Reproductive biology of the horned viper,Cerastes cerastes gasperettii in the central region of Saudi Arabia

The reproductive biology of the horned viper, Cerastes cerastes gasperettii, in Riyadh region of Saudi Arabia was investigated over a period of one year. Study of reproductive cycle of male and female C. c. gasperettii revealed that the breeding season is relatively short (April and May). Thereafter females laid eggs by mid of July and hatching probably had taken place by the end of September. No activity was observed during winter, this may indicate just a single clutch per year. Relative testis weight to body weight was drastically increased (X¯ = 0.88%) during the peak of reproductive activity (May) where maximal expansion of seminiferous tubules was also attained during April and May (X¯ = 209 μm and 191 μm, respectively). Likewise, the ovarian activity was the highest during May where ovarian parameters were greater in terms of relative ovarian weight to body weight and ova diameter being 0.46% and 2.29 mm, respectively. Fat body weight was increased drastically just before the peak of reproductive activity then started to decline during June. It could be concluded that the harsh desert conditions and similar environments certainly affect reproductive activity of Saudi Arabian reptiles including snakes.     

A Comparison between Conductive and Infrared Devices for Measuring Mean Skin Temperature at Rest,during Exercise in the Heat,and Recovery

PurposeSkin temperature assessment has historically been undertaken with conductive devices affixed to the skin. With the development of technology, infrared devices are increasingly utilised in the measurement of skin temperature. Therefore, our purpose was to evaluate the agreement between four skin temperature devices at rest, during exercise in the heat, and recovery.MethodsMean skin temperature (T-sk) was assessed in thirty healthy males during 30 min rest (24.0 ± 1.2°C, 56 ± 8%), 30 min cycle in the heat (38.0 ± 0.5°C, 41 ± 2%), and 45 min recovery (24.0 ± 1.3°C, 56 ± 9%). T-sk was assessed at four sites using two conductive devices (thermistors, iButtons) and two infrared devices (infrared thermometer, infrared camera).ResultsBland–Altman plots demonstrated mean bias ± limits of agreement between the thermistors and iButtons as follows (rest, exercise, recovery): -0.01 ± 0.04, 0.26 ± 0.85, -0.37 ± 0.98°C; thermistors and infrared thermometer: 0.34 ± 0.44, -0.44 ± 1.23, -1.04 ± 1.75°C; thermistors and infrared camera (rest, recovery): 0.83 ± 0.77, 1.88 ± 1.87°C. Pairwise comparisons of T-sk found significant differences (p < 0.05) between thermistors and both infrared devices during resting conditions, and significant differences between the thermistors and all other devices tested during exercise in the heat and recovery.ConclusionsThese results indicate poor agreement between conductive and infrared devices at rest, during exercise in the heat, and subsequent recovery. Infrared devices may not be suitable for monitoring T-sk in the presence of, or following, metabolic and environmental induced heat stress.     

Ion Selectivity in the KcsA Potassium Channel from the Perspective of the Ion Binding Site

To understand the thermodynamic exclusion of Na⁺ relative to K⁺ from the S₂ site of the selectivity filter, the distribution P_X(ɛ) (X = K⁺ or Na⁺) of the binding energy (ɛ) of the ion with the channel is analyzed using the potential distribution theorem. By expressing the excess chemical potential of the ion as a sum of mean-field 〈ɛ〉 and fluctuation μ^ex_flux,X contributions, we find that selectivity arises from a higher value of μflux,Na+ex relative to μflux,K+ex. To understand the role of site-site interactions on μ^ex_flux,X, we decompose P_X(ɛ) into n-dependent distributions, where n is the number of ion-coordinating ligands within a distance λ from the ion. For λ comparable to typical ion-oxygen bond distances, investigations building on this multistate model reveal an inverse correlation between favorable ion-site and site-site interactions: the ion-coordination states that most influence the thermodynamics of the ion are also those for which the binding site is energetically less strained and vice versa. This correlation motivates understanding entropic effects in ion binding to the site and leads to the finding that μ^ex_flux,X is directly proportional to the average site-site interaction energy, a quantity that is sensitive to the chemical type of the ligand coordinating the ion. Increasing the coordination number around Na⁺ only partially accounts for the observed magnitude of selectivity; acknowledging the chemical type of the ion-coordinating ligand is essential.     

DNA,Flexibly Flexible

Investigators have constructed dsDNA molecules with several different base modifications and have characterized their bending and twisting flexibilities using atomic force microscopy, DNA ring closure, and single-molecule force spectroscopy with optical tweezers. The three methods provide persistence length measurements that agree semiquantitatively, and they show that the persistence length is surprisingly similar for all of the modified DNAs. The circular dichroism spectra of modified DNAs differ substantially. Simple explanations based on base stacking strength, polymer charge, or groove occupancy by functional groups cannot explain the results, which will guide further high-resolution theory and experiments.Real double-stranded DNA molecules differ from the idealized zero-Kelvin A, B, and Z forms. They can adopt deformed average conformations, as in bent A-tract DNA or protein-DNA complexes. The path of the DNA helix axis also varies due to thermal energy, so at very long lengths DNA behaves as a random coil. The term “long lengths” is relative to the persistence length P of the wormlike chain model. P is the average offset of the end of a chain along its initial direction, or alternatively the length over which the unit vectors μ1→ and μ2→ tangent to the helix axis lose colinearity according to〈μ1→⋅μ2→〉=〈cosθ〉=e−d12/P,where d₁₂ is the contour length from point 1 to point 2, as in Fig. 1. P can be measured by hydrodynamics (1), atomic force microscopy (AFM) (2), DNA ring closure (3) or protein-DNA looping (4), tethered particle microscopy (5), or single-molecule optical tweezers experiments (6). The long-range loss of memory of DNA direction grows out of local variations in the helix axis direction specified by roll, tilt, and twist angles that parameterize changes in the helix axis direction. For harmonic bending potentials, the bending persistence length is related to roll and tilt according toσroll2+σtilt2=2ℓ/P,where ℓ = 3.4 Å, so for P ∼ 50 nm (147 bp) the average standard deviations in the roll and tilt angles σ_roll and σ_tilt are ∼4.7°, although in real DNA, roll varies more than tilt. Similar relationships hold for twist flexibility (7).Open in a separate windowFigure 1The base modifications studied by Peters et al. (13,14) affect both Watson-Crick hydrogen bonding and groove occupancy. They used AFM, DNA ring closure, single-molecule force spectroscopy, and circular dichroism spectroscopy (not shown) to characterize the resulting changes in bending and twisting flexibility. DNA molecules are not shown to scale. To see this figure in color, go online.DNA flexibility can be studied at contour length scales from Ångstroms to microns. Flexibility at the atomic scale accessed by nuclear magnetic resonance, x-ray crystallography, cryo-electron microscopy, and molecular dynamics simulations (8) refers to many aspects of conformational variability. One active thread of research at this scale concerns interconversion among helical forms, base flipping, DNA kinking, changes in backbone torsion angles, and the sequence dependence of all of these local properties. Local fluctuations in the basepair roll, tilt, and twist angles do seem to predict the correct long-range behavior (9). A second thread asks whether the wormlike chain model holds at DNA lengths shorter than P (2,10); the active controversy concerning enhanced bendability at short lengths has recently been reviewed by Vologodskii and Frank-Kamenetskii (11). A third thread asks whether we can understand the underlying biophysical causes of long-range DNA flexibility. These presumably include base stacking, electrostatic repulsion along the backbone, changes in the counterion atmosphere (12), occupancy of the major and minor grooves by functional groups, conformational entropy, the strength of Watson-Crick hydrogen bonding, and water structure. Helical polymorphisms and the junctions between polymorphs presumably affect the sequence dependence of the persistence length.Peters et al. (13,14) have attempted to understand bending and twisting flexibility by characterizing a variety of modified nucleic acids using DNA ring closure, AFM, and optical tweezer methods, sketched in Fig. 1. In previous work (13), they used ring closure to show that major groove substituents that alter the charge on the polymer do not have substantial effects on the bending persistence length, and that the effects were not correlated in an obvious way to the stacking propensity of the modified bases. The work described in this issue of the Biophysical Journal (14) uses all three methods to demonstrate that DNA with 2-amino-adenosine (a.k.a., 2,6-diaminopurine) substituted for adenosine has an increased persistence length, whereas inosine substitution for guanosine reduces the persistence length, as would be expected if groove occupancy (or the number of Watson-Crick hydrogen bonds) affects flexibility. However, the authors did one experiment too many—when they measured the effects of the earlier major groove substituents (13) using AFM, the correlation with groove occupancy disappeared. This could be because changes in helical geometry, as evidenced by the circular dichroism spectroscopy also reported in the article, alter the grooves sufficiently to prevent a straightforward connection to flexibility.The magnitude of the effect of base modifications on P is the largest for the optical tweezers and the smallest for DNA ring closure, showing that no more than one of the experiments is perfect. The Supporting Material for both articles (13,14) offers valuable resources for the careful evaluation of experimental results and possible sources of error within and between experiments. For example, the DNA lengths and the ionic conditions required by the different methods differ. Ring closure results depend critically on the purity of the DNA and appropriate ligation conditions. Analysis of AFM results averaged several different statistical measures of decaying angular correlations and end-to-end distance, which did not individually always agree. In force spectroscopy there are variations in the bead attachment for each molecule, errors in the stretch modulus can affect the measured persistence length, force can induce DNA melting, and very few molecules can be observed. Rare kinking events proposed to explain enhanced bendability should affect the cyclization experiment most markedly; no evidence for enhanced flexibility was seen. Finally, Peters et al. (14) have observed that DNA twist and twisting flexibility seem to be more sensitive than the persistence length to base modifications.Taken as a whole, this extremely thorough series of experiments shows that we still do not understand the fundamental origins of the remarkable stiffness of double-stranded DNA. There may be compensating effects that make the dissection difficult. For example, changing the charge on the polymer may induce a corresponding adjustment in the counterion condensation atmosphere, leading to a relatively constant residual charge. Groove substituents that enhance basepair stability could enhance bendability for steric reasons. Stacking thermodynamics may not change very much for the very small bend angles at any individual basepair. Locally stiff regions may introduce nearby junctions that are flexible.The stiffness of DNA relative to other biopolymers inspired the development of DNA nanotechnology (although that field has adopted bridged synthetic constructs that are even more rigid). Further research on the biophysics, and specifically the long-range mechanical properties of DNA, will be essential as we build better models of DNA in the cell, which has evolved many proteins that act to increase apparent flexibility. The various aspects of DNA flexibility influence the protein-DNA complexes that mediate DNA’s informational role, the induction of and responses to supercoiling used for long-range communication among sites (15), and chromosome structure and genome organization.     

Type-3 BRET,an Improved Competition-Based Bioluminescence Resonance Energy Transfer Assay

The heart adjusts its power output to meet specific physiological needs through the coordination of several mechanisms, including force-induced changes in contractility of the molecular motor, the β-cardiac myosin (βCM). Despite its importance in driving and regulating cardiac power output, the effect of force on the contractility of a single βCM has not been measured. Using single molecule optical-trapping techniques, we found that βCM has a two-step working stroke. Forces that resist the power stroke slow the myosin-driven contraction by slowing the rate of ADP release, which is the kinetic step that limits fiber shortening. The kinetic properties of βCM are affected by load, suggesting that the properties of myosin contribute to the force-velocity relationship in intact muscle and play an important role in the regulation of cardiac power output.The cardiac cycle is a tightly regulated process in which the heart generates power during systole and relaxes during diastole. Appropriate power must be generated to effectively pump blood against cardiac afterload. Dysfunction of this cycle has devastating consequences for affected individuals.Cardiac power output is regulated by several feedback mechanisms (e.g., neuronal, hormonal, mechanical) that ultimately lead to changes in the force and power output of the molecular motor, β-cardiac myosin (βCM). In isolated cardiac fibers and cardiomyocytes, loading the muscle during systole slows contraction and alters power output. It is widely believed that this slowing is partially due to force-induced inhibition of myosin ATPase kinetics, similar to the Fenn Effect in skeletal muscle. However, this hypothesis has not been directly tested at the molecular level. Much of our contemporary view of how power is generated in cardiac muscle is due to in vivo and isolated muscle-fiber studies (1). Substantial progress has been made in understanding the actomyosin interactions required for power generation, but resolving the molecular effects of mechanical load on the ATPase properties of βCM in intact muscle has been challenging. Nevertheless, determining the biophysical parameters that define βCM contractility is key to understanding cardiac regulation and the etiology of several muscle diseases (1).In vitro assays using isolated contractile proteins have been central to advancing our understanding of contractility, although most experiments have been conducted at low resisting loads that do not mimic working conditions. Elegant optical trapping experiments have imposed loads on small ensembles of murine α-cardiac myosin at subsaturating [ATP] (2), and these experiments suggest that force slows α-cardiac myosin kinetics. The kinetic properties of α-cardiac myosin are substantially different from βCM, the primary isoform in the adult human myocardium (3). Thus, experiments using βCM must be performed to determine the unitary force-dependent kinetic parameters of this key molecular motor. We used optical trapping to measure the working-stroke displacement and force dependence of actin-detachment kinetics of single porcine βCM molecules at saturating ATP concentrations. These experiments allow direct measurement of the force-velocity relationship for single βCM molecules and reveal the mechanism of how loads regulate βCM-driven power output.Using the three-bead geometry (4) in which an actin filament is strung between two optically-trapped beads and then lowered over a bead that is sparsely coated with purified full-length porcine ventricular βCM, interactions between single βCM molecules and actin were recorded at 10 μM ATP (Fig. 1 A) (5, 6). Ensemble averages of these interactions were constructed to determine the size and kinetics of the working stroke (7, 8). βCM has an average displacement (6.8 ± 0.04 nm) that is similar to previously characterized muscle myosins (9, 10). Similar to skeletal muscle myosin (10), ensemble averages clearly show that the βCM working stroke is composed of two substeps with average displacements of 4.7 ± 0.05 nm and 1.9 ± 0.05 nm (Fig. 1 B). A single exponential function was fit to the rising-phase of the time-forward ensemble averages, yielding a rate (74 ± 2 s⁻¹) for the transition from state 1 to state 2 (Fig. 1 C). This rate is similar to the biochemical rate of ADP release measured for βCM (64 s⁻¹) (3), indicating that this structural transition is associated with the release of ADP. The rate of the rising phase of the time-reversed ensemble averages (22 ± 0.7 s⁻¹) reports the rate of exit from state 2 and is consistent with the biochemical rate of ATP binding and actomyosin detachment at 10 μM ATP (16 s⁻¹) (3) (Fig. 1 C).Open in a separate windowFigure 1(A) Representative data trace showing actomyosin displacements generated by βCM at 10 μM ATP. (Blue lines) Individual binding events. (B) Ensemble averages of the βCM working stroke generated from averaging 1295 binding interactions collected at 10 μM ATP. Single exponential functions were fit to the data (red lines) and the reported errors are the standard errors from the fit. (C) Cartoon showing an idealized actomyosin interaction with the corresponding mechanical and biochemical states. To see this figure in color, go online.To examine actomyosin detachment kinetics under working conditions, a positional feedback optical clamp was used to apply a dynamic load to the myosin, keeping the myosin at an isometric position during its working stroke (11). We measured the effect of force on the actin-attachment duration at 4 mM Mg.ATP to ensure that the rate of ATP binding is not rate-limiting for detachment. Increases in attachment durations are observed as the force on the myosin is increased (Fig. 2 A, inset). Assuming a two-state model (12), we expect the attachment durations to be exponentially distributed at each force with the force-dependent actin detachment rate, k(F), given by (13)k(F)=k0∗e−F·ddetkB∗T,(1)where k₀ is the rate of the primary force-sensitive transition in the absence of force, F is the force on the myosin, d_det is the distance to the transition state (a measurement of force sensitivity), k_B is Boltzmann’s constant, and T is the temperature. Maximum likelihood estimation (MLE) fitting Eq. 1 to the data yields a detachment rate (k₀ = 71 (−1.0/+0.8 s⁻¹)) that is similar to the rate of ADP release measured for βCM (64 s⁻¹) (3) and the rate of the time-forward ensemble averages (74 ± 2 s⁻¹). Thus, the ADP release step (and the accompanying state-1 to state-2 mechanical transition) is force-sensitive (d_det = 0.97 (−0.014/+0.011) nm). The value of d_det indicates that the ADP release step slows with increasing force, but less than some other characterized myosins (14). Using the values determined from the MLE fitting and the measured size of the working stroke, it is possible to calculate a force-velocity relationship for βCM, assuming the rate of ADP release limits actin motility (Fig. 2 A).Open in a separate windowFigure 2(A, Inset) Single molecule actomyosin interactions were collected in the presence of the isometric optical clamp. The scatter plot shows 262 binding events. Attachment durations are exponentially distributed at each force. (A) The detachment rate as a function of force as determined by MLE fitting. (Black line) Best fit; (small gray shaded area) 95% confidence interval. (Right axis) Velocity, calculated by multiplying the displacement of the working stroke by the detachment rate. (B) The calculated mean detachment rate as a function of force. Attachment durations were binned according to the average force experienced by the myosin during the binding event. Error bars were calculated via bootstrapping simulations of each force bin. (Blue line) Expected mean detachment rate based on the MLE fitting and the limited temporal resolution of our experiment (see the Supporting Material for details). (C) Proposed model for how force slows shortening velocity. Force inhibits the mechanical transition associated with ADP release, slowing the rate of actomyosin detachment. To see this figure in color, go online.The MLE fitting of Eq. 1 assumes an exponential distribution of attachment durations at every force. As such, the MLE fitting of the raw data should yield correct values of the parameters k₀ and d_det, despite limitations of the temporal resolution of our experiment (see Supporting Material for detailed discussion of MLE fitting). Frequently, groups report the mean attachment duration as a function of force. However, the mean attachment duration at each force will be overestimated because some shorter binding events cannot be resolved. We provide a method for calculating the expected mean detachment rate based on the parameters determined from the MLE fitting, given the limited temporal resolution of the experiment, and verify the robustness of the MLE fitting (see the Supporting Material). For demonstration purposes only, Fig. 2 B shows that the measured mean detachment rate agrees well with the expected mean detachment rate based on the MLE fitting and the temporal resolution of the experiment. It should be emphasized that the relevant dissociation values are obtained from the MLE fitting in Fig. 2 A (see also Figs. S1–S3).Our data demonstrate that at saturating [ATP], the detachment rate is limited by the ADP release step, which is the same transition that limits fiber shortening velocity (15). We propose that resisting loads slow ADP release and actin detachment by slowing the mechanical transition that accompanies ADP release (Fig. 2 C), thereby reducing the shortening velocity of muscle fibers. Thus, our data demonstrate that the intrinsic force-dependent properties of βCM contribute to the force-velocity relationship in the heart. It is important to note that our proposed mechanism does not rule out additional mechanisms by which force could directly modulate the activity of actomyosin such as force-induced reversal of the power stroke (11) or population of branched pathways (16, 17).Are the loads in our experiments physiologically relevant to contracting muscle? Modeling of the force per cross-bridge generated in isometric soleus muscle, which contains the βCM isoform, suggests a load of 2–4 pN per myosin (18). At these loads, we expect actin-detachment to slow up to threefold. Interestingly, βCM is substantially less force-sensitive than smooth muscle myosin (d_det = 2.7), suggesting that βCM can generate more power (the product of force and velocity) under load.In conclusion, our data show that cardiac power output can be directly modulated by force at the level of single myosin molecules. These data will enable the comparison of how molecular changes, such as light-chain phosphorylation, pharmacological treatments, or mutations associated with cardiomyopathies, affect the ability of the myosin to generate power against the afterload.     

Performance Metrics for Liquid Chromatography-Tandem Mass Spectrometry Systems in Proteomics Analyses

A major unmet need in LC-MS/MS-based proteomics analyses is a set of tools for quantitative assessment of system performance and evaluation of technical variability. Here we describe 46 system performance metrics for monitoring chromatographic performance, electrospray source stability, MS1 and MS2 signals, dynamic sampling of ions for MS/MS, and peptide identification. Applied to data sets from replicate LC-MS/MS analyses, these metrics displayed consistent, reasonable responses to controlled perturbations. The metrics typically displayed variations less than 10% and thus can reveal even subtle differences in performance of system components. Analyses of data from interlaboratory studies conducted under a common standard operating procedure identified outlier data and provided clues to specific causes. Moreover, interlaboratory variation reflected by the metrics indicates which system components vary the most between laboratories. Application of these metrics enables rational, quantitative quality assessment for proteomics and other LC-MS/MS analytical applications.LC-MS/MS provides the most widely used technology platform for proteomics analyses of purified proteins, simple mixtures, and complex proteomes. In a typical analysis, protein mixtures are proteolytically digested, the peptide digest is fractionated, and the resulting peptide fractions then are analyzed by LC-MS/MS (1, 2). Database searches of the MS/MS spectra yield peptide identifications and, by inference and assembly, protein identifications. Depending on protein sample load and the extent of peptide fractionation used, LC-MS/MS analytical systems can generate from hundreds to thousands of peptide and protein identifications (3). Many variations of LC-MS/MS analytical platforms have been described, and the performance of these systems is influenced by a number of experimental design factors (4).Comparison of data sets obtained by LC-MS/MS analyses provides a means to evaluate the proteomic basis for biologically significant states or phenotypes. For example, data-dependent LC-MS/MS analyses of tumor and normal tissues enabled unbiased discovery of proteins whose expression is enhanced in cancer (5–7). Comparison of data-dependent LC-MS/MS data sets from phosphotyrosine peptides in drug-responsive and -resistant cell lines identified differentially regulated phosphoprotein signaling networks (8, 9). Similarly, activity-based probes and data-dependent LC-MS/MS analysis were used to identify differentially regulated enzymes in normal and tumor tissues (10). All of these approaches assume that the observed differences reflect differences in the proteomic composition of the samples analyzed rather than analytical system variability. The validity of this assumption is difficult to assess because of a lack of objective criteria to assess analytical system performance.The problem of variability poses three practical questions for analysts using LC-MS/MS proteomics platforms. First, is the analytical system performing optimally for the reproducible analysis of complex proteomes? Second, can the sources of suboptimal performance and variability be identified, and can the impact of changes or improvements be evaluated? Third, can system performance metrics provide documentation to support the assessment of proteomic differences between biologically interesting samples?Currently, the most commonly used measure of variability in LC-MS/MS proteomics analyses is the number of confident peptide identifications (11–13). Although consistency in numbers of identifications may indicate repeatability, the numbers do not indicate whether system performance is optimal or which components require optimization. One well characterized source of variability in peptide identifications is the automated sampling of peptide ion signals for acquisition of MS/MS spectra by instrument control software, which results in stochastic sampling of lower abundance peptides (14). Variability certainly also arises from sample preparation methods (e.g. protein extraction and digestion). A largely unexplored source of variability is the performance of the core LC-MS/MS analytical system, which includes the LC system, the MS instrument, and system software. The configuration, tuning, and operation of these system components govern sample injection, chromatography, electrospray ionization, MS signal detection, and sampling for MS/MS analysis. These characteristics all are subject to manipulation by the operator and thus provide means to optimize system performance.Here we describe the development of 46 metrics for evaluating the performance of LC-MS/MS system components. We have implemented a freely available software pipeline that generates these metrics directly from LC-MS/MS data files. We demonstrate their use in characterizing sources of variability in proteomics platforms, both for replicate analyses on a single instrument and in the context of large interlaboratory studies conducted by the National Cancer Institute-supported Clinical Proteomic Technology Assessment for Cancer (CPTAC)1 Network.     

Cluster size distribution of cells disseminating from a primary tumor

The first stage of the metastatic cascade often involves motile cells emerging from a primary tumor either as single cells or as clusters. These cells enter the circulation, transit to other parts of the body and finally are responsible for growth of secondary tumors in distant organs. The mode of dissemination is believed to depend on the EMT nature (epithelial, hybrid or mesenchymal) of the cells. Here, we calculate the cluster size distribution of these migrating cells, using a mechanistic computational model, in presence of different degree of EMT-ness of the cells; EMT is treated as given rise to changes in their active motile forces (μ) and cell-medium surface tension (Γ). We find that, for (μ > μ_min, Γ > 1), when the cells are hybrid in nature, the mean cluster size, N¯∼Γ2.0/μ2.8, where μ_min increases with increase in Γ. For Γ ≤ 0, N¯=1, the cells behave as completely mesenchymal. In presence of spectrum of hybrid states with different degree of EMT-ness (motility) in primary tumor, the cells which are relatively more mesenchymal (higher μ) in nature, form larger clusters, whereas the smaller clusters are relatively more epithelial (lower μ). Moreover, the heterogeneity in μ is comparatively higher for smaller clusters with respect to that for larger clusters. We also observe that more extended cell shapes promote the formation of smaller clusters. Overall, this study establishes a framework which connects the nature and size of migrating clusters disseminating from a primary tumor with the phenotypic composition of the tumor, and can lead to the better understanding of metastasis.     

Indolicidin Binding Induces Thinning of a Lipid Bilayer

We use all-atom molecular dynamics simulations on a massive scale to compute the standard binding free energy of the 13-residue antimicrobial peptide indolicidin to a lipid bilayer. The analysis of statistical convergence reveals systematic sampling errors that correlate with reorganization of the bilayer on the microsecond timescale and persist throughout a total of 1.4 ms of sampling. Consistent with experimental observations, indolicidin induces membrane thinning, although the simulations significantly overestimate the lipophilicity of the peptide.Antimicrobial peptides are a component of the innate immune system of eukaryotes (1). As such, they must interact with pathogenic membranes, either during translocation or by disrupting their structural integrity (2). Here we examine the binding of the 13-residue cationic antimicrobial peptide indolicidin (3) (ILPWKWPWWPWRR-NH₂) to a lipid membrane as a first step towards elucidating its mechanism of action.Molecular solutes interact with lipid membranes in many cellular processes (4). Computational approaches such as molecular dynamics simulations have been widely used to characterize these interactions (5). However, molecular dynamics simulations can require unfeasibly long times to reach equilibrium (6). Therefore, it is common to compute equilibrium properties of solute insertion into lipid bilayers using umbrella sampling (7) simulations in which the solute is restrained along the bilayer normal using harmonic restraining potentials, or umbrellas, centered at zi0 values distributed between bulk water and the bilayer center.It is often assumed that equilibrium properties rapidly attain convergence in umbrella sampling simulations; accordingly, convergence measures are rarely published (8). However, we have recently shown that umbrella sampling simulations require up to 100 ns per umbrella (3 μs in total) to eliminate systematic sampling errors in the standard free energy of binding, ΔGbind0, of an arginine side-chain analog from bulk water to a lipid bilayer (8). The fact that umbrella sampling has been used to investigate the bilayer insertion of substantially larger solutes (9) motivates a systematic evaluation of statistical sampling convergence of ΔGbind0 for indolicidin in a lipid bilayer.To estimate ΔGbind0 of indolicidin to a lipid bilayer, we conducted 60 sets of umbrella-sampling simulations while systematically varying the initial conformation. In each umbrella sampling simulation, each umbrella was simulated for 1.5 μs, yielding a total simulation time of 1.4 ms and 60 independent free energy or potential of mean force (PMF) profiles from bulk water to the center of a POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine) lipid bilayer.The PMF profiles indicate that indolicidin strongly binds to the bilayer, partitioning inside the lipid headgroups (Fig. 1, A and E). Importantly, the mean estimate of ΔGbind0 decays exponentially with equilibration time t_eq, indicating that systematic sampling errors in individual simulations continued to decrease throughout the 1.5-μs interval as rare events led to more favorable states (Fig. 1 B). The low frequency of transitions to more favorable states exacerbates the requirement for massive sampling using multiple independent simulations.Open in a separate windowFigure 1PMF for indolicidin partitioning into a POPC bilayer. (A) Average PMF from 60 independent umbrella-sampling simulations based on 1 < t ≤ 1.5 μs/umbrella. (B) Average ΔGbind0 from 50-ns time intervals per umbrella (t_eq < t ≤ t_eq+50 ns) as a function of equilibration time, t_eq. (Solid line) Single exponential fit to the mean over 0.5 < t_eq ≤ 1.5 μs. (C) Mean values of ΔGbind0 from the 10-μs/umbrella simulations (crosses) together with the mean values of ΔGbind0 (triangles) and exponential fit from panel B. PMF and ΔGbind0 profiles obtained from each of the 60 independent simulations are shown in Fig. S1 in the Supporting Material. (D–F) Representative conformations after 1.5 μs of simulation at zi0 = (D) 3 nm, (E) 1.2 nm, and (F) 0.0 nm. To see this figure in color, go online.Computational limitations precluded extending all 60 sets of umbrella-sampling simulations to even longer times. Instead, we identified the two simulations at each umbrella that appeared to be most representative of equilibrium and extended each to 10 μs per umbrella (see Methods in the Supporting Material). The resulting estimates of ΔGbind0 continued to decrease until t_eq = 4 μs (68 μs in total), after which they stabilized at the asymptotic limit of the exponential fit of the shorter simulation data (ΔGbind0 = −26 ± 5 kcal/mol; Fig. 1 C).As indolicidin approaches the bilayer, it is drawn closer (Fig. 2 A) as salt bridges form between the peptide and the phospholipid headgroups (Fig. 2 B), inducing their protrusion (Figs. 1 D and ​and22 C). At large separation distances, this state is attained only when the peptide becomes highly extended (Fig. 2, D and E). As indolicidin is inserted more deeply, the surface of the lipid bilayer invaginates (Figs. 1 E and ​and22 C), maintaining peptide-lipid salt bridges (Fig. 2 B) and leading to the formation of a pore when the solute is near the bilayer center (Figs. 1 F and ​and22 C, and see Fig. S2, Fig. S3, Fig. S4, and Fig. S5 in the Supporting Material). These Boltzmann-weighted ensemble averages may not be mechanistically representative of nonequilibrium binding events (8,10).Open in a separate windowFigure 2Slow equilibration of bilayer and peptide. (A–D) Color quantifies conformational reorganization for t_eq < t ≤ t_eq + 100 ns as a function of t_eq and |zi0|. (A) Deviation of insertion depth, z, from zi0, Δz ≡ z − zi0; (B) number of peptide-lipid salt bridges, N_SB; (C) volume change of the bilayer’s proximal leaflet in the radial vicinity of the solute, V_ε; and (D) peptide end-to-end distance (EED). There is no sampling for t > 0.5 μs at |zi0| ≥ 4.5 nm. (E) Representative time-series of a trajectory at zi0 = 3.9 nm. (F) Representative conformation at 10 μs for |zi0| = 1.2 nm. To see this figure in color, go online.The reorganization of the peptide, the bilayer, and the ionic interactions between them became more pronounced with increasing simulation time at peptide insertion depths shallower than the global free energy minimum (|zi0| >1.4 nm; Fig. 1 A and Fig. 2, B–D). These conformational transitions are likely the source of the systematic drift of ΔGbind0. Reorganization of the bilayer also controls the rate of equilibration during membrane insertion of an arginine side chain (8,9) and a cyclic arginine nonamer (11), suggesting that slow reorganization of lipids around cationic solutes presents a general impediment to simulation convergence.Consistent with the perturbation of membrane thickness observed by in situ atomic force microscopy (12), our results suggest that indolicidin insertion induces local thinning of the bilayer (Fig. 1, E and F, and Fig. 2, C and F). The different conformational ensembles sampled by the peptide in water and in the lipid bilayer (Fig. 2 D) are consistent with the observations that indolicidin is disordered in solution (13) and adopts stable conformations in the presence of detergent (14). Although the peptide’s conformation continued to change when it was deeply inserted (Fig. 2 D), the amount of water in the bilayer’s hydrophobic core converged relatively rapidly (see Fig. S2). Indolicidin can induce the formation of hydrated, porelike defects (see Fig. S2, Fig. S3, Fig. S4, and Fig. S5) but does not act as a chloride carrier (see Fig. S6 and Fig. S7). Future studies of the mechanism of indolicidin action will examine the effect of multiple peptide binding.The PMF profile presented in this Letter is strikingly different from that computed by Yeh et al. (15) using different force field parameters for indolicidin partitioning into a DMPC (1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine) bilayer, from which the binding free energy was estimated to be 0 kcal/mol (15). However, that study comprised only 25 ns per umbrella and likely suffers from systematic sampling errors induced by initial conditions (see Fig. S8).Our estimate of the binding affinity is much larger than the values obtained for indolicidin and large unilamellar POPC vesicles using isothermal titration calorimetry, −7.4 kcal/mol (16), and equilibrium dialysis, −8.8 kcal/mol (13). Such a discrepancy suggests that the relative accuracy of binding free energies for amino-acid side-chain analogs (8,9,17) does not necessarily extend to polypeptides. Although more work is needed to elucidate the source of this discrepancy, this study underlines the importance of attaining convergence before evaluating force-field accuracy.Importantly, this work also highlights the extensive sampling required to remove systematic errors induced by initial conditions in atomistic simulations of peptides in membranes. Slow equilibration of the system is due to rare transitions across hidden free energy barriers involving reorganization of the membrane. Two simple recommendations are 1), evaluating the time-dependence of ensemble averages, and 2), conducting multiple simulations with different initial conditions. We have recently shown that by using enhanced sampling techniques it is possible to identify the locations of hidden free energy barriers without a priori knowledge (9). Future research will examine strategies for speeding up the crossing of these barriers, such as optimized order parameters including bilayer reorganization and enhanced sampling techniques including a random walk along the order parameter (9).     

A Microscopic Multiphase Diffusion Model of Viable Epidermis Permeability

A microscopic model of passive transverse mass transport of small solutes in the viable epidermal layer of human skin is formulated on the basis of a hexagonal array of cells (i.e., keratinocytes) bounded by 4-nm-thick, anisotropic lipid bilayers and separated by 1-μm layers of extracellular fluid. Gap junctions and tight junctions with adjustable permeabilities are included to modulate the transport of solutes with low membrane permeabilities. Two keratinocyte aspect ratios are considered to represent basal and spinous cells (longer) and granular cells (more flattened). The diffusion problem is solved in a unit cell using a coordinate system conforming to the hexagonal cross section, and an efficient two-dimensional treatment is applied to describe transport in both the cell membranes and intercellular spaces, given their thinness. Results are presented in terms of an effective diffusion coefficient, D¯epi, and partition coefficient, K¯epi/w, for a homogenized representation of the microtransport problem. Representative calculations are carried out for three small solutes—water, L-glucose, and hydrocortisone—covering a wide range of membrane permeability. The effective transport parameters and their microscopic interpretation can be employed within the context of existing three-layer models of skin transport to provide more realistic estimates of the epidermal concentrations of topically applied solutes.     

Higher ventilatory responses during and after passive walking-like leg movement in older individuals

Background

Minute ventilation (V·E) during walking has been shown to be higher in older individuals than in young individuals, but the mechanisms underlying the higher ventilatory response is unclear. Central command and peripheral neural reflex are important neural control mechanisms underlying ventilatory response during exercise. Passive leg movement has been used to exclude the influence of central command due to the lack of voluntary activation of muscles. The aim of the present study was to compare the ventilatory response during and after passive walking-like leg movement (PWM) in young and older individuals.

Methods

Eight young subjects (20 ± 2 years) and seven older subjects (70 ± 1 years) participated in this study. Subjects spent 7 minutes in a quiet standing (QS) position. Thereafter, they performed 14-minute rhythmic PWM at 1 Hz and this was followed by 7 minutes of QS.

Results

V·E values during pre-PWM QS were calculated as 1-minute averages using data obtained between 5 and 6 minutes. V·E values at pre-PWM QS in the young and older groups were 8.4 ± 2.1 and 7.5 ± 1.2 l/minute, respectively. V·E values increased significantly at the first minute of PWM to 11.4 ± 2.2 and 10.4 ± 2.5 l/minute in the young and older groups, respectively (P <0.001). In the young group, V·E at the last minute of PWM (9.2 ± 2.0 l/minute) was not significantly different from that at pre-PWM QS due to a decline in V·E, whereas V·E at the last minute of PWM in the older group (9.4 ± 2.2 l/minute) was still significantly higher (P <0.01). On the other hand, V·E at the first minute of post-PWM QS (7.2 ± 1.8 l/minute) was significantly lower than that during pre-PWM QS in the young group (P <0.05) but not in the older group.

Conclusions

Ventilatory response during and after PWM is higher in older individuals than in young individuals. This may be associated with a mechanism(s) other than central command. Our findings may explain part of the higher V·E response while walking in older individuals.     

Evaluation of enzyme-linked immunosorbent assay and liquid chromatography-tandem mass spectrometry methodology for the analysis of 8-oxo-7,8-dihydro-2'-deoxyguanosine in saliva and urine

While ELISA is a frequently used means of assessing 8-oxo-7,8-dihydro-2-deoxyguanosine (8-oxodG) in biological fluids, differences in baseline urinary 8-oxodG levels, compared to chromatographic techniques, have raised questions regarding the specificity of immunoassays. Recently, ELISA of salivary 8-oxodG has been used to report on periodontal disease. We compared salivary 8-oxodG levels, determined by two commercial ELISA kits, to liquid chromatography-tandem mass spectrometry (LC-MS/MS) with prior purification using solid-phase extraction. While values were obtained with both ELISA kits, salivary 8-oxodG values were below or around the limit of detection of our LC-MS/MS assay. As the limit of detection for the LC-MS/MS procedure is much lower than ELISA, we concluded that the assessment of salivary 8-oxodG by ELISA is not accurate. In contrast to previous studies, ELISA levels of urinary 8-oxodG (1.67 ± 0.53 pmol/μmol creatinine) were within the range reported previously only for chromatographic assays, although still significantly different than LC-MS/MS (0.41 ± 0.39 pmol/μmol creatinine; p = 0.002). Furthermore, no correlation with LC-MS/MS was seen. These results question the ability of ELISA approaches, at present, to specifically determine absolute levels of 8-oxodG in saliva and urine. Ongoing investigation in our laboratories aims to identify the basis of the discrepancy between ELISA and LC-MS/MS.     

The limitations,dangers, and benefits of simple methods for testing identifiability

In their Commentary paper, Villaverde and Massonis (On testing structural identifiability by a simple scaling method: relying on scaling symmetries can be misleading) have commented on our paper in which we proposed a simple scaling method to test structural identifiability. Our scaling invariance method (SIM) tests for scaling symmetries only, and Villaverde and Massonis correctly show the SIM may fail to detect identifiability problems when a model has other types of symmetries. We agree with the limitations raised by these authors but, also, we emphasize that the method is still valuable for its applicability to a wide variety of models, its simplicity, and even as a tool to introduce the problem of identifiability to investigators with little training in mathematics.

In their Commentary paper, Villaverde and Massonis (On testing structural identifiability by a simple scaling method: relying on scaling symmetries can be misleading [1]) have commented on our paper in which we proposed a simple scaling method to test structural identifiability [2]. Our scaling invariance method (SIM) tests for scaling symmetries only, and Villaverde and Massonis correctly show the SIM may fail to detect identifiability problems when a model has other types of symmetries (we indeed indicated but not investigated the importance of generalizing the method to other symmetries). Thus, we agree that our simple method provides a necessary but not sufficient condition for identifiability, and we appreciate their careful analysis and constructive criticism.We nevertheless think that the simple method remains useful because it is so simple. Even for investigators with little training in mathematics, the method provides a necessary condition for structural identifiability that can be derived in a few minutes with pen and paper. Similarly, we have found its pedagogic strength by teaching the method to our own graduate students and colleagues. More advanced methods (such as STRIKE-GOLDD [3,4], COMBOS [5], or SIAN [6]) are typically intimidating for researchers with a background in Biology or Bioinformatics. This simple method can help those practitioners to familiarize themselves with the identifiability problem and better understand their models.Finally, it is worth noting that if scaling invariance is the only symmetry (as it was in all the cases we analyzed), our SIM remains valuable (albeit uncontrolled), and surprisingly effective for a wide variety of problems (as the extensive list collected in the Supplementary Material our paper [2]). We guess that the SIM especially fails when applied to linear models (as more potential rotations of the variables leave the system invariant), and in non-linear scenarios where some parameters are identical. For instance, the FitzHugh-Nagumo model raised by Villaverde and Massonis, x˙1(t)=c(x1(t)−x13(t)3−x2(t)+d),x˙2(t)=1c(x1(t)+a−b·x2(t)),y(t)=x1(t), could have been written as x˙1(t)=λ1x1(t)−λ2x13(t)3−λ3x2(t)+d,x˙2(t)=λ4x1(t)+a−b·x2(t),y(t)=x1(t) where λ₁ = λ₂ = λ₃ = 1/λ₄ = c. One of the reasons why our method fails, in this case, might be these additional symmetries introduced in this more elaborate notation of the model.Hence, it is worth understanding generic conditions under which the SIM method is expected to be fragile, possibly using STRIKE-GOLDD to test large families of nonlinear models.As a final remark, we appreciate that Villaverde and Massonis have shared their source code, so researchers might have a gold standard to test identifiability.     

A Variable Sampling Interval Synthetic Xbar Chart for the Process Mean

The usual practice of using a control chart to monitor a process is to take samples from the process with fixed sampling interval (FSI). In this paper, a synthetic X¯ control chart with the variable sampling interval (VSI) feature is proposed for monitoring changes in the process mean. The VSI synthetic X¯ chart integrates the VSI X¯ chart and the VSI conforming run length (CRL) chart. The proposed VSI synthetic X¯ chart is evaluated using the average time to signal (ATS) criterion. The optimal charting parameters of the proposed chart are obtained by minimizing the out-of-control ATS for a desired shift. Comparisons between the VSI synthetic X¯ chart and the existing X¯, synthetic X¯, VSI X¯ and EWMA X¯ charts, in terms of ATS, are made. The ATS results show that the VSI synthetic X¯ chart outperforms the other X¯ type charts for detecting moderate and large shifts. An illustrative example is also presented to explain the application of the VSI synthetic X¯ chart.     

Partitioning Heritability of Regulatory and Cell-Type-Specific Variants across 11 Common Diseases

Regulatory and coding variants are known to be enriched with associations identified by genome-wide association studies (GWASs) of complex disease, but their contributions to trait heritability are currently unknown. We applied variance-component methods to imputed genotype data for 11 common diseases to partition the heritability explained by genotyped SNPs (hg2) across functional categories (while accounting for shared variance due to linkage disequilibrium). Extensive simulations showed that in contrast to current estimates from GWAS summary statistics, the variance-component approach partitions heritability accurately under a wide range of complex-disease architectures. Across the 11 diseases DNaseI hypersensitivity sites (DHSs) from 217 cell types spanned 16% of imputed SNPs (and 24% of genotyped SNPs) but explained an average of 79% (SE = 8%) of hg2 from imputed SNPs (5.1× enrichment; p = 3.7 × 10⁻¹⁷) and 38% (SE = 4%) of hg2 from genotyped SNPs (1.6× enrichment, p = 1.0 × 10⁻⁴). Further enrichment was observed at enhancer DHSs and cell-type-specific DHSs. In contrast, coding variants, which span 1% of the genome, explained <10% of hg2 despite having the highest enrichment. We replicated these findings but found no significant contribution from rare coding variants in independent schizophrenia cohorts genotyped on GWAS and exome chips. Our results highlight the value of analyzing components of heritability to unravel the functional architecture of common disease.     

The Physical Foundation of Vasoocclusion in Sickle Cell Disease

The pathology of sickle cell disease arises from the occlusion of small blood vessels because of polymerization of the sickle hemoglobin within the red cells. We present measurements using a microfluidic method we have developed to determine the pressure required to eject individual red cells from a capillary-sized channel after the cell has sickled. We find that the maximum pressure is only ∼100 Pa, much smaller than typically found in the microcirculation. This explains why experiments using animal models have not observed occlusion beginning in capillaries. The magnitude of the pressure and its dependence on intracellular concentration are both well described as consequences of sickle hemoglobin polymerization acting as a Brownian ratchet. Given the recently determined stiffness of sickle hemoglobin gels, the observed obstruction seen in sickle cell disease as mediated by adherent cells can now be rationalized, and surprisingly suggests a window of maximum vulnerability during circulation of sickle cells.Human capillaries are narrower than the erythrocytes they convey. In sickle cell disease, red cells can become rigid in those capillaries, because the hemoglobin inside the red cell will aggregate into stiff polymers. This happens once the molecules deliver their oxygen, and led to the long-held view that capillary occlusion was central to the pathophysiology of the disease (1,2). This was challenged when microscopic study of animal model tissues perfused with sickle blood revealed blockages that began further downstream, in the somewhat larger venules (3–5), at the site of adherent red or white cells which diminished the vessel lumen without fully obstructing the flow. Yet no rationale has been presented for the failure of the prior assumption of capillary blockage. Microfluidic methods (6) are ideally suited to discover why cells don’t get stuck in the capillaries, yet occlude subsequent vessels, and we have constructed a system to address this question. Our measurements show that the pressure differences across capillaries in vivo can easily dislodge a cell sickled within a capillary, giving an experimental answer to the question of why sickled cells don’t stick in capillaries. It turns out that the pressure a cell can withstand is quantitatively explained by the Brownian ratchet behavior of sickle hemoglobin polymerization.We constructed single-cell channels in transparent polydimethylsiloxane, with a cross section (1.5 μm × 4 μm) that is smaller than the resting diameter of red cells (Fig. 1). These channels are much narrower than those that have been employed in other recent studies of the sickling process (7,8), and they resemble human capillaries in permitting only one cell at a time to pass through them. We used a laser photolysis method to create ligand free (deoxygenated) cells, and this requires that the hemoglobin bind CO, which can then be readily removed by strong illumination, in contrast to bound O₂ which is released with far lower efficiency than CO. The microfluidic chips were enclosed in a gas-tight chamber flushed with CO to avoid introduction of oxygen and keep the cells fully ligated before photolysis. The profiles of the channels were confirmed by microscopic observation. To confirm that liquid did not pass around the cells when they were trapped in the channels, fluorescent beads were introduced into some cell solutions. The beads did not pass the cells, nor did they approach the cell when it was occluded, verifying that no significant flow occurred around the cell when it was stuck.Open in a separate windowFigure 1An erythrocyte enters a channel (moving left to right) and is positioned in the center, where it will be photolyzed. The channel cross section is 1.5 μm × 4 μm, smaller than a resting red cell diameter.Optical measurements were carried out on a microspectrophotometer constructed on an optical table. The system employed ×32 LWD objectives (Leitz, Wetzlar, Germany), which were autofocused during collection of absorption spectra to minimize aberrations. Spectra were obtained using a series 300 camera (Photometrics, Tucson, AZ); video imaging was done with a high-speed camera (Photron, San Diego, CA). Photolysis was provided by a 2020 Argon Ion laser (Spectra Physics, Houston, TX). Sickle cells were obtained from patients at the Marian Anderson Sickle Cell Center at St. Christopher''s Hospital for Children, Philadelphia, PA by phlebotomy into EDTA-containing tubes. The blood was centrifuged at 5°C at 1200g for 4 min, and then the pellet was washed 4× with 15 volumes of buffer (120 mM NaCl, 2 mM KCl, 10 mM dibasic Na Phosphate, 7 mM monobasic Na Phosphate, 3.4 mM Na Bicarbonate, and 6 mM Dextrose) by repeated suspension and centrifugation at 30g for 4 min. This minimizes fibrinogen and platelets in the final suspension, to insure that these studies are controlled by the mechanical properties of the cells themselves.Our experiment began by parking a cell in the center of a channel (Fig. 1). The cell, its hemoglobin, and the microchannel environment all were saturated with CO. Because the thickness of the channel is known, we were able to determine the hemoglobin concentration inside the cell from its absorption spectrum (Fig. 2 A). Steady-state laser illumination then removed the CO, allowing the hemoglobin to polymerize, in which condition it remained while the laser was kept on. Removal of CO was confirmed by observing the spectral difference between COHb and deoxyHb. Photolysis of COHb generates negligible heating (9–11). During illumination, hydrostatic pressure was applied until the cell broke free.Open in a separate windowFigure 2(A) Absorption of the cell (points), fit to a standard spectrum (9). (B) Pressure to dislodge a cell sickled in the microchannel, as a function of intracellular concentration. Note that typical intracellular concentrations are ∼32 g/dL. (Line) Brownian-ratchet theory described in the text. The coefficient of friction (0.036) is within the observed range, and is the only parameter varied.The magnitude of the dislodging pressure, measured by simple height difference between input and output cell reservoirs, is shown in Fig. 2 B. The pressure needed to dislodge the cell increased with increasing intracellular Hb concentration, implying that an increased mass of polymerized hemoglobin is more difficult to dislodge. A clear concentration threshold for capture is apparent. While there is a well-known solubility below which polymers cannot form (18.5 g/dL for the 22°C of this experiment (12)), the threshold here is significantly higher.Central to explaining these observations is a Brownian ratchet mechanism (13) which derives from the metastable nature of this polymerization process. Unless disrupted, as by centrifugation, polymerization in sickle hemoglobin terminates before the thermodynamic limit of monomer solubility is reached (14,15). This arises from the fact that polymers only grow at their ends, which are easily occluded in the dense mass of polymers that form. This end obstruction leaves the system in a metastable state and fluctuations accordingly provide polymers with space into which they can incrementally grow. This Brownian ratchet has been shown to lead to dramatic fiber buckling when individual fibers are isolated in sickle cells (16). The force can be simply expressed as f = (kT/δ) ln S(c), where k is Boltzmann’s constant, T the absolute temperature, δ the net spatial elongation from addition of a single monomer, and S is the supersaturation of the solution when the metastable limit is reached, at monomer concentration c. In this calculation, c is taken as the terminal concentration, computed from our empirical finding (15) that in this metastable system the amount of polymerized hemoglobin Δ is Δ(∞) = 2/3 (c_o-c_s), rather than the expected thermodynamic limit c_o-c_s, where c_o is the initial concentration and c_s is the solubility.For determining the net force, the total number of fibers must be known, and can be calculated based on the double nucleation mechanism (17) which has been quantitatively successful in describing polymerization. The concentration of polymers [p(t)] initially grows exponentially, described by[p(t)]=(AB2J)exp(Bt),where A and B are parameters related to nucleation, and J is the polymer elongation rate, as described in Ferrone et al. (17). Because A and B are both extremely concentration-dependent (9), they will drop dramatically once monomers begin to add to polymers in any significant numbers, and thereby diminish the remaining monomer pool. Thanks to the extreme concentration dependence of the reaction, this rapidly shuts off further polymerization. This happens at approximately the 10th time (the time when the reaction has reached 1/10 of its maximum). Thus, the [p(t_1/10)] ≈ [p(∞)]. Moreover, at one-tenth of the reaction,Δ(t1/10)=12Aexp(Bt1/10)=Δ(∞)10,and thus[p(∞)]=(BJ)(Δ(∞)10)=(BJ)((co−cs)15).For computing the number of fibers, the volume of the cell was taken as 90 μm³. This calculation shows, as expected, that the number of polymers in the cell is highly concentration-dependent, and very few fibers are produced at concentrations just above solubility, but the number grows sharply as concentration rises. This is the main contribution to the threshold in holding force shown by the data.With the force per fiber, and the total number of fibers, the net force against the wall is known. With a coefficient of friction, this reveals the force that a trapped cell can withstand. If the force is divided by the cross-sectional area across which the force is applied, we get a prediction of the dislodging pressure, which can be compared to the data. For a quantitative comparison with the results, two further corrections, of order unity, were applied. Because only normal force will contribute to friction, the calculated force was determined by integrating cos θ. This integration is not over all angles (π) because of the possibility that large incidence angles of the fibers against the wall will lead to fiber runaway (18). Therefore, the integration described is taken to the runaway threshold, here ∼1 rad. Finally, it is necessary to assign a coefficient of friction. Known values span the range of 0.03–0.06 (19). We therefore selected a value within the range, 0.036, as the best match for the data. The predicted pressures match the measurements well, as the line in Fig. 2 B shows.Because the flow resistance is comparable for red cells traversing glass channels and endothelial-lined capillaries (20), we conclude that in vivo the pressures a sickled cell inside a capillary can withstand are no more than hundreds of Pa. This is significantly smaller than typical arteriovenous pressure differentials that have been measured, which range from 0.7 kPa (in hamster skin (21)) to 7.9 kPa (in rat mesentery (22)).Our measurements coupled with recent determination of the stiffness of sickle hemoglobin gels (23) provide the missing physical basis for the processes of vasoocclusion seen in ex vivo tissue and animal models of sickle cell disease, arguing that these observations indeed represent fundamental behavior of sickle cell disease. We now understand this behavior in terms of three possible outcomes, all intimately connected with kinetics:

• 1.Certain escape: A cell that does not polymerize until after passing the obstruction can reach the lungs where it reoxygenates and resets its polymerization clock.
• 2.Possible escape: A cell that polymerizes within the capillary will assume an elongated sausage shape. The forces that it can exert against the wall cannot hold it there, and it will emerge into the postcapillary venule. There it has some chance of passing a subsequent obstruction, though it might also obstruct flow were it to rotate before reaching the adherent cell, so as to present its long dimension to the reduced space it must traverse.
• 3.Certain occlusion: A cell that does not polymerize in the capillary reassumes a larger diameter as soon as it escapes. If the cell then polymerizes before it encounters a cell attached to the venule wall, this rigidified cell will not be able to squeeze past the adherent cell, because that kind of deformation takes MPa (23). This would precipitate the type of blockage that is observed. This suggests that there is a window of greatest vulnerability, toward which therapies might be addressed.

     

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

Kinetics of H2O2-driven catalysis by a lytic polysaccharide monooxygenase from the fungus Trichoderma reesei

Owing to their ability to break glycosidic bonds in recalcitrant crystalline polysaccharides such as cellulose, the catalysis effected by lytic polysaccharide monooxygenases (LPMOs) is of major interest. Kinetics of these reductant-dependent, monocopper enzymes is complicated by the insoluble nature of the cellulose substrate and parallel, enzyme-dependent, and enzyme-independent side reactions between the reductant and oxygen-containing cosubstrates. Here, we provide kinetic characterization of cellulose peroxygenase (oxidative cleavage of glycosidic bonds in cellulose) and reductant peroxidase (oxidation of the reductant) activities of the LPMO TrAA9A of the cellulose-degrading model fungus Trichoderma reesei. The catalytic efficiency (kcat/Km(H2O2)) of the cellulose peroxygenase reaction (k_cat = 8.5 s⁻¹, and Km(H2O2)=30μM) was an order of magnitude higher than that of the reductant (ascorbic acid) peroxidase reaction. The turnover of H₂O₂ in the ascorbic acid peroxidase reaction followed the ping-pong mechanism and led to irreversible inactivation of the enzyme with a probability of 0.0072. Using theoretical analysis, we suggest a relationship between the half-life of LPMO, the values of kinetic parameters, and the concentrations of the reactants.