Influence of Adjuvant Therapy in Cancer Survivors on Endothelial Function and Skeletal Muscle Deoxygenation

The cardiotoxic effects of adjuvant cancer treatments (i.e., chemotherapy and radiation treatment) have been well documented, but the effects on peripheral cardiovascular function are still unclear. We hypothesized that cancer survivors i) would have decreased resting endothelial function; and ii) altered muscle deoxygenation response during moderate intensity cycling exercise compared to cancer-free controls. A total of 8 cancer survivors (~70 months post-treatment) and 9 healthy controls completed a brachial artery FMD test, an index of endothelial-dependent dilation, followed by an incremental exercise test up to the ventilatory threshold (VT) on a cycle ergometer during which pulmonary V˙O2 and changes in near-infrared spectroscopy (NIRS)-derived microvascular tissue oxygenation (TOI), total hemoglobin concentration ([Hb]_total), and muscle deoxygenation ([HHb] ≈ fractional O₂ extraction) were measured. There were no significant differences in age, height, weight, and resting blood pressure between cancer survivors and control participants. Brachial artery FMD was similar between groups (P = 0.98). During exercise at the VT, TOI was similar between groups, but [Hb]_total and [HHb] were significantly decreased in cancer survivors compared to controls (P < 0.01) The rate of change for TOI (ΔTOIΔ/V˙O2) and [HHb] (Δ[HHb]/ΔV˙O2) relative to ΔV˙O2 were decreased in cancer survivors compared to controls (P = 0.02 and P = 0.03 respectively). In cancer survivors, a decreased skeletal muscle microvascular function was observed during moderate intensity cycling exercise. These data suggest that adjuvant cancer therapies have an effect on the integrated relationship between O₂ extraction, V˙O2 and O₂ delivery during exercise.     

Validation of Walking Trails for the Urban TrainingTM of Chronic Obstructive Pulmonary Disease Patients

Purpose

Accessible interventions to train patients with chronic obstructive pulmonary disease (COPD) are needed. We designed urban trails of different intensities (low, moderate and high) in different types of public spaces (boulevard, beach and park). We aimed to validate the trails’ design by assessing the physiological response to unsupervised walking trails of: (1) different intensities in COPD patients, and (2) same intensity from different public spaces in healthy adults.

Methods

On different days and under standardized conditions, 10 COPD patients walked the three intensity trails designed in a boulevard space, and 10 healthy subjects walked the three intensity trails in three different spaces. We measured physiological response and energy expenditure using a gas analyzer. We compared outcomes across trails intensity and/or spaces using mixed-effects linear regression.

Results

In COPD patients, physiological response and energy expenditure increased significantly according to the trails intensity: mean (SD) peak V˙O₂ 15.9 (3.5), 17.4 (4.7), and 17.7 (4.4) mL/min/kg (p-trend = 0.02), and MET-min 60 (23), 64 (26), 72 (31) (p-trend<0.01) in low, moderate and high intensity trails, respectively. In healthy subjects there were no differences in physiological response to walking trails of the same intensity across different spaces.

Conclusions

We validated the trails design for the training of COPD patients by showing that the physiological response to and energy expenditure on unsupervised walking these trails increased according to the predefined trails’ intensity and did not change across trails of the same intensity in different public space. Walkable public spaces allow the design of trails that could be used for the training of COPD patients in the community.     

Effects of Acute Endurance Exercise Performed in the Morning and Evening on Inflammatory Cytokine and Metabolic Hormone Responses

Purpose

To compare the effects of endurance exercise performed in the morning and evening on inflammatory cytokine responses in young men.

Methods

Fourteen healthy male participants aged 24.3 ± 0.8 years (mean ± standard error) performed endurance exercise in the morning (0900–1000 h) on one day and then in the evening (1700–1800 h) on another day with an interval of at least 1 week between each trial. In both the morning and evening trials, the participants walked for 60 minutes at approximately 60% of the maximal oxygen uptake (V·O2max) on a treadmill. Blood samples were collected to determine hormones and inflammatory cytokines at pre-exercise, immediately post exercise, and 2 h post exercise.

Results

Plasma interleukin (IL)-6 and adrenaline concentrations were significantly higher immediately after exercise in the evening trial than in the morning trial (P < 0.01, both). Serum free fatty acids concentrations were significantly higher in the evening trial than in the morning trial at 2 h after exercise (P < 0.05). Furthermore, a significant correlation was observed between the levels of IL-6 immediately post-exercise and free fatty acids 2 h post-exercise in the evening (r = 0.68, P < 0.01).

Conclusions

These findings suggest that the effect of acute endurance exercise in the evening enhances the plasma IL-6 and adrenaline concentrations compared to that in the morning. In addition, IL-6 was involved in increasing free fatty acids, suggesting that the evening is more effective for exercise-induced lipolysis compared with the morning.     

Correlation of a Decline in Aerobic Capacity with Development of Emphysema in Patients with Chronic Obstructive Pulmonary Disease: A Prospective Observational Study

In patients with COPD, CT assessment of emphysema and airway disease is known to be associated with lung function and 6-minute walk distance. However, it remains to be determined whether low attenuation area (LAA) on CT is associated with aerobic capacity assessed using cardiopulmonary exercise testing (CPET). In this prospective observational study, we repeatedly conducted high-resolution CT and CPET using a treadmill in 81 COPD patients over a median interval of 3.5 years. Two investigators independently scored LAA on images obtained at the aortic arch level, tracheal bifurcation level, and supradiaphragmatic level. Grades for the images of each lung were added to yield the total LAA score. Total LAA score was negatively correlated with peak aerobic capacity (V˙O2) (p<0.001, r = -0.485). LAA scores of the upper (aortic arch level) and the lower (supradiaphragmatic level) lungs were both significantly associated with peak V˙O2. There was a significant correlation between total LAA score and peak CO₂ output (V˙CO2) (p<0.001, r = -0.433). Total LAA score was correlated with oxygen saturation at peak exercise (p<0.001, r = -0.634) and the estimated dead space fraction (p<0.001, r = 0.416). The mean annual change in total LAA score was significantly correlated with those in peak V˙O2 (p<0.001, r = -0.546) and peak V˙CO2 (p<0.001, r = -0.488). The extent of emphysema measured by CT was associated with the results of CPET. The time-dependent changes in CPET data were also correlated with that in total LAA score. CT assessment could be a non-invasive tool to predict aerobic capacity in patients with COPD.     

Endurance Training-Induced Increase in Circulating Irisin Levels Is Associated with Reduction of Abdominal Visceral Fat in Middle-Aged and Older Adults

To elucidate the effects of endurance training on circulating irisin levels in young and middle-aged/older adults, and to determine the association between endurance training-induced alteration of irisin and reduction in body fat. Twenty-five healthy young (age 21 ± 1 years; 16 men, 9 women) and 28 healthy middle-aged/older adults (age 67 ± 8 years; 12 men, 16 women) participated in the study. Each age cohort was divided into two groups: the endurance-training group (14 young, 14 middle-aged/older) and the control group. Subjects in the training groups completed an 8-week endurance-training program (cycling at 60-70% peak oxygen uptake [V˙O_2peak] for 45 min, 3 days/week). Before and after the intervention, we evaluated serum irisin level, V˙O_2peak, and body composition. The increase in V˙O_2peak in the young and middle-aged/older training groups after the intervention period was significantly greater than those in the young and middle-aged/older control groups (P < 0.05). Serum irisin level was significantly increased in the middle-aged/older training group after the intervention period (P < 0.01), but not in the young training group. Furthermore, in the middle-aged/older training group, the endurance training-induced reduction in visceral adipose tissue area was negatively correlated with the change in serum irisin level (r = −0.54, P < 0.05). These results suggest a possible role for secreted irisin in the exercise-induced alteration of abdominal visceral fat in middle-aged and older adults.     

Relationship of aerobic and anaerobic parameters with 400 m front crawl swimming performance

The aims of the present study were to investigate the relationship of aerobic and anaerobic parameters with 400 m performance, and establish which variable better explains long distance performance in swimming. Twenty-two swimmers (19.1±1.5 years, height 173.9±10.0 cm, body mass 71.2±10.2 kg; 76.6±5.3% of 400 m world record) underwent a lactate minimum test to determine lactate minimum speed (LMS) (i.e., aerobic capacity index). Moreover, the swimmers performed a 400 m maximal effort to determine mean speed (S400m), peak oxygen uptake (V.O2PEAK) and total anaerobic contribution (C_ANA). The C_ANA was assumed as the sum of alactic and lactic contributions. Physiological parameters of 400 m were determined using the backward extrapolation technique (V.O2PEAK and alactic contributions of C_ANA) and blood lactate concentration analysis (lactic anaerobic contributions of C_ANA). The Pearson correlation test and backward multiple regression analysis were used to verify the possible correlations between the physiological indices (predictor factors) and S400m (independent variable) (p < 0.05). Values are presented as mean ± standard deviation. Significant correlations were observed between S400m (1.4±0.1 m·s^-1) and LMS (1.3±0.1 m·s^-1; r = 0.80), V.O2PEAK (4.5±3.9 L·min^-1; r = 0.72) and C_ANA (4.7±1.5 L·O₂; r= 0.44). The best model constructed using multiple regression analysis demonstrated that LMS and V.O2PEAK explained 85% of the 400 m performance variance. When backward multiple regression analysis was performed, C_ANA lost significance. Thus, the results demonstrated that both aerobic parameters (capacity and power) can be used to predict 400 m swimming performance.     

Cardiorespiratory Adaptations during Concurrent Aerobic and Strength Training in Men and Women

This study investigated the effects of endurance followed by strength training (ES, men n = 16; women n = 15), the reverse exercise order (SE, men n = 18, women n = 13) and concurrent endurance and strength training performed on alternating days (AD, men n = 21, women n = 18) on cardiorespiratory parameters. Peak oxygen consumption (V˙O_2peak) and oxygen consumption at sub-maximal power outputs (V˙O_2submax) of 50 to 175 Watts in men and 50 to 125 Watts in women were assessed during an incremental cycling test both before and after 24 weeks of training. Increases in V˙O_2peak in both men and women were statistically larger in AD (18±9% and 25±11%) compared to ES (7±9% and 12±12%, p = 0.002 and 0.009, respectively) and SE (7±9% and 10±8%, p = 0.005 and 0.008, respectively). No statistical group interaction was observed for V˙O_2submax in men, but in women V˙O_2submax was statistically lower at week 24 in ES compared to AD at 75 W (-2±6% vs. +3±6%, p = 0.027) and 125 W (-4±5% vs. +2±5%, p = 0.010). These findings indicate that endurance and strength training performed on alternating days may optimize the adaptations in V˙O_2peak in both sexes, while performing ES training in women may optimize cardiorespiratory fitness at sub-maximal power outputs.     

Exercise Tolerance Can Be Enhanced through a Change in Work Rate within the Severe Intensity Domain: Work above Critical Power Is Not Constant

Introduction

The characterization of the hyperbolic power-time (P-t _lim) relationship using a two-parameter model implies that exercise tolerance above the asymptote (Critical Power; CP), i.e. within the severe intensity domain, is determined by the curvature (W’) of the relationship.

Purposes

The purposes of this study were (1) to test whether the amount of work above CP (W>CP) remains constant for varied work rate experiments of high volatility change and (2) to ascertain whether W’ determines exercise tolerance within the severe intensity domain.

Methods

Following estimation of CP (208 ± 19 W) and W’ (21.4 ± 4.2 kJ), 14 male participants (age: 26 ± 3; peak V˙O2: 3708 ± 389 ml.min^-1) performed two experimental trials where the work rate was initially set to exhaust 70% of W’ in 3 (‘THREE’) or 10 minutes (‘TEN’) before being subsequently dropped to CP plus 10 W.

Results

W>CP for TEN (104 ± 22% W’) and W’ were not significantly different (P>0.05) but lower than W>CP for THREE (119 ± 17% W’, P<0.05). For both THREE (r = 0.71, P<0.01) and TEN (r = 0.64, P<0.01), a significant bivariate correlation was found between W’ and t _lim.

Conclusion

W>CP and t _lim can be greater than predicted by the P-t _lim relationship when a decrement in the work rate of high-volatility is applied. Exercise tolerance can be enhanced through a change in work rate within the severe intensity domain. W>CP is not constant.     

Perspectives on: Conformational coupling in ion channels: Conformational coupling in BK potassium channels

Large conductance calcium- and voltage-dependent BK potassium channels (aka BK_Ca, MaxiK, Slo1, KCa1.1, and KCNMA1) are expressed in a wide variety of tissues throughout the body and are activated by both intracellular Ca²⁺ and membrane depolarization. Owing to these properties, BK channels participate in diverse physiological processes from electrical excitability in neurons and secretory cells, and regulation of smooth muscle tone to tuning of auditory hair cells (Vergara et al., 1998; Ghatta et al., 2006). The response to voltage and Ca²⁺ allows BK channels to integrate electrical and calcium signaling, which is central to their physiological role. Understanding how BK and other multimodal channels are regulated by and integrate diverse stimuli is not only physiologically important but also relevant to the topic of conformational coupling. As a voltage- and ligand-dependent channel, BK channels contain both voltage-sensor and ligand-binding domains as well as a gate to regulate the flow of K⁺ through the pore. Coupling of conformational changes in one domain to another provides the basis for transducing voltage and ligand binding into channel opening and, therefore, defines, together with the functional properties of the gate and sensors, the signal transduction properties of the channel. The goal of this perspective is to provide an overview on the role and molecular basis of conformational coupling between functional domains in BK channels and outline some of the questions that remain to be answered.

BK channel structure

The BK channel is a member of the superfamily of voltage-gated channels that assembles as a homotetramer of pore-forming Slo1 (α) subunits. Each subunit contains seven transmembrane segments (S0–S6), including an S5–S6 pore gate domain (PGD) and voltage-sensor domain (VSD) that is likely to include S0–S4 segments (Liu et al., 2008) with charged voltage-sensing residues in S2, S3, and S4 (Fig. 1 A; Ma et al., 2006). In addition, a large C-terminal cytoplasmic domain (CTD) consisting of two homologous regulator of K⁺ conductance domains (RCK1 and RCK2) contains binding sites for Ca²⁺ and other ligands (Hou et al., 2009). The CTDs form a tetrameric gating-ring structure whose conformation changes upon Ca²⁺ binding. Crystal structures of the isolated BK channel gating ring and related prokaryotic Ca²⁺-activated K⁺ channel MthK have been solved in the presence and absence of Ca²⁺ (Jiang et al., 2002; Ye et al., 2006; Wu et al., 2010; Yuan et al., 2010, 2012). The atomic structure of the transmembrane domain has yet to be determined but is assumed to be homologous with that of voltage-gated potassium (K_V) channels, consistent with a low resolution cryo-EM structure of the entire channel(Wang and Sigworth, 2009). Although BK channels formed from Slo1 alone are fully functional, each channel may also coassemble with up to four regulatory subunits of which several subtypes exist (β1–4 and γ1–4; Brenner et al., 2000; Yan and Aldrich, 2012). Regulatory subunits tune BK channel function in different tissues, contain one or two transmembrane segments, occupy sites adjacent to the VSD (Liu et al., 2010), and act in part to regulate voltage-dependent gating (Bao and Cox, 2005; Yan and Aldrich, 2010).Open in a separate windowFigure 1.BK channel structure. (A) Topology of the pore-forming Slo1 subunit, including VSD, PGD, and CTD. Charged residues in the VSD that are important for voltage sensing are highlighted in yellow. The CTD contains binding sites for Ca²⁺, Mg²⁺, and heme. (B) Schematic organization of functional domains in the tetrameric channel. S6 segments in the PDG are connected to the CTD gating ring through S6-RCK1 linkers.

BK channel function

The response of BK channels to voltage and Ca²⁺ is illustrated in Fig. 2 by plotting steady-state open probability (P_O; Fig. 2 A) and Log(P_O) (Fig. 2 B) versus voltage at different [Ca²⁺]_i (0–100 µM) for heterologously expressed Slo1 channels (Horrigan and Aldrich, 2002). The P_o-V relation in 0 Ca²⁺ (∼0.5 nM) shows channels can be fully activated in the absence of Ca²⁺ binding, but only at voltages approaching +300 mV. Calcium, to a first approximation, shifts P_o-V to more negative voltages (Fig. 2 A), allowing the channel to activate in a physiological voltage range. However, plotting the data on a log scale reveals that Ca²⁺ does not simply shift the curve but rather increases Log(P_O) in a nearly voltage-independent manner until P_O saturates (Fig. 2 B). This response indicates that BK channels are activated independently by voltage- and Ca²⁺-sensors. Furthermore, Log(P_O) becomes almost voltage independent at extreme negative voltages indicating that channels can open in the absence of voltage-sensor activation, a conclusion supported by gating current measurements (Horrigan and Aldrich, 1999).Open in a separate windowFigure 2.Voltage- and Ca²⁺-gating of BK channels. (A) P_O-V relations for mSlo1 estimated as G_K/G_Kmax from macroscopic tail currents after 30 ms voltage pulses in 0–100 µM Ca²⁺. (B) Log(P_o)-V relations extend P_O to <10⁻² using steady-state unitary current recordings from macropatches. A and B represent mean ± SEM and are fit (solid curves) by the HA model (Horrigan and Aldrich, 2002). The increase in Log(P_o) from 0 Ca²⁺ to saturating 100 µM Ca²⁺ at −120 mV (where voltage-sensors are in the resting state) reflects Ca²⁺-sensor/gate coupling energy (ΔΔGCOCa). The increase in Log(P_o) in 0 Ca²⁺ from −120 mV to ∼+300 mV (where voltage sensors are fully activated) reflects voltage-sensor/gate coupling (ΔΔGCOV). The values of ΔΔGCOCa and ΔΔGCOV are determined from the change in the free energy of the gate (e.g., ΔΔGCOCa=ΔGCO[100 Ca]−ΔGCO[0 Ca], where ΔG_CO = kTln[P_O/(1 ? P_O)]), and, in the case of ΔΔGCOV, the measurement at −120 mV must be extrapolated to positive voltages (dashed line) to correct for the weak voltage dependence of the C-O transition (z_L = 0.3 e). (C) Allosteric model indicates the possible conformations of the gate (C and O), voltage sensors (R and A), and Ca²⁺ sensors (X and X-Ca²⁺) in each of four subunits and allosteric factors (C, D, and E) that describe the energetic coupling between these three parts of the channel. J and L are voltage-dependent equilibrium constants with zero-voltage values J₀ and L₀ and partial charges (z_J, z_L), K = [Ca²⁺]/K_D, where K_D is the elementary Ca²⁺ dissociation constant for the closed channel.

An allosteric mechanism of BK channel gating

That BK channels exhibit basal activity in the absence of voltage-sensor activation and Ca²⁺ binding implies that sensor/gate coupling is not an obligatory process. That is, sensor activation promotes but is not required for channel opening. The ability of voltage or Ca²⁺ sensors in different subunits to influence a concerted conformational change (opening) in a nonobligatory fashion is well described in terms of allosteric mechanisms (Monod et al., 1965). A dual allosteric model (Fig. 2 C, HA model) was used to fit the steady-state data in Fig. 2 (A and B, curves), accounts for many other features of Slo1 gating (Horrigan and Aldrich, 1999, 2002; Horrigan et al., 1999), and provides a useful framework for analyzing BK channel gating in terms of domain/domain interactions. The HA (Horrigan-Aldrich) model asserts that the channel gate can undergo a closed to open (C-O) conformational change that is regulated by four independent and identical voltage- and Ca²⁺-sensors. Voltage sensors can be in a resting (R) or activated (A) conformation, whereas Ca²⁺ sensors can be Ca²⁺ free (X) or Ca²⁺ bound (X-Ca²⁺). The function of each domain is defined by equilibrium constants for gate opening (L), voltage-sensor activation (J), and Ca²⁺ binding (K). The coupling, or energy transfer, between domains is represented by allosteric factors (C, D, and E) which define the ability of a transition in one domain to affect the equilibrium constant in another.

The energetics of conformational coupling

The structures of BK and homologous channels provide important clues concerning the molecular basis of conformational coupling, as discussed below. However, many features of coupling can only be resolved through structure-function analysis using site-directed mutagenesis. A prerequisite to such analysis is to quantify coupling interactions represented by allosteric factors C, D, and E in the HA model. Mutations that alter channel activity may perturb sensors, the gate, or their coupling. Therefore, it is crucial to distinguish changes in coupling from changes in the function of sensor or gate. One way to do this is by fitting steady-state data over a wide range of voltage and [Ca²⁺] as in Fig. 2 (A and B) to determine all parameters in the HA model. However, a more direct and model-independent approach to measure coupling is to determine the energetic effect on one domain of forcing coupled domains into defined conformations (e.g., all activated or deactivated) under extreme stimulus conditions (see also Chowdhury and Chanda in this issue). For example, the total coupling between all Ca²⁺ sensors and the gate (ΔΔGCOCa=5.0 kcal mol−1) can be determined by comparing Log(P_o) in 0 Ca²⁺ and saturating 100 µM Ca²⁺ at extreme negative voltages where voltage sensors are in the resting state, and voltage-sensor/gate coupling (ΔΔGCOV=7.6 kcal mol−1) can be determined by comparing Log(P_o) at extreme negative and positive voltages in 0 Ca²⁺ (Fig. 2 B; Horrigan and Aldrich, 2002). In general, the HA model predicts that channels can occupy many different open and closed states, defined by the number of voltage- and Ca²⁺-sensors activated in each channel. But under extreme stimulus conditions, where all voltage- or Ca²⁺-sensors are either activated or deactivated, gating reduces to a single closed and open state. For a two-state process, the free energy difference between closed and open (ΔG_CO) can be defined in terms of the equilibrium constant (P_o/1-P_o) for the C-O transition (i.e., ΔG_CO = kTln[P_O/(1 ? P_O)]; Chowdhury and Chanda, 2010, 2012). Thus, changes in Log(P_o) in Fig. 2 B reflect the energetic effects of voltage- and Ca²⁺-sensor activation on the gate. Similarly, a weak coupling between voltage- and Ca²⁺-sensors (ΔΔGRACa=0.5 kcal mol−1) has been measured by comparing the effects of 0 Ca²⁺ and saturating Ca²⁺ on voltage-sensor activation measured with gating currents while the gate is closed (Horrigan and Aldrich, 2002).Although measurement of Ca²⁺-sensor/gate coupling as in Fig. 2 B is relatively straightforward, measurement of voltage-sensor/gate coupling is subject to several challenges (Fig. 3). The relationship between gating and voltage-sensor/gate coupling is illustrated in Fig. 3 A by expanding the HA model to show the four combinations of states that the gate (C and O) and voltage-sensor (R and A) can assume in a single subunit (RC, RO, AC, and AO) together with the equilibrium constants between them. The equilibrium constant for the C-O transition increases from L when the voltage sensor is in the resting state (Fig. 3 A, #1) to LD when a voltage sensor is activated (Fig. 3 A, #2). Thus the voltage-sensor/gate coupling factor D can be determined by comparing P_o at extreme voltages (Fig. 3 B, #1 and 2), with the expectation that P_o/(1-P_o) will increase by a factor of D⁴ when all four voltage sensors are activated. One challenge is the large dynamic range of these measurements, which span a seven-order-of-magnitude change in P_o and require both macroscopic and unitary current recordings in the same patch and a high level of expression that cannot always be achieved with mutant channels. A related challenge is that P_o in 0 Ca²⁺ approaches saturation near unity at +300 mV as voltage sensors become fully activated (Fig. 2 A). As P_o approaches unity, determination of the equilibrium constant P_o/(1-P_o) becomes problematic and coupling energy can therefore be underestimated, especially in the presence of Ca²⁺ or with mutants that are easier to open than the WT because P_o may saturate before voltage sensors are fully activated. Finally, the C-O conformational change, as in many ion channels, has a weak intrinsic voltage dependence (L(V)) that must be taken into account when comparing P_o at extreme voltages (Figs. 2 B and 3 B, dashed lines).Open in a separate windowFigure 3.The energetics of voltage sensor/gate coupling. (A) Voltage sensor/gate states in a single subunit. Numbers refer to data in B, C, and D used to determine the indicated equilibrium constants. (B) P_O-V determines L (1) and LD⁴ (2). Dashed lines indicate the predicted voltage dependence of P_O with all voltage sensors either in the resting or activated state and z_L = 0.3 e. (C) Normalized Q_C-V for closed channels determined from ON gating currents (inset) is fit by a Boltzmann function with z_J = 0.58 e and defines J (3). (D) Q_O-V relation for open channels defines JD (4). Q_O is estimated by fitting the foot of the q_a-V relation (q_a = kTdln(P_O)/dV) with a Boltzmann function. The shift between Q_O and Q_C relations defines the coupling factor D.A complementary approach to measure voltage-sensor/gate coupling is to determine the effect of channel opening on voltage-sensor activation. The equilibrium constant for the R-A transition increases from J when channels are closed to JD when channels are open (Fig. 3 A, #3 and 4). The equilibrium constant J is determined from the charge distribution for closed channels (Q_C-V; Fig. 3 C). Q_c can be measured by integrating ON gating currents (Fig. 3 B, inset) because voltage-sensor activation in BK channels is rapid and occurs while most channels remain closed. The equilibrium constant JD is determined from the charge distribution for open channels (Q_O-V; Fig. 3 D). Q_O cannot be determined from gating currents because BK channels close rapidly. However, Q_O can be estimated in a model-independent fashion from the log-slope of the P_o-V relation (q_a = kTdln(P_O)/dV), as shown in Fig. 3 D (Horrigan and Aldrich, 2002). The Q_O-V and Q_C-V relations have the same shape but are shifted relative to each other by a voltage directly proportional to coupling energy for a single voltage sensor (ΔV=kT ln(D)/zJ=ΔΔGCOV/4zJ; Ma et al., 2006). This method yields similar results as in Fig. 3 B and avoids challenges relating to the voltage dependence of L(V), or P_O saturation. However, gating currents are difficult to measure in BK channels and require an even higher level of expression than in Fig. 3 B.

Molecular mechanisms of conformational coupling

Although the energetics and biophysical mechanisms of sensor/gate and sensor/sensor coupling in BK channels are well defined, many fundamental questions remain concerning the molecular basis of these interactions. Where in the channel do they occur? What are the identity and nature of amino acid interactions involved? When do the interactions occur during channel activation? These questions are broad because many potential sites of domain/domain interaction exist, the conformational changes that these domains and their interfaces undergo during gating are not all understood in detail, and insight provided by the structure of BK or homologous channels is in many cases limited. For example, although voltage-sensor/gate coupling is likely to be mediated in large part by interfaces between the VSD and PGD as in Kv channels, there is also a unique interface between the VSD and CTD in BK channels that may contribute to this process. Intracellular Mg²⁺ is a BK channel activator that is coordinated by residues in both VSD and CTD and interacts electrostatically with the voltage sensor, indicating (together with cross-linking experiments) that these domains come in contact (Yang et al., 2007, 2008). The primary functional effect of Mg²⁺ is to enhance voltage-sensor/gate coupling, suggesting that VSD/CTD interaction could provide a basis for this process (Horrigan and Ma, 2008). VSD/CTD interaction must also mediate coupling between voltage and Ca²⁺ sensors. However information about the VSD/CTD interface is incomplete. Structures of BK and MthK channel CTDs and the Kv channel VSD help identifying residues that may lie at this interface. But the complete BK channel structure including the VSD/CTD interface has yet to be determined, and neither MthK nor Kv channels contain a homologous interface.Because most domain/domain interactions involved in conformational coupling remain to be identified, it is useful to consider what properties such interactions must have. In general, coupling may occur through linkers that directly connect two domains or through noncovalent interactions at domain/domain interfaces. In BK channels, Ca²⁺-sensor/gate coupling is thought to be mediated by the S6-RCK1 linker connecting CTD to PGD (Jiang et al., 2002; Niu et al., 2004). However multiple domain/domain interfaces are also involved in coupling, as noted above. Structural information has helped to identify where these interfaces are and to locate potential interaction partners. But elucidating the basis of conformational coupling is more complex than simply identifying domain/domain interactions. Coupling is necessarily a state-dependent process that depends on the conformations of two coupled domains. To understand the possible interaction mechanisms, it is useful to consider the energetics of coupling in the context of a gating cycle such as that describing voltage-sensor/gate coupling in Fig. 3 A. The coupling energy between a single voltage sensor and gate (ΔΔGCORA=kTln(D)) can be expressed in terms of the free energies of the four states involved (AC, AO, RC, and RO):ΔΔGCORA=[ΔGCOA−ΔGCOR]=[(GCA−GOA)−(GCR−GOR)]=GCA−GOA−GCR+GOR(1)Therefore, the change in coupling produced by changes in the free energy of each state is:ΔΔΔGCORA=[ΔGCA−ΔGOA−ΔGCR+ΔGOR](2)Eq. 2 indicates that coupling is enhanced (ΔΔΔGCORA>0) by decreasing GCR or GOA (stabilizing the RC or AO state) or by increasing GCA or GOR (destabilizing the AC or RO state). Coupling could also be enhanced by changing the free energy of multiple states, provided the net contribution (Eq. 2) is positive. However, interactions that are state independent or depend on the conformation of only one domain (e.g., ΔGCA=ΔGCR or ΔG0R=ΔGCR) will have no effect on coupling (i.e.,ΔΔGCORA=0).This analysis has several important implications for elucidating mechanisms of conformational coupling. First, to identify coupling interactions by structural methods requires that structures be solved in four conformations defined by two domains and have sufficient resolution to observe state-dependent changes in interaction. In practice, because changes in interaction energy may be subtle or difficult to estimate based on structure, coupling interactions would have to be verified and quantified by structure-function analysis. When only one or two structures of a channel are available, as is currently the case for BK and homologous channels, then structure-function analysis is required to determine if observed interactions participate in coupling, and residues that do not interact in an observed structure may still mediate coupling by interacting in other conformations. Second, structure-function analysis involving site-directed mutagenesis and measurements of coupling energy, as in Figs. 2 and ​and3,3, should be sufficient to identify residues involved in coupling interactions. However, such experiments must be interpreted cautiously. Allosteric proteins are often sensitive to modulation at domain interfaces by heterotropic ligands that bind and introduce interactions that do not normally exist, and mutations can have similar effects. For example, introduction of a positively charged residue near the BK channel Mg²⁺-binding site (Q397R) mimics the effect of Mg²⁺ by introducing an electrostatic interaction (Yang et al., 2007). Thus, the ability of Q397R to enhance coupling does not indicate that Q397 is normally involved in this process, just that it is located at a sensitive interface where conformational changes associated with voltage-sensor activation and channel opening both occur. Such false positives cannot be avoided simply by restricting analysis to mutations that reduce coupling because, based on Eq. 2, coupling can be reduced by introducing interactions that destabilize the RC or AO states or stabilize the AC or RO states. Intracellular heme, which inhibits voltage-sensor/gate coupling in BK channels, may act in this way (Horrigan et al., 2005). Consequently, whether a mutation increases or decreases coupling is less critical than the use of mutations such as Ala that are least likely to introduce interactions. Finally, to define the mechanism of voltage-sensor/gate coupling we must not only identify mutations that alter coupling but also characterize those changes in terms of the effect on individual states (i.e., RC, RO, AC, and AO) to determine when during activation the interactions occur. Although the change in free energy of any particular state cannot be determined directly, the equilibria between states can be evaluated as in Fig. 3 to define the change in free energy of individual states relative to each other. Such analysis has indicated that Mg²⁺ enhances voltage-sensor/gate coupling by preferentially stabilizing the AO state (Horrigan and Ma, 2008), whereas a stabilization of the RO state is consistent with the inhibitory effect of heme (Horrigan et al., 2005). It is worth noting that, depending on their state dependence, coupling interactions may influence open probability when sensors are in a resting conformation. Thus, the basal activity of BK channels in the absence of sensor activation defined by the equilibrium constant L in the HA model cannot be interpreted simply as the intrinsic stability of the gate because it also reflects any state-dependent interactions between the gate and resting sensors.

Mechanisms of voltage-sensor/gate coupling

Kv channel structures reveal two interfaces between VSD and PGD: intrasubunit contacts between the S4–S5 linker and S6 and intersubunit contacts between S4 and S5 (Long et al., 2005a, 2007). In BK channels, additional intersubunit interactions occur between the VSD and CTD (Yang et al., 2008). All of these interfaces potentially play a role in voltage-sensor/gate coupling in BK channels, but their relative contributions and mechanisms remain unknown. The S4/S5 interface is implicated because a mutation near the top of S4 (R210E) reduces coupling energy by half (Ma et al., 2006). However, we cannot rule out that this is a false positive produced by introducing rather than disrupting an interaction because other mutations at this site (R210C and R210N) appear to constitutively activate the channel preventing measurement of voltage-sensor/gate coupling (Ma et al., 2006). Similarly, the VSD/CTD interface is implicated indirectly based on the ability of Mg²⁺, Q397R, and heme to modulate coupling by introducing interactions at or near this interface.Interactions between the S4–S5 linker and S6 are widely considered to underlie voltage-sensor/gate coupling, also known as electromechanical coupling, in Kv channels (Lu et al., 2002; Tristani-Firouzi et al., 2002; Long et al., 2005b; Chowdhury and Chanda, 2012) and are also likely to be important in BK channels (Sun et al., 2012). However, even in Kv channels many of the questions raised above remain to be answered, such as what are the individual residues and nature of interactions that contribute to coupling and when do they occur during gating? The importance of these questions can be illustrated by comparing three hypothetical mechanisms of voltage-sensor/gate coupling that include S4–S5/S6 interactions and are consistent with the allosteric nature of voltage gating in Slo1 (Fig. 4). Fig. 4 (A–C) depicts the four combinations of states the gate and voltage-sensor can assume in a single subunit. The possibility that S4–S5/S6 forms a rigid connection that forces sensor and gate to move as a unit can be ruled out because voltage sensors can activate while channels remain closed. However, it is conceivable that the S4–S5 linker remains bound to S6 at all times, whereas flexibility in adjoining regions allows sensor and gate to move as if coupled by a spring (Fig. 4 A). Another possibility is the S4–S5 linker binds to the open gate only when the voltage sensor is activated, stabilizing the AO state (Fig. 4 B). Alternatively, the S4–S5 linker of the resting voltage sensor might clash with the open gate to destabilize the RO state (Fig. 4 C). These and other mechanisms could account for the ability of voltage-sensor activation to promote opening but make different predictions concerning the source of coupling and the role of S4–S5/S6 interaction. Fig. 4 A suggests that many parts of the S4–S5 linker could contribute to coupling by influencing the mechanical properties of the linkage. In this case, S4–S5/S6 interaction acts merely as a passive connection that affects coupling only to the extent that it is intact or disrupted. In contrast, Fig. 4 (B and C) predicts that the S4–S5/S6 interaction energy is the main determinant of coupling energy. However, the panels in Fig. 4 differ in the nature of the proposed interaction (Fig. 4 B, binding; Fig. 4 C, steric hindrance) and the state dependence of the interaction. The analysis of coupling energy and equilibria for such gating cycles, as outlined above, should allow such mechanisms and predictions to be distinguished in BK channels.Open in a separate windowFigure 4.Three models of voltage-sensor/gate coupling. Interaction of S4–S5 linker with the S6 gate in a single subunit. The voltage sensor can be in a resting (R) or activated (A) state, and the gate is closed (C) or open (O). (A) Flexible linkage with S4–S5/S6 interacting in all states. (B) S4–S5/S6 binding stabilizes AO state. (C) Steric hindrance destabilizes the RO state.Despite substantial homology between BK and K_V channels, important differences also exist that could be relevant to voltage-sensor/gate coupling. First, BK channels are weakly voltage dependent compared with Kv channels and exhibit a different pattern and contribution of voltage-sensing residues in the VSD, suggesting that conformational changes associated with voltage-sensor activation may differ (Ma et al., 2006). Second, the ability of intracellular blockers and Cys-modifying reagents to access the inner pore of closed BK channels (Wilkens and Aldrich, 2006; Zhou et al., 2011) suggests that the BK channel gate may be formed by the selectivity filter (Cox and Hoshi, 2011; Thompson and Begenisich, 2012), as in cyclic-nucleotide–gated channels (Contreras et al., 2008), rather than by crossing of S6 segments at the inner mouth of the pore, as in Kv channels (del Camino and Yellen, 2001). These differences do not require that voltage-sensor/gate coupling occurs through fundamentally different mechanisms. For example, if the BK channel gate is in the selectivity filter it is still likely to be strongly coupled to S6 movement, as in CNG channels (Flynn and Zagotta, 2001), and therefore subject to control by S4–S5/S6 interaction. Indeed, there is considerable evidence for S6 movement associated with BK channel opening (Li and Aldrich, 2006; Wu et al., 2009; Chen and Aldrich, 2011). However, the coupling mechanisms for BK and Kv channels may differ in detail, and a selectivity gate in the BK channel could potentially support a larger role for S4/S5 interaction in voltage-sensor/gate coupling. It should also be noted that regulatory β and γ subunits have been reported to modulate voltage-sensor/gate coupling (Bao and Cox, 2005; Yan and Aldrich, 2010); thus, additional state-dependent interactions may form in BK channels between the VSD and regulatory subunits.

Mechanisms of coupling Ca²⁺ sensors to the gate and voltage sensors

Of the three coupling interactions in the HA model, Ca²⁺-sensor/gate coupling is easiest to measure and best understood at a molecular level. Nonetheless, many questions and controversies remain to be resolved concerning the conformational changes that occur upon Ca²⁺ binding and the mechanisms coupling these changes to the gate and voltage sensors.Ca²⁺-dependent activation is generally consistent with the idea, originally proposed for MthK, that Ca²⁺ binding causes a conformational change in the gating ring that opens the channel by pulling on the RCK1-S6 linker (Jiang et al., 2002). Crystal structures in the presence and absence of Ca²⁺ suggest that MthK and BK channel gating rings expand in diameter by 8 and 12 Å, respectively, upon Ca²⁺ binding (Ye et al., 2006; Wu et al., 2010; Yuan et al., 2012). Experimental evidence in BK channels shows a monotonic relationship between channel activation and linker length, suggesting that the linker is under constant tension in the presence or absence of Ca²⁺, like a spring (Niu et al., 2004). Likewise, effects on Ca²⁺-sensor/gate coupling and Ca² sensitivity of mutations in the N-terminal AC region of the BK channel RCK1 domain suggest that the flexibility of this region is important for transmitting Ca²⁺-dependent conformational changes to the gate (Yang et al., 2010). Although the latter results are consistent with the linker hypothesis, they also have raised the possibility that conformational changes in the AC region could be coupled to the gate through direct contact with the PGD. Consistent with this possibility, the N-terminal half of RCK1 undergoes a substantial reorientation relative to the rest of the BK channel gating ring upon Ca²⁺ binding (Yuan et al., 2012). However, determining whether a CTD/PDG interface exists and contributes to coupling may have to wait until a complete BK channel structure is available.The BK channel CTD contains two high affinity Ca²⁺-binding sites (one in each RCK domain) that have been identified by site-directed mutagenesis (Bao et al., 2004; Zhang et al., 2010). By using mutations to eliminate each site individually and carefully measuring the effects of Ca²⁺ on P_o at −80 mV (similar to Fig. 2 B), Sweet and Cox (2008) determined that the contribution to Ca²⁺-sensor/gate coupling of the RCK1 site (3.74 kCal mol⁻¹) was slightly greater than that of the RCK2 Ca²⁺ bowl site (3.04 kCal mol⁻¹), but the RCK2 site has a higher affinity for Ca²⁺. In addition, the summed contribution of the individual sites exceeded their combined effect in the WT channel (ΔΔGCOCa=5.0 kcal mol−1; Fig. 2 B), consistent with negative cooperativity between sites in the same subunit (Sweet and Cox, 2008). In contrast, another group performing similar experiments at +50 mV concluded that positive cooperativity exists between the two binding sites (Qian et al., 2006). In the latter case, positive cooperativity could potentially be accounted for if both Ca²⁺ sites were coupled to the voltage sensor because the voltage sensor is not held in a resting state at +50 mV. However Sweet and Cox (2008) concluded that the RCK1 site is solely responsible for Ca²⁺-sensor/voltage-sensor coupling. A recent study combining Ca²⁺ site mutations and voltage clamp fluorometry to monitor the effects of Ca²⁺ on steady-state voltage-sensor activation and P_o reached conclusions similar to that of Sweet and Cox (2008) regarding intrasubunit cooperativity and Ca²⁺-sensor/voltage-sensor coupling (Savalli et al., 2012). However, this study also suggested that Ca²⁺ site mutations may have effects other than elimination of Ca²⁺ binding. This caveat, together with the fact that none of the studies mentioned measured Ca²⁺-sensor/voltage-sensor coupling directly, suggests that the extent to which the individual Ca²⁺-binding sites are coupled to the voltage sensor or to each other, as well as the molecular mechanisms mediating such interactions, is still open to question.Although the CTD contains two high affinity Ca²⁺-binding sites, only the Ca²⁺ bowl is occupied in the Ca²⁺-bound gating-ring structure (Yuan et al., 2012), raising questions of to what extent this structure resembles the Ca²⁺-saturated conformation in the intact channel. In principal, the two Ca²⁺ sites could have independent effects on activation by stabilizing a single Ca²⁺-bound open conformation. However, mutations in the AC region of RCK1 selectively alter the Ca²⁺ sensitivity of the RCK1 site (Yang et al., 2010), suggesting that some conformational changes may be coupled to RCK1 occupancy alone. This, together with the fact that the gating ring of the intact channel is expected to contact the VSD, suggests that significant differences in structure could exist between the crystal structure and intact Ca²⁺-saturated gating ring. A related question is to what extent gating ring expansion is determined by channel opening (i.e., RCK1-S6 linker tension) versus Ca²⁺ binding. Because gating ring expansion is observed upon Ca²⁺ binding in isolated gating rings, it seems reasonable to suppose that expansion and channel opening might not occur simultaneously. If the gating ring could expand into a high-Ca²⁺-affinity conformation while the channel is closed, it could have important implications for gating models and for the possible state dependence of CTD/VSD coupling. However, there is as yet no evidence supporting this possibility. Indeed Sweet and Cox (2008) concluded that their results were best fit by assuming gating-ring expansion is tightly coupled to channel opening, consistent with the HA model.A final question relates to conformational events that occur in Ca²⁺-binding sites during channel opening. As in any allosteric model of ligand-dependent gating, the HA model predicts that Ca²⁺-binding sites must have a higher affinity for Ca²⁺ in the open than the closed conformation. Therefore, understanding how Ca²⁺ coordination changes upon channel opening is fundamental to the mechanism of Ca²⁺-sensor/gate coupling. In principal, the contribution of individual Ca²⁺-coordinating residues to state-dependent binding can be evaluated by determining the effect on coupling energy of mutating such sites (Purohit et al., 2012). Previous studies have generally identified likely Ca²⁺-coordination sites based on a reduced sensitivity of mutated channels to Ca²⁺ in the physiological range (≤100 µM). However, experiments at higher [Ca²⁺] may be required to saturate mutated sites and determine if Ca²⁺-sensor/gate coupling is altered.

Summary

The BK channel is an important example of a voltage- and ligand-gated channel whose function depends on conformational coupling between multiple domains. Many questions remain about the molecular basis of domain–domain coupling, but this channel represents a favorable system for studying such processes owing to its unique functional properties and methods that have allowed the energetics of coupling to be studied in detail. Combining these methods with emerging structural information about domain/domain interfaces and conformational changes in the channel should provide further insight into coupling mechanisms that are important in BK channels and in other voltage-gated or ligand-gated channels. BK channels also constitute a powerful system for understanding the interplay between ligand- and voltage-dependent gating. Defining the interactions that mediate coupling between voltage and Ca²⁺ sensors in this channel should provide unique insight into processes that may be relevant to other multimodal channels such as HCN or TRP.This Perspectives series includes articles by Andersen, Colquhoun and Lape, and Chowdury and Chanda.     

Plasma Levels of Middle Molecules to Estimate Residual Kidney Function in Haemodialysis without Urine Collection

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 (GFR_Residual = mean of urea and creatinine clearance). The relationships of plasma Cystatin C and β2-microglobulin levels to GFR_Residual 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 GFR_Residual were 1/β2-micoglobulin (r² 0.67) and 1/Cystatin C (r² 0.50). Both these relationships were weaker at low GFR_Residual. The best regression model for GFR_Residual, 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.     

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

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.     

Detection of MET Gene Copy Number in Cancer Samples Using the Droplet Digital PCR Method

Purpose

The analysis of MET gene copy number (CN) has been considered to be a potential biomarker to predict the response to MET-targeted therapies in various cancers. However, the current standard methods to determine MET CN are SNP 6.0 in the genomic DNA of cancer cell lines and fluorescence in situ hybridization (FISH) in tumor models, respectively, which are costly and require advanced technical skills and result in relatively subjective judgments. Therefore, we employed a novel method, droplet digital PCR (ddPCR), to determine the MET gene copy number with high accuracy and precision.

Methods

The genomic DNA of cancer cell lines or tumor models were tested and compared with the MET gene CN and MET/CEN-7 ratio determined by SNP 6.0 and FISH, respectively.

Results

In cell lines, the linear association of the MET CN detected by ddPCR and SNP 6.0 is strong (Pearson correlation = 0.867). In tumor models, the MET CN detected by ddPCR was significantly different between the MET gene amplification and non-amplification groups according to FISH (mean: 15.4 vs 2.1; P = 0.044). Given that MET gene amplification is defined as MET CN >5.5 by ddPCR, the concordance rate between ddPCR and FISH was 98.0%, and Cohen''s kappa coefficient was 0.760 (95% CI, 0.498–1.000; P <0.001).

Conclusions

The results demonstrated that the ddPCR method has the potential to quantify the MET gene copy number with high precision and accuracy as compared with the results from SNP 6.0 and FISH in cancer cell lines and tumor samples, respectively.     

Controlling Electron Transfer between the Two Cofactor Chains of Photosystem I by the Redox State of One of Their Components

Two functional electron transfer (ET) chains, related by a pseudo-C₂ symmetry, are present in the reaction center of photosystem I (PSI). Due to slight differences in the environment around the cofactors of the two branches, there are differences in both the kinetics of ET and the proportion of ET that occurs on the two branches. The strongest evidence that this is indeed the case relied on the observation that the oxidation rates of the reduced phylloquinone (PhQ) cofactor differ by an order of magnitude. Site-directed mutagenesis of residues involved in the respective PhQ-binding sites resulted in a specific alteration of the rates of semiquinone oxidation. Here, we show that the PsaA-F689N mutation results in an ∼100-fold decrease in the observed rate of PhQA− oxidation. This is the largest change of PhQA− oxidation kinetics observed so far for a single-point mutation, resulting in a lifetime that exceeds that of the terminal electron donor, P700+. This situation allows a second photochemical charge separation event to be initiated before PhQA− has decayed, thereby mimicking in PSI a situation that occurs in type II reaction centers. The results indicate that the presence of PhQA− does not impact the overall quantum yield and leads to an almost complete redistribution of the fractional utilization of the two functional ET chains, in favor of the one that does not bear the charged species. The evolutionary implications of these results are also briefly discussed.     

Physicochemical Properties and Amino Acid Composition of Alkaline Proteinase from Aspergillus sojae

Some physicochemical properties and amino acid composition of alkaline proteinase from Aspergillus sojae were found to be as follows: The isoelectric point was at pH 5.1. The molecular weight was 25,500 using the Sheraga-Mandelkern’s formula, based upon the values of the sedimentation coefficient $(s_{20,w}^{°}=\text{?}2.82\text{?}\text{S})$, the intrinsic viscosity ([η] = 0.027 dl/g), and the partial specific volume $({\displaystyle \overline{V}}\text{?}=\text{?}0.726\text{?}\text{ml}/\text{g})$. The enzyme contains 16.8% of nitrogen and is composed of 250 residues of amino acid; Asp₃₁ Glu₁₉, Gly₂₇, Ala₃₂, Val₁₈, Leu₁₄, Ile₁₄, Ser₂₈, Thr₁₈, ${\text{(}{\displaystyle \stackrel{}{{\displaystyle \stackrel{?}{\text{Cys C}}}}}\text{ys})}_1$, Met₂, Pro₆, Phe₇, Tyr₈, Trp₂, His₅, Lys₁₄, Arg₃, (amide-NH₃)₂₀.     

Increased labile iron pool in sorghum embryonic axes after the exogenous application of nitric oxide is independent on the nature of the NO donor

The objective of this work was to explore the hypothesis that nitric oxide (NO) affects Fe bioavailability in sorghum (Sorghum bicolor (L.) Moench) embryonic axes. NO content was assessed in embryonic axes isolated from seeds control or exposed to NO-donors, employing spin trapping electron paramagnetic resonance (EPR) methodology. NO donors such as sodium nitroprusside (SNP) and diethylenetriamine NONOate (DETA NONOate), released NO that permeated inside the axes increasing NO content. Under these conditions low temperature EPR was employed to study the labile iron pool. A 2.5 fold increase was observed in NO steady state concentration after 24 h of exposure to NO donors that was correlated to a 2 fold increase in the Fe labile pool, as compared to control axes. This observation provides experimental evidence for a potential role of NO in Fe homeostasis.Key words: iron, labile iron pool, nitric oxide, sorghumNitric oxide (NO) has a wide range of functions, among them promotion of growth and seed germination were described in several plant species.¹ Evidences for its participation in Fe homeostasis in planta arise from the fact that Fe deficiency can be reverted enhancing NO level.² Moreover, it is expected that NO acts as intercellular messenger³ being transported from the site of its synthesis. Nitrosylated Fe complexes, formed by reaction of NO with Fe²⁺ and biological thiols, have been proposed as NO carriers, since they are relative stable molecules.⁴The ability of Fe of changing its oxidation state and redox potential in response to changes in the nature of the ligand makes this metal essential for almost all living organisms.⁵ Fe-containing enzymes are the key components of many essential biological reactions. However, the same biochemical properties that make Fe beneficial might be a drawback in some particular conditions, when improperly shielded Fe can catalyze one-electron reductions of O₂ species that lead to the production of reactive free radicals. The toxicity of Fe depends on the Fenton reaction, which produces the hydroxyl radical (·OH) or an oxoiron compound (LFeO²⁺) and on its reactions with lipid hydroperoxides.⁶Most of the current information about NO functions in plants comes from pharmacological studies using NO donors, which generate NO either spontaneously, or after metabolic activation. Moreover, NO production from numerous compounds strongly depends on pH, temperature, light and the presence of reductants.⁷ SNP and DETA NONOate have different kinetics and mechanisms of NO release. However, both are suitable compounds for long-term treatments, since their stability is higher than other NO donors.In this work we evaluated NO steady state concentration in sorghum embryonic axes 24 h after imbibition, in control seeds (distilled water) and in seeds placed either in 1 mM SNP or DETA NONOate. SNP contains Fe in its chemical structure, thus a control was carried out employing photodegraded SNP, which consist of 1 mM SNP solution which had been left under light until all NO was released from the molecule. As it is shown in

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.     

A Novel Method for Quantifying the Inhaled Dose of Air Pollutants Based on Heart Rate,Breathing Rate and Forced Vital Capacity

To better understand the interaction of physical activity and air pollution exposure, it is important to quantify the change in ventilation rate incurred by activity. In this paper, we describe a method for estimating ventilation using easily-measured variables such as heart rate (HR), breathing rate (f_B), and forced vital capacity (FVC). We recruited healthy adolescents to use a treadmill while we continuously measured HR, f_B, and the tidal volume (V_T) of each breath. Participants began at rest then walked and ran at increasing speed until HR was 160–180 beats per minute followed by a cool down period. The novel feature of this method is that minute ventilation (V˙E) was normalized by FVC. We used general linear mixed models with a random effect for subject and identified nine potential predictor variables that influence either V˙E or FVC. We assessed predictive performance with a five-fold cross-validation procedure. We used a brute force selection process to identify the best performing models based on cross-validation percent error, the Akaike Information Criterion and the p-value of parameter estimates. We found a two-predictor model including HR and f_B to have the best predictive performance (V˙E/FVC = -4.247+0.0595HR+0.226f_B, mean percent error = 8.1±29%); however, given the ubiquity of HR measurements, a one-predictor model including HR may also be useful (V˙E/FVC = -3.859+0.101HR, mean percent error = 11.3±36%).