Strain-driven criticality underlies nonlinear mechanics of fibrous networks

Networks with only central force interactions are floppy when their average connectivity is below an isostatic threshold. Although such networks are mechanically unstable, they can become rigid when strained. It was recently shown that the transition from floppy to rigid states as a function of simple shear strain is continuous, with hallmark signatures of criticality [Sharma et al., Nature Phys. 12, 584 (2016)1745-247310.1038/nphys3628]. The nonlinear mechanical response of collagen networks was shown to be quantitatively described within the framework of such mechanical critical phenomenon. Here, we provide a more quantitative characterization of critical behavior in subisostatic networks. Using finite-size scaling we demonstrate the divergence of strain fluctuations in the network at well-defined critical strain. We show that the characteristic strain corresponding to the onset of strain stiffening is distinct from but related to this critical strain in a way that depends on critical exponents. We confirm this prediction experimentally for collagen networks. Moreover, we find that the apparent critical exponents are largely independent of the spatial dimensionality. With subisostaticity as the only required condition, strain-driven criticality is expected to be a general feature of biologically relevant fibrous networks.

Nonlinear Mechanics of Athermal Branched Biopolymer Networks

Naturally occurring biopolymers such as collagen and actin form branched fibrous networks. The average connectivity in branched networks is generally below the isostatic threshold at which central force interactions marginally stabilize the network. In the submarginal regime, for connectivity below this threshold, such networks are unstable toward small deformations unless stabilized by additional interactions such as bending. Here we perform a numerical study on the elastic behavior of such networks. We show that the nonlinear mechanics of branched networks is qualitatively similar to that of filamentous networks with freely hinged cross-links. In agreement with a recent theoretical study,1 we find that branched networks also exhibit nonlinear mechanics consistent with athermal critical phenomena controlled by strain. We obtain the critical exponents capturing the nonlinear elastic behavior near the critical point by performing scaling analysis of the stiffening curves. We find that the exponents evolve with the connectivity in the network. We show that the nonlinear mechanics of disordered networks, independent of the detailed microstructure, can be characterized by a strain-driven second-order phase transition, and that the primary quantitative differences among different architectures are in the critical exponents describing the transition.

On-site residence time in a driven diffusive system: Violation and recovery of a mean-field description

We investigate simple one-dimensional driven diffusive systems with open boundaries. We are interested in the average on-site residence time defined as the time a particle spends on a given site before moving on to the next site. Using mean-field theory, we obtain an analytical expression for the on-site residence times. By comparing the analytic predictions with numerics, we demonstrate that the mean-field significantly underestimates the residence time due to the neglect of time correlations in the local density of particles. The temporal correlations are particularly long-lived near the average shock position, where the density changes abruptly from low to high. By using domain wall theory, we obtain highly accurate estimates of the residence time for different boundary conditions. We apply our analytical approach to residence times in a totally asymmetric exclusion process (TASEP), TASEP coupled to Langmuir kinetics (TASEP+LK), and TASEP coupled to mutually interactive LK (TASEP+MILK). The high accuracy of our predictions is verified by comparing these with detailed Monte Carlo simulations.

Transmission of HIV Drug Resistance and the Predicted Effect on Current First-line Regimens in Europe

Transmitted human immunodeficiency virus drug resistance in Europe is stable at around 8%. The impact of baseline mutation patterns on susceptibility to antiretroviral drugs should be addressed using clinical guidelines. The impact on baseline susceptibility is largest for nonnucleoside reverse transcriptase inhibitors.

Background. Numerous studies have shown that baseline drug resistance patterns may influence the outcome of antiretroviral therapy. Therefore, guidelines recommend drug resistance testing to guide the choice of initial regimen. In addition to optimizing individual patient management, these baseline resistance data enable transmitted drug resistance (TDR) to be surveyed for public health purposes. The SPREAD program systematically collects data to gain insight into TDR occurring in Europe since 2001.

Methods. Demographic, clinical, and virological data from 4140 antiretroviral-naive human immunodeficiency virus (HIV)–infected individuals from 26 countries who were newly diagnosed between 2008 and 2010 were analyzed. Evidence of TDR was defined using the WHO list for surveillance of drug resistance mutations. Prevalence of TDR was assessed over time by comparing the results to SPREAD data from 2002 to 2007. Baseline susceptibility to antiretroviral drugs was predicted using the Stanford HIVdb program version 7.0.

Results. The overall prevalence of TDR did not change significantly over time and was 8.3% (95% confidence interval, 7.2%–9.5%) in 2008–2010. The most frequent indicators of TDR were nucleoside reverse transcriptase inhibitor (NRTI) mutations (4.5%), followed by nonnucleoside reverse transcriptase inhibitor (NNRTI) mutations (2.9%) and protease inhibitor mutations (2.0%). Baseline mutations were most predictive of reduced susceptibility to initial NNRTI-based regimens: 4.5% and 6.5% of patient isolates were predicted to have resistance to regimens containing efavirenz or rilpivirine, respectively, independent of current NRTI backbones.

Conclusions. Although TDR was highest for NRTIs, the impact of baseline drug resistance patterns on susceptibility was largest for NNRTIs. The prevalence of TDR assessed by epidemiological surveys does not clearly indicate to what degree susceptibility to different drug classes is affected.

Driven diffusive systems with mutually interactive Langmuir kinetics

We investigate the simple one-dimensional driven model, the totally asymmetric exclusion process, coupled to mutually interactive Langmuir kinetics. This model is motivated by recent studies on clustering of motor proteins on microtubules. In the proposed model, the attachment and detachment rates of a particle are modified depending upon the occupancy of neighboring sites. We first obtain continuum mean-field equations and in certain limiting cases obtain analytic solutions. We show how mutual interactions increase (decrease) the effects of boundaries on the phase behavior of the model. We perform Monte Carlo simulations and demonstrate that our analytical approximations are in good agreement with the numerics over a wide range of model parameters. We present phase diagrams over a selective range of parameters.