Specificity and Affinity Quantification of Flexible Recognition from Underlying Energy Landscape Topography

Flexibility in biomolecular recognition is essential and critical for many cellular activities. Flexible recognition often leads to moderate affinity but high specificity, in contradiction with the conventional wisdom that high affinity and high specificity are coupled. Furthermore, quantitative understanding of the role of flexibility in biomolecular recognition is still challenging. Here, we meet the challenge by quantifying the intrinsic biomolecular recognition energy landscapes with and without flexibility through the underlying density of states. We quantified the thermodynamic intrinsic specificity by the topography of the intrinsic binding energy landscape and the kinetic specificity by association rate. We found that the thermodynamic and kinetic specificity are strongly correlated. Furthermore, we found that flexibility decreases binding affinity on one hand, but increases binding specificity on the other hand, and the decreasing or increasing proportion of affinity and specificity are strongly correlated with the degree of flexibility. This shows more (less) flexibility leads to weaker (stronger) coupling between affinity and specificity. Our work provides a theoretical foundation and quantitative explanation of the previous qualitative studies on the relationship among flexibility, affinity and specificity. In addition, we found that the folding energy landscapes are more funneled with binding, indicating that binding helps folding during the recognition. Finally, we demonstrated that the whole binding-folding energy landscapes can be integrated by the rigid binding and isolated folding energy landscapes under weak flexibility. Our results provide a novel way to quantify the affinity and specificity in flexible biomolecular recognition.     

Substrate Affinity and Specificity of the ScSth1p Bromodomain Are Fine-Tuned for Versatile Histone Recognition

1. Download : Download high-res image (238KB)
2. Download : Download full-size image

     

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 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.     

Kinetics of Fast Changing Intramolecular Distance Distributions Obtained by Combined Analysis of FRET Efficiency Kinetics and Time-Resolved FRET Equilibrium Measurements

Detailed studies of the mechanisms of macromolecular conformational transitions such as protein folding are enhanced by analysis of changes of distributions for intramolecular distances during the transitions. Time-resolved Förster resonance energy transfer (FRET) measurements yield such data, but the more readily available kinetics of mean FRET efficiency changes cannot be analyzed in terms of changes in distances because of the sixth-power dependence on the mean distance. To enhance the information obtained from mean FRET efficiency kinetics, we combined the analyses of FRET efficiency kinetics and equilibrium trFRET experiments. The joint analysis enabled determination of transient distance distributions along the folding reaction both in cases where a two-state transition is valid and in some cases consisting of a three-state scenario. The procedure and its limits were tested by simulations. Experimental data obtained from stopped-flow measurements of the refolding of Escherichia coli adenylate kinase were analyzed. The distance distributions between three double-labeled mutants, in the collapsed transient state, were determined and compared to those obtained experimentally using the double-kinetics technique. The proposed method effectively provides information on distance distributions of kinetically accessed intermediates of fast conformational transitions induced by common relaxation methods.     

Kinetics of Fast Changing Intramolecular Distance Distributions Obtained by Combined Analysis of FRET Efficiency Kinetics and Time-Resolved FRET Equilibrium Measurements

Detailed studies of the mechanisms of macromolecular conformational transitions such as protein folding are enhanced by analysis of changes of distributions for intramolecular distances during the transitions. Time-resolved Förster resonance energy transfer (FRET) measurements yield such data, but the more readily available kinetics of mean FRET efficiency changes cannot be analyzed in terms of changes in distances because of the sixth-power dependence on the mean distance. To enhance the information obtained from mean FRET efficiency kinetics, we combined the analyses of FRET efficiency kinetics and equilibrium trFRET experiments. The joint analysis enabled determination of transient distance distributions along the folding reaction both in cases where a two-state transition is valid and in some cases consisting of a three-state scenario. The procedure and its limits were tested by simulations. Experimental data obtained from stopped-flow measurements of the refolding of Escherichia coli adenylate kinase were analyzed. The distance distributions between three double-labeled mutants, in the collapsed transient state, were determined and compared to those obtained experimentally using the double-kinetics technique. The proposed method effectively provides information on distance distributions of kinetically accessed intermediates of fast conformational transitions induced by common relaxation methods.     

Enzyme Kinetics for Complex System Enables Accurate Determination of Specificity Constants of Numerous Substrates in a Mixture by Proteomics Platform

Many important experiments in proteomics including protein digestion, enzyme substrate screening, enzymatic labeling, etc., involve the enzymatic reactions in a complex system where numerous substrates coexists with an enzyme. However, the enzyme kinetics in such a system remains unexplored and poorly understood. Herein, we derived and validated the kinetics equations for the enzymatic reactions in complex system. We developed an iteration approach to depict the enzymatic reactions in complex system. It was validated by 630 time-course points from 24 enzymatic reaction experiments and was demonstrated to be a powerful tool to simulate the reactions in the complex system. By applying this approach, we found that the ratio of substrate depletion is independent of other coexisted substrates under specific condition. This observation was then validated by experiments. Based on this striking observation, a simplified model was developed to determine the catalytic efficiencies of numerous competing substrates presented in the complex enzyme reaction system. When coupled with high-throughput quantitative proteomics technique, this simplified model enabled the accurate determination of catalytic efficiencies for 2369 peptide substrates of a protease by using only one enzymatic reaction experiment. Thus, this study provided, in the first time, a validated model for the large scale determination of specificity constants which could enable the enzyme substrate screening approach turned from a qualitative method of identifying substrates to a quantitative method of identifying and prioritizing substrates. Data are available via ProteomeXchange with identifier PXD004665.     

Crucial Roles of Single Residues in Binding Affinity,Specificity, and Promiscuity in the Cellulosomal Cohesin-Dockerin Interface

Interactions between cohesin and dockerin modules play a crucial role in the assembly of multienzyme cellulosome complexes. Although intraspecies cohesin and dockerin modules bind in general with high affinity but indiscriminately, cross-species binding is rare. Here, we combined ELISA-based experiments with Rosetta-based computational design to evaluate the contribution of distinct residues at the Clostridium thermocellum cohesin-dockerin interface to binding affinity, specificity, and promiscuity. We found that single mutations can show distinct and significant effects on binding affinity and specificity. In particular, mutations at cohesin position Asn³⁷ show dramatic variability in their effect on dockerin binding affinity and specificity: the N37A mutant binds promiscuously both to cognate (C. thermocellum) as well as to non-cognate Clostridium cellulolyticum dockerin. N37L in turn switches binding specificity: compared with the wild-type C. thermocellum cohesin, this mutant shows significantly increased preference for C. cellulolyticum dockerin combined with strongly reduced binding to its cognate C. thermocellum dockerin. The observation that a single mutation can overcome the naturally observed specificity barrier provides insights into the evolutionary dynamics of this system that allows rapid modulation of binding specificity within a high affinity background.     

Binding Specificity and Affinity of Acriflavine for Nucleic Acids

A set of conditions was developed for the specific binding of acriflavine to the DNA of intact squamous cells. This was achieved through a series of studies into the relative affinities for dye between DNA and various biopolymers by an agar gel diffusion technique. Specificity was ascertained by DNase and RNase treatment of the cells. The final conditions, based on an estimated DNA-to-dye ratio of 4:1, required a constant cell count of 100,000 and dye at a concentration of 0.0025 μg per ml in 10 ml of phosphate buffer, pH 6.0-7.4. These quantities were dictated by the sensitivity limitations of the analytical apparatus. To make use of standard fluorometric instrumentation, the whole cell population method for determining average values was followed. Free dye was analyzed after cell samples were stained, and the difference between this value and that of an aliquot of working dye was taken as the amount of bound dye. To ensure cell-free residues of dye, cells were removed by centrifugation through Teflon membrane filters. The average amount of dye which was bound to the DNA of normal squamous cells was 1.6 × 10^-7 μg (0.7 × 10^-15 mole) per cell, and the amount bound to HeLa cells was 2.3 × 10^-7 μg (1 × 10^-15 mole). These values were highly replicable, making it possible to use them as an expression of the DNA content of the cells. The mildness of the staining conditions, and the preservation of cellular integrity in this technique may permit quantitative measurements of the DNA content of living cells.     

The Estimation of Rapid Rate Constants from Current-Amplitude Frequency Distributions of Single-Channel Recordings

A method is described for estimating rapid rate constants from the distributions of current amplitude observed in single-channel electrical recordings. It has the advantages over previous, similar approaches that it can accommodate both multistate kinetic models and adjustable filtering of the data using an 8-pole Bessel filter. The method is conceptually straightforward: the observed distributions of current amplitude are compared with theoretical distributions derived by combining several simplifying assumptions about the underlying stochastic process with a model of the filter and electrical noise. Parameters are estimated by approximate maximum likelihood. The method was used successfully to estimate rate constants for both a simple two-state kinetic model (the transitions between open and closed states during the rapid gating of an outward-rectifying K⁺-selective channel in the plasma membrane of Acetabularia) and a complex multistate kinetic model (the blockade of the maxi cation channel in the plasma membrane of rye roots by verapamil). For the two-state model, parameters were estimated well, provided that they were not too fast or too slow in relation to the sampling rate. In the three-state model the precision of estimates depended in a complex way on the values of all rate parameters in the model. Received: 4 October 1996/Revised: 2 September 1997     

Binding Mechanism of the Peptidoglycan Hydrolase Acm2: Low Affinity,Broad Specificity

Peptidoglycan hydrolases are bacterial secreted enzymes that cleave covalent bonds in the cell-wall peptidoglycan, thereby fulfilling major physiological functions during cell growth and division. Although the molecular structure and functional roles of these enzymes have been widely studied, the molecular details underlying their interaction with peptidoglycans remain largely unknown, mainly owing to the paucity of appropriate probing techniques. Here, we use atomic force microscopy to explore the binding mechanism of the major autolysin Acm2 from the probiotic bacterium Lactobacillus plantarum. Atomic force microscopy imaging shows that incubation of bacterial cells with Acm2 leads to major alterations of the cell-surface nanostructure, leading eventually to cell lysis. Single-molecule force spectroscopy demonstrates that the enzyme binds with low affinity to structurally different peptidoglycans and to chitin, and that glucosamine in the glycan chains is the minimal binding motif. We also find that Acm2 recognizes mucin, the main extracellular component of the intestinal mucosal layer, thereby suggesting that this enzyme may also function as a cell adhesion molecule. The binding mechanism (low affinity and broad specificity) of Acm2 may represent a generic mechanism among cell-wall hydrolases for guiding cell division and cell adhesion.     

Binding Mechanism of the Peptidoglycan Hydrolase Acm2: Low Affinity,Broad Specificity

Peptidoglycan hydrolases are bacterial secreted enzymes that cleave covalent bonds in the cell-wall peptidoglycan, thereby fulfilling major physiological functions during cell growth and division. Although the molecular structure and functional roles of these enzymes have been widely studied, the molecular details underlying their interaction with peptidoglycans remain largely unknown, mainly owing to the paucity of appropriate probing techniques. Here, we use atomic force microscopy to explore the binding mechanism of the major autolysin Acm2 from the probiotic bacterium Lactobacillus plantarum. Atomic force microscopy imaging shows that incubation of bacterial cells with Acm2 leads to major alterations of the cell-surface nanostructure, leading eventually to cell lysis. Single-molecule force spectroscopy demonstrates that the enzyme binds with low affinity to structurally different peptidoglycans and to chitin, and that glucosamine in the glycan chains is the minimal binding motif. We also find that Acm2 recognizes mucin, the main extracellular component of the intestinal mucosal layer, thereby suggesting that this enzyme may also function as a cell adhesion molecule. The binding mechanism (low affinity and broad specificity) of Acm2 may represent a generic mechanism among cell-wall hydrolases for guiding cell division and cell adhesion.     

Distributions of Potential in Cylindrical Coordinates and Time Constants for a Membrane Cylinder

A mathematical problem relating to membrane cylinders is stated and solved; its implications are illustrated and discussed. The problem concerns the volume distribution, in cylindrical coordinates, of the electric potential inside and outside a membrane cylinder of finite length (with sealed ends), during passive decay of an initially nonuniform membrane potential. The time constants for equalization with respect to the angle, theta, are shown to be typically about ten thousand times smaller than the time constant, tau(m) = R(m)C(m), for uniform passive membrane potential decay. The time constants for equalization with respect to length are shown to agree with those from one-dimensional cable theory; typically, they are smaller than tau(m) by a factor between 2 and 10. The relation of the membrane current density, I(m)(theta, x, t), to the values (at the outer membrane surface) of the extracellular potential phi(e)(r, theta, x, t) and of partial differential(2)phi(e)/ partial differentialx(2), is examined and it is shown that these quantities are not proportional to each other, in general; however, under certain specified conditions, all three of these quantities are proportional with each other and with phi(i)(r, theta, x, t) and partial differential(2)phi(i)/ partial differentialx(2) (at the inner membrane surface). The relation of these results to those of one-dimensional cable theory is discussed.     

Bayesian Estimation of the Active Concentration and Affinity Constants Using Surface Plasmon Resonance Technology

Surface plasmon resonance (SPR) has previously been employed to measure the active concentration of analyte in addition to the kinetic rate constants in molecular binding reactions. Those approaches, however, have a few restrictions. In this work, a Bayesian approach is developed to determine both active concentration and affinity constants using SPR technology. With the appropriate prior probabilities on the parameters and a derived likelihood function, a Markov Chain Monte Carlo (MCMC) algorithm is applied to compute the posterior probability densities of both the active concentration and kinetic rate constants based on the collected SPR data. Compared with previous approaches, ours exploits information from the duration of the process in its entirety, including both association and dissociation phases, under partial mass transport conditions; do not depend on calibration data; multiple injections of analyte at varying flow rates are not necessary. Finally the method is validated by analyzing both simulated and experimental datasets. A software package implementing our approach is developed with a user-friendly interface and made freely available.     

Rank Distributions in Community Ecology from the Statistical Viewpoint

Traditional statistical methods for definition of empirical functions of abundance distribution (population, biomass, production, etc.) of species in a community are applicable for processing of multivariate data contained in the above quantitative indices of the communities. In particular, evaluation of moments of distribution suffices for convolution of the data contained in a list of species and their abundance. At the same time, the species should be ranked in the list in ascending rather than descending population and the distribution models should be analyzed on the basis of the data on abundant species only.     

Computational Design of the Affinity and Specificity of a Therapeutic T Cell Receptor

T cell receptors (TCRs) are key to antigen-specific immunity and are increasingly being explored as therapeutics, most visibly in cancer immunotherapy. As TCRs typically possess only low-to-moderate affinity for their peptide/MHC (pMHC) ligands, there is a recognized need to develop affinity-enhanced TCR variants. Previous in vitro engineering efforts have yielded remarkable improvements in TCR affinity, yet concerns exist about the maintenance of peptide specificity and the biological impacts of ultra-high affinity. As opposed to in vitro engineering, computational design can directly address these issues, in theory permitting the rational control of peptide specificity together with relatively controlled increments in affinity. Here we explored the efficacy of computational design with the clinically relevant TCR DMF5, which recognizes nonameric and decameric epitopes from the melanoma-associated Melan-A/MART-1 protein presented by the class I MHC HLA-A2. We tested multiple mutations selected by flexible and rigid modeling protocols, assessed impacts on affinity and specificity, and utilized the data to examine and improve algorithmic performance. We identified multiple mutations that improved binding affinity, and characterized the structure, affinity, and binding kinetics of a previously reported double mutant that exhibits an impressive 400-fold affinity improvement for the decameric pMHC ligand without detectable binding to non-cognate ligands. The structure of this high affinity mutant indicated very little conformational consequences and emphasized the high fidelity of our modeling procedure. Overall, our work showcases the capability of computational design to generate TCRs with improved pMHC affinities while explicitly accounting for peptide specificity, as well as its potential for generating TCRs with customized antigen targeting capabilities.     

Humoral Recognition Factors in the Arthropoda. The Specificity of Chelicerata Serum Lectins

Arthropods have the capacity of recognizing self from non-selfin various defense phenomena including hemolymph clotting, phagocytosis,encapsulation, melanization and clearance of the foreign matterwhich must be initiated by a first step of molecular recognition."Natural" and experimentally induced humoral factors have beendescribed which act as hemagglutinins, bacterial agglutinins,precipitins, bactericidal factors, bacteriolysins, hemolysins,opsonins, clotting factors, and lysozymes. Their exact rolein recognition functions has not been fully explored and theirfunction remains unclear. Among these factors, the carbohydrate-bindingmolecules (lectins) are the best characterized in their specificity,physicochemical properties and molecular structure. Arthropodlectins are multimeric, high molecular weight protein (glycoprotein)molecules with a certain degree of heterogeneity in their specificityand structure. In particular, serum lectins from chelicerates(horseshoe crabs, scorpions and spiders) share a common property:the specificity for sialic acids. Arachnids and merostomes divergedin the earliest Cambrian. Since they occupy markedly differenthabitats, the sialic acid specific lectins most probably area relict rather than an adaptative character. In addition tothis common feature of specificity, lectins from cheliceratesand other arthropods represent heterogeneous populations whichcan bind a wide variety of carbohydrates, many of them presenton bacteria as D-galactose, 2-keto-3-deoxyoctonate, glucuronicacid, N-acetylmuramic acid, and colominic acid. Multiplicityin specificity suggests that serum lectins might contributeas a carbohydrate-based recognition system for the non-self.The requirement for avoiding self recognition would be thatcarbohydrate structures potentially recognized by the systemwould be absent, masked or out of reach of this humoral factoror cell associated recognition factors.