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1.
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 (Qmax) 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 Qmax 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 Qmax VM, where VM is the median voltage of charge transfer, a value that is only equal to the half-point of activation V1/2 for symmetrical Q-V curves. VM is easily estimated from the Q-V curve, but Qmax 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 Qmax 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 Qmax (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(VV1/2)kT],(1)where V1/2 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 Qmax. 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 V1/2 (V1/2) and an apparent QMAX (Qmax), and this last value is then attributed to be the total charge moving Qmax. Indeed, this is correct but only for the case of a charge moving between two positions in a single step. However, the value of Qmax 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 Qmax 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 zi (in units of electronic charge e0) that will add up to the total charge Qmax.S1μ1S2μ2SiμiSi+1SnμnSn+1The probability of being in each of the states Si is labeled as Pi, and the equilibrium constant of each step is given byμi=exp[zi(VVi)kT],i=1n,where zi is the charge (in units of e0) of step i, and Vi is the membrane potential that makes the equilibrium constant equal 1. In steady state, the solution of Pi can be obtained by combiningPi+1Pi=μi,i=1nandi=1i=n+1Pi=1,givingPi+1=m=1iμm1+j=1nk=1jμk,i=1nandP1=11+j=1nk=1jμk.We define the reaction coordinate along the moved charged q asqi=j=1izj,i=1n.The Q-V curve is defined asQ(V)=i=1nqiPi+1.Then, replacing Pi yieldsQ(V)=i=1n[j=1izj][m=1iμm]1+j=1nk=1jμk,or written explicitly as a function of V:Q(V)=i=1n[j=1izj][m=1iexp[zm(VVm)kT]]1+j=1nk=1jexp[zk(VVk)kT].(2)Eq. 2 is a general solution of a sequential model with n + 1 states with arbitrary valences and Vi’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 Qmax and V1/2, respectively. For the more general situation where n > 1, if one fits the Q(V) relation obeying Eq. 2 with Eq. 1, the fitted Qmax value will not correspond to the sum of the zi 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 Vi = Vo for all transitions and that the total charge Qmax is evenly divided among those transitions. The limit of the first derivative of the Q(V) with respect to V evaluated at V = Vo 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 Qmax /(4kT) when n = 1 (two states) and a minimum equal to Qmax /(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 Qmax = 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 (Qmax) and half-point (V1/2).

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 makeziQmax/n, ?i = 1…n, ??ViVo, ?i = 1…n, then all µi = µ, and we can write Eq. 2 as the normalized Q(V) in the limit when n goes to infinity:Qnor(V)=limni=1n[j=1iQmaxn]m=1iexp[Qmax(VVo)nkT]Qmax[1+i=1nj=1iexp[Qmax(VVo)nkT]]=[Qmax(VVo)kT]exp[Qmax(VVo)kT]+kTQmax(VVo)[exp[Qmax(VVo)kT]1].(4)Eq. 4 can also be written asQnor(V)=12[1+coth[Qmax(VVo)2kT]2kTQmax(VV0)],(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, Qnor, is obtained by dividing Q(V) by the sum of all the partial charges.Fig. 1 shows Qnor 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 Qmax = 4e0) and also the same Vi = −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 Qmax 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 Qmax 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 V1/2 is very close to the correct value for all cases, but we have only considered cases in which all Vi’s are the same.It should be noted that if µi of the rightmost transition is heavily biased to the last state (Vi is very negative), then the Qmax 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 Qmax 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 Qmax value will be a low estimate of the gating charge Qmax, 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 Qmax 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 = Qmax by means of steps, loops, or branches. In that case, the partition function is given byZ=iexp(qi(VVi)kT).(6)We can compute the mean gating charge, also called the Q-V curve, asQ(V)=q=kTZZ=kTdlnZdV=iqiexp(qi(VVi)kT)iexp(qi(VVi)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=q2q2=(kT)2(ZZ(ZZ)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.  相似文献   

2.

Background

Residual Kidney Function (RKF) is associated with survival benefits in haemodialysis (HD) but is difficult to measure without urine collection. Middle molecules such as Cystatin C and β2-microglobulin accumulate in renal disease and plasma levels have been used to estimate kidney function early in this condition. We investigated their use to estimate RKF in patients on HD.

Design

Cystatin C, β2-microglobulin, urea and creatinine levels were studied in patients on incremental high-flux HD or hemodiafiltration(HDF). Over sequential HD sessions, blood was sampled pre- and post-session 1 and pre-session 2, for estimation of these parameters. Urine was collected during the whole interdialytic interval, for estimation of residual GFR (GFRResidual = mean of urea and creatinine clearance). The relationships of plasma Cystatin C and β2-microglobulin levels to GFRResidual and urea clearance were determined.

Results

Of the 341 patients studied, 64% had urine output>100ml/day, 32.6% were on high-flux HD and 67.4% on HDF. Parameters most closely correlated with GFRResidual were 1/β2-micoglobulin (r2 0.67) and 1/Cystatin C (r2 0.50). Both these relationships were weaker at low GFRResidual. The best regression model for GFRResidual, explaining 67% of the variation, was: GFRResidual=160.3(1β2m)4.2 Where β2m is the pre-dialysis β2 microglobulin concentration (mg/L). This model was validated in a separate cohort of 50 patients using Bland-Altman analysis. Areas under the curve in Receiver Operating Characteristic analysis aimed at identifying subjects with urea clearance≥2ml/min/1.73m2 was 0.91 for β2-microglobulin and 0.86 for Cystatin C. A plasma β2-microglobulin cut-off of ≤19.2mg/L allowed identification of patients with urea clearance ≥2ml/min/1.73m2 with 90% specificity and 65% sensitivity.

Conclusion

Plasma pre-dialysis β2-microglobulin levels can provide estimates of RKF which may have clinical utility and appear superior to cystatin C. Use of cut-off levels to identify patients with RKF may provide a simple way to individualise dialysis dose based on RKF.  相似文献   

3.
In their Commentary paper, Villaverde and Massonis (On testing structural identifiability by a simple scaling method: relying on scaling symmetries can be misleading) have commented on our paper in which we proposed a simple scaling method to test structural identifiability. Our scaling invariance method (SIM) tests for scaling symmetries only, and Villaverde and Massonis correctly show the SIM may fail to detect identifiability problems when a model has other types of symmetries. We agree with the limitations raised by these authors but, also, we emphasize that the method is still valuable for its applicability to a wide variety of models, its simplicity, and even as a tool to introduce the problem of identifiability to investigators with little training in mathematics.

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

4.
5.
6.
7.
The fixation index F st plays a central role in ecological and evolutionary genetic studies. The estimators of Wright (F^st1), Weir and Cockerham (F^st2), and Hudson et al. (F^st3) are widely used to measure genetic differences among different populations, but all have limitations. We propose a minimum variance estimator F^stm using F^st1 and F^st2. We tested F^stm in simulations and applied it to 120 unrelated East African individuals from Ethiopia and 11 subpopulations in HapMap 3 with 464,642 SNPs. Our simulation study showed that F^stm has smaller bias than F^st2 for small sample sizes and smaller bias than F^st1 for large sample sizes. Also, F^stm has smaller variance than F^st2 for small F st values and smaller variance than F^st1 for large F st values. We demonstrated that approximately 30 subpopulations and 30 individuals per subpopulation are required in order to accurately estimate F st.  相似文献   

8.
9.
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)eF0Fk(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) + Gpull(x,t) along the molecular extension x. Here G0(x) is the intrinsic molecular potential and Gpull(x,t) is the potential of the pulling device. When G(x,t) features a high barrier on the scale of kBT (kB 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)=ΔGν1ν(xx)11νΔGν(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 κS is Gpull(x,t) = κS/2(X0Vtx)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))1ν12(1+νFxΔG)1ν1×eβΔG[1(1+κSκU(F))2ν1ν1(1+νFxΔG)1ν],where k0 is the intrinsic on-rate, β ≡ (kBT)−1, andκU(F)=ν(1ν)2ΔGx2(1+νFxΔG)21νis the stiffness of the unfolded biomolecule under force F (see the Supporting Material for details on all derivations). The full nonlinear form of Gpull(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, 1/2κS x‡2(F) << kBT 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 κS/κU(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 Gteth(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)|ek(F)β|F˙(F)|x(1+κSκU(F))νν1(1+νFxΔG)11ν.(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 κSκU (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 κS 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 Gteth(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=α1α2x˜,ΔG=(α1)22(α2)x˜Fteth(Δ+x˜),(3)and the intrinsic unimolecular association rate isk0k˜0(βΔG)32(βΔG˜)1ν12(x˜x)2eβ(ΔG˜ΔG).(4)Here, the force value Fteth(Δ+x˜) is extracted from the force-extension curve of the tether at extension Δ+x˜ andα=2(ΔG˜Gteth(Δ)+Gteth(Δ+x˜))x˜Fteth(Δ+x˜),where Gteth(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
    Foldingk0 (s−1)x (nm)ΔG (kBT)ν
     True9.5 × 1032.22.0
     Fit8 ± 2 × 1032.2 ± 0.21.8 ± 0.50.54a
    Binding (LTR)k˜0 (s−1)x˜ (nm)ΔG˜ (kBT)ν
     True281.561.7
     Fit24 ± 31.57 ± 0.091.8 ± 0.40.53a
    Binding (LR)k0 (s−1)x (nm)ΔG (kBT)
     True2.83.04.0
     Fit2.7 ± 0.22.9 ± 0.14.1 ± 0.1
    Open in a separate windowaFixed at value that minimized least-squares error.  相似文献   

    10.
    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
    Substrate (site)Effect on substrateOutcome
    TSC2 (T1462)GAP activity ↓Rheb, mTOR ↑
    PRAS40 (T246)mTOR binding ↓mTOR ↑
    GSK3α/β (S21/S9)kinase activity ↓β-catenin ↑
    BAD (S136)Bcl-2/xL binding ↓Bcl-2/xL ↑
    Open in a separate windowHere, we use simple kinetic models to elucidate the basic properties of pathway activation by deactivation of a negative regulator (hereafter referred to as mechanism II), as compared with the standard activation of a positive regulator (mechanism I). The analysis is presented in the context of protein phosphorylation, but the conclusions may be generalized to other reversible modifications or to allosteric binding interactions. The common first step is phosphorylation of the regulatory molecule by the kinase. The activity of the upstream kinase such as Akt may be represented by a dimensionless, time (t)-dependent input signal function, s(t). We assume that the total amount of regulator is constant and define its phosphorylated fraction as ϕ(t). Neglecting concentration gradients and saturation of the upstream kinase and of the opposing (constitutively active) phosphatase(s), the conservation of phosphorylated regulator is expressed as follows (see Text S1 in the Supporting Material):dϕdt=kp[s(1ϕ)ϕ];ϕ(0)=0.(1)The parameter kp is the pseudo-first-order rate constant of protein dephosphorylation. In the case of s = constant (i.e., subject to a step change at t = 0), the properties of this simplified kinetic equation are well known (5) and may be summarized as follows. As the magnitude of the signal strength s increases, the steady-state value of ϕ, ϕss, increases in a saturable fashion; when s >> 1, ϕss approaches its maximum value of 1 and is insensitive to further increases in s. The kinetics of ϕ(t) approaching ϕss become progressively faster as s increases, however.Next, we model the influence of the regulator on a downstream response. Defining the fractional response as ρ and following analogous assumptions as above, we formulate equations for mechanisms I and II as follows:dρdt={[ka,0+(ka,maxka,0)ϕ](1ρ)kd,0ρ(I)ka,0(1ρ)[kd,0(kd,0kd,min)ϕ]ρ(II).(2)In each equation, the first term on the right-hand side describes activation, and the second, deactivation. In mechanism I, the effective rate constant of activation increases linearly with ϕ, from a minimum value of ka,0 when ϕ = 0 up to a maximum value of ka,max when ϕ = 1; the deactivation rate constant is fixed at kd,0. Conversely, in mechanism II, the effective rate constant of deactivation decreases linearly with ϕ, from a maximum value of kd,0 when ϕ = 0 down to a minimum value of kd,min when ϕ = 1; in this mechanism, the activation rate constant is fixed at ka,0. The initial condition is assigned so that ρ is stationary when ϕ = 0. To further set the two mechanisms on a common basis, we define dimensionless parameters such that the maximum steady-state value of ρ (with ϕss = 1) is the same for both mechanisms I and II,gka,max/ka,0kd,0/kd,minKka,0/kd,0.(3)With these definitions, each conservation equation is reduced to the following dimensionless form:1kd,0dρdt={K[1+(g1)ϕ](1ρ)ρ(I)K(1ρ)[1(1g1)ϕ]ρ(II).(4)Mechanisms I and II (Fig. 1 a) are compared first at the level of their steady-state solutions, ρss, for stationary s. Equation 1 yields the familiar hyperbolic dependence of ϕss on s, and ρss(s) has the same shape for both mechanisms. However, whereas ρss of mechanism I shows saturation at a lower value of s than ϕss, the opposite is true of mechanism II (Fig. 1 b). Thus, mechanism II retains sensitivity to the input even while phosphorylation of the upstream regulator shows saturation. This is perhaps more readily seen when ϕss(s) is replaced with a sigmoidal Hill function (i.e., with s replaced by sn in Eq. 1) (Fig. 1 c). The key parameter that affects the relative sensitivities of mechanisms I and II and the disparity between them is the gain constant, g (see Text S1 in the Supporting Material). As this parameter is increased, ρss of mechanism I becomes increasingly saturable with respect to ϕss (Fig. 1 d), whereas ρss of mechanism II gains sensitivity as ϕss approaches 1 (Fig. 1 e). As an illustrative example, consider that when ϕss is increased from 0.90 to 0.95, or from 0.98 to 0.99, the amount of the negative regulator in the active state is reduced by a factor of 2 (see Fig. S2).Open in a separate windowFigure 1Steady-state properties of mechanisms I and II. (a) Schematics of direct (I) and indirect (II) activation. (b) Steady-state dose responses, ρss(s), of mechanisms I and II along with phosphorylation of the upstream regulator, ϕss(s) (Eq. 1 at steady state); K = 0.05, g = 100. (c) Same as panel b, except with a sigmoidal ϕss(s) (Hill function with n = 4). (d) Steady-state output, ρss, of mechanism I vs. ϕss for K = 0.05 and indicated values of the gain constant, g. (e) Same as panel d, but for mechanism II. To see this figure in color, go online.The two mechanisms also show distinct temporal responses. In the response of mechanism I to a step increase in s, ρ(t) approaches ρss with a timescale that generally becomes faster as s increases. Unless the kinetics of ϕ(t) are rate-limiting, the timescale is ∼kd,0–1(1–ρss) (Fig. 2 a; see also Text S1 and Fig. S3 in the Supporting Material). Conversely, the response of mechanism II generally becomes slower as s increases, inasmuch as the frequency of deactivation decreases whereas that of activation is constant, with a timescale of ∼ka,0–1ρss (Fig. 2 b). To approximate a transient input, we model s(t) as a step increase followed by a decay. For mechanism I, the response ρ(t) is such that the variation in the time of the peak, as a function of the step size, is modest. The subsequent decay is prolonged when ϕ(t) hovers close to saturation (Fig. 2 c). Such kinetic schemes have been analyzed in some detail previously (6,7). In contrast, the response of mechanism II to the transient input is such that the system retains sensitivity and consistent decay kinetics beyond the saturation of ϕ(t). The distinctive feature is that ρ(t) peaks noticeably later in time as the magnitude of the peak increases (Fig. 2 d).Open in a separate windowFigure 2Kinetic properties of mechanisms I and II. (a) Response of mechanism I to a step change in s from zero to the indicated s(0). Time is given in units of kpt; parameters are K = 0.05, g = 10, and kd,0 = 0.1kp. (b) Same as panel a, but for mechanism II. (c) Same as panel a, but for a transient input, s(t) = s(0)exp(–0.03kpt). d) Same as panel c, but for mechanism II. To see this figure in color, go online.Having established the basic steady state and kinetic properties of mechanism II as compared with the canonical mechanism I, we considered what outcomes could be achieved by linking these motifs in series or in parallel. Such schemes are identified in the Akt/mTOR signaling network, for example (see Fig. S4). In a standard kinase activation cascade, it is understood that the properties of saturation and sensitivity are compounded with each step of the cascade (8). Thus, two sequential steps of mechanism I yield progressive saturation of the steady-state output at lower s (Fig. 3 a), and the desaturating effect of mechanism II is likewise compounded (Fig. 3 b). By corollary it follows that a sequence of mechanisms I and II will show an intermediate dose response; that is, the mechanism II step offsets the saturation effect of mechanism I.Open in a separate windowFigure 3Serial and parallel schemes incorporating mechanism I or/and II. (a) Steady-state outputs of two response elements, ρ1 and ρ2, activated by mechanism I in series. At each level, K = 0.05, g = 100. (b) Same as panel a, but for mechanism II in series. (c) Incoherent feedforward loop (FFL) in which mechanisms I and II are activated in parallel to activate and inhibit, respectively, the terminal output. For both mechanisms I and II, K = 0.05, g = 100. The parameters for Eq. 5 are α = 2.5, β = 50. To see this figure in color, go online.A more complex scheme is to combine the two mechanisms in parallel, as in an incoherent feedforward loop (FFL) connected to an “AND NOT” output as follows:Output = αρI/(1 + αρIβρII).(5)Given the differential saturation properties of mechanisms I and II, this scheme readily yields the expected biphasic dose response (9) without the need for disparate values of the parameters (Fig. 3 c). Regarding the kinetics, the analysis shown in Fig. 2 makes it clear that mechanism II naturally introduces time delays in cascades or network motifs. Thus, for the incoherent FFL at high, constant s, activation of inhibition by mechanism II would tend to yield a dynamic response marked by a peak followed by adaptation (see Fig. S5). Analogous calculations were carried out for a coherent FFL as well (see Fig. S6).To summarize our conclusions and their implications for signaling downstream of Akt and other kinases, we have described a distinct, indirect signal transduction mechanism characterized by deactivation of a negative regulator. This motif shows steady-state sensitivity beyond saturation, and therefore the activity of the upstream kinase, such as Akt, can be relatively high. By comparison, the direct activation of signaling by phosphorylation requires that activity of the kinase be regulated, or specifically countered by high phosphatase activity, to maintain sensitivity and avoid saturation of the response. The mechanism described here also introduces relatively slow kinetics (for comparable parameter values). This property, together with its extended range of sensitivity, would allow the motif to be incorporated in signaling networks to yield desired steady and unsteady responses in a robust manner. Considering that key signaling processes mediated by Akt (notably activation of the mammalian target of rapamycin (mTOR) pathway) are achieved by deactivation of negative regulators, we assert that greater recognition of this mechanism and of its distinct properties is warranted.  相似文献   

    11.
    12.
    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 (kcat = 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.  相似文献   

    13.
    14.
    15.
    16.
    Identifying the three-dimensional molecular organization of subcellular organelles in intact cells has been challenging to date. Here we present an analysis approach for three-dimensional localization microscopy that can not only identify subcellular objects below the diffraction limit but also quantify their shape and volume. This approach is particularly useful to map the topography of the plasma membrane and measure protein distribution within an undulating membrane.Single molecule localization microscopy (SMLM) (1–3) is a superresolution fluorescence microscopy technique that produces coordinate data for single molecule localizations with a precision of tens of nanometers in live and fixed cells. These methods have mainly been performed with total internal reflectance fluorescence microscopy and therefore have generated two-dimensional molecular coordinates. Such two-dimensional data sets have revealed nanosized clusters of membrane proteins at the cell surface (4–7). This was achieved with analysis routines based on pair-correlation analysis (8), Ripley’s K function (9), and related techniques. While three-dimensional localization microscopy techniques such as biplane imaging (10), astigmatic spot analysis (11), and depth-encoding point-spread functions (12) have now been developed, quantitative analysis approaches of three-dimensional coordinate patterns have not.Here, we describe an approach based on Getis and Franklin''s local point pattern analysis to quantitatively analyze three-dimensional subcellular structures and map plasma membrane topography. The latter can also be used to account for topography-induced clustering of membrane proteins in an undulating membrane. To illustrate the approach, we generated three-dimensional SMLM data of the membrane dye DiI and the protein Linker for Activation of T cells (LAT) fused to the photoswitchable fluorescent protein mEos2 in T cells. It has been previously shown that LAT resides within the plasma membrane as well as membrane-proximal vesicles (5,13). The data were acquired using the biplane SMLM technique and highly inclined and laminated optical sheet illumination (14). Three-dimensional molecular coordinates were calculated by fitting a three-dimensional theoretical point-spread-function to the acquired data.As previously described for two-dimensional SMLM data analysis (5), Ripley’s K-function is calculated according to Eq. 1 where V is the analyzed volume, n is the total number of points, and r is the radius of a sphere (a circle for the two-dimensional case) centered on each point. The value K(r) is thus a measure of how many points are encircled within a sphere of radius r:K(r)=Vi=1nj=1n(δij/n2);δij=1ifd(pointi,pointj)<r,0else.(1)For completely spatially random (CSR) data, K(r) scales with the volume of the sphere. We therefore linearize the K-function such that it scales with radius (the L-function) using:L(r)=(3K(r)4π)1/3.(2)The value of L(r)−r is then zero for the CSR case. Values of L(r)−r above zero indicate clustering at the length scale, r.Next we used the related Getis and Franklin''s local point pattern analysis to generate a clustering value (L(r) at r = 50 nm; L(50)) for each point, j, based on the local three-dimensional molecular density. This was calculated using:Lj(50)=((3V4π)i=1n(δijn))1/3;δij=1ifd(pointi,pointj)<50,0else.(3)These values can then be interpolated such that every voxel in a volume is assigned a cluster value based on the number of encircled points, relative to the expected CSR case. This allows construction of isosurfaces where all points on the surface have an identical L(50) value. A high threshold imparts a strict criterion for cluster detection compared to a lower one, and this allows users to, for example, determine the efficiency of sequestration into clusters by quantifying the cluster number and size as a function of the threshold.To illustrate the identification of subcellular structures, Lat-mEos2 was imaged by three-dimensional SMLM in activated T cells at the immunological synapse (Fig. 1 A). Three-dimensional projections of isosurfaces (for L(50) = 200) clearly identified intracellular LAT vesicles at varying depths within the synapse (Fig. 1, B and C). Cluster statistics were extracted from this data set to quantify the distribution of clusters in the z direction as well as the volume and sphericity of the LAT objects themselves (Fig. 1, DF).Open in a separate windowFigure 1Identification of subcellular objects in three dimensions by isosurface rendering of molecular distribution. (A) Schematic of a T cell synapse formed against an activating coverslip where subsynaptic LAT vesicles (red dots) can be imaged with three-dimensional SMLM. (B and C) Isosurfaces, shown in x,z view (B) and as projection (C), identify T cell vesicles as LAT objects with L(50) > 200 (Eq. 3). (DF) Distribution of LAT objects in z direction (D), volume (E), and sphericity (F) of LAT objects in T cells.Membrane undulations can cause clustering artifacts when the distribution of membrane proteins is recorded as a two-dimensional projection (15) (Fig. 2 A), as is the case in two-dimensional SMLM under total internal reflectance fluorescence illumination. To illustrate a solution to this problem, we obtained three-dimensional SMLM data sets of the membrane dye DiI (16) in resting T cells adhered onto nonactivating coverslips. With appropriately short labeling times to prevent dye internalization, it can be assumed that all DiI molecules reside in the plasma membrane. In this case, as is the case for plasma membrane proteins, neither two-dimensional nor three-dimensional analysis is appropriate, as it is a priori known the points must be derived from a two-dimensional membrane folded in three-dimensional space. To correct for membrane undulations, the plasma membrane topography must first be mapped so that molecular coordinates of membrane molecules can be appropriately corrected in two-dimensional projections. The position of the plasma membrane in three dimensions, i.e., the membrane topography, was determined by averaging the z position of all DiI molecules within a 100-nm radius in x-y at each point. The averaged z-position of DiI molecules was then displayed as a map, which exhibits a smooth, undulating profile (Fig. 2 B). The selection of this radius determines the accuracy of the assigned z position but also causes smoothing of the membrane profile.Open in a separate windowFigure 2Mapping of membrane topography and correction of molecular distributions in undulating membranes. (A) Two-dimensional projections can cause cluster artifacts, for example in membrane ruffles. Molecules (red rectangles) in the upper image are equally spaced along the membrane but appear as clusters in two-dimensional projections in areas with high gradient. (B) Three-dimensional membrane topography of a 2 × 2 μm plasma membrane area of a resting T cell obtained from averaged z positions of DiI molecules. Note that membrane undulation is ∼100 nm. (C) Map of membrane gradient, corresponding to the topography map shown in panel B, with an area of high gradient highlighted (dashed red box). (D) Correction of the circle radii in the Getis and Franklin cluster map calculations to account for projection artifacts. (E and F) Cluster map of data shown in panel C before (E) and after (F) correction for membrane gradient. Boxes in panels C, E, and F highlight the regions with high membrane gradient.Next, the gradient at the position of each DiI molecule was determined and interpolated into a gradient map (Fig. 2 C). Here, blue represents horizontal, i.e., flat membrane areas, whereas red regions indicate areas of high gradient. The information from the gradient map was then used to ensure that the two-dimensional circles in the Getis and Franklin cluster map calculations each correspond to an identical area of membrane, hence accounting for two-dimensional projection artifacts. To do this, the size of the circle (r) used to calculate the L value for each molecule was modified using Eq. 4, where c is calculated for the surface, S, using Eq. 5:r(corr)=r(uncorr)(1+c2)1/4,(4)c=((Sx)2+(Sy)2)1/2.(5)This operation is shown schematically in Fig. 2. The comparison of Getis and Franklin cluster maps before (Fig. 2 E) and after (Fig. 2 F) correction for the gradient shows that cluster values for DiI molecules were substantially reduced by up to 5–10% at sites where the plasma membrane had a high gradient (area highlighted in red box), and where the two-dimensional projection of three-dimensional structures caused an overestimation of clustering.In conclusion, we demonstrated that three-dimensional superresolution localization microscopy data can be used to identify and quantify subcellular structures. The approach has the distinct advantage that subcellular structures are solely identified by the distribution of the fluorescent marker so that no a priori knowledge of the structure is necessary. How precisely the subcellular structures are identified only depends on how efficiently the fluorescent maker is recruited to the structure, and hence does not depend on the resolution limits of optical microscopy. We applied the methods to two very different structures in T cells: small intracellular vesicles and the undulating plasma membrane. Importantly, the topography of plasma membrane can also be used to correct clustering artifacts in two-dimensional projections, which may be useful for distribution analysis within membranes.  相似文献   

    17.
    Population bottlenecks followed by re-expansions have been common throughout history of many populations. The response of alleles under selection to such demographic perturbations has been a subject of great interest in population genetics. On the basis of theoretical analysis and computer simulations, we suggest that this response qualitatively depends on dominance. The number of dominant or additive deleterious alleles per haploid genome is expected to be slightly increased following the bottleneck and re-expansion. In contrast, the number of completely or partially recessive alleles should be sharply reduced. Changes of population size expose differences between recessive and additive selection, potentially providing insight into the prevalence of dominance in natural populations. Specifically, we use a simple statistic, BRxipop1/xjpop2, where x i represents the derived allele frequency, to compare the number of mutations in different populations, and detail its functional dependence on the strength of selection and the intensity of the population bottleneck. We also provide empirical evidence showing that gene sets associated with autosomal recessive disease in humans may have a B R indicative of recessive selection. Together, these theoretical predictions and empirical observations show that complex demographic history may facilitate rather than impede inference of parameters of natural selection.  相似文献   

    18.
    19.

    Background

    Obesity is a global public health challenge. In the US, for instance, obesity prevalence remains high at more than one-third of the adult population, while over two-thirds are obese or overweight. Obesity is associated with various health problems, such as diabetes, cardiovascular diseases (CVDs), depression, some forms of cancer, sleep apnea, osteoarthritis, among others. The body mass index (BMI) is one of the best known measures of obesity. The BMI, however, has serious limitations, for instance, its inability to capture the distribution of lean mass and adipose tissue, which is a better predictor of diabetes and CVDs, and its curved (“U-shaped”) relationship with mortality hazard. Other anthropometric measures and their relation to obesity have been studied, each with its advantages and limitations. In this work, we introduce a new anthropometric measure (called Surface-based Body Shape Index, SBSI) that accounts for both body shape and body size, and evaluate its performance as a predictor of all-cause mortality.

    Methods and Findings

    We analyzed data on 11,808 subjects (ages 18–85), from the National Health and Human Nutrition Examination Survey (NHANES) 1999–2004, with 8-year mortality follow up. Based on the analysis, we introduce a new body shape index constructed from four important anthropometric determinants of body shape and body size: body surface area (BSA), vertical trunk circumference (VTC), height (H) and waist circumference (WC). The surface-based body shape index (SBSI) is defined as follows: SBSI=(H7/4)(WC5/6)BSAVTC(1) SBSI has negative correlation with BMI and weight respectively, no correlation with WC, and shows a generally linear relationship with age. Results on mortality hazard prediction using both the Cox proportionality model, and Kaplan-Meier curves each show that SBSI outperforms currently popular body shape indices (e.g., BMI, WC, waist-to-height ratio (WHtR), waist-to-hip ratio (WHR), A Body Shape Index (ABSI)) in predicting all-cause mortality.

    Conclusions

    We combine measures of both body shape and body size to construct a novel anthropometric measure, the surface-based body shape index (SBSI). SBSI is generally linear with age, and increases with increasing mortality, when compared with other popular anthropometric indices of body shape.  相似文献   

    20.
    The purpose of this study was to explore the association of the MCT1 gene Glu490Asp polymorphism (rs1049434) with athletic status and performance of endurance athletes. A total of 1,208 Brazilians (318 endurance athletes and 890 non-athletes) and 867 Europeans (315 endurance athletes and 552 non-athletes) were evaluated in a case–control approach. Brazilian participants were classified based on self-declared ethnicity to test whether the polymorphism was different between Caucasians and Afro-descendants. Moreover, 66 Hungarian athletes underwent an incremental test until exhaustion to assess blood lactate levels, while 46 Russian athletes had their maximum oxygen uptake (VO2max ) compared between genotypes. In the Brazilian cohort, the major T-allele was more frequent in Caucasian top-level competitors compared to their counterparts of lower competitive level (P = 0.039), and in Afro-descendant athletes compared to non-athletes (P = 0.015). Similarly, the T-allele was more frequent in European athletes (P = 0.029). Meta-analysis of the Brazilian and European cohorts confirmed that the T-allele is over-represented in endurance athletes (OR: 1.48, P = 0.03), especially when Afro-descendant athletes were included in the meta-analysis (OR: 1.58, P = 0.005). Furthermore, carriers of the T/T genotype accumulated less blood lactate in response to intense effort (P < 0.01) and exhibited higher VO2max (P = 0.04). In conclusion, the Glu490Asp polymorphism was associated with endurance athletic status and performance. Our findings suggest that, although ethnic differences may exist, the presence of the major T-allele (i.e., the Glu-490 allele) favours endurance performance more than the mutant A-allele (i.e., the 490-Asp allele).  相似文献   

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