Harnessing fluctuation theorems to discover free energy and dissipation potentials from non-equilibrium data.

The Jarzynski relation, as an equality form of the second law of thermodynamics, represents an exact thermodynamic statement that is valid arbitrarily far away from equilibrium. This remarkable relation directly links the equilibrium free energy difference between two states and the probability distribution of the work done along a process that drives the system from one state to the other. Here, we leverage the Jarzynski equality and a local equilibrium assumption, to go beyond the calculation of free energy differences and also extract the dissipation potential from additional measurements of kinematic field variables (strain and velocity fields). The proposed strategy is exemplified over pulling experiments of mass-spring models obeying overdamped Langevin dynamics, which is a prototype for nanorods, fibrous macro-molecules and the Rouse model of polymers. Different interaction potentials, fluid viscosities and bath temperatures are studied, so as to intrinsically control how close or far away the system is from equilibrium. The data-inferred continuum models are then validated against processes governed by different pulling protocols, thereby demonstrating their predictive capability. The methods presented here represent a first step toward full material characterization from non-equilibrium data of macroscopic observables, which could potentially be obtained from experimental observations.

Stick-slip kinetics in a bistable bar immersed in a heat bath.

Structural transitions in some rod-like biological macromolecules under tension are known to proceed by the propagation through the length of the molecule of an interface separating two phases. A continuum mechanical description of the motion of this interface, or phase boundary, takes the form of a kinetic law which relates the thermodynamic driving force across it with its velocity in the reference configuration. For biological macromolecules immersed in a heat bath, thermally activated kinetics described by the Arrhenius law is often a good choice. Here we show that 'stick-slip' kinetics, characteristic of friction, can also arise in an overdamped bistable bar immersed in a heat bath. To mimic a rod-like biomolecule we model the bar as a chain of masses and bistable springs moving in a viscous fluid. We conduct Langevin dynamics calculations on the chain and extract a temperature dependent kinetic relation by observing that the dissipation at a phase boundary can be estimated by performing an energy balance. Using this kinetic relation we solve boundary value problems for a bistable bar immersed in a constant temperature bath and show that the resultant force-extension relation matches very well with the Langevin dynamics results. We estimate the force fluctuations at the pulled end of the bar due to thermal kicks from the bath by using a partition function. We also show rate dependence of hysteresis in cyclic loading of the bar arising from the stick-slip kinetics. Our kinetic relation could be applied to rod-like biomolecules, such as, DNA and coiled-coil proteins which exhibit structural transitions that depend on both temperature and loading rate.

Rheology of fibrous gels under compression.

A number of biological tissues and synthetic gels consist of a fibrous network infused with liquid. There have been a few experimental studies of the rheological properties of such gels under applied compressive strain. Their results suggest that a plot of rheological moduli as a function of applied compressive strain has a long plateau flanked by a steeply increasing curve for large compressive strains and a slowly decreasing curve for small strains. In this paper we explain these trends in rheological properties using a chemo-elastic model characterized by a double-well strain energy function for the underlying fibrous network. The wells correspond to rarefied and densified phases of the fibrous network at low and high strains, respectively. These phases can co-exist across a movable transition front in the gel in order to accommodate overall applied compression. We find that the rheological properties of fibrous gels share similarities with a Kelvin-Voigt visco-elastic solid. The storage modulus has its origins in the elasticity of the fibrous network, while the loss modulus is determined by the dissipation caused by liquid flow through pores. The rheological properties can depend on the number of phase transition fronts present in a compressed sample. Our analysis may explain the dependence of storage and loss moduli of fibrin gels on the loading history. We also point to the need for combining rheological measurements on gels with a microstructural analysis that could shed light on various dissipation mechanisms.

Effects of laparoscopic radical surgery in the treatment of colorectal cancer and correlations of VEGF and TGF-ß1 with prognosis.

OBJECTIVE: To investigate the effects of laparoscopic radical surgery on the treatment of colorectal cancer (CRC) and explore the correlations of vascular endothelial growth factor (VEGF) and transforming growth factor-ß1 (TGF-ß1) with prognosis. METHODS: The clinical data of 210 patients with CRC admitted to the Yantai Zhifu Hospital from February 2015 to February 2018 were analyzed retrospectively. Among them, 110 patients were treated with laparoscopic radical surgery and assigned to the observation group, and the rest 100 patients were treated with routine open surgery and included in the open group. The two groups were compared in terms of operation time (OT), intraoperative blood loss (IBL), postoperative exhaust time (PET), length of hospital stays (LOS) and incidence of complications. Patients were also followed up for 3 years to count their survival rates. Serum expression levels of VEGF and TGF-ß1, detected by enzyme-linked immunosorbent assays (ELISAs), were compared before and after treatment, and their correlations with patients' clinicopathological data and prognosis were analyzed. RESULTS: Compared with the open group, patients in the observation group had longer OT, but lower IBL, PET, LOS, and overall incidence of complications. In the observation group, VEGF and TGF-ß1 expression after treatment was remarkably lower than that before treatment and that in the open group. A 3-year survival rate of 80.0% was observed in the observation group. Univariate analysis showed that serum VEGF and TGF-ß1 expression levels were closely related to Dukes staging and lymph node metastasis (LNM) (P<0.05). The Log-Rank test showed that the survival rate of patients with high VEGF and TGF-ß1 expression was remarkably lower than that of those with low expression (P<0.05). According to Cox model multivariate analysis, Dukes staging, LNM, surgical methods and high VEGF and TGF-ß1 expression were all independent risk factors for the prognosis of CRC patients (P<0.05). CONCLUSION: Laparoscopic radical surgery is effective and safe in treating CRC. VEGF and TGF-ß1 are highly expressed in the serum of CRC patients, and are closely related to the tumor staging, LNM and prognosis of patients, which are of great significance for evaluating the condition and prognosis of CRC patients.

Fibrous gels modelled as fluid-filled continua with double-well energy landscape.

Several biological materials are fibre networks infused with fluid, often referred to as fibrous gels. An important feature of these gels is that the fibres buckle under compression, causing a densification of the network that is accompanied by a reduction in volume and release of fluid. Displacement-controlled compression of fibrous gels has shown that the network can exist in a rarefied and a densified state over a range of stresses. Continuum chemo-elastic theories can be used to model the mechanical behaviour of these gels, but they suffer from the drawback that the stored energy function of the underlying network is based on neo-Hookean elasticity, which cannot account for the existence of multiple phases. Here we use a double-well stored energy function in a chemo-elastic model of gels to capture the existence of two phases of the network. We model cyclic compression/decompression experiments on fibrous gels and show that they exhibit propagating interfaces and hysteretic stress-strain curves that have been observed in experiments. We can capture features in the rate-dependent response of these fibrous gels without recourse to finite-element calculations. We also perform experiments to show that certain features in the stress-strain curves of fibrous gels predicted by our model can be found in the compression response of blood clots. Our methods may be extended to other tissues and synthetic gels that have a fibrous structure.