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Entropy-driven instability and rupture of fluid membranes.

A computer simulation is used to investigate hole formation in a model membrane. The model parameters are the stress applied to the membrane, and the edge energy per unit length along the hole boundary (edge tension). Even at zero stress, the membrane has an entropically driven instability against hole formation. Within the model, the minimum edge tension required for the stability of a typical biological membrane is in the region of 1 x 10(-11) J/m, which is similar to the edge tension obtained in many measurements of biomembranes. At the zero-stress instability threshold, the hole shape is the same as a self-avoiding ring, but under compression, the hole shape assumes a branched polymer form. In the presence of large holes at zero stress, the membrane itself behaves like a branched polymer. The boundaries of the phase diagram for membrane stability are obtained, and general features of the rate of membrane rupture under stress are investigated. A model in which the entropy of hole formation is proportional to the hole perimeter is used to interpret the simulation results at small stress near the instability threshold.

Biomechanical Phenomena↗

Obfuscation of allosteric structure-function relationships by enthalpy-entropy compensation.

The pH and temperature dependence of the allosteric properties of phosphofructokinase (PFK) from Bacillus stearothermophilus have been studied from 5 to 9 and 6 to 40 degrees C, respectively. Throughout this pH and temperature range the allosteric ligands MgADP and phospho(enol)pyruvate (PEP) have no effect on kcat. The dissociation constants of the substrate, fructose 6-phosphate, and the allosteric ligands, as well as the absolute value of the coupling free energies between these ligands, all increase when the pH is raised, indicating that the inhibition by PEP and the activation by MgADP increase despite each ligand's somewhat lower affinity. However, the constituent coupling enthalpies and entropies substantially diminish in absolute value as pH is increased, suggesting that the magnitudes of molecular perturbations engendered by the binding of allosteric ligands do not correlate with the magnitudes of the functional consequences of those perturbations. Temperature and pH exert their influence on the observed allosteric behavior by changing the relative contributions made by the largely compensating DeltaH and TDeltaS terms to the coupling free energy.

Allosteric Regulation↗

Effect of volatile anesthetics on interhemispheric EEG cross-approximate entropy in the rat.

Dissimilarity of the electroencephalogram (EEG) between the two hemispheres was characterized by cross-approximate entropy (C-ApEn), an information statistical parameter applicable to nonlinear, aperiodic signals. EEGs were recorded bipolarly with pairs of epidural electrodes in the left and right frontal cortices. The signals were filtered for 1-100 Hz and digitized at 200 Hz. Inhaled anesthetic concentration was varied between 0.3 and 2.1% with 45-min equilibration periods while the rats were breathing spontaneously. Anesthetics produced concentration-dependent changes in C-ApEn. A greater dynamic range of C-ApEn was obtained by reducing the epoch length from 2 s to 100 ms. At a 0.4% inspired agent concentration halothane caused an increase of C-ApEn, whereas isoflurane did not. When the inspired concentrations of both agents were greater than 0.4%, C-ApEn dose-dependently decreased as agent concentrations increased. Isoflurane depressed C-ApEn more than did halothane at all equivalent minimum alveolar concentration levels, but the two agents became equipotent at 1.5% inspired concentration. C-ApEn fell below the awake baseline at 0.8% anesthetic concentration that also abolished the righting reflex. C-ApEn increased after high-pass filtering (>20 Hz) and decreased after-low pass filtering (<20 Hz) of the digitized EEG; the anesthetic dependence of C-ApEn was diminished by both filters. The results suggest that C-ApEn of bihemispheric EEG is a sensitive, agent-specific correlate of anesthetics' central effect.

Anesthetics, Inhalation↗

Use of approximate entropy measurements to classify ventricular tachycardia and fibrillation.

Implantable cardiac devices which treat arrhythmias require automated detection to decide when to deliver therapy and, in some devices like the implantable cardioverter-defibrillator (ICD), to determine which therapy to deliver. This type of detection often requires the separation of fibrillatory chaotic rhythms from coherent tachycardias. In the ICD, multiple rate zones can be programmed for detection of ventricular tachycardia (VT) and ventricular fibrillation (VF) and for delivery of therapy: antitachycardia pacing and cardioversion for VT, and defibrillation for VF. Previous research determined that current technology is unable to uniquely classify VF. Analysis of typical settings of the ICD revealed that 40% to 80% of VTs were misclassified as VF (depending on device/setting). Improved detection of VF must be sought in order to capitalize on the cost effectiveness of low-energy VT therapies, potentially saving up to 20% of the life of the battery. In this study, a statistical measure of variability, called approximate entropy (ApEn), has been applied to separate fibrillatory and nonfibrillatory rhythms. Although standard deviation is often used as a measure of variability, it fails to capture the level of regularity or complexity. ApEn improves upon standard deviation by quantifying differences between random and regular signals. ApEn was tested on a small patient set containing VF, VT, and sinus rhythm (SR). Intracardiac recordings (bipolar, ventricular) were selected from the Ann Arbor Electrogram Library (Ann Arbor, MI) where filtering (1-500 Hz), amplification (approximately 1000), and digitization (1000 Hz) are tightly controlled. Results demonstrated that ApEn has the ability to quantify subtle differences between VF and other rhythms.

Cost-Benefit Analysis↗

Enzyme catalysis via control of activation entropy: site-directed mutagenesis of 6,7-dimethyl-8-ribityllumazine synthase.

6,7-Dimethyl-8-ribityllumazine synthase (lumazine synthase) catalyses the penultimate step in the biosynthesis of riboflavin. In Bacillus subtilis, 60 lumazine synthase subunits form an icosahedral capsid enclosing a homotrimeric riboflavin synthase unit. The ribH gene specifying the lumazine synthase subunit can be expressed in high yield. All amino acid residues exposed at the surface of the active site cavity were modified by PCR assisted mutagenesis. Polar amino acid residues in direct contact with the enzyme substrates, 5-amino-6-ribitylamino-2,4(1H,3H)-pyrimidinedione and 3,4-dihydroxy-2-butanone 4-phosphate, could be replaced with relative impunity with regard to the catalytic properties. Only the replacement of Arg127, which forms a salt bridge with the phosphate group of 3,4-dihydroxy-2-butanone 4-phosphate, reduced the catalytic rate by more than one order of magnitude. Replacement of His88, which is believed to assist in proton transfer reactions, reduced the catalytic activity by about one order of magnitude. Surprisingly, the activation enthalpy deltaH of the lumazine synthase reaction exceeds that of the uncatalysed reaction. On the other hand, the free energy of activation deltaG of the uncatalysed reaction is characterised by a large entropic term (TdeltaS) of -37.8 kJmol(-1), whereas the entropy of activation (TdeltaS) of the enzyme-catalysed reaction is -6.7 kJmol(-1). This suggests that the rate enhancement by the enzyme is predominantly achieved by establishing a favourable topological relation of the two substrates, whereas acid/base catalysis may play a secondary role.

Bacillus subtilis↗

Investigations into sequence and conformational dependence of backbone entropy, inter-basin dynamics and the Flory isolated-pair hypothesis for peptides.

The populations and transitions between Ramachandran basins are studied for combinations of the standard 20 amino acids in monomers, dimers and trimers using an implicit solvent Langevin dynamics algorithm and employing seven commonly used force-fields. Both the basin populations and inter-conversion rates are influenced by the nearest neighbor's conformation and identity, contrary to the Flory isolated-pair hypothesis. This conclusion is robust to the choice of force-field, even though the use of different force-fields produces large variations in the populations and inter-conversion rates between the dominant helical, extended beta, and polyproline II basins. The computed variation of conformational and dynamical properties with different force-fields exceeds the difference between explicit and implicit solvent calculations using the same force-field. For all force-fields, the inter-basin transitions exhibit a directional dependence, with most transitions going through extended beta conformation, even when it is the least populated basin. The implications of these results are discussed in the context of estimates for the backbone entropy of single residues, and for the ability of all-atom simulations to reproduce experimental protein folding data.

Algorithms↗

The method to compare nucleotide sequences based on the minimum entropy principle.

A new method to compare two (or several) symbol sequences is developed. The method is based on the comparison of the frequencies of the small fragments of the compared sequences; it requires neither string editing, nor other transformations of the compared objects. The comparison is executed through a calculation of the specific entropy of a frequency dictionary against the special dictionary called the hybrid one; this latter is the statistical ancestor of the group of sequences under comparison. Some applications of the developed method in the fields of genetics and bioinformatics are discussed.

Animals↗

Maximum-entropy determination of self-association distribution functions; daunorubicin and ATP.

In the present paper we show how one can use the perturbation of some molecular optical property (for example circular dichroism or chemical shift) as a function of concentration to construct cluster distribution functions describing the self-association of molecules in solution. The optical data are first converted into data giving the variation of the average extent of clustering as a function of the total concentration and then, using straightforward thermodynamics, a set of moments of the cluster distribution function can be obtained. Utilizing the maximum-entropy method, the moments are then used to calculate approximate distribution functions, where the more moments that are used the better the approximation obtained. Given the probability distribution for clusters of different sizes one can then calculate the equilibrium constant for each stage of association. Thus one converts average degree of association into equilibrium constants without having to use any specific model. By this method one can clearly tell whether the equilibrium constants remain constant, increase, or decrease with the number of molecules in a cluster. We apply the method to literature data for two systems, namely daunorubicin, which has a strong tendency to cluster in solution, and Mg(ATP)(2-) which forms weaker clusters. We find that the successive equilibrium constants for adding a monomer to a cluster are approximately constant for daunorubicin but clearly decrease as a function of increasing cluster size for Mg(ATP)(2-).

Adenosine Triphosphate↗

Intravenous cocaine decreases cardiac vagal tone, vagal index (derived in lorenz space), and heart period complexity (approximate entropy) in cocaine abusers.

We assessed the effects of i.v. cocaine on parasympathetic and sympathetic nervous system activity, and on the complexity vs. regularity of changes in heart rate over time. Fourteen otherwise healthy men with histories of i.v. cocaine abuse received bolus injections of cocaine (20 mg or 40 mg) and placebo (saline) on different days. Cardiovascular measures derived from the electrocardiogram, including heart rate, Porges' vagal tone (respiratory sinus arrhythmia), the 0.10 Hz rhythm, Toichi's vagal index, Toichi's sympathetic index, and approximate entropy (ApEn), were measured continuously. As predicted, cocaine produced tachycardia, accompanied by pronounced decreases in response to 40 mg cocaine in two different vagal tone indexes that precisely mirrored the increases in heart rate. The measure of sympathetic (and vagal) neural influences on the heart (0.10 Hz wave) also decreased in response to cocaine. Converging evidence from Toichi's vagal index supported the conclusion that the tachycardia from cocaine was due to withdrawal of cardiac vagal tone. These findings, and evidence that cocaine decreased cardiovascular complexity, contradict the prevailing assumption that the mechanism by which cocaine produces tachycardia is sympathetic (beta-adrenergic). We discuss implications for cardiac arrhythmias associated with cocaine abuse and death due to overdose.

Adult↗

Shannon entropy applied to the analysis of event-related fMRI time series.

Event-related functional magnetic resonance imaging (ER-fMRI) refers to the blood oxygen level-dependent (BOLD) signal in response to a short stimulus followed by a long period of rest. These paradigms have become more popular in the last few years due to some advantages over standard block techniques. Most of the analysis of the time series generated in such exams is based on a model of specific hemodynamic response function. In this paper we propose a new method for the analysis of ER-fMRI based in a specific aspect of information theory: the entropy of a signal using the Shannon formulation, which makes no assumption about the shape of the response. The results show the ability to discriminate between activated and resting cerebral regions for motor and visual stimuli. Moreover, the results of simulated data show a more stable pattern of the method, if compared to typical algorithms, when the signal to noise ratio decreases.

Adult↗

Distributed source imaging of alpha activity using a maximum entropy principle.

OBJECTIVE: We present a method based on the distributed dipole source model to localize sources of spontaneous human brain activity, such as the alpha rhythm. The proposed method relies on the generalized maximum entropy principle and is implemented in frequency-domain. METHODS: Several computer simulation studies of synchronous and asynchronous distributed dipole sources were carried out to test the validity of the method. The method was also applied to spontaneous electroencephalographic (EEG) recordings from human subjects to estimate the sources of alpha activity. The locations of these sources were registered with actual magnetic resonance images for anatomical visualization. RESULTS: The simulation studies suggest the validity of the proposed method and its capability to detect distributed and fairly deep synchronous dipole sources. Results of human studies with 6 subjects suggest that the generators of alpha rhythm are mainly concentrated over the posterior regions of the cortex. CONCLUSION: The proposed distributed source imaging method is a promising technique for localizing rhythmic brain activity.

Adult↗

Thermodynamics of electron transfer in oxygenic photosynthetic reaction centers: volume change, enthalpy, and entropy of electron-transfer reactions in manganese-depleted photosystem II core complexes.

We have previously reported the thermodynamic data of electron transfer in photosystem I using pulsed time-resolved photoacoustics [Hou et al. (2001) Biochemistry 40, 7109-7116]. In the present work, using preparations of purified manganese-depleted photosystem II (PS II) core complexes from Synechocystis sp. PCC 6803, we have measured the DeltaV, DeltaH, and estimated TDeltaS of electron transfer on the time scale of 1 micros. At pH 6.0, the volume contraction of PS II was determined to be -9 +/- 1 A3. The thermal efficiency was found to be 52 +/- 5%, which corresponds to an enthalpy change of -0.9 +/- 0.1 eV for the formation of the state P680+Q(A-) from P680*. An unexpected volume expansion on pulse saturation of PS II was observed, which is reversible in the dark. At pH 9.0, the volume contraction, the thermal efficiency, and the enthalpy change were -3.4 +/- 0.5 A3, 37 +/- 7%, and -1.15 +/- 0.13 eV, respectively. The DeltaV of PS II, smaller than that of PS I and bacterial centers, is assigned to electrostriction and analyzed using the Drude-Nernst equation. To explain the small DeltaV for the formation of P680+Q(A-) or Y(Z*)Q(A-), we propose that fast proton transfer into a polar region is involved in this reaction. Taking the free energy of charge separation of PS II as the difference between the energy of the excited-state P680* and the difference in the redox potentials of the donor and acceptor, the apparent entropy change (TDeltaS) for charge separation of PS II is calculated to be negative, -0.1 +/- 0.1 eV at pH 6.0 (P680+Q(A-)) and -0.2 +/- 0.15 eV at pH 9.0 (Y(Z*)Q(A-)). The thermodynamic properties of electron transfer in PS II core reaction centers thus differ considerably from those of bacterial and PS I reaction centers, which have DeltaV of approximately -27 A3, DeltaH of approximately -0.4 eV, and TDeltaS of approximately +0.4 eV.

Cyanobacteria↗

Thermodynamics of electron transfer in oxygenic photosynthetic reaction centers: volume change, enthalpy, and entropy of electron-transfer reactions in the intact cells of the cyanobacterium Synechocystis PCC 6803.

The volume and enthalpy changes for charge transfer in the 0.1-10 micros time window in photosynthetic reaction centers of the intact cells of Synechocystis PCC 6803 were determined using pulsed, time-resolved photoacoustics. This required invention of a method to correct for the cell artifact at the temperature of maximum density of water caused by the heterogeneous system. Cells grown under either white or red light had different PS I/PS II molar ratios, approximately 3 and approximately 1.7, respectively, but invariable action spectra and effective antenna sizes of the photosystems. In both cultures, the photoacoustic measurements revealed that their thermodynamic parameters differed strongly in the spectral regions of predominant excitation of PS I (680 nm) and PS II (625 nm). On correcting for contribution of the two photosystems at these wavelengths, the volume change was determined to be -27 +/- 3 and -2 +/- 3 A3 for PS I and PS II, respectively. The energy storage on the approximately 1 micros time scale was estimated to be 80 +/- 15% and 45 +/- 10% per trap in PS I and PS II, respectively. These correspond to enthalpies of -0.33 +/- 0.2 and -1 +/- 0.2 eV for the assumed formation of ion radical pairs P700+F(AB-) and Y(Z*)P680Q(A-), respectively. Taking the free energy of the above reactions as the differences of their redox potentials in situ, apparent entropy changes were estimated to be +0.4 +/- 0.2 and -0.2 +/- 0.2 eV for PS I and PS II, respectively. These values are similar to that obtained in vitro for the purified reaction center complexes on the microsecond time scale [Hou et al. (2001) Biochemistry 40, 7109-7116, 7117-7125]. The constancy of these thermodynamic values over a 2-fold change of the ratio of PS I/PS II is support for this method of in vivo analysis. Our pulsed PA method can correct the "cell" or heterogeneous artifact and thus opens a new route for studying the thermodynamics of electron transfer in vivo.

Calorimetry↗

Energetics of domain-domain interactions and entropy driven association of beta-crystallins.

Beta-crystallins are major protein constituents of the mammalian lens, where their stability and association into higher order complexes are critical for lens clarity and refraction. They undergo modification as the lens ages, including cleavage of their terminal extensions. The energetics of betaA3- and betaB2-crystallin association was studied using site-directed mutagenesis and analytical ultracentrifugation. Recombinant (r) murine wild type betaA3- and betaB2-crystallins were modified by removal of either the N-terminal extension of betaA3 (rbetaA3Ntr) or betaB2 (rbetaB2Ntr), or both the N- and C-terminal extensions of betaB2 (rbetaB2NCtr). The proteins were expressed in Sf9 insect cells or Escherichia coli and purified by gel-filtration and ion-exchange chromatography. All beta-crystallins studied demonstrated fast reversible monomer-dimer equilibria over the temperature range studied (5-35 degrees C) with a tendency to form tighter dimers at higher temperatures. The N-terminal deletion of rbetaA3 (rbetaA3Ntr) significantly increases the enthalpy (+10.9 kcal/mol) and entropy (+40.7 cal/deg mol) of binding relative to unmodified protein. Removal of both N- and C-terminal extensions of rbetaB2 also increases these parameters but to a lesser degree. Deletion of the betaB2-crystallin N-terminal extension alone (rbetaB2Ntr) gave almost no change relative to rbetaB2. The resultant net negative changes in the binding energy suggest that betaAlpha3- and betaB2-crystallin association is entropically driven. The thermodynamic consequences of the loss of betaAlpha3-crystallin terminal extensions by in vivo proteolytic processing could increase their tendency to associate and so promote the formation of higher order associates in the aging and cataractous lens.

Amino Acid Sequence↗

Entropy-enthalpy compensation in ionic interactions probed in a zinc finger peptide.

Zinc(II) and cobalt(II) binding to a series of zinc finger peptides with different charged residue pairs across from one another in a beta-sheet were examined. Previous studies revealed a narrow range of interaction free energies (<0.5 kcal/mol) between these residues. Here, isothermal titration calorimetry studies were performed, revealing a range of over 3 kcal/mol in relative binding enthalpies. Double mutant cycle analysis revealed a range of interaction enthalpies ranging from -3.1 to -3.4 kcal/mol for the Arg-Asp pair to -0.8 kcal/mol for the Lys-Glu pair. The large range of interaction enthalpies coupled with the small range of interaction free energies reveals substantial entropy-enthalpy compensation. The magnitudes of the effects are consistent with the formation of a structurally rigid Arg-Asp contact ion pair but less direct and more mobile interactions involving the other combinations.

Calorimetry↗

Unusual entropy-driven affinity of Chromobacterium violaceum lectin CV-IIL toward fucose and mannose.

The purple pigmented bacterium Chromobacterium violaceum is a dominant component of tropical soil microbiota that can cause rare but fatal septicaemia in humans. Its sequenced genome provides insight into the abundant potential of this organism for biotechnological and pharmaceutical applications and allowed an ORF encoding a protein that is 60% identical to the fucose binding lectin (PA-IIL) from Pseudomonas aeruginosa and the mannose binding lectin (RS-IIL) from Ralstonia solanacearum to be identified. The lectin, CV-IIL, has recently been purified from C. violaceum [Zinger-Yosovich, K., Sudakevitz, D., Imberty, A., Garber, N. C., and Gilboa-Garber, N. (2006) Microbiology 152, 457-463] and has been confirmed to be a tetramer with subunit size of 11.86 kDa and a binding preference for fucose. We describe here the cloning of CV-IIL and its expression as a recombinant protein. A complete structure-function characterization has been made in an effort to analyze the specificity and affinity of CV-IIL for fucose and mannose. Crystal structures of CV-IIL complexes with monosaccharides have yielded the molecular basis of the specificity. Each monomer contains two close calcium cations that mediate the binding of the monosaccharides, which occurs in different orientations for fucose and mannose. The thermodynamics of binding has been analyzed by titration microcalorimetry, giving dissociation constants of 1.7 and 19 microM for alpha-methyl fucoside and alpha-methyl mannoside, respectively. Further analysis demonstrated a strongly favorable entropy term that is unusual in carbohydrate binding. A comparison with both PA-IIL and RS-IIL, which have binding preferences for fucose and mannose, respectively, yielded insights into the monosaccharide specificity of this important class of soluble bacterial lectins.

Bacterial Proteins↗

Characterization of the backbone and side chain dynamics of the CaM-CaMKIp complex reveals microscopic contributions to protein conformational entropy.

Calmodulin is a central mediator of calcium-dependent signal transduction pathways and regulates the activity of a large number of diverse targets. Calcium-dependent interactions of calmodulin with regulated proteins are of generally high affinity but of quite variable thermodynamic origins. Here we investigate the influence of the binding of the calmodulin-binding domain of calmodulin kinase I on the fast internal dynamics of calcium-saturated calmodulin. NMR relaxation was used to probe motion on the backbone (viewed through the backbone amide NH group) and the side chains (viewed through methyl groups). The distribution of the amplitudes of side chain dynamics is trimodal. The microscopic details of side chain motion are compared with those of a thermodynamically and structurally similar complex of calmodulin with the calmodulin-binding domain of the smooth muscle myosin light chain kinase. While there are no significant differences in backbone dynamics and no net change in methyl-bearing side chain dynamics, a large redistribution of the amplitude of methyl dynamics is observed between the two complexes. The variation in dynamics was largely localized to the heterogeneously dynamic target-binding interface, suggesting that differential dynamics of the binding surface plays a functional role in the high-affinity binding interactions of calmodulin. These results begin to reveal a fundamental role for residual protein entropy in molecular recognition by calmodulin.

Amino Acid Sequence↗

15N NMR relaxation studies of free and inhibitor-bound 4-oxalocrotonate tautomerase: backbone dynamics and entropy changes of an enzyme upon inhibitor binding.

The solution secondary structure of 4-oxalocrotonate tautomerase (4-OT), a 41 kDa homohexamer with 62 residues per subunit, consists of an alpha-helix, two beta-strands, a beta-hairpin, two loops, two turns, and a C-terminal coil [Stivers et al. (1996) Protein Sci. 5, 729-741]. The general base, proline-1, as well as the two loops and the beta-hairpin have been shown to comprise the active site [Stivers et al. (1996) Biochemistry 35, 814-823]. The backbone dynamics of both the free enzyme and its complex with a substrate analog have been studied by 1H-detected 15N relaxation rates and NOE determinations at 500 and 600 MHz. Analysis of the data using the model-free formalism showed that the nanosecond to picosecond motion of 53 of the 60 backbone 15N-H vectors was highly restricted with a mean order parameter mean value of S2 = 0.87 +/- 0.03. The lowest backbone mobility (S2 > 0.90) is found in the beta 1-strand, loop 2, and turn 2. Greater backbone mobility is found in the active site (0.5 < or = S2 < or = 0.83) and at C-terminal residues 58-62 (0.03 < or = S2 < or = 0.70). A tau m value for the free hexamer of 13.7 ns at 42 degrees C was determined, consistent with a compact globular molecule of 41 kDa. Saturation of 4-OT with the analog of the dienolic intermediate and linear competitive inhibitor cis, cis-muconate (4) (KD = 0.59 mM) increased the backbone S2 of seven residues and decreased the backbone S2 of another eight residues, both at the active site and at the antiparallel beta 1-beta 1 interface. The S2 values of the other 44 detectable NH vectors were not altered by the binding of 4. The increases in S2, resulting from the "freezing" of the backbone NH vectors of seven residues upon the binding of 4, correspond to an unfavorable entropic contribution to delta Gbinding of 3.2 +/- 1.1 kcal/mol. This freezing is partially compensated for by the mobilization of the other eight residues, since the decreases in S2 for these residues correspond to an entropic contribution to binding of -1.9 +/- 0.1 kcal/mol. These entropy changes, resulting solely from alterations in high-frequency motion, are significant compared to the overall delta Gbinding = -4.6 kcal/mol for 4. Other effects of the binding of 4 include (1) changes in 15N and NH chemical shifts localized to the active site and (2) increases in the exchange contributions (R(ex)) to 1/T2 of backbone 15N resonances at the active site and at the subunit interface, reflecting microsecond to millisecond motions which may play a role in substrate binding (k(on) > or = 4 x 10(6) M-1 s-1) and/or catalysis (kcat = 10(3) s-1).

Binding Sites↗