is known regarding the torsional elasticity of DNA, at least in part due to difficulties in making direct torque measurements. The most prevalent method to twist DNA is to use magnetic tweezers to rotate a magnetic bead via rotation of a magnetic field [3,4]. Twisting DNA can also be achieved by rotation of a micropipette cantilever [5]. These approaches have provided many important insights into DNA torsional properties even without torque detection. A recent and novel technique directly measured torque in DNA via viscous drag force on a small bead attached to the side of a DNA molecule [6]. This approach requires taut DNA to minimize writhe and thus is more suited for measurements under high force ( > 15 pN). More recently, an angular optical trap that we developed has permitted simultaneous and direct measurements of force and torque for concurrent observation of the tensile and torsional behaviors of DNA over broad ranges of forces and torques [7,8]. In addition, its wider bandwidth is well suited for detection of highly kinetic processes. Previously we showed that nanofabricated quartz cylinders are ideally suited as handles for angular trapping. During DNA supercoiling, the torque, angle, force, and extension of a DNA molecule can be simultaneously monitored at kHz rates. In this work, we have directly measured the torsional modulus of DNA in the intermediate force regime, determined basic relations regarding the dependence of torque on applied force, made the first observation of the abrupt formation of the initial plectoneme † Corresponding author. mwang@physics.cornell.edu. * Present address: Mayo Clinic, Rochester, Minnesota 55902, USA. (interwound loop) in positively supercoiled DNA, and mo...

Large scale models of physical phenomena demand the development of new statistical and computational tools in order to be effective. Many such models are 'sloppy', i.e., exhibit behavior controlled by a relatively small number of parameter combinations. We review an information theoretic framework for analyzing sloppy models. This formalism is based on the Fisher Information Matrix, which we interpret as a Riemannian metric on a parameterized space of models. Distance in this space is a measure of how distinguishable two models are based on their predictions. Sloppy model manifolds are bounded with a hierarchy of widths and extrinsic curvatures. We show how the manifold boundary approximation can extract the simple, hidden theory from complicated sloppy models. We attribute the success of simple effective models in physics as likewise emerging from complicated processes exhibiting a low effective dimensionality. We discuss the ramifications and consequences of sloppy models for biochemistry and science more generally. We suggest that the reason our complex world is understandable is due to the same fundamental reason: simple theories of macroscopic behavior are hidden inside complicated microscopic processes.

The functioning of many biochemical networks is often robust-remarkably stable under changes in external conditions and internal reaction parameters. Much recent work on robustness and evolvability has focused on the structure of neutral spaces, in which system behavior remains invariant to mutations. Recently we have shown that the collective behavior of multiparameter models is most often sloppy: insensitive to changes except along a few 'stiff' combinations of parameters, with an enormous sloppy neutral subspace. Robustness is often assumed to be an emergent evolved property, but the sloppiness natural to biochemical networks offers an alternative nonadaptive explanation. Conversely, ideas developed to study evolvability in robust systems can be usefully extended to characterize sloppy systems.

Dynamics of complex systems is often driven by large and intricate networks of microscopic interactions, whose sheer size obfuscates understanding. With limited experimental data, many parameters of such dynamics are unknown, and thus detailed, mechanistic models risk overfitting and making faulty predictions. At the other extreme, simple ad hoc models often miss defining features of the underlying systems. Here we develop an approach that instead constructs phenomenological, coarse-grained models of network dynamics that automatically adapt their complexity to the available data. Such adaptive models produce accurate predictions even when microscopic details are unknown. The approach is computationally tractable, even for a relatively large number of dynamical variables. Using simulated data, it correctly infers the phase space structure for planetary motion, avoids overfitting in a biological signalling system and produces accurate predictions for yeast glycolysis with tens of data points and over half of the interacting species unobserved.