Glassy State and Seed Storage Stability: A Viability Equation Analysis

Dry seeds exist generally in a glassy (or vitrified) state.The high viscosity of the glassy state would be expected tohave a retarding effect on deteriorative reactions in the cytoplasm.Thus the glassy state may be considered to be a biophysicalbarrier for seed deterioration. The present study aims to testthe hypothesis that seed storage stability is associated withthe glassy state. With the equations derived from the seed viabilityequation, we have calculated the maximum temperature (Tmax)for long-term storage of corn, pea and soybeans. The Tmax forlong-term seed storage is found to be in a good agreement withthe glass transition temperature (Tg) in each instance, suggestingthat seed deterioration would be accelerated when seeds arenot in the glassy state. Experiments with soybeans given acceleratedageing show that the loss of glassy state is followed by a rapiddecrease in seed viability. These observations provide indirectevidence that the glassy state may play a significant role inseed storage stability.Copyright 1994, 1999 Academic Press Glassy state, seed longevity, storage stability, viability analysis     

An Unusual Hydrophobic Core Confers Extreme Flexibility to HEAT Repeat Proteins

Alpha-solenoid proteins are suggested to constitute highly flexible macromolecules, whose structural variability and large surface area is instrumental in many important protein-protein binding processes. By equilibrium and nonequilibrium molecular dynamics simulations, we show that importin-β, an archetypical α-solenoid, displays unprecedentedly large and fully reversible elasticity. Our stretching molecular dynamics simulations reveal full elasticity over up to twofold end-to-end extensions compared to its bound state. Despite the absence of any long-range intramolecular contacts, the protein can return to its equilibrium structure to within 3 Å backbone RMSD after the release of mechanical stress. We find that this extreme degree of flexibility is based on an unusually flexible hydrophobic core that differs substantially from that of structurally similar but more rigid globular proteins. In that respect, the core of importin-β resembles molten globules. The elastic behavior is dominated by nonpolar interactions between HEAT repeats, combined with conformational entropic effects. Our results suggest that α-solenoid structures such as importin-β may bridge the molecular gap between completely structured and intrinsically disordered proteins.     

Stochastic Dynamics Underlying Cognitive Stability and Flexibility

Cognitive stability and flexibility are core functions in the successful pursuit of behavioral goals. While there is evidence for a common frontoparietal network underlying both functions and for a key role of dopamine in the modulation of flexible versus stable behavior, the exact neurocomputational mechanisms underlying those executive functions and their adaptation to environmental demands are still unclear. In this work we study the neurocomputational mechanisms underlying cue based task switching (flexibility) and distractor inhibition (stability) in a paradigm specifically designed to probe both functions. We develop a physiologically plausible, explicit model of neural networks that maintain the currently active task rule in working memory and implement the decision process. We simplify the four-choice decision network to a nonlinear drift-diffusion process that we canonically derive from a generic winner-take-all network model. By fitting our model to the behavioral data of individual subjects, we can reproduce their full behavior in terms of decisions and reaction time distributions in baseline as well as distractor inhibition and switch conditions. Furthermore, we predict the individual hemodynamic response timecourse of the rule-representing network and localize it to a frontoparietal network including the inferior frontal junction area and the intraparietal sulcus, using functional magnetic resonance imaging. This refines the understanding of task-switch-related frontoparietal brain activity as reflecting attractor-like working memory representations of task rules. Finally, we estimate the subject-specific stability of the rule-representing attractor states in terms of the minimal action associated with a transition between different rule states in the phase-space of the fitted models. This stability measure correlates with switching-specific thalamocorticostriatal activation, i.e., with a system associated with flexible working memory updating and dopaminergic modulation of cognitive flexibility. These results show that stochastic dynamical systems can implement the basic computations underlying cognitive stability and flexibility and explain neurobiological bases of individual differences.     

Coexistence of Fluid and Crystalline Phases of Proteins in Photosynthetic Membranes

Photosystem II (PSII) and its associated light-harvesting complex II (LHCII) are highly concentrated in the stacked grana regions of photosynthetic thylakoid membranes. PSII-LHCII supercomplexes can be arranged in disordered packings, ordered arrays, or mixtures thereof. The physical driving forces underlying array formation are unknown, complicating attempts to determine a possible functional role for arrays in regulating light harvesting or energy conversion efficiency. Here, we introduce a coarse-grained model of protein interactions in coupled photosynthetic membranes, focusing on just two particle types that feature simple shapes and potential energies motivated by structural studies. Reporting on computer simulations of the model’s equilibrium fluctuations, we demonstrate its success in reproducing diverse structural features observed in experiments, including extended PSII-LHCII arrays. Free energy calculations reveal that the appearance of arrays marks a phase transition from the disordered fluid state to a system-spanning crystal. The predicted region of fluid-crystal coexistence is broad, encompassing much of the physiologically relevant parameter regime; we propose experiments that could test this prediction. Our results suggest that grana membranes lie at or near phase coexistence, conferring significant structural and functional flexibility to this densely packed membrane protein system.     

Coexistence of Fluid and Crystalline Phases of Proteins in Photosynthetic Membranes

Photosystem II (PSII) and its associated light-harvesting complex II (LHCII) are highly concentrated in the stacked grana regions of photosynthetic thylakoid membranes. PSII-LHCII supercomplexes can be arranged in disordered packings, ordered arrays, or mixtures thereof. The physical driving forces underlying array formation are unknown, complicating attempts to determine a possible functional role for arrays in regulating light harvesting or energy conversion efficiency. Here, we introduce a coarse-grained model of protein interactions in coupled photosynthetic membranes, focusing on just two particle types that feature simple shapes and potential energies motivated by structural studies. Reporting on computer simulations of the model’s equilibrium fluctuations, we demonstrate its success in reproducing diverse structural features observed in experiments, including extended PSII-LHCII arrays. Free energy calculations reveal that the appearance of arrays marks a phase transition from the disordered fluid state to a system-spanning crystal. The predicted region of fluid-crystal coexistence is broad, encompassing much of the physiologically relevant parameter regime; we propose experiments that could test this prediction. Our results suggest that grana membranes lie at or near phase coexistence, conferring significant structural and functional flexibility to this densely packed membrane protein system.     

Gibbs Ensemble Calculations with an Equation of State: An Application to Vapor-Liquid Equilibria

Abstract

A new modification of the Gibbs ensemble Monte Carlo computer simulation method for fluid phase equilibria is described. The modification is based on a thermodynamic model for the vapor phase, and uses an equation of state to account for the weak interactions between the vapor phase molecules. Reductions in the computational time by 30–40% as compared to the original Gibbs ensemble method are obtained. The algorithm is applied to Lennard-Jones - (12,6) fluids and their mixtures and the results are in good agreement with results obtained from simulations using the full Gibbs ensemble method.     

Thermal and Structural Stability of Adsorbed Proteins

Experimental evidence suggests that proteins adsorbed to hydrophobic surfaces at low coverages are stabilized relative to the bulk. For larger coverages, proteins unfold and form β-sheets. We performed computer simulations on model proteins and found that: 1), For weakly adsorbing surfaces, unfolded conformations lose more entropy upon adsorption than folded ones. 2), The melting temperature, both in the bulk and at surfaces, decreases with increasing protein concentration because of favorable interprotein interactions. 3), Proteins in the bulk show large unfolding free energy barriers; this barrier decreases at stronger adsorbing surfaces. We conjecture that typical experimental temperatures appear to be below the bulk melting temperature for a single protein, but above the melting temperature for concentrated protein solutions. Purely thermodynamic factors then explain protein stabilization on adsorption at low concentrations. However, both thermodynamic and kinetic factors are important at higher concentrations. Thus, proteins in the bulk do not denature with increasing concentration due to large kinetic barriers, even though the aggregated state is thermodynamically preferred. However, they readily unfold upon adsorption, with the surface acting as a heterogeneous catalyst. The thermal behavior of proteins adsorbed to hydrophobic surfaces thus appears to follow behavior independent of their chemical specificity.     

Autophagy-related Proteins in Genome Stability: Autophagy-Dependent and Independent Actions

It is emerging that autophagy-related proteins regulate the adaptive response to DNA damage in maintaining genome stability at multiple pathways. Here, we discuss recent insights into how autophagy-related proteins participate in DNA damage repair processes, influence chromosomal instability, and regulate the cell cycle through autophagy-dependent and independent actions. There is increasing awareness of the importance of these pathways mediated by autophagy-related proteins to DNA damage response (DDR), and disturbances in these regulatory connections may be linked to genomic instability participated in various human diseases, such as cancer and aging.     

时滞逻辑斯谛方程的稳定性和振动性

本文研究时滞逻辑斯谛方程其中得到方程（E）关于正常数平衡点为渐近稳定和振动的条件,也得到方程（E）存在正周期解的条件,所得结果发展和推广了文献［1］,［2］的结果。     

Predicting Important Residues and Interaction Pathways in Proteins Using Gaussian Network Model: Binding and Stability of HLA Proteins

A statistical thermodynamics approach is proposed to determine structurally and functionally important residues in native proteins that are involved in energy exchange with a ligand and other residues along an interaction pathway. The structure-function relationships, ligand binding and allosteric activities of ten structures of HLA Class I proteins of the immune system are studied by the Gaussian Network Model. Five of these models are associated with inflammatory rheumatic disease and the remaining five are properly functioning. In the Gaussian Network Model, the protein structures are modeled as an elastic network where the inter-residue interactions are harmonic. Important residues and the interaction pathways in the proteins are identified by focusing on the largest eigenvalue of the residue interaction matrix. Predicted important residues match those known from previous experimental and clinical work. Graph perturbation is used to determine the response of the important residues along the interaction pathway. Differences in response patterns of the two sets of proteins are identified and their relations to disease are discussed.     

LCP-Tm: An Assay to Measure and Understand Stability of Membrane Proteins in a Membrane Environment

Structural and functional studies of membrane proteins are limited by their poor stability outside the native membrane environment. The development of novel methods to efficiently stabilize membrane proteins immediately after purification is important for biophysical studies, and is likely to be critical for studying the more challenging human targets. Lipidic cubic phase (LCP) provides a suitable stabilizing matrix for studying membrane proteins by spectroscopic and other biophysical techniques, including obtaining highly ordered membrane protein crystals for structural studies. We have developed a robust and accurate assay, LCP-T_m, for measuring the thermal stability of membrane proteins embedded in an LCP matrix. In its two implementations, protein denaturation is followed either by a change in the intrinsic protein fluorescence on ligand release, or by an increase in the fluorescence of a thiol-binding reporter dye that measures exposure of cysteines buried in the native structure. Application of the LCP-T_m assay to an engineered human β₂-adrenergic receptor and bacteriorhodopsin revealed a number of factors that increased protein stability in LCP. This assay has the potential to guide protein engineering efforts and identify stabilizing conditions that may improve the chances of obtaining high-resolution structures of intrinsically unstable membrane proteins.     

时滞Logistic型差分方程的振动及稳定性

本文获得了如下Xn 1=xnexp(a bxn-k^p-cxn-1^q）时滞Logistic型差分方程所有正解关于其平衡点振动的充要条件，同时还获得了一个正平衡点渐近稳定的充分条件，其中A∈（0，∞），B∈（-∞，O]，C∈（0，∞），K,l∈N。     

An Ultrahigh Energy Density Quasi‐Solid‐State Zinc Ion Microbattery with Excellent Flexibility and Thermostability

The rapid development of smart wearable and integrated electronic products has urgently increased the requirement for high‐performance microbatteries. Although few lithium ion microbatteries based on organic electrolytes have been reported so far, the problems, such as undesirable energy density, poor flexibility, inflammability, volatility toxicity, and high cost restrict their practical applications in the above‐mentioned electronic products. In order to overcome these problems, a low cost quasi‐solid‐state aqueous zinc ion microbattery (ZIMB) assembled by a vanadium dioxide (B)‐multiwalled carbon nanotubes (VO₂ (B)‐MWCNTs) cathode, a zinc nanoflakes anode, and a zinc trifluoromethanesulfonate‐polyvinyl alcohol (Zn(CF₃SO₃)₂‐PVA) hydrogel electrolyte is exploited. As expected, the ZIMB exhibits excellent electrochemical performance, e.g., a high capacity of 314.7 µAh cm^?2, an ultrahigh energy density of 188.8 µWh cm^?2, and a high power density of 0.61 mW cm^?2. Furthermore, the ZIMB also shows high flexibility and excellent high temperature stability: the capacity has no obvious decay when the bending angle is up to 150° and the temperature reaches 100 °C. The ZIMB provides a way to develop next‐generation miniature energy storage devices with high performance.     

Co-Crystallization with Conformation-Specific Designed Ankyrin Repeat Proteins Explains the Conformational Flexibility of BCL-W

BCL-W is a member of the BCL-2 family of anti-apoptotic proteins. A key event in the regulation of apoptosis is the heterodimerization between anti-apoptotic and pro-apoptotic family members, which involves a conserved surface-exposed groove on the anti-apoptotic proteins. Crystal structures of the ligand binding-competent conformation exist for all anti-apoptotic family members, with the exception of BCL-W, due to the flexibility of the BCL-W groove region. Existing structures had suggested major deviations of the BCL-W groove region from the otherwise structurally highly related remaining anti-apoptotic family members. To capture its ligand binding-competent conformation by counteracting the conformational flexibility of the BCL-W groove, we had selected high-affinity groove-binding designed ankyrin repeat proteins (DARPins) using ribosome display. We now determined two high-resolution crystal structures of human BCL-W in complex with different DARPins at resolutions 1.5 and 1.85 Å, in which the structure of BCL-W is virtually identical, and BCL-W adopts a conformation extremely similar to the ligand-free conformation of its closest relative BCL-XL in both structures. However, distinct differences to all previous BCL-W structures are evident, notably in the ligand-binding region. We provide the first structural explanation for the conformational flexibility of the BCL-W groove region in comparison to other BCL-2 family members. Due to the importance of the anti-apoptotic BCL-2 family as drug targets, the presented crystal structure of ligand binding-competent BCL-W may serve as a valuable basis for structure-based drug design in the future and provides a missing piece for the structural characterization of this protein family.     

Predicting Evolutionary Site Variability from Structure in Viral Proteins: Buriedness,Packing, Flexibility,and Design

Several recent works have shown that protein structure can predict site-specific evolutionary sequence variation. In particular, sites that are buried and/or have many contacts with other sites in a structure have been shown to evolve more slowly, on average, than surface sites with few contacts. Here, we present a comprehensive study of the extent to which numerous structural properties can predict sequence variation. The quantities we considered include buriedness (as measured by relative solvent accessibility), packing density (as measured by contact number), structural flexibility (as measured by B factors, root-mean-square fluctuations, and variation in dihedral angles), and variability in designed structures. We obtained structural flexibility measures both from molecular dynamics simulations performed on nine non-homologous viral protein structures and from variation in homologous variants of those proteins, where they were available. We obtained measures of variability in designed structures from flexible-backbone design in the Rosetta software. We found that most of the structural properties correlate with site variation in the majority of structures, though the correlations are generally weak (correlation coefficients of 0.1–0.4). Moreover, we found that buriedness and packing density were better predictors of evolutionary variation than structural flexibility. Finally, variability in designed structures was a weaker predictor of evolutionary variability than buriedness or packing density, but it was comparable in its predictive power to the best structural flexibility measures. We conclude that simple measures of buriedness and packing density are better predictors of evolutionary variation than the more complicated predictors obtained from dynamic simulations, ensembles of homologous structures, or computational protein design.     

未折叠蛋白质的普遍初始热力学亚稳态

探索和理解蛋白质折叠问题一直是分子生物学、结构生物学和生物物理学的终极挑战.未折叠的蛋白质应该存在一种普遍初始热力学亚稳态,否则无法解释蛋白质是如何在剧烈的热振动干扰下完成快速精确折叠的.本文通过分析水溶液环境和蛋白质折叠的相关性,揭示了一种由水分子屏蔽效应引起的未折叠蛋白质的普遍初始热力学亚稳态,该亚稳态的存在是水溶液环境中水分子的物理性质决定,并赋予未折叠蛋白质抵抗热扰动和避免错误折叠的能力.我们通过研究已发表的实验数据和建立分子模型,找到了该初始热力学亚稳态存在的相关证据,并推测了该亚稳态导致蛋白质精确折叠的相关物理学机制.     

Redefining the Dry Molten Globule State of Proteins

Dynamics and function of proteins are governed by the structural and energetic properties of the different states they adopt and the barriers separating them. In earlier work, native-state triplet–triplet energy transfer (TTET) on the villin headpiece subdomain (HP35) revealed an equilibrium between a locked native state and an unlocked native state, which are structurally similar but have different dynamic properties. The locked state is restricted to low amplitude motions, whereas the unlocked state shows increased conformational flexibility and undergoes local unfolding reactions. This classified the unlocked state as a dry molten globule (DMG), which was proposed to represent an expanded native state with loosened side-chain interactions and a solvent-shielded core. To test whether the unlocked state of HP35 is actually expanded compared to the locked state, we performed high-pressure TTET measurements. Increasing pressure shifts the equilibrium from the locked toward the unlocked state, with a small negative reaction volume for unlocking (ΔV⁰ = − 1.6 ± 0.5 cm³/mol). Therefore, rather than being expanded, the unlocked state represents an alternatively packed, compact state, demonstrating that native proteins can exist in several compact folded states, an observation with implications for protein function. The transition state for unlocking/locking, in contrast, has a largely increased volume relative to the locked and unlocked state, with respective activation volumes of 7.1 ± 0.4 cm³/mol and 8.7 ± 0.9 cm³/mol, indicating an expansion of the protein during the locking/unlocking transition. The presented results demonstrate the existence of both compact, low-energy and expanded, high-energy DMGs, prompting a broader definition of this state.     

Substrate Binding Tunes Conformational Flexibility and Kinetic Stability of an Amino Acid Antiporter

We used single molecule dynamic force spectroscopy to unfold individual serine/threonine antiporters SteT from Bacillus subtilis. The unfolding force patterns revealed interactions and energy barriers that stabilized structural segments of SteT. Substrate binding did not establish strong localized interactions but appeared to be facilitated by the formation of weak interactions with several structural segments. Upon substrate binding, all energy barriers of the antiporter changed thereby describing the transition from brittle mechanical properties of SteT in the unbound state to structurally flexible conformations in the substrate-bound state. The lifetime of the unbound state was much shorter than that of the substrate-bound state. This leads to the conclusion that the unbound state of SteT shows a reduced conformational flexibility to facilitate specific substrate binding and a reduced kinetic stability to enable rapid switching to the bound state. In contrast, the bound state of SteT showed an increased conformational flexibility and kinetic stability such as required to enable transport of substrate across the cell membrane. This result supports the working model of antiporters in which alternate substrate access from one to the other membrane surface occurs in the substrate-bound state.The amino acid/polyamine/organocation (APC)² superfamily comprises about 250 members that occur in all phyla from prokaryotes to higher eukaryotes. These membrane proteins function as solute/cation symporters or solute/solute antiporters (1). One APC subfamily is established by l-amino acid transporters (LATs), which correspond to the light subunits of eukaryotic heteromeric amino acid transporters (2, 3). Heteromeric amino acid transporters are composed of a light subunit that provides transport activity and a disulfide-linked heavy subunit that shows responsibility for plasma membrane targeting. Genetic defects in light and heavy subunits cause a number of inherited human diseases. Mutations in the light as well as the heavy subunit of system b^0,+ lead to cystinuria (4, 5), whereas mutations in the light subunit y⁺LAT1 cause lysinuric protein intolerance (6, 7). Another light subunit, xCT that mediates cysteine uptake and glutamate efflux (8, 9), is involved in vivo in cocaine relapse (10) and maintenance of the plasma redox balance (11). LAT1, the light subunit of system L, is overexpressed in certain primary human tumors. It transports essential neutral amino acids with long, branched, or aromatic side chains required by tumor cells to support their unabated growth (12). Therefore, amino acid transporters like LAT1 are attractive anticancer drug targets.So far a high resolution structure of a eukaryotic LAT family member is not available. However, studies on xCT revealed a membrane topology of 12 transmembrane helices (TMHs) with cytosolic N and C termini and a re-entrant loop structure between TMHs II and III (13). The identified first prokaryotic member of the LAT family, SteT from Bacillus subtilis, is a serine/threonine antiporter, which shows high sequence identity (∼30%) to the light subunits of eukaryotic heteromeric amino acid transporters. Moreover SteT exhibits a similar putative membrane topology and sequential mode of obligate exchange (14). Thus, SteT is an excellent model for studying the structure-function relationship of LAT family members.According to current models, transport proteins undergo functionally related conformational changes. Transporters alternate between two conformations to expose their binding sites to the cytoplasmic and extracellular side (15–22). However, prior to conformational changes substrates have to be recognized and bound. If substrates are amino acids, three main features can be used for specific selection and binding: (i) the negatively charged α-carboxyl group, (ii) the positively charged α-amino group, and (iii) the electrostatic, hydrophobic, or spatial properties of the side chain (22–24). α-Carboxyl and α- amino groups of l-amino acids possess similar structural and chemical characteristics (except for proline); however, their side chains differ in shape, size, and electrostatic properties. Combinations of these features are assumed to establish different interactions within the side chain binding pocket, which determines the substrate specificity of the transporter. The two main substrates of SteT, l-serine and l-threonine, differ by only one methylene group in their side chain; thus they have similar properties. Additionally SteT transports aromatic l-amino acids (Trp, Tyr, and Phe) albeit less efficiently (14).Since its invention, the atomic force microscope (AFM) (25) has evolved from a surface imaging device to a versatile tool for studying interactions of manifold biological systems (26–31). Introduced to characterize interactions between receptor-ligand complexes (32, 33) and complementary DNA strands (34), AFM-based single molecule force spectroscopy (SMFS) has been exploited to explore antibody-antigen recognition (35) and unfolding and refolding of soluble proteins (29, 36) and to probe the adhesion of living cells at molecular resolution (37). Applied to membrane proteins, SMFS uses the AFM stylus to exert a mechanical pulling force to the terminal end of a protein that is embedded and anchored by the lipid membrane (see Fig. 1A) (38). Sufficiently high stretching forces initiate sequential unfolding of the membrane protein with each step indicating the unfolding of a structural segment (39). Recording the applied force over pulling distance results in a force-distance (F-D) curve in which individual force peaks represent the rupture of intra- and intermolecular interactions. The height of a force peak measures the strength of an interaction with piconewton accuracy, and the pulling distance, at which the force peak occurs, allows the interaction within the membrane protein structure to be located (38).Open in a separate windowFIGURE 1.SMFS of SteT. A, pushing the AFM stylus onto the proteoliposomes promotes contacting single transporters to the stylus. This molecular link allows exertion of a mechanical pulling force that initiates stepwise unfolding of SteT. During the experiments, sample and cantilever are immersed in buffer solution. B, F-D curves recorded while unfolding single substrate-free SteT molecules. C, superimpositions of F-D curves recorded while unfolding SteT in buffer lacking any substrate (top) and supplemented with 5 mm l-serine (middle) or 5 mm l-threonine (bottom). Superimpositions are represented as density plots, each calculated from 60 F-D curves. Gray lines represent WLC curves with a persistence length of 0.4 nm and contour length (in amino acids) as indicated by the numbers next to the lines. The contour lengths were obtained from the Gaussian fits shown in D. F-D curves were obtained at room temperature at a pulling velocity of 654 nm/s in buffer solution (150 mm NaCl, 20 mm Tris-HCl, pH 8.0, substrate as indicated). D, frequency of force peaks detected at different positions of the stretched polypeptide. Every force peak detected in individual F-D curves (B) was fitted using the WLC model with the contour length of the stretched polypeptide as the only fitting parameter. The frequency at which the force peaks appeared is plotted in the histogram: substrate-free, n = 132; 5 mm l-serine, n = 128; and 5 mm l-threonine, n = 127. The bin size of the histograms is 3 aa and reflects the accuracy of fitting the WLC model (55) to individual force peaks. Error bars representing the S.E. were calculated using S.E. = (p(1 − p)/n)^0.5 where p is the probability and n is the total number of F-D curves. The width of each force peak distribution is given by the experimental noise, conformational variability of the structural segments, and fitting accuracy of the force peaks (53, 99–102). The gray solid curve represents the sum of seven Gaussian fits to the seven main peaks from the histograms and superimpositions (C). Numbers next to peaks denote peak positions (measured in amino acids) obtained from Gaussian fits.Besides quantification and localization of molecular interactions in membrane proteins, SMFS provides information about their energy landscape. For that purpose, the interactions of membrane proteins are probed over a range of different time scales by dynamic force spectroscopy (DFS). Bell (40) and Evans and co-worker (41, 42) provided the most commonly used theoretical framework to analyze DFS data. Their model describes the deformation of the energy landscape by an externally applied force, F. Such force-induced deformations reduce the energy barriers that separate bound and unbound states (see Fig. 2). Consequently transition rates over such energy barriers are force-dependent. Probing the interactions at different pulling velocities and thus at different force loading rates, r_f, leads to a so-called dynamic force spectrum in which the most probable force, F*, of rupture is plotted versus the logarithm of r_f. In these dynamic force spectra, each linear regime represents an energy barrier. Energy barriers located closer to the bound state are probed at higher pulling velocities because the energy barriers located further from the bound state are suppressed by increasingly applied forces (see Fig. 2) (41). The slope of each linear regime measures the distance from the ground state to the transition state, whereas extrapolation of a linear regime to zero force provides the rate constant of crossing the corresponding barrier in the absence of any load. These two parameters allow an estimate of the rigidity of the probed structure (43, 44).Open in a separate windowFIGURE 2.Energy landscape tilted by force. Schematic representation of the free energy profile along the reaction coordinate and applied force according to the Bell-Evans theory (40–42). The potential along the reaction coordinate (vector of force) in the absence of force (black curve) exhibits two energy barriers separating the folded from the unfolded state. Application of an external force, F, changes the thermal likelihood of reaching the top of the energy barrier(s). Although for a sharp barrier the position, x_u, of the energy barrier relative to the folded state is not changed, the thermally averaged projection of the energy profile along the pulling direction is tilted by the mechanical energy (−F·cos θ)x (long-dashed line). This tilt decreases the energy barriers (short-dashed curve). Consequently the relevant energy barrier that has to be overcome is the outermost barrier. At slow pulling velocities, the thermal contribution is higher, and therefore, the mechanical energy required to overcome the barrier is smaller. With increasing pulling velocities, the barriers are further lowered. At some velocity, the height of the outer barrier will be lower than that of the inner barrier (short-dashed curve), which then becomes the relevant energy barrier to be overcome. Each energy barrier manifests as a linear regime in dynamic force spectra (Fig. 3).In this study, we applied SMFS to characterize molecular interactions that stabilize SteT in the absence and in the presence of its substrates, l-serine and l-threonine. We used DFS to characterize how substrate binding changes the energy landscape and the mechanical properties of the antiporter. It was observed that the structural regions stabilized within SteT did not depend on substrate binding. However, substrate binding dynamically changed the energy landscape of these structures. In the absence of substrate all structural regions within SteT were stabilized by a narrow inner energy barrier and co-stabilized by a second outer energy barrier. The unique properties of these energy barriers restricted the conformation of SteT thereby trapping the antiporter in a kinetically instable and mechanically rigid conformation. In contrast, substrate binding sets SteT into a different energy minimum that significantly increased the kinetic stability and conformational flexibility of the antiporter.