Mechanical Conformers of Keyring Catenanes.

Interlocked molecules exhibit structural isomerization that is different from that of molecules whose connectedness is solely through covalent bonds. A mechanical bond, or the interlocking of components, provides a rich conformational landscape. The ability of synthetic chemists to design directional motion between these mechanical conformers suggests mechanical bonds as building blocks in the design of synthetic molecular motors and machines. Here we examine the complexity of mechanical conformers of radial catenanes with n anisotropically repulsive rings (coined "keyrings") threaded onto a single central ring for n ≤ 10. For a given number of rings, n, the ratio of the key length to the main ring radius, λ, determines the mechanical conformer. We show that this system displays symmetrical in-plane conformers for short keys and co-conformers of lower symmetry where the keys lie out of the plane for longer keys.

Equilibrium binding energies from fluctuation theorems and force spectroscopy simulations.

Brownian dynamics simulations are used to study the detachment of a particle from a substrate. Although the model is simple and generic, we attempt to map its energy, length and time scales onto a specific experimental system, namely a bead that is weakly bound to a cell and then removed by an optical tweezer. The external driving force arises from the combined optical tweezer and substrate potentials, and thermal fluctuations are taken into account by a Brownian force. The Jarzynski equality and Crooks fluctuation theorem are applied to obtain the equilibrium free energy difference between the final and initial states. To this end, we sample non-equilibrium work trajectories for various tweezer pulling rates. We argue that this methodology should also be feasible experimentally for the envisioned system. Furthermore, we outline how the measurement of a whole free energy profile would allow the experimentalist to retrieve the unknown substrate potential by means of a suitable deconvolution. The influence of the pulling rate on the accuracy of the results is investigated, and umbrella sampling is used to obtain the equilibrium probability of particle escape for a variety of trap potentials.

Non-equilibrium umbrella sampling applied to force spectroscopy of soft matter.

Physical systems often respond on a timescale which is longer than that of the measurement. This is particularly true in soft matter where direct experimental measurement, for example in force spectroscopy, drives the soft system out of equilibrium and provides a non-equilibrium measure. Here we demonstrate experimentally for the first time that equilibrium physical quantities (such as the mean square displacement) can be obtained from non-equilibrium measurements via umbrella sampling. Our model experimental system is a bead fluctuating in a time-varying optical trap. We also show this for simulated force spectroscopy on a complex soft molecule--a piston-rotaxane.

Piston-rotaxanes as molecular shock absorbers.

We describe the thermomechanical response of a new molecular system that behaves as a shock absorber. The system consists of a rodlike rotaxane connected to a piston and tethered to a surface. The response of this system is dominated by the translational entropy of the rotaxane rings and can be calculated exactly. The force laws are contrasted with those for a rigid rod and a polymer. In some cases, the rotaxanes undergo a sudden transition to a tilted state when compressed. These piston-rotaxanes provide a potential motif for the design of a new class of materials with a novel thermomechanical response.

Hydrodynamic mobility of an optically trapped colloidal particle near fluid-fluid interfaces.

Using optical tweezers, we measure the anisotropic hydrodynamic mobility of a colloidal particle by tracking its thermal motion in an optical trap located near fluid-fluid interfaces, namely, liquid-vapor and liquid-liquid interfaces. The method requires no controlled fluid flow, is independent of conservative interactions between particle and interface, and resolves distance dependent friction to within a fraction of the particle radius. Near the liquid-vapor interface, the friction decreases below that in the bulk, corresponding to predictions of a "perfect-slip" surface.

Coarse-graining intramolecular hydrodynamic interaction in dilute solutions of flexible polymers.

We present a scheme for coarse-graining hydrodynamic interactions in an isolated flexible homopolymer molecule in solution. In contrast to the conventional bead-spring model that employs spherical beads of fixed radii to represent the hydrodynamic characteristics of coarse-grained segments, we show that our procedure leads naturally to a discrete model of a polymer molecule as a chain of orientable and stretchable Gaussian blobs. This model accounts for both intrablob and interblob hydrodynamic interactions, which depend on the instantaneous shapes of the blobs. In Brownian dynamics simulations of initially stretched chains relaxing under quiescent conditions, the transient evolution of the mean-square end-to-end distance and first normal stress difference obtained with the Gaussian-blob model are found to be less sensitive to the degree of coarse graining, in comparison with the conventional bead-spring model with Rotne-Prager-Yamakawa hydrodynamic interactions.

Effect of red blood cell rigidity on tumor blood flow: increase in viscous resistance during hyperglycemia.

Elevated glucose level and low pH have been shown to increase red blood cell (RBC) rigidity. This increased rigidity has been proposed as one factor which mediates the tumor blood flow (TBF) reduction during hyperglycemia by (a) causing RBC entrapment and hence increasing geometric resistance and (b) increasing viscous resistance to blood flow. However, due to the inability to measure these resistances in vivo in tumors directly, the relative contribution of RBC rigidity in TBF reduction has not been quantified. In the present study, blood flow resistance was measured in "tissue-isolated" mammary adenocarcinoma R3230AC perfused ex vivo with (a) normally deformable, (b) glutaraldehyde-hardened, and (c) glucose-incubated RBC suspensions. Flow resistance measured during tumor perfusion with Krebs-Henseleit buffer prior to and following perfusion with the glutaraldehyde-hardened RBC suspensions showed no significant change, suggesting constant geometric resistance and lack of RBC entrapment. Instead, our measurements indicated increased viscous resistance with loss of deformability due to glutaraldehyde and glucose incubation even though glucose incubation did not significantly alter the apparent blood viscosity measured in vitro. Thus, the TBF reduction during hyperglycemia may be due to subtle changes in RBC deformability. These results suggest the development of strategies to increase the delivery of drugs or oxygen must take into account any changes in intratumor viscous resistance. For example, the increase in the oxygen-carrying capacity of blood using RBC transfusion or fluorocarbon emulsions may be offset by the increase in viscous resistance and the corresponding reduction in TBF.

Measurement of capillary filtration coefficient in a solid tumor.

The net transvascular filtration rate, JF (ml/min/100 g), in an isolated, RBC-free perfused R3230AC mammary adenocarcinoma tumor was measured using a gravimetric method whereby changes in tissue weight over time were monitored. From the gravimetric measurements of JF following changes in venous pressure, the capillary filtration coefficient (ml/min/mm Hg/100 g) was found to be 2.2 (range, 0.8-2.8), i.e., 10 to 1000 times higher than those found in several normal tissues and within the range of those reported for glomerular capillaries. These measurements of capillary filtration coefficient are consistent with elevated tumor interstitial fluid pressure, interstitial fluid flow, and peritumor edema.

Geometric resistance to blood flow in solid tumors perfused ex vivo: effects of tumor size and perfusion pressure.

In a vascular network blood flow rate is proportional to the arteriovenous pressure difference and inversely proportional to the viscous and geometric resistances. The geometric resistance to tumor blood flow was determined by perfusing tissue-isolated mammary adenocarcinoma (R3230AC; N = 40; tumor weight, 1.8 +/- 1.2 (SD) g; range, 0.5-6.6 g) ex vivo with an acellular Krebs-Henseleit medium (viscosity, 0.9 g/m/s) at rates of 0.1 to 60 ml/h and arteriovenous pressure differences of 0 to 120 mm Hg. Below perfusion pressures of 40 mm Hg, pressure-flow behavior was always nonlinear, indicating elevated geometric resistance and a reduction in vascular cross-sectional area with decreasing microvessel pressure. However, above 40 mm Hg, pressure-flow behavior was linear demonstrating a constant geometric resistance, z0 and a constant vascular cross-sectional area for flow. z0 increased linearly from 1.6 to 17.3 X 10(8) g/cm3 as tumor weight increased from 0.5 to 6.6 g. This dependence of z0 upon tumor size is in agreement with the decrease in tumor perfusion rates with tumor growth observed in vivo. Comparison with previous studies of normal organs and tissues shows that z0 in tumors can be as much as 1-2 orders of magnitude higher, depending upon tumor weight. This dependence of geometric resistance on perfusion pressure and tumor size offers novel insights into the dynamics of tumor microcirculation and has significant clinical implications.

Viscous resistance to blood flow in solid tumors: effect of hematocrit on intratumor blood viscosity.

Blood flow rate in a vascular network is proportional to the arteriovenous pressure difference and inversely proportional to the geometric and viscous resistances. We have recently shown that the geometric resistance to blood flow increases with increasing tumor size and/or decreasing arterial pressure. In this study, the viscous resistance to blood flow within tumor microvasculature was determined by alternately perfusing mammary adenocarcinoma [R3230AC; N = 12; tumor weight, 2.2 +/- 1.6 (SD) g] ex vivo with Krebs-Henseleit solution and with RBC suspensions at hematocrits between 1 and 60%. Our results demonstrate that: (a) intratumor blood viscosity increases with increasing hematocrit; and (b) for fixed hematocrits between 10 and 60%, the intratumor blood viscosity is significantly reduced (P less than 0.0001) compared to bulk viscosity measured at shear rates of 460 s-1 using a cone/plate viscometer. However, this reduction of intratumor blood viscosity is not as pronounced as in a previous study of skeletal muscle. Further comparison shows that as arterial pressure is lowered, intratumor blood viscosity increases at a greater rate and at lower hematocrits than in normal tissues. We attribute the increased viscous resistance in tumor microvasculature to (a) a less pronounced Fahraeus effect (i.e., reduction in hematocrit in small vessels) and a less pronounced Fahraeus-Lindqvist effect (i.e., reduction in blood viscosity in small vessels) in dilated tumor microvessels compared to normal microvessels; (b) low shear rates (i.e., velocity gradients) associated with tumor vessels which may facilitate rouleaux formation at moderate pressures and even at low hematocrits; and (c) vascular fluid losses of 5-14% which may also increase microvessel hematocrit. We also propose that intratumor blood viscosity may be even higher in vivo than ex vivo due to the presence of WBC and cancer cells in vivo; considerably more rigid than RBC, these cells may cause increased viscous resistance and transient vascular stasis in tumors. The implications of these results in tumor blood flow modulation using chemical and physical agents are discussed.

Blood flow and venous pH of tissue-isolated Walker 256 carcinoma during hyperglycemia.

Hemodynamic (blood flow rate, hematocrit, hemoglobin concentration, and blood viscosity) and pH responses to glucose (6 g/kg, i.p.) injections were studied in ten Walker 256 carcinoma tumors (0.5-1.8 g) grown in the "tissue-isolated" tumor preparation. A maximum blood flow reduction of 57 +/- 19% (SD) occurred concurrently with an increase in tumor arterial-venous blood pH difference 20-30 min after glucose administration. Tumor venous blood pH dropped significantly by 0.15 +/- 0.07 pH unit to 7.15 +/- 0.01, while systemic blood pH dropped by 0.06 +/- 0.02 pH unit to 7.38 +/- 0.03. Arteriovenous blood pH differences were found to correlate with blood flow rates; however, both the small magnitude of the pH reduction and the immediate blood flow response argue against the hypothesis of increased resistance to flow caused by low pH-stiffened RBC membranes. Significant increases in systemic and tumor efferent whole blood viscosities at 2.25 and 4.5s-1 occurred after glucose administration, while hemoglobin concentrations of systemic and tumor efferent blood increased by as much as 11 +/- 1 and 16 +/- 2%, respectively. Venous to arterial hematocrit and hemoglobin ratios remained unchanged with glucose administration. These data suggest local tumor blood flow reductions are caused by increased viscous resistance to flow within the tortuous microvasculature of tumor, not as a result of low pH RBC rigidity, but rather from other mechanisms such as glucose-mediated RBC rigidity and systemic hemoconcentration.

Microvascular architecture in a mammary carcinoma: branching patterns and vessel dimensions.

The objective of this work was to introduce a tumor vessel classification scheme and to provide the first quantitative measurements of vessel branching patterns and the related vascular dimensions in a mammary carcinoma. Mammary adenocarcinoma R3230AC tumors, grown in the rat ovarian tissue-isolated tumor preparation, were infused with Batson's No. 17 polymer and maintained at an intravascular pressure of 50 mm Hg during polymerization. Maceration of the tumor in KOH allowed visualization of the vasculature. The vessel branching patterns, lengths, and diameters were measured in four tumors (4-5 g). A centrifugal ordering scheme was devised specifically to account for the unique features of tumor microvascular network topology. The arterial networks revealed two types of branching patterns. One type of arteriolar network exhibited decreasing vessel diameters and lengths with increasing branch order. In a second type of network, the diameter and length of the vessels displayed fluctuations in both variables at higher generations. Avascular and poorly vascularized regions with sparse capillary supply were present in the tumors, but analysis of several capillary networks in vascularized regions revealed a nonplanar meshwork of interconnected vessels. The meshworks were composed of vessels with a mean segment length of 67 microns, a mean diameter of 10 microns, and a mean intercapillary distance of 49 microns. Capillary path lengths ranged from 0.5 to 1.5 mm. Thus, tumor capillary diameter was greater than that in most normal tissues and, in the regions where capillary networks existed, intercapillary spacing was in the normal range. In the venous network, diameters decreased from 650 to 20 microns for the first to ninth order venules. Venule length decreased from 5 to 0.5 mm for first to fourth order but was fairly uniform (less than 500 microns) for higher orders. In conclusion, solid tumor vascular architecture, while exhibiting several features that are similar to those observed in normal tissues, has others that are not commonly seen in normal tissues. These features of the tumor microcirculation may lead to heterogeneous local hematocrits, oxygen tensions, and drug concentrations, thus reducing the efficacy of present day cancer therapies.

Experimental study of the fluctuation theorem in a nonequilibrium steady state.

The fluctuation theorem (FT) quantifies the probability of second law violations in small systems over short time scales. While this theorem has been experimentally demonstrated for systems that are perturbed from an initial equilibrium state, there are a number of studies suggesting that the theorem applies asymptotically in the long time limit to systems in a nonequilibrium steady state. The asymptotic application of the FT to such nonequilibrium steady states has been referred to in the literature as the steady-state fluctuation theorem (or SSFT). In this paper, we demonstrate experimentally the application of the FT to nonequilibrium steady states, using a colloidal particle localized in a translating optical trap. Furthermore, we show, for this colloidal system, that the FT holds under nonequilibrium steady states for all time, and not just in the long time limit, as in the SSFT.

Frequency domain imaging of absorbers obscured by scattering.

Multiple pixel, frequency domain measurements of phase shift, theta, and modulation, m, in a phantom containing an absorber obscured by a relatively non-absorbing scattering solution are presented in combination with a theory of photon migration imaging. Results employing a single point source show that two dimensional theta measurements made in the presence (theta presence) and in the absence (theta absence) of an absorber can be used to create delta theta images. delta theta (theta absence-theta presence) images can be used to detect as well as locate the three dimensional position of the absorber. Images of mpresence measured in the presence of the absorber normalized by mabsence also provided detection and two dimensional location of its position. Images of % mpresence/mabsence at higher modulation frequencies provided greater resolution as predicted by photon migration theory. Neither theta nor m images alone could be used to detect or locate the presence of the absorber.

Reversibility in nonequilibrium trajectories of an optically trapped particle.

The fluctuation theorem (FT) describes how a system's thermodynamic irreversibility develops in time from a completely thermodynamically reversible system at short observation times, to a thermodynamically irreversible one at infinitely long times. In this paper, we present a general definition of the dissipation function Omega(t), the quantitative argument in the fluctuation theorem (FT), that is a measure of a system's irreversibility. Originally cast for deterministic systems, we demonstrate, through the example of two recent experiments, that the dissipation function can be defined for stochastic systems. While the ensemble average of Omega(t) is positive definite irrespective of the system for which it is constructed, different expressions for Omega(t) can arise in stochastic and deterministic systems. Moreover, within the stochastic framework, Omega(t) is not unique. Nevertheless, each of these expressions for Omega(t) satisfies the FT.

Near-infrared optical imaging of tissue phantoms with measurement in the change of optical path lengths.

Using 2-D Monte Carlo simulations, we have demonstrated that values of delta < L > at varying delta t, T1 and T2 can contain significant information concerning the presence and location of a light absorbing volume in scattering media such as tissue. Specifically, we have illustrated that relationships exist between ZPW measured in x,y reflectance geometries and the absorber x,y,z position. These relationships are predictable yet can be expected to furthermore vary with (i) absorber z-dimensions, (ii) the optical properties of the surrounding media, and (iii) the source/detector separation, rho. In addition, while we have reported absorber positions located within 1 cm of tissue thickness for rho = 2 cm, One can expect interrogation of absorbers located at greater tissue thicknesses with greater rho 4. Most importantly, it is noteworthy that there exists greater opportunity to monitor specific population of photons in time-domain PMI than in frequency-domain PMI. Therefore, time-domain localization may be more sensitive than in the frequency-domain. From comparison to PMI, Figure 8 illustrates the values of delta I* computed from equation (1) versus absorber position for the same values T1 and T2 as in Figure 3. Upon inspection of Figures 3 and 8, one can see that it is easier to infer the relationship between the PSV and the absorber position from delta < L > than from delta I*. As a consequence, the measurement of delta < L > may enable creation of an inverse localization algorithm for photon migration imaging.(ABSTRACT TRUNCATED AT 250 WORDS)

Fluctuation theorems.

Fluctuation theorems, developed over the past 15 years, have resulted in fundamental breakthroughs in our understanding of how irreversibility emerges from reversible dynamics and have provided new statistical mechanical relationships for free-energy changes. They describe the statistical fluctuations in time-averaged properties of many-particle systems such as fluids driven to nonequilibrium states and provide some of the few analytical expressions that describe nonequilibrium states. Quantitative predictions on fluctuations in small systems that are monitored over short periods can also be made, and therefore the fluctuation theorems allow thermodynamic concepts to be extended to apply to finite systems. For this reason, we anticipate an important role for fluctuation theorems in the design of nanotechnological devices and in the understanding of biological processes. This review discusses these theorems, their physical significance, and results for experimental and model systems.

Compression of a polymer chain by a small obstacle: the effect of fluctuations on the escape transition.

We describe the escape transition of an ideal chain compressed between finite-sized obstacles. Three different theoretical methods are used and each provides a similar description of the escape transition, as predicted by earlier and less detailed mean-field theories. The first two methods show that thermal fluctuations near the transition can blur what was previously described as a sharp transition. The last method is an exact calculation of the partition function that shows unambiguously the character of the escape transition. This exact calculation overcomes the inherent uncertainties associated with previous theory and computer simulation.

Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales.

We experimentally demonstrate the fluctuation theorem, which predicts appreciable and measurable violations of the second law of thermodynamics for small systems over short time scales, by following the trajectory of a colloidal particle captured in an optical trap that is translated relative to surrounding water molecules. From each particle trajectory, we calculate the entropy production/consumption over the duration of the trajectory and determine the fraction of second law-defying trajectories. Our results show entropy consumption can occur over colloidal length and time scales.