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

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

The pH dependence of peptide hydrolysis by nitrocarboxypeptidase A

Hydrolysis of benzyloxycarbonyl-GlyGlyPhe by nitro(Tyr 248)carboxypeptidase A over the pH range 4.88–8.04 has been examined. The nitroenzyme retains appreciable activity near pH 6.5, and the limiting value of K_m is scarcely affected. The peptidase activity has a pH dependence characterized by the following parameters: pK_E1 of 6.37 ± 0.19 and pK_E2 of 6.60 ± 0.17 in $\text{k}{}_{\mathrm{<mtext>cat</mtext>}}\text{K}{}_{\mathrm{m}}$, and apparent pK of 5.59 ± 0.06 in K_cat. A spectroscopic pK of 6.75 ± 0.01, attributable to the nitro-Tyr 248 residue, has been determined. This correlates with the base-limb pK_E2 in the $\text{k}{}_{\mathrm{<mtext>cat</mtext>}}\text{K}{}_{\mathrm{m}}$ profile, which appears to be shifted from a higher value, pK_E2 of 9.0, for the native enzyme. The single (acid-limb) pK which characterizes the k_cat profile of the native enzyme is also found to be perturbed to a lesser extent by nitration. A kinetically competent reverse protonation mechanism, based on chemical modification and crystallographic evidence for the enzyme, is described.     

Bacillus subtilis aminopeptidase: specificity toward amino acyl-beta-naphthylamides.

The kinetic parameters for the hydrolyses of different l-α-amino acid-β-naphthylamides by Bacillus subtilis aminopeptidase have been measured for the native enzyme and for the enzyme activated in 5 mm Co(NO₃)₂. In most cases Co²⁺ activation decreased K_m(app) values and increased k_cat values, in other cases k_m(app) and k_cat values were increased; for the remainder of the substrates tested k_m(app) values and k_cat values were decreased. In all cases tested the ratios of $\text{(}\text{k}\text{cat}\text{K}{}_{\mathrm{<mtext>m(</mtext><mtext>app</mtext><mtext>)</mtext>}}\text{)}\text{CO}{}^{\mathrm{2+}}\text{/(}\text{k}{}_{\mathrm{<mtext>cat</mtext>}}\text{K}{}_{\mathrm{<mtext>m(</mtext><mtext>app</mtext><mtext>)nativ</mtext>}}\text{)}$ were increased (2- to 108-fold). For the native enzyme the order of specificity toward the l-amino acid-β-naphthylamides was Arg > Met > Trp > Lys > Leu and for the Co²⁺ activated enzyme the order of specificity was Lys > Arg > Met > Trp > Leu. The native enzyme hydrolyzed Pro-β-naphthylamide, but not α-Glu-β-naphthylamide; Co²⁺ activation of the enzyme affected an appreciable rate of hydrolysis of the latter substrate.     

The gating charge should not be estimated by fitting a two-state model to a Q-V curve

The voltage dependence of charges in voltage-sensitive proteins, typically displayed as charge versus voltage (Q-V) curves, is often quantified by fitting it to a simple two-state Boltzmann function. This procedure overlooks the fact that the fitted parameters, including the total charge, may be incorrect if the charge is moving in multiple steps. We present here the derivation of a general formulation for Q-V curves from multistate sequential models, including the case of infinite number of states. We demonstrate that the commonly used method to estimate the charge per molecule using a simple Boltzmann fit is not only inadequate, but in most cases, it underestimates the moving charge times the fraction of the field.Many ion channels, transporters, enzymes, receptors, and pumps are voltage dependent. This voltage dependence is the result of voltage-induced translocation of intrinsic charges that, in some way, affects the conformation of the molecule. The movement of such charges is manifested as a current that can be recorded under voltage clamp. The best-known examples of these currents are “gating” currents in voltage-gated channels and “sensing” currents in voltage-sensitive phosphatases. The time integral of the gating or sensing current as a function of voltage (V) is the displaced charge Q(V), normally called the Q-V curve.It is important to estimate how much is the total amount of net charge per molecule (Q_max) that relocates within the electric field because it determines whether a small or a large change in voltage is necessary to affect the function of the protein. Most importantly, knowing Q_max is critical if one wishes to correlate charge movement with structural changes in the protein. The charge is the time integral of the current, and it corresponds to the product of the actual moving charge times the fraction of the field it traverses. Therefore, correlating charge movement with structure requires knowledge of where the charged groups are located and the electric field profile. In recent papers by Chowdhury and Chanda (2012) and Sigg (2013), it was demonstrated that the total energy of activating the voltage sensor is equal to Q_max V_M, where V_M is the median voltage of charge transfer, a value that is only equal to the half-point of activation V_1/2 for symmetrical Q-V curves. V_M is easily estimated from the Q-V curve, but Q_max must be obtained with other methods because, as we will show here, it is not directly derived from the Q-V curve in the general case.The typical methods used to estimate charge per molecule Q_max include measurements of limiting slope (Almers, 1978) and the ratio of total charge divided by the number of molecules (Schoppa et al., 1992). The discussion on implementation, accuracy, and reliability of these methodologies has been addressed many times in the literature, and it will not be discussed here (see Sigg and Bezanilla, 1997). However, it is worth mentioning that these approaches tend to be technically demanding, thus driving researchers to seek alternative avenues toward estimating the total charge per molecule. Particularly, we will discuss here the use of a two-state Boltzmann distribution for this purpose. Our intention is to demonstrate that this commonly used method to estimate the charge per molecule is generally incorrect and likely to give a lower bound of the moving charge times the fraction of the field.The two-state Boltzmann distribution describes a charged particle that can only be in one of two positions or states that we could call S₁ and S₂. When the particle with charge Q_max (in units of electronic charge) moves from S₁ to S₂, or vice versa, it does it in a single step. The average charge found in position S₂, Q(V), will depend on the energy difference between S₁ and S₂, and the charge of the particle. The equation that describes Q(V) is:Q(V)=Qmax1+exp[−Qmax(V−V1/2)kT],(1)where V_1/2 is the potential at which the charge is equally distributed between S₁ and S₂, and k and T are the Boltzmann constant and absolute temperature, respectively. The Q(V) is typically normalized by dividing Eq. 1 by the total charge Q_max. The resulting function is frequently called a “single Boltzmann” in the literature and is used to fit normalized, experimentally obtained Q-V curves. The fit yields an apparent V_1/2 (V∼1/2) and an apparent Q_MAX (Q−max), and this last value is then attributed to be the total charge moving Q_max. Indeed, this is correct but only for the case of a charge moving between two positions in a single step. However, the value of Q−max thus obtained does not represent the charge per molecule for the more general (and frequent) case when the charge moves in more than one step.To demonstrate the above statement and also estimate the possible error in using the fitted Q−max from Eq. 1, let us consider the case when the gating charge moves in a series of n steps between n + 1 states, each step with a fractional charge z_i (in units of electronic charge e₀) that will add up to the total charge Q_max.S1↔μ1S2↔μ2…Si↔μiSi+1…Sn↔μnSn+1The probability of being in each of the states S_i is labeled as P_i, and the equilibrium constant of each step is given byμi=exp[zi(V−Vi)kT], i=1…n,where z_i is the charge (in units of e₀) of step i, and V_i is the membrane potential that makes the equilibrium constant equal 1. In steady state, the solution of P_i can be obtained by combiningPi+1Pi=μi, i=1…n and ∑i=1i=n+1Pi=1,givingPi+1=∏m=1iμm1+∑j=1n∏k=1jμk, i=1…n and P1=11+∑j=1n∏k=1jμk.We define the reaction coordinate along the moved charged q asqi=∑j=1izj, i=1…n.The Q-V curve is defined asQ(V)=∑i=1nqiPi+1.Then, replacing P_i yieldsQ(V)=∑i=1n[∑j=1izj][∏m=1iμm]1+∑j=1n∏k=1jμk,or written explicitly as a function of V:Q(V)=∑i=1n[∑j=1izj][∏m=1iexp[zm(V−Vm)kT]]1+∑j=1n∏k=1jexp[zk(V−Vk)kT].(2)Eq. 2 is a general solution of a sequential model with n + 1 states with arbitrary valences and V_i’s for each transition. We can easily see that Eq. 2 has a very different form than Eq. 1, except when there is only a single transition (n = 1). In this latter case, Eq. 2 reduces to Eq. 1 because z₁ and V₁ are equal to Q_max and V_1/2, respectively. For the more general situation where n > 1, if one fits the Q(V) relation obeying Eq. 2 with Eq. 1, the fitted Q−max value will not correspond to the sum of the z_i values (see examples below and Fig. 1). A simple way to visualize the discrepancy between the predicted value of Eqs. 1 and 2 is to compute the maximum slope of the Q-V curve. This can be done analytically assuming that V_i = V_o for all transitions and that the total charge Q_max is evenly divided among those transitions. The limit of the first derivative of the Q(V) with respect to V evaluated at V = V_o is given by this equation:dQ(V)dV|V=V0=Qmax(n+2)12nkT.(3)From Eq. 3, it can be seen that the slope of the Q-V curve decreases with the number of transitions being maximum and equal to Q_max /(4kT) when n = 1 (two states) and a minimum equal to Q_max /(12kT) when n goes to infinity, which is the continuous case (see next paragraph).Open in a separate windowFigure 1.Examples of normalized Q-V curves for a Q_max = 4 computed with Eq. 2 for the cases of one, two, three, four, and six transitions and the continuous case using Eq. 5 (squares). All the Q-V curves were fitted with Eq. 1 (lines). The insets show the fitted valence (Q−max) and half-point (V∼1/2).

Infinite number of steps

Eq. 2 can be generalized to the case where the charge moves continuously, corresponding to an infinite number of steps. If we makez_i = Q_max/n, ?i = 1…n, ??V_i = V_o, ?i = 1…n, then all µ_i = µ, and we can write Eq. 2 as the normalized Q(V) in the limit when n goes to infinity:Qnor(V)=limn→∞∑i=1n[∑j=1iQmaxn]∏m=1iexp[Qmax(V−Vo)nkT]Qmax[1+∑i=1n∏j=1iexp[Qmax(V−Vo)nkT]]=[Qmax(V−Vo)−kT]exp[Qmax(V−Vo)kT]+kTQmax(V−Vo)[exp[Qmax(V−Vo)kT]−1].(4)Eq. 4 can also be written asQnor(V)=12[1+coth[Qmax(V−Vo)2kT]−2kTQmax(V−V0)],(5)which is of the same form of the classical equation of paramagnetism (see Kittel, 2005).

Examples

We will illustrate now that data generated by Eq. 2 can be fitted quite well by Eq. 1, thus leading to an incorrect estimate of the total charge moved. Typically, the experimental value of the charge plotted is normalized to its maximum because there is no knowledge of the absolute amount of charge per molecule and the number of molecules. The normalized Q-V curve, Q_nor, is obtained by dividing Q(V) by the sum of all the partial charges.Fig. 1 shows Q_nor computed using Eq. 2 for one, two, three, four, and six transitions and for the continuous case using Eq. 5 (squares) with superimposed fits to a two-state Boltzmann distribution (Eq. 1, lines). The computations were done with equal charge in each step (for a total charge Q_max = 4e₀) and also the same V_i = −25 mV value for all the steps. It is clear that fits are quite acceptable for cases up to four transitions, but the fit significantly deviates in the continuous case.Considering that experimental data normally have significant scatter, it is then quite likely that the experimenter will accept the single-transition fit even for cases where there are six or more transitions (see Fig. 1). In general, the case up to four transitions will look as a very good fit, and the fitted Q−max value may be inaccurately taken and the total charge transported might be underestimated. To illustrate how bad the estimate can be for these cases, we have included as insets the fitted value of Q−max for the cases presented in Fig. 1. It is clear that the estimated value can be as low as a fourth of the real total charge. The estimated value of V∼1/2 is very close to the correct value for all cases, but we have only considered cases in which all V_i’s are the same.It should be noted that if µ_i of the rightmost transition is heavily biased to the last state (V_i is very negative), then the Q−max estimated by fitting a two-state model is much closer to the total gating charge. In a three-state model, it can be shown that the fitted value is exact when V₁→∞ and V₂→−∞ because in that case, it converts into a two-state model. Although these values of V are unrealistic, the fitted value of Q−max can be very close to the total charge when V₂ is much more negative than V₁ (that is, V₁ >> V₂). On the other hand, If V₁ << V₂, the Q-V curve will exhibit a plateau region and, as the difference between V₁ and V₂ decreases, the plateau becomes less obvious and the curve looks monotonic. These cases have been discussed in detail for the two-transition model in Lacroix et al. (2012).We conclude that it is not possible to estimate unequivocally the gating charge per sensor from a “single-Boltzmann” fit to a Q-V curve of a charge moving in multiple transitions. The estimated Q−max value will be a low estimate of the gating charge Q_max, except in the case of the two-state model or the case of a heavily biased late step, which are rare occurrences. It is then safer to call “apparent gating charge” the fitted Q−max value of the single-Boltzmann fit.

Addendum

The most general case in which transitions between states include loops, branches, and steps can be derived directly from the partition function and follows the general thermodynamic treatment by Sigg and Bezanilla (1997), Chowdhury and Chanda (2012), and Sigg (2013). The reaction coordinate is the charge moving in the general case where it evolves from q = 0 to q = Q_max by means of steps, loops, or branches. In that case, the partition function is given byZ=∑iexp(qi(V−Vi)kT).(6)We can compute the mean gating charge, also called the Q-V curve, asQ(V)=〈q〉=kTZ’Z=kTdlnZdV=∑iqiexp(qi(V−Vi)kT)∑iexp(qi(V−Vi)kT).(7)The slope of the Q-V is obtained by taking the derivative of 〈q〉 with respect to V:dQ(V)dV=(kT)2d2lnZdV2.(8)Let us now consider the gating charge fluctuation. The charge fluctuation will depend on the number of possible conformations of the charge and is expected to be a maximum when there are only two possible charged states to dwell. As the number of intermediate states increases, the charge fluctuation decreases. Now, a measure of the charge fluctuation is given by the variance of the gating charge, which can be computed from the partition function as:〈Δq2〉=〈q2〉−〈q〉2=(kT)2(Z’’Z−(Z’Z)2)=(kT)2d2lnZdV2.(9)But the variance (Eq. 9) is identical to the slope of Q(V) (Eq. 8). This implies that the slope of the Q-V is maximum when there are only two states.     

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

Mechanism of action of thrombin on fibrinogen. The reaction of thrombin with fibrinogen-like peptides containing 11, 14, and 16 residues

The following peptides were synthesized by classical methods in solution: Ac-Gly-Gly- Val-Arg-Gly-Pro-Arg-Val-Val-Glu-Arg-NHCH₃ (A), Ac-Ala-Glu-Gly-Gly-Gly-Val- Arg-Gly-Pro-Arg-Val-Val-Glu-Arg-NHCH₃ (B), and Ac-Phe-Leu-Ala-Glu-Gly-Gly- Gly-Val-Arg-Gly-Pro-Arg-Val-Val-Glu-Arg-NHCH₃ (C). The rates of hydrolysis of the Arg-Gly bond of these three peptides by thrombin were measured, and the values of $\text{k}{}_{\mathrm{<mtext>cat</mtext>}}\text{K}{}_{\mathrm{m}}$ were found to be 0.05 × 10^?7 (A), 0.02 × 10^?7 (B), and 1.6 × 10^?7 (C) [(NIH units/ liter)s]^?1. The value of$\text{k}{}_{\mathrm{<mtext>cat</mtext>}}\text{K}{}_{\mathrm{m}}$ for peptide C is less than 1% of that for fibrinogen [although the value of k_cat itself, for peptide C (but not for A or B), is comparable to that for fibrinogen]. These results indicate that phenylanine and leucine at positions P₉ and P₈, respectively, play a key role in the reaction of thrombin with fibrinogen. The data also show that factors outside of the 16 residues of peptide C are important in determining the rate of hydrolysis of fibrogen by thrombin.     

Dependence on pH of the activity of pig liver esterase

The dependence on pH of the kinetic parameters for the hydrolysis of phenyl acetate catalyzed by pig liver carboxylesterase was examined for purified high-isoelectric point and low-isoelectric point fractions of enzyme that were separated by isoelectric focusing. The values of k_cat are half-maximal at pH 4.3 and 5.1 for the high- and low-isoelectric point forms, respectively, and show a shallow dependence on pH with a value of n = 0.5. The absence of a change in the pH dependence of k_cat for the high-isoelectric point enzyme in the presence of high concentrations of methanol, which reacts with the acetyl-enzyme intermediate to give methyl acetate, provides evidence that the pH dependence is not caused by a change in rate-determining step. This means that if an imidazole group is involved in catalysis its pK must be perturbed downward by 2–3 units. The pH dependence of $\text{k}{}_{\mathrm{<mtext>cat</mtext>}}\text{K}{}_{\mathrm{m}}$ is biphasic with apparent pK values for dissociations of the free enzyme near 7 and 4 for both the high- and low-isoelectric point enzymes. Inhibition by a second molecule of substrate and by methanol are strongest for high-pH forms of the enzyme.     

Deactivation of a Negative Regulator: A Distinct Signal Transduction Mechanism,Pronounced in Akt Signaling

Kinase cascades, in which enzymes are sequentially activated by phosphorylation, are quintessential signaling pathways. Signal transduction is not always achieved by direct activation, however. Often, kinases activate pathways by deactivation of a negative regulator; this indirect mechanism, pervasive in Akt signaling, has yet to be systematically explored. Here, we show that the indirect mechanism has properties that are distinct from direct activation. With comparable parameters, the indirect mechanism yields a broader range of sensitivity to the input, beyond saturation of regulator phosphorylation, and kinetics that become progressively slower, not faster, with increasing input strength. These properties can be integrated in network motifs to produce desired responses, as in the case of feedforward loops.Phosphorylation of proteins and lipids, catalyzed by specific kinase enzymes, is ubiquitous in intracellular signal transduction. A classic example in eukaryotes is the canonical structure of the mitogen-activated protein kinase cascades, in which three kinases are sequentially activated by phosphorylation (1). Another example is the PI3K (phosphoinositide 3-kinase)/Akt pathway, which (like the mammalian mitogen-activated protein kinases) is prominently dysregulated in human cancers (2). Type-I PI3Ks phosphorylate a lipid substrate to produce the lipid second messenger, PIP₃, which recruits the protein kinase Akt and mediates its activation by phosphorylation (3,4). In no small part because of these important pathways, we typically think of phosphorylation as a direct means of activating molecular interactions and reactions in signal transduction. This is not the only way to increase the flux through a signaling pathway, however. Consider signaling downstream of Akt, which phosphorylates a host of protein substrates to affect diverse functions. A survey of the Akt signaling hub shows that many of these reactions result in a decrease, rather than an increase, in activity/function of the substrates (3). And, among those substrates, the four listed in Fig. S1 in the Supporting Material). Whereas negative regulators are appreciated for their roles in feedback adaptation of signaling, the implications of deactivating a negative regulator as an indirect mechanism of pathway activation has yet to be explored.

Table 1

Survey of Akt substrates and downstream signaling

Structure-activity relationships in papain and bromelain ligand interactions

The parameters K_m and k_cat were determined for 16 methyl hippurates (CH₃OCOCH₂NHCOC₆H₄-X) hydrolyzed by papain. A simple linear relationship is found between log $\text{1}\text{K}{}_{\mathrm{m}}$ and the hydrophobic substituent constant π. It is found that log k_cat is parabolically related to π. The results with papain are compared with results obtained by Hawkins and Williams with the enzyme bromelain. The two enzymes behave in a similar fashion.     

Analysis of Amylose-borate Interaction by Frontal Gel Filtration

Amylose-borate interaction has been analyzed by frontal gel chromatography, using the constituent velocity data alone. The constituent Velocity equation was reformulated in terms of elution volume for a type of interacting system described by$\text{A}+i\text{B}={\text{AB}}_i(i=1,2,3\dots n)$

Detailed examination of the binding data indicates that, in the complex formation between amylose and borate, this type of equilibria operates predominantly, if not solely. Use of the constituent elution volume equation enabled us, for the first time, to evaluate the association constant (K) and number of binding site pertaining to this system, i.e., K = 4.9 10² and n = 1. There was no evidence indicating the occurrence of the formation of inclusion complex.     

Energy fluxes and driving forces for photosynthesis in Lemna minor exposed to herbicides

Analysis of fast chlorophyll fluorescence rise OJIP was carried out to assess the impact of diuron, paraquat and flazasulfuron on energy fluxes and driving forces for photosynthesis in Lemna minor. Results showed that diuron and paraquat treatment produced major changes in electron transport in active reaction centres (RCs). However, diuron had a more pronounced effect on the yield of electron transport per trapped exciton (ψ₀) than on the yield of primary electron transport (φP₀)$({\phi }_{{\text{P}}_0})$ showing that dark reactions are more sensitive to diuron than light-dependent reactions. In contrast, paraquat treatment effects were not due to a target-specific action on those dark and light reactions. Paraquat also induced a marked surge in the total absorption of photosystem II (PSII) antenna chlorophyll per active RC displaying a large increase of the dissipation of excess energy through non-photochemical pathways (thermal dissipation processes). Flazasulfuron induced a slight decrease of both the total driving force for photosynthesis and the quantum yield of electron transport beyond Q_A⁻ combined to a small but significant increase of the non-photochemical energy dissipation per RC (DI₀/RC). We conclude that energy fluxes and driving force for photosynthesis generate useful information about the behaviour of aquatic plant photosystems helping to localize different target sites and to distinguish heterogeneities inside the PSII complexes. Regardless of the active molecule tested, the DF_ABS, φE₀${\phi }_{{\text{E}}_0}$, DI₀/RC and/or ET₀/RC parameters indicated a significant variation compared to control while φP₀${\phi }_{{\text{P}}_0}$ (F_V/F_M) showed no significant inhibition suggesting that those parameters are more sensitive for identifying a plant’s energy-use efficiency than the maximum quantum yield of primary PS II photochemistry alone.     

Base-group specificity at the primary recognition site of ribonuclease T1 for minimal RNA substrates

Kinetic studies on the RNase T₁-catalyzed transesterification of 12 dinucleoside monophosphates, N_p¹N² (N¹ = A, C, and U; N² = A, C, G, and U) at pH 5, 25 °C, and 0.2 m ionic strength, revealed that the catalytic efficiency ($\text{k}{}_{\mathrm{<mtext>cat</mtext>}}\text{K}{}_{\mathrm{m}}$) for GpN substrates (H. L. Osterman, and F. G. Walz, Jr., 1978, Biochemistry, 17, 4142) was ~10⁶-fold greater than corresponding ApNs and at least 10⁸-fold greater than corresponding CpNs and UpNs. The catalytic activity with ApN substrates survives phenol extraction which indicates (along with other criteria) that it is intrinsic to RNase T₁ and is not due to trace contamination by other nucleases. Circumstantial evidence is presented which suggests that homologous GpN and ApN substrates bind productively at different sites on the enzyme. The results of steady-state kinetic studies of RNase T₁ with IpNs (N = C and U) were compared with those for GpNs and indicated that the primary effect of the guanine 2-NH₂ group is to enhance substrate binding at the primary recognition site by ~2.6 kcal/mol. Values of ($\text{k}{}_{\mathrm{<mtext>cat</mtext>}}\text{K}{}_{\mathrm{m}}$) showed the order NpC > NpU (N = A, G, and I) which evidences the existence of a subsite for the leaving nucleoside group that prefers cytidine: interactions at this subsite are reflected in k_cat rather than K_m.     

Reactive Nitrogen Species-Dependent Effects on Soybean Chloroplasts

Nitric oxide (NO) generation by soybean (Glycine max, var ADM 4800) chloroplasts was studied by electron paramagnetic resonance (EPR) spin-trapping technique.¹ Both nitrite and L-arginine (arg) are the required substrates for enzymatic activities considered as possible sources of NO in plants. Soybean chloroplasts showed a NO production of 3.2 ± 0.2 nmol min⁻¹ mg⁻¹ protein in the presence of 1 mM NaNO₂. Chloroplasts incubated with 1 mM arg showed a NO production of 0.76 ± 0.04 nmol min⁻¹ mg⁻¹ protein. This production was inhibited when chloroplasts were incubated in presence of NOS-inhibitors L-NAME and L-NNA. In vitro exposure of chloroplasts to a NO-donor (GSNO) decreased both ascorbyl radical content and the activity of ascorbate peroxidase, without modification of the total ascorbate content. Exposure of the isolated chloroplasts to a NO-donor decreased lipid radical content in membranes, however, incubation in the presence of 25 µM peroxynitrite (ONOO⁻) led to an increase in lipid-derived radicals (34%). The effect of ONOO⁻ on protein oxidation was determined by western blotting, showing an increase in carbonyl content either in stroma or thylakoid proteins as compared to control. Taken as a whole, NO seems to be an endogenous metabolite in soybean chloroplasts and reactive nitrogen species could exert either antioxidant or prooxidant effects on chloroplasts, since both a decreased lipid radical content in membranes and a decrease in the activity of ascorbate peroxidase were observed after exposure to a NO donor.Key Words: ascorbate, ascorbate peroxidase, chloroplasts, nitric oxide, peroxynitriteThe origin of nitric oxide (NO) in plants under aerobic conditions is currently under study. Although plants with low level of arginine shows arg-stimulated NO accumulation,² the mechanism for arginine-dependent NO synthesis in plants is still unknown, because the detection of an animal-type NOS remains elusive to date.^3,4 Even though assimilatory nitrate reductase is an enzymatic source of NO, its role in vivo would be limited by both its cytosolic localization which difficult the availability for nitrite, and the relative high K_m for nitrite (100 µM).⁵Chloroplasts have been previously marked as NO sources based in nonquantitative studies employing fluorescence microscopy^6,7 and immunogold electron microscopy.⁸ In our work we employed an specific technique (EPR, electron paramagnetic resonance with spin trap⁹) to detect NO as an endogenous metabolite and to quantify its generation in the presence of different substrates. In order to gain insight on the mechanism leading to NO production both nitrite-dependent and arg-dependent pathways were evaluated. In the presence of 1 mM arg and 0.1 mM NADPH the rate of NO generation was 0.76 ± 0.04 nmol min⁻¹ mg⁻¹ prot (arg-dependent synthesis). The synthesis of NO resulted completely blocked in the presence of arg analogs (L-NAME and L-NNA). It is important to point out that the content of arg in the chloroplasts stroma is high as compared to the content of other amino acids (56.7 ± 0.8 nmol mg⁻¹ prot), suggesting that this pathway could be operative under physiological conditions.Soybean chloroplasts showed a NO production of 3.2 ± 0.2 nmol min⁻¹ mg⁻¹ prot in the presence of 1 mM NaNO₂. Furthermore, NO generation was detected in the presence of nitrite concentrations as low as 25 mM. Since nitrite-dependent NO generation resulted inhibited by 50% by the addition of DCMU, and no NO generation was measured in the stroma fraction, thylakoidal electron transport seems to be a key feature in NO synthesis.According to this scenario and assuming that the two independent pathways for NO generation in chloroplasts are operative, the total rate of production of NO could be understood as the generation by the activity of an arg-dependent enzyme and by a NO₂⁻ dependent pathway, as indicated by eq. 1.d[NO]dt=(d[NO]dt)NOS like+(d[NO]dt)NO2−(1)Regarding the NO disappearance, from a kinetic point of view, the rate of the reaction of NO with O₂⁻ to generate peroxynitrite seems to be the main pathway, since the reaction is diffusionally controlled. Thus, the rate of disappearance of NO could be estimated from the rate of generation of ONOO⁻ (eq. 2); however, other reactions should be considered under nonphysiological conditions.−d[NO]dt=d⌊ONOO−⌋dt=k[NO][O2−](2)NO generation rate should be equal to NO consumption rate in order to keep a physiological NO steady state concentration (eq. 3)d[NO]dt=−d[NO]dt(3)Thus, replacing NO generation and disappearance rates by those rates indicated in equations 1 and 2, (d[NO]dt)NOS like+(d[NO]dt)NO2−=k[NO][O2−](4) The data obtained under unrestricted availability of substrates, indicate a generation rate of NO by the activity of a NOS-like enzyme of 13 × 10⁻⁹ M s⁻¹. Chloroplastic NO generation rate in the presence of 100 µM NO₂⁻ was 14 × 10⁻⁹ M s⁻¹. Thus, according to equation 1, the rate of generation of NO is approximately 3 × 10⁻⁸ M s⁻¹. Assuming a steady state concentration for O₂⁻ of 1 nM in chloroplasts¹⁰ and a rate constant (k) of 6.9 × 10⁹ M⁻¹ s⁻¹ for the reaction between O₂⁻ and NO,¹¹ a steady state concentration of 4 nM for NO in the chloroplast could be estimated. Since under in vivo conditions chloroplasts may content the required substrates for the NO synthesis, the assays presented here strongly suggest that a feasible NO production could take place inside the chloroplasts. However, nonsupplemented chloroplasts did not show any NO-dependent EPR signal. This observation agrees with the fact that NO steady state concentration under physiological conditions as was calculated here (4 nM) is below the EPR detection limit (500 nM).¹²Further studies should be performed to characterize NO oxidative effects on chloroplasts. Scavenging of O₂⁻ and H₂O₂ is essential for chloroplasts to maintain their ability to fix CO₂ since several enzymes in the CO₂-reduction cycle are sensitive to active oxygen species.¹³ These organelles lacking catalase, contain a significant peroxidase activity.¹⁴ H₂O₂-reduction catalized by ascorbate peroxidase (AP) lead to ascorbate oxidation and produces ascorbyl radical (A^.).¹⁵ In isolated chloroplast the content of A^.. was evaluated in DMSO based extract by EPR¹⁶. Quantification of EPR signals indicated that A^. content in control chloroplasts (123 ± 5 pmol mg⁻¹ prot) decreased after exposure to NO (Fig. 1). The total content of ascorbate, assessed by an HPLC technique¹⁷ in chloroplasts isolated from soybean leaves exposed to NO was not significantly different from the measured content in chloroplasts not exposed to the NO donor (Fig. 1). The activity of AP was significantly decreased by 48, 53 and 54% after exposure of the chloroplasts to NO-donor. Previous data suggested that AP could be inactivated by NO via oxidation of functional thiols.¹⁸ Besides, the reversible inhibition of AP could be due to the formation of Fe-nitrosyl complexes between NO and the Fe atom of the heme group, as it was previously described for NO-mediated activation of guanylate cyclase and the inhibition of cytochrome P₄₅₀ and catalase in mammals.¹⁹ The data presented here showed that in isolated chloroplasts exposed to a NO donor, there could be either a limited damage associated to the decrease in the content of A^.. or an increased cellular deterioration by the decrease in the activity of the enzyme responsible for the scavenging of H₂O₂.Open in a separate windowFigure 1Ascorbate metabolism in soybean chloroplasts after NO exposure. A^.. content (▪), ascorbate content (▪), and AP activity (*) as a function of the exposure of isolated chloroplasts to GSNO in the presence of 50 µM DTT. * = significantly different at p ≥ 0.05 from the value obtained in the absence of GSNO + 50 µM DTT.Thus, in situ generation of NO could play a protective role in preventing the oxidation of chloroplastic lipids; however, the reaction of NO with O₂⁻ leading to ONOO⁻ production may result in a potential source of damage or as it is shown here by the significant decrease of the AP activity that consumes H₂O₂. NO is a suitable candidate to modulate cellular H₂O₂ level through the chloroplast function, as an initial step to regulate complex metabolic pathways directed to activate physiological responses, defense pathways or deleterious effects in the cytosol. Furthermore, an integrated study on the effect of nitrogen reactive species is required under stress conditions to characterize the metabolic pathways involved in the resulting cellular damage.     

Kinetic studies on the reaction of ethylenediaminetetraacetatochromium(III) complex with hydrogen peroxide

The rate of reaction of [Cr(III)Y]_aq (Y is EDTA anion) with hydrogen peroxide was studied in aqueous nitrate media [μ = 0.10 M (KNO₃)] at various temperatures. The general rate equation, Rate = $\text{k}{}_1\text{+}\text{k}{}_2\text{K}{}_1\text{[H}{}^{\mathrm{+}}\text{]}{}^{\mathrm{?1}}\text{1 +}\text{K}{}_1\text{[H}{}^{\mathrm{+}}\text{]}{}^{\mathrm{?1}}$ [Cr(III)Y]_aq[H₂O₂] holds over the pH range 5–9. The decomposition reaction of H₂O₂ is believed to proceed via two pathways where both the aquo and hydroxo-quinquedentate EDTA complexes are acting as the catalyst centres. Substitution-controlled mechanisms are suggested and the values of the second-order rate constants k₁ and k₂ were found to be 1.75 × 10^?2 M^?1 s^?1 and 0.174 M^?1 s^?1 at 303 K respectively, where k₂ is the rate constant for the aquo species and k₂ is that for the hydroxo complex. The respective activation enthalpies (ΔH^*₁ = 58.9 and ΔH^*₂ = 66.5 KJ mol^?1) and activation entropies (ΔS^*₁ = ?85 and ΔS^*₂ = ?40 J mol^?1 deg^?1) were calculated from a least-squares fit to the Eyring plot. The ionisation constant pK₁, was inferred from the kinetic data at 303 K to be 7.22. Beyond pH 9, the reaction is markedly retarded and ceases completely at pH ? 11. This inhibition was attributed in part to the continuous loss of the catalyst as a result of the simultaneous oxidation of Cr(III) to Cr(VI).     

On the mechanism of the reaction of tris(hydroxymethyl)aminomethane with activated carbonyl compounds: A model for the serine proteinases

The pH dependence of the reaction of tris(hydroxymethyl)aminomethane (Tris) with the activated carbonyl compound 4-trans-benzylidene-2-phenyloxazolin-5-one (I) is given by the equation $\text{k′}{}_2\text{=}\text{k}{}_{\mathrm{<mtext>b</mtext>}}\text{K}{}_{\mathrm{<mtext>a</mtext>}}\text{(K}{}_{\mathrm{<mtext>a</mtext>}}\text{+ [}\text{H}{}^{\mathrm{+}}\text{])}\text{+}\text{k}{}_{\mathrm{<mtext>a</mtext>}}\text{[}\text{OH}{}^{\mathrm{?}}\text{]K}{}_{\mathrm{<mtext>a</mtext>}}\text{(K}{}_{\mathrm{<mtext>a</mtext>}}\text{+ [}\text{H}{}^{\mathrm{+}}\text{])}$, where K_a is the dissociation constant of TrisH⁺. Spectrophotometric experiments show that the Tris ester of α-benzamido-trans-cinnamic acid is formed quantitatively over a range of pH values, regardless of the relative contribution of k_b and k_a terms to k′₂. Hence, both terms refer to alcoholysis. While the mechanism of the reaction is not determined unequivocally in the present work, the magnitude of the k_b term, together with its dependence on the basic form of Tris, suggests that ester formation is occurring by nucleophilic attack of a Tris hydroxyl group on the carbonyl carbon of the oxazolinone, with intramolecular catalysis by the Tris amino group. The rate enhancement due to this group is at least 10² and possibly of the order 10⁶. This system is compared with other model systems for the acylation step of catalysis by serine esterases and proteinases.