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.     

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.     

A Variable Sampling Interval Synthetic Xbar Chart for the Process Mean

The usual practice of using a control chart to monitor a process is to take samples from the process with fixed sampling interval (FSI). In this paper, a synthetic X¯ control chart with the variable sampling interval (VSI) feature is proposed for monitoring changes in the process mean. The VSI synthetic X¯ chart integrates the VSI X¯ chart and the VSI conforming run length (CRL) chart. The proposed VSI synthetic X¯ chart is evaluated using the average time to signal (ATS) criterion. The optimal charting parameters of the proposed chart are obtained by minimizing the out-of-control ATS for a desired shift. Comparisons between the VSI synthetic X¯ chart and the existing X¯, synthetic X¯, VSI X¯ and EWMA X¯ charts, in terms of ATS, are made. The ATS results show that the VSI synthetic X¯ chart outperforms the other X¯ type charts for detecting moderate and large shifts. An illustrative example is also presented to explain the application of the VSI synthetic X¯ chart.     

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.     

Hunting,Exotic Carnivores,and Habitat Loss: Anthropogenic Effects on a Native Carnivore Community,Madagascar

The wide-ranging, cumulative, negative effects of anthropogenic disturbance, including habitat degradation, exotic species, and hunting, on native wildlife has been well documented across a range of habitats worldwide with carnivores potentially being the most vulnerable due to their more extinction prone characteristics. Investigating the effects of anthropogenic pressures on sympatric carnivores is needed to improve our ability to develop targeted, effective management plans for carnivore conservation worldwide. Utilizing photographic, line-transect, and habitat sampling, as well as landscape analyses and village-based bushmeat hunting surveys, we provide the first investigation of how multiple forms of habitat degradation (fragmentation, exotic carnivores, human encroachment, and hunting) affect carnivore occupancy across Madagascar’s largest protected area: the Masoala-Makira landscape. We found that as degradation increased, native carnivore occupancy and encounter rates decreased while exotic carnivore occupancy and encounter rates increased. Feral cats (Felis species) and domestic dogs (Canis familiaris) had higher occupancy than half of the native carnivore species across Madagascar’s largest protected landscape. Bird and small mammal encounter rates were negatively associated with exotic carnivore occupancy, but positively associated with the occupancy of four native carnivore species. Spotted fanaloka (Fossa fossana) occupancy was constrained by the presence of exotic feral cats and exotic small Indian civet (Viverricula indica). Hunting was intense across the four study sites where hunting was studied, with the highest rates for the small Indian civet (x¯ = 90 individuals consumed/year), the ring-tailed vontsira (Galidia elegans) (x¯ = 58 consumed/year), and the fosa (Cryptoprocta ferox) (x¯ = 31 consumed/year). Our modeling results suggest hunters target intact forest where carnivore occupancy, abundance, and species richness, are highest. These various anthropogenic pressures and their effects on carnivore populations, especially increases in exotic carnivores and hunting, have wide-ranging, global implications and demand effective management plans to target the influx of exotic carnivores and unsustainable hunting that is affecting carnivore populations across Madagascar and worldwide.     

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%).     

The Effects of Exercise Intensity vs. Metabolic State on the Variability and Magnitude of Left Ventricular Twist Mechanics during Exercise

Increased left ventricular (LV) twist and untwisting rate (LV twist mechanics) are essential responses of the heart to exercise. However, previously a large variability in LV twist mechanics during exercise has been observed, which complicates the interpretation of results. This study aimed to determine some of the physiological sources of variability in LV twist mechanics during exercise. Sixteen healthy males (age: 22 ± 4 years, V˙O_2peak: 45.5 ± 6.9 ml∙kg^-1∙min^-1, range of individual anaerobic threshold (IAT): 32–69% of V˙O_2peak) were assessed at rest and during exercise at: i) the same relative exercise intensity, 40%_peak, ii) at 2% above IAT, and, iii) at 40%_peak with hypoxia (40%_peak+HYP). LV volumes were not significantly different between exercise conditions (P > 0.05). However, the mean margin of error of LV twist was significantly lower (F_2,47 = 2.08, P < 0.05) during 40%peak compared with IAT (3.0 vs. 4.1 degrees). Despite the same workload and similar LV volumes, hypoxia increased LV twist and untwisting rate (P < 0.05), but the mean margin of error remained similar to that during 40%peak (3.2 degrees, P > 0.05). Overall, LV twist mechanics were linearly related to rate pressure product. During exercise, the intra-individual variability of LV twist mechanics is smaller at the same relative exercise intensity compared with IAT. However, the absolute magnitude (degrees) of LV twist mechanics appears to be associated with the prevailing rate pressure product. Exercise tests that evaluate LV twist mechanics should be standardised by relative exercise intensity and rate pressure product be taken into account when interpreting results.     

A Global Analysis of Deforestation in Moist Tropical Forest Protected Areas

Protected areas (PAs) have been established to conserve tropical forests, but their effectiveness at reducing deforestation is uncertain. To explore this issue, we combined high resolution data of global forest loss over the period 2000–2012 with data on PAs. For each PA we quantified forest loss within the PA, in buffer zones 1, 5, 10 and 15 km outside the PA boundary as well as a 1 km buffer within the PA boundary. We analysed 3376 tropical and subtropical moist forest PAs in 56 countries over 4 continents. We found that 73% of PAs experienced substantial deforestation pressure, with >0.1% a⁻¹ forest loss in the outer 1 km buffer. Forest loss within PAs was greatest in Asia (0.25% a⁻¹) compared to Africa (0.1% a⁻¹), the Neotropics (0.1% a⁻¹) and Australasia (Australia and Papua New Guinea; 0.03% a⁻¹). We defined performance (P) of a PA as the ratio of forest loss in the inner 1 km buffer compared to the loss that would have occurred in the absence of the PA, calculated as the loss in the outer 1 km buffer corrected for any difference in deforestation pressure between the two buffers. To remove the potential bias due to terrain, we analysed a subset of PAs (n = 1804) where slope and elevation in inner and outer 1 km buffers were similar (within 1° and 100 m, respectively). We found 41% of PAs in this subset reduced forest loss in the inner buffer by at least 25% compared to the expected inner buffer forest loss (P<0.75). Median performance (P˜) of subset reserves was 0.87, meaning a reduction in forest loss within the PA of 13%. We found PAs were most effective in Australasia (P˜=0.16), moderately successful in the Neotropics (P˜=0.72) and Africa (P˜=0.83), but ineffective in Asia (P˜=1). We found many countries have PAs that give little or no protection to forest loss, particularly in parts of Asia, west Africa and central America. Across the tropics, the median effectiveness of PAs at the national level improved with gross domestic product per capita. Whilst tropical and subtropical moist forest PAs do reduce forest loss, widely varying performance suggests substantial opportunities for improved protection, particularly in Asia.     

A Comparison between Conductive and Infrared Devices for Measuring Mean Skin Temperature at Rest,during Exercise in the Heat,and Recovery

PurposeSkin temperature assessment has historically been undertaken with conductive devices affixed to the skin. With the development of technology, infrared devices are increasingly utilised in the measurement of skin temperature. Therefore, our purpose was to evaluate the agreement between four skin temperature devices at rest, during exercise in the heat, and recovery.MethodsMean skin temperature (T-sk) was assessed in thirty healthy males during 30 min rest (24.0 ± 1.2°C, 56 ± 8%), 30 min cycle in the heat (38.0 ± 0.5°C, 41 ± 2%), and 45 min recovery (24.0 ± 1.3°C, 56 ± 9%). T-sk was assessed at four sites using two conductive devices (thermistors, iButtons) and two infrared devices (infrared thermometer, infrared camera).ResultsBland–Altman plots demonstrated mean bias ± limits of agreement between the thermistors and iButtons as follows (rest, exercise, recovery): -0.01 ± 0.04, 0.26 ± 0.85, -0.37 ± 0.98°C; thermistors and infrared thermometer: 0.34 ± 0.44, -0.44 ± 1.23, -1.04 ± 1.75°C; thermistors and infrared camera (rest, recovery): 0.83 ± 0.77, 1.88 ± 1.87°C. Pairwise comparisons of T-sk found significant differences (p < 0.05) between thermistors and both infrared devices during resting conditions, and significant differences between the thermistors and all other devices tested during exercise in the heat and recovery.ConclusionsThese results indicate poor agreement between conductive and infrared devices at rest, during exercise in the heat, and subsequent recovery. Infrared devices may not be suitable for monitoring T-sk in the presence of, or following, metabolic and environmental induced heat stress.     

The Impact of Prior Information on Estimates of Disease Transmissibility Using Bayesian Tools

The basic reproductive number (R₀) and the distribution of the serial interval (SI) are often used to quantify transmission during an infectious disease outbreak. In this paper, we present estimates of R₀ and SI from the 2003 SARS outbreak in Hong Kong and Singapore, and the 2009 pandemic influenza A(H1N1) outbreak in South Africa using methods that expand upon an existing Bayesian framework. This expanded framework allows for the incorporation of additional information, such as contact tracing or household data, through prior distributions. The results for the R₀ and the SI from the influenza outbreak in South Africa were similar regardless of the prior information (R^0 = 1.36–1.46, μ^ = 2.0–2.7, μ^ = mean of the SI). The estimates of R₀ and μ for the SARS outbreak ranged from 2.0–4.4 and 7.4–11.3, respectively, and were shown to vary depending on the use of contact tracing data. The impact of the contact tracing data was likely due to the small number of SARS cases relative to the size of the contact tracing sample.     

Higher ventilatory responses during and after passive walking-like leg movement in older individuals

Background

Minute ventilation (V·E) during walking has been shown to be higher in older individuals than in young individuals, but the mechanisms underlying the higher ventilatory response is unclear. Central command and peripheral neural reflex are important neural control mechanisms underlying ventilatory response during exercise. Passive leg movement has been used to exclude the influence of central command due to the lack of voluntary activation of muscles. The aim of the present study was to compare the ventilatory response during and after passive walking-like leg movement (PWM) in young and older individuals.

Methods

Eight young subjects (20 ± 2 years) and seven older subjects (70 ± 1 years) participated in this study. Subjects spent 7 minutes in a quiet standing (QS) position. Thereafter, they performed 14-minute rhythmic PWM at 1 Hz and this was followed by 7 minutes of QS.

Results

V·E values during pre-PWM QS were calculated as 1-minute averages using data obtained between 5 and 6 minutes. V·E values at pre-PWM QS in the young and older groups were 8.4 ± 2.1 and 7.5 ± 1.2 l/minute, respectively. V·E values increased significantly at the first minute of PWM to 11.4 ± 2.2 and 10.4 ± 2.5 l/minute in the young and older groups, respectively (P <0.001). In the young group, V·E at the last minute of PWM (9.2 ± 2.0 l/minute) was not significantly different from that at pre-PWM QS due to a decline in V·E, whereas V·E at the last minute of PWM in the older group (9.4 ± 2.2 l/minute) was still significantly higher (P <0.01). On the other hand, V·E at the first minute of post-PWM QS (7.2 ± 1.8 l/minute) was significantly lower than that during pre-PWM QS in the young group (P <0.05) but not in the older group.

Conclusions

Ventilatory response during and after PWM is higher in older individuals than in young individuals. This may be associated with a mechanism(s) other than central command. Our findings may explain part of the higher V·E response while walking in older individuals.     

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.     

GEDAE-LaB: A Free Software to Calculate the Energy System Contributions during Exercise

Purpose

The aim of the current study is to describe the functionality of free software developed for energy system contributions and energy expenditure calculation during exercise, namely GEDAE-LaB.

Methods

Eleven participants performed the following tests: 1) a maximal cycling incremental test to measure the ventilatory threshold and maximal oxygen uptake (V˙O₂max); 2) a cycling workload constant test at moderate domain (90% ventilatory threshold); 3) a cycling workload constant test at severe domain (110% V˙O₂max). Oxygen uptake and plasma lactate were measured during the tests. The contributions of the aerobic (A_MET), anaerobic lactic (LA_MET), and anaerobic alactic (AL_MET) systems were calculated based on the oxygen uptake during exercise, the oxygen energy equivalents provided by lactate accumulation, and the fast component of excess post-exercise oxygen consumption, respectively. In order to assess the intra-investigator variation, four different investigators performed the analyses independently using GEDAE-LaB. A direct comparison with commercial software was also provided.

Results

All subjects completed 10 min of exercise at moderate domain, while the time to exhaustion at severe domain was 144 ± 65 s. The A_MET, LA_MET, and AL_MET contributions during moderate domain were about 93, 2, and 5%, respectively. The A_MET, LA_MET, and AL_MET contributions during severe domain were about 66, 21, and 13%, respectively. No statistical differences were found between the energy system contributions and energy expenditure obtained by GEDAE-LaB and commercial software for both moderate and severe domains (P > 0.05). The ICC revealed that these estimates were highly reliable among the four investigators for both moderate and severe domains (all ICC ≥ 0.94).

Conclusion

These findings suggest that GEDAE-LaB is a free software easily comprehended by users minimally familiarized with adopted procedures for calculations of energetic profile using oxygen uptake and lactate accumulation during exercise. By providing availability of the software and its source code we hope to facilitate future related research.     

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.     

Rhinos in the Parks: An Island-Wide Survey of the Last Wild Population of the Sumatran Rhinoceros

In the 200 years since the Sumatran rhinoceros was first scientifically described (Fisher 1814), the range of the species has contracted from a broad region in Southeast Asia to three areas on the island of Sumatra and one in Kalimantan, Indonesia. Assessing population and spatial distribution of this very rare species is challenging because of their elusiveness and very low population number. Using an occupancy model with spatial dependency, we assessed the fraction of the total landscape occupied by Sumatran rhinos over a 30,345-km² survey area and the effects of covariates in the areas where they are known to occur. In the Leuser Landscape (surveyed in 2007), the model averaging result of conditional occupancy estimate was ψ^(SE[ψ^])=0.151(0.109) or 2,371.47 km², and the model averaging result of replicated level detection probability p^(SE[p^])=0.252(0.267); in Way Kambas National Park—2008: ψ^(SE[ψ^])=0.468(0.165) or 634.18 km², and p^(SE[p^])=0.138(0.571); and in Bukit Barisan Selatan National Park—2010: ψ^(SE[ψ^])=0.322(0.049) or 819.67 km², and p^(SE[p^])=0.365(0.42). In the Leuser Landscape, rhino occurrence was positively associated with primary dry land forest and rivers, and negatively associated with the presence of a road. In Way Kambas, occurrence was negatively associated with the presence of a road. In Bukit Barisan Selatan, occurrence was negatively associated with presence of primary dryland forest and rivers. Using the probabilities of site occupancy, we developed spatially explicit maps that can be used to outline intensive protection zones for in-situ conservation efforts, and provide a detailed assessment of conserving Sumatran rhinos in the wild. We summarize our core recommendation in four points: consolidate small population, strong protection, determine the percentage of breeding females, and recognize the cost of doing nothing. To reduce the probability of poaching, here we present only the randomized location of site level occupancy in our result while retaining the overall estimation of occupancy for a given area.     

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

Enhancement of Chemotactic Cell Aggregation by Haptotactic Cell-To-Cell Interaction

The crawling of biological cell is a complex phenomenon involving various biochemical and mechanical processes. Some of these processes are intrinsic to individual cells, while others pertain to cell-to-cell interactions and to their responses to extrinsically imposed cues. Here, we report an interesting aggregation dynamics of mathematical model cells, when they perform chemotaxis in response to an externally imposed global chemical gradient while they influence each other through a haptotaxis-mediated social interaction, which confers intriguing trail patterns. In the absence of the cell-to-cell interaction, the equilibrium population density profile fits well to that of a simple Keller-Segal population dynamic model, in which a chemotactic current density J→chemo∼∇p competes with a normal diffusive current density J→diff∼∇ρ, where p and ρ refer to the concentration of chemoattractant and population density, respectively. We find that the cell-to-cell interaction confers a far more compact aggregation resulting in a much higher peak equilibrium cell density. The mathematical model system is applicable to many biological systems such as swarming microglia and neutrophils or accumulating ants towards a localized food source.