Increasing the concentration of counterions (salt) is known to reduce the bending persistence length of DNA. Here we use atomistic molecular dynamics simulations to predict that multivalent counterions have the opposite effect on double-stranded RNA, increasing its bending rigidity by at least 30%. This counterintuitive effect is observed for various tri- and tetravalent ions alike, and is robust to methodological details and the RNA sequence. In contrast to DNA, multivalent counterions bind inside the RNA major groove, causing significant contraction of the molecule along its helical axis—as a result, its further deformation due to bending becomes energetically more expensive compared to bending without bound multivalent ions. Thus, the relationship between mechanical properties of a charged polymer and its ionic atmosphere may be richer than previously thought.

We report a novel superresolution microscopy approach for imaging fluorescence samples. The reported approach, termed virtual $k$-space modulation optical microscopy (VIKMOM), is able to improve the lateral resolution by a factor of 2, reduce the background level, improve the optical sectioning effect and correct for unknown optical aberrations. In the acquisition process of VIKMOM, we used a scanning confocal microscope setup with a 2D detector array to capture sample information at each scanned $x\text{−}y$ position. In the recovery process of VIKMOM, we first modulated the captured data by virtual $k$-space coding and then employed a ptychography-inspired procedure to recover the sample information and correct for unknown optical aberrations. We demonstrated the performance of the reported approach by imaging fluorescent beads, fixed bovine pulmonary artery endothelial (BPAE) cells, and living human astrocytes (HA). As the VIKMOM approach is fully compatible with conventional confocal microscope setups, it may provide a turn-key solution for imaging biological samples with $\sim 100\mathrm{nm}$ lateral resolution, in two or three dimensions, with improved optical sectioning capabilities and aberration correcting.

We consider epidemic extinction in finite networks with a broad variation in local connectivity. Generalizing the theory of large fluctuations to random networks with a given degree distribution, we are able to predict the most probable, or optimal, paths to extinction in various configurations, including truncated power laws. We find that paths for heterogeneous networks follow a limiting form in which infection first decreases in low-degree nodes, which triggers a rapid extinction in high-degree nodes, and finishes with a residual low-degree extinction. The usefulness of our approach is further demonstrated through optimal control strategies that leverage the dependence of finite-size fluctuations on network topology. Interestingly, we find that the optimal control is a mix of treating both high- and low-degree nodes based on theoretical predictions, in contrast to methods that ignore dynamical fluctuations.

We show that highly twisted minimal strips can undergo a nonsingular transition, unlike the singular transitions seen in the Möbius strip and the catenoid. If the strip is nonorientable, this transition is topologically frustrated, and the resulting surface contains a helicoidal defect. Through a controlled analytic approximation, the system can be mapped onto a scalar ${\varphi }^4$ theory on a nonorientable line bundle over the circle, where the defect becomes a topologically protected kink soliton or domain wall, thus establishing their existence in minimal surfaces. Demonstrations with soap films confirm these results and show how the position of the defect can be controlled through boundary deformation.

We investigate the dynamics of the heterodimer autorepression loop (HAL), a small genetic module in which a protein $A$ acts as an autorepressor and binds to a second protein $B$ to form an $AB$ dimer. For suitable values of the rate constants, the HAL produces pulses of $A$ alternating with pulses of $B$. By means of analytical and numerical calculations, we show that the duration of $A$ pulses is extremely robust against variation of the rate constants while the duration of the $B$ pulses can be flexibly adjusted. The HAL is thus a minimal genetic module generating robust pulses with a tunable duration, an interesting property for cellular signaling.

We propose a stochastic model for gene transcription coupled to DNA supercoiling, where we incorporate the experimental observation that polymerases create supercoiling as they unwind the DNA helix and that these enzymes bind more favorably to regions where the genome is unwound. Within this model, we show that when the transcriptionally induced flux of supercoiling increases, there is a sharp crossover from a regime where torsional stresses relax quickly and gene transcription is random, to one where gene expression is highly correlated and tightly regulated by supercoiling. In the latter regime, the model displays transcriptional bursts, waves of supercoiling, and up regulation of divergent or bidirectional genes. It also predicts that topological enzymes which relax twist and writhe should provide a pathway to down regulate transcription.

Negative autoregulation is universally found across organisms. In the bacterium Escherichia coli, transcription factors often repress their own expression to form a negative feedback network motif that enables robustness to changes in biochemical parameters. Here we present a simple phenomenological model of a negative feedback transcription factor repressing both itself and another target gene. The strength of the negative feedback is characterized by three parameters: the cooperativity in self-repression, the maximal expression rate of the transcription factor, and the apparent dissociation constant of the transcription factor binding to its own promoter. Analysis of the model shows that the target gene levels are robust to mutations in the transcription factor, and that the robustness improves as the degree of cooperativity in self-repression increases. The prediction is tested in the LexA transcriptional network of E. coli by altering cooperativity in self-repression and promoter strength. Indeed, we find robustness is correlated with the former. Considering the proposed importance of gene regulation in speciation, parameters governing a transcription factor’s robustness to mutation may have significant influence on a cell or organism’s capacity to evolve.

We derive a reduced quasi-one-dimensional theory of geometrically frustrated elastic ribbons. Expressed in terms of geometric properties alone, it applies to ribbons over a wide range of scales, allowing the study of their elastic equilibrium, as well as thermal fluctuations. We use the theory to account for the twisted-to-helical transition of ribbons with spontaneous negative curvature and the effect of fluctuations on the corresponding critical exponents. The persistence length of such ribbons changes nonmonotonically with the ribbon’s width, dropping to zero at the transition. This and other statistical properties qualitatively differ from those of nonfrustrated fluctuating filaments.

To understand DNA elasticity at high forces ($F>30\mathrm{pN}$), its helical nature must be taken into account, as a coupling between twist and stretch. The prevailing model, the wormlike chain, was previously extended to include this twist-stretch coupling. Motivated by DNA’s charged nature, and the known effects of ionic charges on its elasticity, we set out to systematically measure the impact of buffer ionic conditions on twist-stretch coupling. After developing a robust fitting approach, we show, using our new data set, that DNA’s helical twist is stabilized at high concentrations of the magnesium divalent cation. DNA’s persistence length and stretch modulus are, on the other hand, relatively insensitive to the applied range of ionic strengths.

Biological systems are characterized by compartmentalization from the subcellular to the tissue level, and thus reactions in small volumes are ubiquitous in living systems. Under such conditions, statistical number fluctuations, which are commonly negligible in bulk reactions, can become dominant and lead to stochastic behavior. We present here a stochastic model of protein filament formation in small volumes. We show that two principal regimes emerge for the system behavior, a small fluctuation regime close to bulk behavior and a large fluctuation regime characterized by single rare events. Our analysis shows that in both regimes the reaction lag-time scales inversely with the system volume, unlike in bulk. Finally, we use our stochastic model to connect data from small-volume microdroplet experiments of amyloid formation to bulk aggregation rates, and show that digital analysis of an ensemble of protein aggregation reactions taking place under microconfinement provides an accurate measure of the rate of primary nucleation of protein aggregates, a process that has been challenging to quantify from conventional bulk experiments.

The susceptible-infected-susceptible (SIS) model is a canonical model for emerging disease outbreaks. Such outbreaks are naturally modeled as taking place on networks. A theoretical challenge in network epidemiology is the dynamic correlations coming from that if one node is infected, then its neighbors are likely to be infected. By combining two theoretical approaches—the heterogeneous mean-field theory and the effective degree method—we are able to include these correlations in an analytical solution of the SIS model. We derive accurate expressions for the average prevalence (fraction of infected) and epidemic threshold. We also discuss how to generalize the approach to a larger class of stochastic population models.

Myosin motor proteins drive vigorous steady-state fluctuations in the actin cytoskeleton of cells. Endogenous embedded semiflexible filaments such as microtubules, or added filaments such as single-walled carbon nanotubes are used as novel tools to noninvasively track equilibrium and nonequilibrium fluctuations in such biopolymer networks. Here, we analytically calculate shape fluctuations of semiflexible probe filaments in a viscoelastic environment, driven out of equilibrium by motor activity. Transverse bending fluctuations of the probe filaments can be decomposed into dynamic normal modes. We find that these modes no longer evolve independently under nonequilibrium driving. This effective mode coupling results in nonzero circulatory currents in a conformational phase space, reflecting a violation of detailed balance. We present predictions for the characteristic frequencies associated with these currents and investigate how the temporal signatures of motor activity determine mode correlations, which we find to be consistent with recent experiments on microtubules embedded in cytoskeletal networks.

We derive an unbiased information theoretic energy landscape for chromosomes at metaphase using a maximum entropy approach that accurately reproduces the details of the experimentally measured pairwise contact probabilities between genomic loci. Dynamical simulations using this landscape lead to cylindrical, helically twisted structures reflecting liquid crystalline order. These structures are similar to those arising from a generic ideal homogenized chromosome energy landscape. The helical twist can be either right or left handed so chiral symmetry is broken spontaneously. The ideal chromosome landscape when augmented by interactions like those leading to topologically associating domain formation in the interphase chromosome reproduces these behaviors. The phase diagram of this landscape shows that the helical fiber order and the cylindrical shape persist at temperatures above the onset of chiral symmetry breaking, which is limited by the topologically associating domain interaction strength.

We implement and optimize a particle-swap Monte Carlo algorithm that allows us to thermalize a polydisperse system of hard spheres up to unprecedentedly large volume fractions, where previous algorithms and experiments fail to equilibrate. We show that no glass singularity intervenes before the jamming density, which we independently determine through two distinct nonequilibrium protocols. We demonstrate that equilibrium fluid and nonequilibrium jammed states can have the same density, showing that the jamming transition cannot be the end point of the fluid branch.