Switching of Swimming Modes in Magnetospirillium gryphiswaldense

The microaerophilic magnetotactic bacterium Magnetospirillum gryphiswaldense swims along magnetic field lines using a single flagellum at each cell pole. It is believed that this magnetotactic behavior enables cells to seek optimal oxygen concentration with maximal efficiency. We analyze the trajectories of swimming M. gryphiswaldense cells in external magnetic fields larger than the earth’s field, and show that each cell can switch very rapidly (in <0.2 s) between a fast and a slow swimming mode. Close to a glass surface, a variety of trajectories were observed, from straight swimming that systematically deviates from field lines to various helices. A model in which fast (slow) swimming is solely due to the rotation of the trailing (leading) flagellum can account for these observations. We determined the magnetic moment of this bacterium using a to our knowledge new method, and obtained a value of (2.0 ± 0.6) × 10^?16 A · m². This value is found to be consistent with parameters emerging from quantitative fitting of trajectories to our model.     

Ultrashort echo imaging of cyclically loaded rabbit patellar tendon

Tendinopathy affects individuals who perform repetitive joint motion. Magnetic resonance imaging (MRI) is frequently used to qualitatively assess tendon health, but quantitative evaluation of inherent MRI properties of loaded tendon has been limited. This study evaluated the effect of cyclic loading on _T2^?${T_2}^{?}$ values of fresh and frozen rabbit patellar tendons using ultra short echo (UTE) MRI. Eight fresh and 8 frozen rabbit lower extremities had MR scans acquired for tendon _T2^?${T_2}^{?}$ evaluation. The tendons were then manually cyclically loaded for 100 cycles to 45 N at approximately 1 Hz. The MR scanning was repeated to reassess the _T2^?${T_2}^{?}$ values. Analyses were performed to detect differences of tendon _T2^?${T_2}^{?}$ values between fresh and frozen samples prior to and after loading, and to detect changes of tendon _T2^?${T_2}^{?}$ values between the unloaded and loaded configurations. No difference of _T2^?${T_2}^{?}$ was found between the fresh and frozen samples prior to or after loading, p=0.8 and p  =0.1, respectively. The tendons had significantly shorter _T2^?${T_2}^{?}$ values, p  =0.023, and reduced _T2^?${T_2}^{?}$ variability, p  =0.04, after cyclic loading. Histologic evaluation confirmed no induced tendon damage from loading. Shorter _T2^?${T_2}^{?}$, from stronger spin–spin interactions, may be attributed to greater tissue organization from uncrimping of collagen fibrils and lateral contraction of the tendon during loading. Cyclic tensile loading of tissue reduces patellar tendon _T2^?${T_2}^{?}$ values and may provide a quantitative metric to assess tissue organization.     

Generation of RNA pseudoknot structures with topological genus filtration

In this paper we present a sampling framework for RNA structures of fixed topological genus. We introduce a novel, linear time, uniform sampling algorithm for RNA structures of fixed topological genus g  , for arbitrary g>0$g>0$. Furthermore we develop a linear time sampling algorithm for RNA structures of fixed topological genus g   that are weighted by a simplified, loop-based energy functional. For this process the partition function of the energy functional has to be computed once, which has O(n²)$O(n^2)$ time complexity.     

Critical Behaviour in DOPC/DPPC/Cholesterol Mixtures: Static H NMR Line Shapes Near the Critical Point

Static ²H NMR spectroscopy is used to study the critical behavior of mixtures of 1,2-dioleoyl-phosphatidylcholine/1,2-dipalmitoyl-phosphatidylcholine (DPPC)/cholesterol in molar proportion 37.5:37.5:25 using either chain perdeuterated DPPC-d₆₂ or chain methyl deuterated DPPC-d₆. The temperature dependence of the first moment of the ²H spectrum of the sample made with DPPC-d₆₂ and of the quadrupolar splittings of the chain-methyl-labeled DPPC-d₆ sample are directly related to the temperature dependence of the critical order parameter η  , which scales as [(Tc−T)/Tc]^βc${\left[\left(T_c-T\right)/T_c\right]}^{{\beta }_c}$ near the critical temperature. Analysis of the data reveals that for the chain perdeuterated sample, the value of T_c is 301.51 ± 0.1 K, and that of the critical exponent, β_c = 0.391 ± 0.02. The line shape analysis of the methyl labeled (d₆) sample gives T_c = 303.74 ± 0.07 K and β_c = 0.338 ± 0.009. These values obtained for β_c are in good agreement with the predictions of a three-dimensional Ising model. The difference in critical temperature between the two samples having nominally the same molar composition arises because of the lowering of the phase transition temperature that occurs due to the perdeuteration of the DPPC.     

Ionic microenvironmental effects on triplex DNA stabilization: Cationic counterion effects on poly(dT)·poly(dA)·poly(dT)

The structure and conformation of nucleic acids are influenced by metal ions, polyamines, and the microenvironment. In poly(purine) · poly(pyrimidine) sequences, triplex DNA formation is facilitated by metal ions, polyamines and other ligands. We studied the effects of mono- and di-valent metal ions, and ammonium salts on the stability of triple- and double-stranded structures formed from poly(dA) and poly(dT) by measuring their respective melting temperatures. In the presence of metal ions, the absorbance versus temperature profile showed two transitions: T_m1 for triplex to duplex and single stranded DNA, and T_m2 for duplex DNA melting to single stranded DNA. Monovalent cations (Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺ and ₄NH⁺${{\text{NH}}_4}^{+}$) promoted triplex DNA at concentrations ≥150 mM. T_m1 varied from 49.8 °C in the presence of 150 mM Li⁺ to 30.6 °C in the presence of 150 mM K⁺. ₄NH⁺${{\text{NH}}_4}^{+}$ was very effective in stabilizing triplex DNA and its efficacy decreased with increasing substitution of the hydrogen atoms with methyl, ethyl, propyl and butyl groups. As in the case of monovalent cations, a concentration-dependent increase in T_m1 was observed with divalent ions and triplex DNA stabilization decreased in the order: Mg²⁺ > Ca²⁺ > Sr²⁺ > Ba²⁺. All positively charged cations increased the melting temperature of duplex DNA. Values of Δn (number of ions released) on triplex DNA melting were 0.46 ± 0.06 and 0.18 ± 0.02, respectively, for mono- and di-valent cations, as calculated from 1/T_m1 versus ln[M^+,2+] plots. The corresponding values for duplex DNA were 0.25 ± 0.02 and 0.12 ± 0.02, respectively, for mono- and di-valent cations. Circular dichroism spectroscopic studies showed distinct conformational changes in triplex DNA stabilized by alkali metal and ammonium ions. Our results might be useful in developing triplex forming oligonucleotide based gene silencing techniques.     

Fast Label-Free Cytoskeletal Network Imaging in Living Mammalian Cells

We present a full-field technique that allows label-free cytoskeletal network imaging inside living cells. This noninvasive technique allows monitoring of the cytoskeleton dynamics as well as interactions between the latter and organelles on any timescale. It is based on high-resolution quantitative phase imaging (modified Quadriwave lateral shearing interferometry) and can be directly implemented using any optical microscope without modification. We demonstrate the capability of our setup on fixed and living Chinese hamster ovary cells, showing the cytoskeleton dynamics in lamellipodia during protrusion and mitochondria displacement along the cytoskeletal network. In addition, using the quantitative function of the technique, along with simulation tools, we determined the refractive index of a single tubulin microtubule to be n_tubu=2.36±0.6$n_{tubu}=2.36\pm 0.6$ at λ=527$\lambda =527$ nm.     

Rectal,telemetry pill and tympanic membrane thermometry during exercise heat stress

We compared the accuracy of an ingestible telemetry pill method of core temperature (T_c) measurement and an infrared tympanic membrane thermometer to values from a rectal thermistor during exercise-induced heat stress. Ten well-trained subjects completed four exercise trials consisting of 40 min constant-load exercise at 63% of maximum work rate followed by a 16.1 km time trial at 30 °C and 70% relative humidity. Temperature at rest was not different between the three methods of T_c measurement (T_re: 37.2±0.3 °C; T_p: 37.2±0.2 °C; T_ty: 37.1±0.3 °C; P=0.40$P=0.40$). Temperature rose continuously during the exercise period (ΔT_re: 2.2±0.5 °C; ΔT_p: 2.2±0.5 °C; ΔT_ty: 1.9±0.5 ±°C and there were no differences between T_re and T_p measurements at any time throughout exercise (P=0.32$P=0.32$). While there were no differences between T_re and T_ty after 10 min (P=0.11$P=0.11$) and 20 min (P=0.06$P=0.06$) of exercise, T_ty was lower than T_re after 30 min of exercise (P<0.01$P<0.01$) and remained significantly lower throughout the remainder of the exercise period. These results demonstrate that the telemetry pill system provides a valid measurement of trunk temperature during rest and exercise-induced thermal strain. T_ty was significantly lower than T_re when temperature exceeded 37.5 °C. However, whether these differences are due to selective brain cooling or imperfections in the tympanic membrane thermometer methodology remains to be determined.     

Kinetics and Energetics of Biomolecular Folding and Binding

The ability of biomolecules to fold and to bind to other molecules is fundamental to virtually every living process. Advanced experimental techniques can now reveal how single biomolecules fold or bind against mechanical force, with the force serving as both the regulator and the probe of folding and binding transitions. Here, we present analytical expressions suitable for fitting the major experimental outputs from such experiments to enable their analysis and interpretation. The fit yields the key determinants of the folding and binding processes: the intrinsic on-rate and the location and height of the activation barrier.Dynamic processes in living cells are regulated through conformational changes in biomolecules—their folding into a particular shape or binding to selected partners. The ability of biomolecules to fold and to bind enables them to act as switches, assembly factors, pumps, or force- and displacement-generating motors (1). Folding and binding transitions are often hindered by a free energy barrier. Overcoming the barrier requires energy-demanding rearrangements such as displacing water from the sites of native contacts and breaking nonnative electrostatic contacts, as well as loss of configurational entropy. Once the barrier is crossed, the folded and bound states are stabilized by short-range interactions: hydrogen bonds, favorable hydrophobic effects, and electrostatic and van der Waals attractions (2).Mechanistic information about folding and binding processes is detailed in the folding and binding trajectories of individual molecules: observing an ensemble of molecules may obscure the inherent heterogeneity of these processes. Single-molecule trajectories can be induced, and monitored, by applying force to unfold/unbind a molecule and then relaxing the force until folding or binding is observed (3–5) (Fig. 1). Varying the force relaxation rate shifts the range of forces at which folding or binding occurs, thus broadening the explorable spectrum of molecular responses to force and revealing conformational changes that are otherwise too fast to detect. The measured force-dependent kinetics elucidates the role of force in physiological processes (6) and provides ways to control the timescales, and even the fate, of these processes. The force-dependent data also provides a route to understanding folding and binding in the absence of force—by extrapolating the data to zero force via a fit to a theory.Open in a separate windowFigure 1Schematic of the output from a force-relaxation experiment. The applied force is continuously relaxed from the initial value F₀ until the biomolecule folds or binds, as signified by a sharp increase in the measured force. From multiple repeats of this experiment, distributions of the folding or binding forces are collected (inset). Fitting the force distributions with the derived analytical expression yields the key parameters that determine the kinetics and energetics of folding or binding.In this letter, we derive an analytical expression for the distribution of transition forces, the major output of force-relaxation experiments that probe folding and binding processes. The expression extracts the key determinants of these processes: the on-rate and activation barrier in the absence of force. The theory is first developed in the context of biomolecular folding, and is then extended to cover the binding of a ligand tethered to a receptor. In contrast to unfolding and unbinding, the reverse processes of folding and binding require a theory that accounts for the compliance of the unfolded state, as well as the effect of the tether, to recover the true kinetic parameters of the biomolecule of interest.In a force-relaxation experiment, an unfolded biomolecule or unbound ligand-receptor complex is subject to a stretching force, which is decreased from the initial value F₀ as the pulling device approaches the sample at speed V until a folding or binding transition is observed (Fig. 1) (3–5). Define S(t) as the probability that the molecule has not yet escaped from the unfolded (implied: or unbound) state at time t. When escape is limited by one dominant barrier, S(t) follows the first-order rate equationS˙(t)≡dS(t)dt=−k←(F(t))S(t),where k_←(F(t)) is the on-rate at force F at time t. Because, prior to the transition, the applied force decreases monotonically with time, the distribution of transition forces, p(F), is related to S(t) through p(F)dF=S˙(t)dt, yieldingp(F)=−k←(F)F˙(F)e−∫F0Fk←(F′)F˙(F′)dF′.(1)Here F˙(F)≡dF(t)/dt<0 is the force relaxation rate. The proper normalization of p(F) is readily confirmed by integrating Eq. 1 from the initial force F₀ to negative infinity, the latter accounting for transitions that do not occur by the end of the experiment. Note that the expression for the distribution of folding/binding forces in Eq. 1 differs from its analog for the unfolding process (7) by the limits of integration and a negative sign, reflecting the property of a relaxation experiment to decrease the survival probability S(t) by decreasing the force. Converting the formal expression in Eq. 1 into a form suitable for fitting experimental data requires establishing functional forms for k_←(F) and F˙(F) and analytically solving the integral. These steps are accomplished below.The on-rate k_←(F) is computed by treating the conformational dynamics of the molecule as a random walk on the combined free energy profile G(x,t) = G₀(x) + G_pull(x,t) along the molecular extension x. Here G₀(x) is the intrinsic molecular potential and G_pull(x,t) is the potential of the pulling device. When G(x,t) features a high barrier on the scale of k_BT (k_B is the Boltzmann constant and T the temperature), the dynamics can be treated as diffusive. The unfolded region of the intrinsic potential for a folding process, unlike that for a barrierless process (8), can be captured by the functionG0(x)=ΔG‡ν1−ν(xx‡)11−ν−ΔG‡ν(xx‡),which has a sharp (if ν = 1/2, Fig. 2, inset) or smooth (if ν = 2/3) barrier of height ΔG^‡ and location x^‡. The potential of a pulling device of stiffness κ_S is G_pull(x,t) = κ_S/2(X₀ – Vt – x)² with an initial minimum at X₀ (corresponding to F₀). Applying Kramers formalism (9) to the combined potential G(x,t), we establish the analytical form of the on-rate at force F(t),k←(F)=k0(1+κSκU(F))1ν−12(1+νFx‡ΔG‡)1ν−1×eβΔG‡[1−(1+κSκU(F))2ν1−ν−1(1+νFx‡ΔG‡)1ν],where k₀ is the intrinsic on-rate, β ≡ (k_BT)⁻¹, andκU(F)=ν(1−ν)2ΔG‡x‡2(1+νFx‡ΔG‡)2−1νis the stiffness of the unfolded biomolecule under force F (see the Supporting Material for details on all derivations). The full nonlinear form of G_pull(x,t) was necessary in the derivation because, in contrast to the typically stiff folded state, the unfolded state may be soft (to be exact, 1/2κ_S x^‡2(F) << k_BT may not be satisfied) and thus easily deformed by the pulling device. Because of this deformation, the folding transition faces an extra contribution (regulated by the ratio κ_S/κ_U(F)) to the barrier height, typically negligible for unfolding, that decreases the on-rate in addition to the applied force F.Open in a separate windowFigure 2Contributions to the free energy profile for folding (inset) and binding (main figure). The derived expression (Eq. 2) extracts the on-rate and the location and height of the activation barrier to folding. When applied to binding data, the expression extracts the parameters of the ligand-tether-receptor (LTR) potential G˜0 (x); the proposed algorithm (Eqs. 3 and 4) removes the contribution of the tether potential G_teth(x) to recover the parameters of the intrinsic ligand-receptor (LR) potential G₀(x).The last piece required for Eq. 1, the loading rate F˙(F), is computed as the time derivative of the force F(t) on the unfolded molecule at its most probable extension at time t:F˙(F)=−κSV1+κS/κU(F).Finally, we realize that the integral in Eq. 1 can be solved analytically exactly, both for ν = 1/2 and ν = 2/3, resulting in the analytical expression for the distribution of folding forces:p(F)=k←(F)|F˙(F)|e−k←(F)β|F˙(F)|x‡(1+κSκU(F))νν−1(1+νFx‡ΔG‡)1−1ν.(2)Equation 2 can be readily applied to (normalized) histograms from force-relaxation experiments to extract the parameters of the intrinsic kinetics and energetics of folding. Being exact for ν = 1/2 and ν = 2/3, Eq. 2 is also an accurate approximation for any ν in the interval 1/2 < ν < 2/3 as long as κ_S ≲ κ_U (F) (see Fig. S1 in the Supporting Material). For simplicity, in Eq. 2 we have omitted the term containing F₀ as negligible if F₀ is large enough to prevent folding events.The solution in Eq. 2 reveals properties of the distribution of folding forces that distinguish it from its unfolding counterpart (7):

• 1.The distribution has a positive skew (Fig. 3), as intuitively expected: the rare folding events occur at high forces when the barrier is still high.Open in a separate windowFigure 3Force histograms from folding (left) and binding (right) simulations at several values of the force-relaxation speed (in nanometers per second, indicated at each histogram). Fitting the histograms with the analytical expression in Eq. 2 (lines) recovers the on-rate and activation barrier for folding or binding (2.Increasing the relaxation speed shifts the distribution to lower forces (Fig. 3): faster force relaxation leaves less time for thermal fluctuations to push the system over a high barrier, causing transitions to occur later (i.e., at lower forces), when the barrier is lower.
• 3.The stiffness κ_S and speed V enter Eq. 2 separately, providing independent routes to control the range of folding forces and thus enhance the robustness of a fit.

The application of the above framework to binding experiments on a ligand and receptor connected by a tether (3) involves an additional step—decoupling the effect of the tether—to reconstruct the parameters of ligand-receptor binding. Indeed, the parameters extracted from a fit of experimental histograms to Eq. 2 characterize the ligand-tether-receptor (LTR) potential (k˜0, x˜‡, ΔG˜‡, ν) (Fig. 2). The parameters of the natural ligand-receptor (LR) potential (k₀, x^‡, ΔG^‡) can be recovered using three characteristics of the tether: contour length L; persistence length p; and extension Δℓ of the tether along the direction of the force in the LTR transition state. The values of L and p can be determined from the force-extension curve of the tether (10); these define the tether potential G_teth(x) (Fig. 2). The value of Δℓ can be found from an unbinding experiment (7) on LTR and the geometry of the tether attachment points (see Fig. S3). Approximating the region of the LR potential between the transition and unbound states as harmonic, with no assumptions about the shape of the potential beyond x^‡, the ligand-receptor barrier parameters are thenx‡=α−1α−2x˜‡,ΔG‡=(α−1)22(α−2)x˜‡Fteth(Δℓ+x˜‡),(3)and the intrinsic unimolecular association rate isk0≈k˜0(βΔG‡)32(βΔG˜‡)1ν−12(x˜‡x‡)2eβ(ΔG˜‡−ΔG‡).(4)Here, the force value Fteth(Δℓ+x˜‡) is extracted from the force-extension curve of the tether at extension Δℓ+x˜‡ andα=2(ΔG˜‡−Gteth(Δℓ)+Gteth(Δℓ+x˜‡))x˜‡Fteth(Δℓ+x˜‡),where G_teth(x) is the wormlike-chain potential (see Eq. S13 in the Supporting Material). Equations 3–4 confirm that a tether decreases the height and width of the barrier (see Fig. 2), thus increasing the on-rate.In Fig. 3, the developed analytical framework is applied to folding and binding force histograms from Brownian dynamics simulations at parameters similar to those in the analogous experimental and computational studies (3,5,11) (for details on simulations and fitting procedure, see the Supporting Material). For the stringency of the test, the simulations account for the wormlike-chain nature of the molecular unfolded and LTR unbound states that is not explicitly accounted for in the theory. With optimized binning (12) of the histograms and a least-squares fit, Eqs. 2–4 recover the on-rate, the location and the height of the activation barrier, and the value of ν that best captures how the kinetics scale with force (

1.Multiple relaxation speeds,

2.Folding/binding events at low forces, and

3.A large number of events at each speed.

Table 1

On-rate and the location and height of the activation barrier from the fit of simulated data to the theory in Eq. 2

Quantifying Cell-to-Cell Variation in Power-Law Rheology

Among individual cells of the same source and type, the complex shear modulus G^∗$G^{\ast }$ exhibits a large log-normal distribution that is the result of spatial, temporal, and intrinsic variations. Such large distributions complicate the statistical evaluation of pharmacological treatments and the comparison of different cell states. However, little is known about the characteristic features of cell-to-cell variation. In this study, we investigated how this variation depends on the spatial location within the cell and on the actin filament cytoskeleton, the organization of which strongly influences cell mechanics. By mechanically probing fibroblasts arranged on a microarray, via atomic force microscopy, we observed that the standard deviation σ   of G^∗$G^{\ast }$ was significantly reduced among cells in which actin filaments were depolymerized. The parameter σ also exhibited a subcellular spatial dependence. Based on our findings regarding the frequency dependence of σ   of the storage modulus G^′$G^{\prime }$, we proposed two types of cell-to-cell variation in G^′$G^{\prime }$ that arise from the purely elastic and the frequency-dependent components in terms of the soft glassy rheology model of cell deformability. We concluded that the latter inherent cell-to-cell variation can be reduced greatly by disrupting actin networks, by probing at locations within the cell nucleus boundaries distant from the cell center, and by measuring at high loading frequencies.     

Study of the motion of magnetotactic bacteria

Motion of flagellate bacteria is considered from the point of view of rigid body mechanics. As a general case we consider a flagellate coccus magnetotactic bacterium swimming in a fluid in the presence of an external magnetic field. The proposed model generalizes previous approaches to the problem and allows one to access parameters of the motion that can be measured experimentally. The results suggest that the strong helical pattern observed in typical trajectories of magnetotactic bacteria can be a biological advantage complementary to magnetic orientation. In the particular case of zero magnetic interaction the model describes the motion of a non-magnetotactic coccus bacterium swimming in a fluid. Theoretical calculations based on experimental results are compared with the experimental track obtained by dark field optical microscopy. Correspondence to: H. G. P. Lins de Barros     

Analysis methods for two types of second-order thermal transients

Methods are developed to find rate constants, asymptotes, and first derivatives of proportional temperature change at time zero for second-order transients when rate of change in core temperature initially is retarded or accelerated. Methods are applied to data for cooling chicken eggs (initially retarded core dynamics) and cooling 1-day-old nestling House Wrens in broods under natural conditions (initially accelerated core dynamics). Asymptotes minus T_e are used to estimate an average net metabolic heat production rate of 0.016 W±0.0108 (S.D., n=10$n=10$) for 1-day-old House Wrens, a value similar to previous estimates using different methods.     

The Wall-stress Footprint of Blood Cells Flowing in Microvessels

It is well known that mechanotransduction of hemodynamic forces mediates cellular processes, particularly those that lead to vascular development and maintenance. Both the strength and space-time character of these forces have been shown to affect remodeling and morphogenesis. However, the role of blood cells in the process remains unclear. We investigate the possibility that in the smallest vessels blood’s cellular character of itself will lead to forces fundamentally different than the time-averaged forces usually considered, with fluctuations that may significantly exceed their mean values. This is quantitated through the use of a detailed simulation model of microvessel flow in two principal configurations: a diameter D=6.5$D=6.5$μ  m tube—a model for small capillaries through which red blood cells flow in single-file—and a D=12$D=12$μm tube—a model for a nascent vein or artery through which the cells flow in a confined yet chaotic fashion. Results in both cases show strong sensitivity to the mean flow speed U  . Peak stresses exceed their means by greater than a factor of 10 when U/D?10$U/D\mathrm{?}10$ s⁻¹, which corresponds to the inverse relaxation time of a healthy red blood cell. This effect is more significant for smaller D cases. At faster flow rates, including those more commonly observed under normal, nominally static physiological conditions, the peak fluctuations are more comparable with the mean shear stress. Implications for mechanotransduction of hemodynamic forces are discussed.