Training-Induced Increase in V·O2max and Critical Power, and Acceleration of V·O2 on-Kinetics Result from Attenuated Pi Increase Caused by Elevated OXPHOS Activity

Computer simulations using a dynamic model of the skeletal muscle bioenergetic system, involving the Pi-double-threshold mechanism of muscle fatigue, demonstrate that the training-induced increase in V·O2max, increase in critical power (CP) and acceleration of primary phase II of the V·O2 on kinetics (decrease in t0.63) is caused by elevated OXPHOS activity acting through a decrease in and slowing of the Pi (inorganic phosphate) rise during the rest-to-work transition. This change leads to attenuation of the reaching by Pi of Pipeak, peak Pi at which exercise is terminated because of fatigue. The delayed (in time and in relation to V·O2 increase) Pi rise for a given power output (PO) in trained muscle causes Pi to reach Pipeak (in very heavy exercise) after a longer time and at a higher V·O2; thus, exercise duration is lengthened, and V·O2max is elevated compared to untrained muscle. The diminished Pi increase during exercise with a given PO can cause Pi to stabilize at a steady state less than Pipeak, and exercise can continue potentially ad infinitum (heavy exercise), instead of rising unceasingly and ultimately reaching Pipeak and causing exercise termination (very heavy exercise). This outcome means that CP rises, as the given PO is now less than, and not greater than CP. Finally, the diminished Pi increase (and other metabolite changes) results in, at a given PO (moderate exercise), the steady state of fluxes (including V·O2) and metabolites being reached faster; thus, t0.63 is shortened. This effect of elevated OXPHOS activity is possibly somewhat diminished by the training-induced decrease in Pipeak.

with mitochondrial myopathies and cardiovascular diseases.Therefore, these properties constitute a good and convenient measure of the efficiency of the human bioenergetic system.
It was also shown that end-exercise P i at work termination because of fatigue is more than twice lower in trained, compared to untrained, rowers [26], while end-exercise P i , H + and H 2 PO 4  -in exhausting exercise are lower in younger individuals than in older people, who can be regarded in a sense as "detrained" individuals [27].
The "P i double-threshold" mechanism of muscle fatigue was postulated recently [28,29].This mechanism assumes that: (1) the additional ATP usage, underlying the slow component of the • VO 2 and metabolites on-kinetics, begins when P i exceeds a critical value, Pi crit [28]; (2) muscle work is terminated because of fatigue when P i reaches a peak value, Pi peak [30]; and (3) the increases in P i and additional ATP usage reciprocally stimulate each other, creating a positive feedback loop (self-driving mechanism) [28].In sufficiently intense exercise, P i ultimately reaches Pi peak (and ), and exercise is terminated because of exhaustion.The first threshold, corresponding to Pi crit (point 1), the second threshold, corresponding to Pi peak (point 2), and positive feedback (point 3) were introduced previously in relation to an abstract fatigue factor F, representing various fatigue-related metabolites: H + , NH 4 + , IMP, AMP, ADP, P i , etc. [31].
The "P i double-threshold" mechanism is able to generate numerous different, apparently unrelated properties of the skeletal muscle bioenergetic system: time courses of relevant variables, including of muscle (and pulmonary) • VO 2 , cytosolic ADP, pH, PCr and P i during the rest-work transition; the constancy of these variable values at the end of exercise at various power outputs above critical power, the hyperbolic power-duration curve with an asymptote in the form of critical power and the decrease or increase in CP and • VO 2max and increase or decrease in t 0.63 caused by hypoxia or hyperoxia, respectively [28].
The discussed mechanism also allows for consideration of the effect of mutations in mitochondrial and nuclear DNA, leading to impairment of OXPHOS in mitochondrial myopathy (MM) patients regarding the skeletal muscle bioenergetic system and exercise tolerance [32].
The discussed mechanism can also explain the changes in • VO 2max , CP and • VO 2 onkinetics (decrease in t 0.63 and the slow component) induced by endurance training in healthy persons [29] and MM patients [33].Computer simulations have predicted that these effects are caused by the training-induced increase in OXPHOS activity.When it is assumed that the increase in OXPHOS activity in vivo corresponds quantitatively to the increase in mitochondria volume density and/or OXPHOS (enzymes) activity in vitro, slightly too great quantitative effects on • VO 2max and CP were predicted [29].Therefore, the possibility was postulated that training also leads to a decrease in Pi peak , which diminishes the effect of the increase in OXPHOS activity and improves the metabolite (ADP, P i , PCr, H + ) homeostasis [29,33].However, alternatively, the increase in the activity of OXPHOS (complexes) measured in a given muscle (e.g., gastrocnemius or quadriceps) in vitro may not be representative of the rise in the (mean) OXPHOS activity in the whole working muscle group (including gluteus, biceps femoris, quadriceps, gastrocnemius and soleus) in vivo [34].If a smaller training-induced increase in OXPHOS activity in power-generating muscles in vivo is assumed, the training-induced increases in • VO 2max and CP encountered in experimental studies can be accounted for quantitatively without the need to decrease Pi peak .This problem will have to be resolved by future experimental studies, in particular directed toward the measurement of the effect of training on the end-exercise concentrations of P i and other metabolites (particularly H 2 PO 4 − and H + ).The present study is intended to demonstrate how (by which mechanism) the traininginduced increase in OXPHOS activity and likely the decrease in Pi peak determine the rises in • VO 2max and CP and fall in t 0.63 .It is hypothesized that these changes occur through a delay and decrease in the P i increase during the rest-to-work transition that leads to attenuation of the reaching of Pi peak by P i (the effect of elevated OXPHOS activity on

Ethical Approval
This study was purely theoretical and did not involve any experiments on humans or animals.

Computer Model
The dynamic computer model of the skeletal muscle bioenergetic system developed previously was used in the present study [28,[34][35][36][37][38].The model involves the each-step activation (ESA) (parallel activation) mechanism of the stimulation of different elements of the bioenergetic system in the cell during work transitions.According to this mechanism, all OXPHOS complexes, NADH supply and glycolysis/glycogenolysis are directly activated by some cytosolic factor/mechanism (which probably involves cytosolic Ca 2+ ions and possibly protein phosphorylation/dephosphorylation) in parallel with ATP usage activation by Ca 2+ ions during rest-to-work or low-to-high-work transitions in skeletal muscle, heart and other tissues [39][40][41][42].Fell and Thomas postulated a similar mechanism, called "multi-site stimulation", for the regulation of glycolysis and TCA (tricarboxylic acid) cycles [43,44].The complete model description was published previously [30] and is available on the author's personal website: http://bernardkorzeniewski.pl(accessed on 22 September 2023).
A general, simplified scheme of the bioenergetic system in skeletal muscle addressed in the present study is shown in Figure 1.The components of the system that appear explicitly within the model are shown.The two main parts of the model are the set of kinetic equations describing the dependence of the rate of particular enzymatic reactions and processes on metabolite concentrations and the set of ordinary differential equations describing the dependence of the rates of the changes in particular metabolite concentrations on the rates of reactions and processes.In each simulation step (very short time interval), new reaction rates are calculated on the basis of current metabolite concentrations, and new metabolite concentrations are calculated on the basis of current reaction rates.

Figure 1.
General scheme of the myocyte bioenergetic system.The components of the system are presented that are considered explicitly in the dynamic computer model used for theoretical studies.Each-step activation (ESA) denotes direct activation of (almost) all elements of the system by some mechanism involving cytosolic Ca 2+ (ATP usage, OXPHOS complexes, malate-aspartate shuttle, MAS and glycolysis) and mitochondrial Ca 2+ (NADH supply system).Some still unknown factor/mechanism cooperating with Ca 2+ , for example, calmodulin-like protein, which "presents" Ca 2+ ions to enzymes/carriers and/or protein (de)phosphorylation, is indicated by the question mark ("?").CI, CIII and CIV indicate complexes I, III and IV of the respiratory chain, respectively; cyt.c, cytochrome c; UQ, ubiquinone.This diagram is taken from [45] (no permission required by the publisher).
The action of Ca 2+ ions and the still unknown additional factor "?" in the system is not involved explicitly in the model but is expressed implicitly as the activity of the regular ATP usage (AUT) and activation by ESA of OXPHOS (AOX) and glycolysis (AGL) (see below).
This model is able to generate a wide range of various kinetic properties and explain many aspects of the functioning of the skeletal muscle bioenergetic system (see [42] for a review and [28][29][30]32,33,46]).

Bioenergetic Molecular Sequence of Events during Rest-to-Work Transition
The model is intended to reproduce the real behavior of the elements of the system presented in Figure 1.During the rest-to-work transition, the subsequent chain (sequence) of biochemical-molecular events in the skeletal muscle cell bioenergetic system is Figure 1.General scheme of the myocyte bioenergetic system.The components of the system are presented that are considered explicitly in the dynamic computer model used for theoretical studies.Each-step activation (ESA) denotes direct activation of (almost) all elements of the system by some mechanism involving cytosolic Ca 2+ (ATP usage, OXPHOS complexes, malate-aspartate shuttle, MAS and glycolysis) and mitochondrial Ca 2+ (NADH supply system).Some still unknown factor/mechanism cooperating with Ca 2+ , for example, calmodulin-like protein, which "presents" Ca 2+ ions to enzymes/carriers and/or protein (de)phosphorylation, is indicated by the question mark ("?").CI, CIII and CIV indicate complexes I, III and IV of the respiratory chain, respectively; cyt.c, cytochrome c; UQ, ubiquinone.This diagram is taken from [45] (no permission required by the publisher).
The action of Ca 2+ ions and the still unknown additional factor "?" in the system is not involved explicitly in the model but is expressed implicitly as the activity of the regular ATP usage (A UT ) and activation by ESA of OXPHOS (A OX ) and glycolysis (A GL ) (see below).
This model is able to generate a wide range of various kinetic properties and explain many aspects of the functioning of the skeletal muscle bioenergetic system (see [42] for a review and [28][29][30]32,33,46]).

Bioenergetic Molecular Sequence of Events during Rest-to-Work Transition
The model is intended to reproduce the real behavior of the elements of the system presented in Figure 1.During the rest-to-work transition, the subsequent chain (sequence) of biochemical-molecular events in the skeletal muscle cell bioenergetic system is initiated.Neural myocyte stimulation by an appropriate motor unit leads to a release of Ca 2+ ions from sarcoplasmic reticulum cisterns.Calcium ions activate actomyosin-ATPase (muscle contraction) and Ca 2+ -ATPase (SERCA; taking up of Ca 2+ ions during muscle relaxation).As a result, intense hydrolysis of ATP to ADP and P i takes place, and the concentrations of ADP and P i increase.The level of ATP remains almost constant, as the resting ATP/ADP ratio is very high (several hundreds), unless the total adenine nucleotide pool is reduced by AMP deamination.Simultaneously, most cytosolic and mitochondrial elements of the system are directly stimulated by some still unknown factor/mechanism, which probably involves (mostly cytosolic) Ca 2+ and possibly calmodulin-like proteins presenting Ca 2+ ions to different enzymes and carriers and/or phosphorylation or dephosphorylation of proteins.The direct stimulation of the ATP supply by ESA attenuates the increases in ADP and P i [40].Because OXPHOS (together with glycolysis and substrate dehydrogenation) is significantly activated by this mechanism, less accumulation of ADP and P i is needed to stimulate the oxidative and glycolytic ATP supply to match the greatly increased ATP usage for muscle contraction.The equilibrium of the very fast reaction catalyzed by creatine kinase (CK) is shifted as a result of the moderate ADP increase.Consequently, a moderate fall in PCr, rise in Cr, consumption of protons (transient initial pH increase) and further moderate rise in P i (resulting from the co-operation of creatine kinase and ATP usage) take place.The rises in ADP and P i further drive OXPHOS, resulting in augmentation of • VO 2 , which is simultaneously stimulated through the direct OXPHOS activation by ESA.As the changes in metabolite concentrations, especially PCr, Cr and P i , are only moderate, the characteristic transition time of primary phase II of the • VO 2 (and metabolites) on-kinetics (t 0.63 ) is rather short.The increases in ADP and AMP (and other metabolites not considered explicitly within the model) additionally stimulate (anaerobic) glycolysis.The production of H + ions by anaerobic glycolysis leads to a decrease in pH to less than its resting value.The magnitude of this acidification depends on exercise intensity: the greater that the power output is, the stronger that the acidification is.However, accumulating H + ions inhibit (anaerobic) glycolysis, preventing further significant cytosol acidification (self-limiting process).In the moderate exercise intensity domain, the system ultimately reaches a steady state (see [45] for more details).
In heavy, very heavy and severe exercise intensity domains [47] additional biochemicalmolecular events in the muscle bioenergetic system form a causal chain (sequence) supplementing the processes occurring in the primary phase II on-kinetics of the system.In particular, the slow component of the • VO 2 and metabolite on-kinetics appears.A sufficiently high work intensity (ATP usage activity) causes P i to exceed Pi crit , which starts the additional ATP usage (as opposed to the regular ATP usage related to power generation).This increase is associated with additional rises in ADP and P i , and P i further enhances the additional ATP usage, leading to the formation of a positive feedback loop (self-driving phenomenon).The additional increase in ADP further affects the creatine kinase equilibrium and results in an additional fall in PCr and rise in Cr.The further elevated ADP and AMP additionally enhance anaerobic glycolysis, leading to greater cytosolic acidification.Accumulating protons in turn recursively inhibit (anaerobic) glycolysis.ADP and P i rise continuously, further stimulating OXPHOS and leading to an additional increase in • VO 2 .Consequently, the slow component of the on-kinetics of oxygen consumption and metabolites appears.The mutual stimulation of the rise in P i and additional ATP usage in heavy exercise are not intense enough to reach Pi peak by P i and to reach of Consequently, exercise is not terminated because of fatigue, and the system finally approaches a steady state, although a higher one than that achieved without the presence of the additional ATP usage and • VO 2 and metabolites' slow components.The heavy/very heavy exercise border constitutes an emerging property of the system that separates work intensities/A UT s, for which this feedback loop leads to P i stabilization at less than Pi peak from those for which it does not.This border represents the critical ATP usage activity (A UTcrit ) at the muscle level and critical power (CP) at the whole-body level.With very heavy and severe exercise, the reciprocal driving of the rises in P i and additional ATP usage is intense enough to prevent reaching of a steady state.Metabolites change, and oxygen consumption increases continuously.Finally, when P i reaches Pi peak , and , muscle work is terminated because of exhaustion (see [45] for more details).
It should be emphasized that the • VO 2 kinetics constitute a result of this sequence of events; therefore, it cannot be a cause of any system property.On the contrary, it is an epiphenomenon (emergent property of the system) that can serve as a non-invasive indicator of the biochemical/kinetic properties/events originating in the muscle, especially of total OXPHOS activity ( [45,46]; see below).

Computer Simulations
The ATP usage activity (A UT , proportional to power output) is scaled to 1 at rest.This regular ATP usage differs from the additional ATP usage, which underlies the slow component of • VO 2 and metabolites.At the onset of constant-power exercise, it is elevated instantaneously to a determined value, for example, 100 for intense exercise.One A UT unit is an equivalent of roughly 3 W (2-4 W depending, for instance, on working muscle mass) in whole-body exercise, such as cycling or running.
Rate constants for OXPHOS complexes and NADH supply block present in kinetic equations in the computer model can be represented as a single rate constant of OXPHOS (k OX ), representing the OXPHOS activity.This rate constant is scaled to 1 in the "standard" version of the model for young, physically active individuals.At the onset of exercise, this "default" OXPHOS activity (at rest and during work) is multiplied by the ESA intensity A OX , being a saturating function of ATP usage activity A UT [37,38].This activity can be called the "work-induced" OXPHOS activity (present only during work).Therefore, the total OXPHOS activity = default OXPHOS activity × induced OXPHOS activity (ESA intensity).During work, OXPHOS is additionally moderately stimulated by the ADP and P i increases.A OX is elevated through an increase in the parameter A OXmax , which can be called the ESA rate constant, at the onset of exercise.OXPHOS complexes, NADH supply block and glycolysis are activated by ESA with some delay in parallel with ATP usage, the activity of which is elevated step-wise (see, e.g., [36,[39][40][41][42]).
Within the model, the "P i double-threshold" mechanism of muscle fatigue is expressed by a fixed Pi crit = 18 mM, Pi peak = 25 mM (in the "standard" version of the model for young physically-active individuals) and kinetic equation for the additional ATP usage (for P i > Pi crit ), in which the additional ATP usage flux is proportional to the current P i −Pi crit difference [28,47].The kinetic equation for the intensity of the additional ATP usage has the following form: where v add is the rate of additional ATP usage (mM min −1 ), k add = 0.2 mM −0.5 is the activity ("rate constant") of the additional ATP usage, v UT is the rate of the regular (as opposed to additional) ATP usage (mM min −1 ), P i is the current inorganic phosphate concentration (mM), t a = 2 min is the characteristic time of the activation of the additional ATP usage, and t add is the time after the onset of exercise.
The computer model involves a constant capillary O 2 concentration during exercise equal to 30 µM in the standard model version.
In the present study, the following simulations demonstrating the effect of endurance training on the key variables of the skeletal muscle bioenergetic system were performed.

In the simulations of the effect of training on
• VO 2max , the activity of ATP usage (work intensity) A UT = 90 was used, representing the very heavy exercise-intensity domain both before and after training.The "default" activity of OXPHOS was augmented by 10% (k OX : 1.0 → 1.1), while ESA intensity ("work-induced" OXPHOS activity) was assumed to be unchanged.The "standard" value of Pi peak = 25 mM was used.
In the simulations of the effect of training on the critical ATP usage activity (A UTcrit , analogous to CP) the activity of ATP usage (work intensity) A UT = 82 was used, which represented the very heavy exercise-intensity domain before training and heavy exerciseintensity domain after training.The "default" activity of OXPHOS was augmented by 10% (k OX : 1.0 → 1.1), while ESA intensity ("work-induced" OXPHOS activity) was assumed to be unchanged.The "standard" value of Pi peak = 25 mM was used.
In the simulations of the effect of training on t 0.63 , the activity of ATP usage (work intensity) A UT = 50 was used, representing the moderate exercise-intensity domain both before and after training.The "default" activity of OXPHOS was augmented by 22% (k OX : 0.9 → 1.1), while ESA intensity ("work-induced" OXPHOS activity) was assumed to be unchanged.The "standard" value of Pi peak = 25 mM was used.
In the simulations of the effect of the Pi peak decrease in trained muscle on • VO 2max , the activity of ATP usage (work intensity) A UT = 90 was used, representing the very heavy exercise-intensity domain.The "trained" OXPHOS activity was used (k OX = 1.1), and Pi peak was decreased: 25 mM → 22.5 mM.
In the simulations of the effect of the Pi peak decrease in trained muscle on CP, the activity of ATP usage (work intensity) A UT = 82 was used, representing the heavy exerciseintensity domain without Pi peak decrease and very heavy exercise-intensity domain with Pi peak decrease.The "trained" OXPHOS activity was used (k OX = 1.1), and Pi peak was decreased: 25 mM → 22 mM.
The values of the parameters A UT , k OX and Pi peak and their changes were chosen arbitrarily to enable a clear presentation.

Results
Muscle training, leading to an increase in OXPHOS activity, elevates • VO 2max is augmented, and the duration of exercise is lengthened.
The training-induced increase in OXPHOS activity also elevates A UTcrit (critical ATP usage activity proportional to critical power, CP) and can lead to the transition of exercise of a given intensity (power output) from the very heavy-intensity domain to heavy-intensity domain.This outcome is demonstrated if Figure 3.It occurs because of a decrease in the P i rise during exercise.Before training, P i was unceasingly rising and ultimately reached P i and thus caused exercise termination because of fatigue at this power output (PO), while after training, P i was increasing at a slower pace and finally stabilized at a steady-state value less than Pi peak , and exercise could be continued potentially ad infinitum.As a result, in trained muscle, • VO 2 does not reach • VO 2max and stabilizes at a steady-state value less than it, in opposition to the situation taking place in untrained muscle.Thus, as the result of training, CP is elevated, and PO, which was greater than CP in untrained muscle, can be less than CP in trained muscle.

Results
Muscle training, leading to an increase in OXPHOS activity, elevates VȮ2max and lengthens the duration of exercise in very heavy exercise.This outcome is demonstrated if Figure 2. It occurs through attenuation (delay and decrease in relation of VȮ2) of the Pi rise during exercise.As a result, in trained muscle, Pi reaches Pipeak ,and exercise is terminated because of fatigue after a longer time and at a higher VȮ2 (VȮ2max) than in untrained muscle.Thus, at a given work intensity (regular ATP usage activity), VȮ2max is augmented, and the duration of exercise is lengthened.The training-induced increase in OXPHOS activity also elevates AUTcrit (critical ATP usage activity proportional to critical power, CP) and can lead to the transition of exercise of a given intensity (power output) from the very heavy-intensity domain to heavy-intensity domain.This outcome is demonstrated if Figure 3.It occurs because of a decrease in the Pi rise during exercise.Before training, Pi was unceasingly rising and ultimately reached Pi and thus caused exercise termination because of fatigue at this power output (PO), while after training, Pi was increasing at a slower pace and finally stabilized at a steady-state value less than Pipeak, and exercise could be continued potentially ad infinitum.As a result, in trained muscle, VȮ2 does not reach VȮ2max and stabilizes at a steadystate value less than it, in opposition to the situation taking place in untrained muscle.Thus, as the result of training, CP is elevated, and PO, which was greater than CP in untrained muscle, can be less than CP in trained muscle.4.This effect is mostly caused by the decrease in the P i increase (associated with a smaller PCr decrease/Cr increase) (e.g., the smaller training-induced increase in ADP plays a minor role, as the ADP concentration is in the micromolar range; see Discussion).Here, both before and after training, exercise is within the moderate-intensity domain.However, for some power outputs, muscle training can bring the system from the (very) heavy exercise-intensity domain to the moderate exercise-intensity domain (see [29], Figure 6 therein).
, x FOR PEER REVIEW 9 of 18 underlying it are absent.This outcome is demonstrated in Figure 4.This effect is mostly caused by the decrease in the Pi increase (associated with a smaller PCr decrease/Cr increase) (e.g., the smaller training-induced increase in ADP plays a minor role, as the ADP concentration is in the micromolar range; see Discussion).Here, both before and after training, exercise is within the moderate-intensity domain.However, for some power outputs, muscle training can bring the system from the (very) heavy exercise-intensity domain to the moderate exercise-intensity domain (see [29], Figure 6 therein).The possible training-induced decrease in Pipeak weakens the rise in VȮ2 caused by the OXPHOS activity increase.This outcome is demonstrated in Figure 5.In the presence of the diminished Pipeak, Pi simply reaches Pipeak, and exercise is terminated because of fatigue earlier after the onset of exercise and at a lower VȮ2.Therefore, timeend and VȮ2max decrease.For this reason, generally, the training-induced increases in VȮ2max and timeend are smaller than they would be if only OXPHOS activity increased, and Pipeak did not decrease.Nevertheless, exercise remains in the very heavy-intensity domain.The possible training-induced decrease in Pipeak diminishes the increase in CP caused by the OXPHOS activity increase.This outcome is demonstrated in Figure 6.In the presence of the diminished Pipeak at a given power output, Pi does not stabilize at a steady state less than Pipeak but reaches Pipeak, and exercise does not continue potentially ad infinitum but is terminated because of fatigue at timeend.PO, which was less than CP in the absence of the Pipeak decrease, is now greater than (diminished) CP when Pipeak falls.Therefore, generally, the training-induced increase in CP is smaller than it would be if only OXPHOS activity increased, and Pipeak did not decrease.Exercise of a given intensity passes from the heavy-intensity domain to the very heavy-intensity domain.The possible training-induced decrease in Pi peak diminishes the increase in CP caused by the OXPHOS activity increase.This outcome is demonstrated in Figure 6.In the presence of the diminished Pi peak at a given power output, P i does not stabilize at a steady state less than Pi peak but reaches Pi peak , and exercise does not continue potentially ad infinitum but is terminated because of fatigue at time end .PO, which was less than CP in the absence of the Pi peak decrease, is now greater than (diminished) CP when Pi peak falls.Therefore, generally, the training-induced increase in CP is smaller than it would be if only OXPHOS activity increased, and Pi peak did not decrease.Exercise of a given intensity passes from the heavy-intensity domain to the very heavy-intensity domain.The decrease in Pipeak does not affect t0.63, as the primary phase II of VȮ2 on-kinetics does not depend on Pipeak.

Mechanism of the Impact of Training-Induced Increase in OXPHOS Activity and Decrease in Pipeak on VȮ2max, CP and t0.63
The aim of the present article is to explain and explicate in detail the mechanisms through which the training-induced increase in OXPHOS activity and likely decrease in Pipeak determine the increases in VȮ2max and CP and decrease in t0.63.Previous in silico studies [29,33,45] demonstrated that the rise in OXPHOS activity led to rises in VȮ2max and CP and a fall in t0.63, while the decrease in Pipeak diminishes the increases in VȮ2max and CP.However, the detailed mechanism underlying this effect was not explicated.Additionally, previous studies did not address the effect of the OXPHOS activity and peak Pi on exercise duration until exhaustion.
The present article demonstrates that the effect of the training-induced increase in OXPHOS activity on VȮ2max, CP and t0.63 and of the decrease in Pipeak on VȮ2max and CP is mediated through the attenuation (decrease and delay) of the Pi increase after the onset of exercise.This attenuation is caused by the increase in OXPHOS activity and is possibly partly compensated for (diminished) by the Pipeak decrease.
The details of the mechanism of the impact of the elevated OXPHOS activity on VȮ2max, CP and t0.63 are presented in Figures 2-4 and are summarized in Figure 7.The decrease in Pi peak does not affect t 0.63 , as the primary phase II of The aim of the present article is to explain and explicate in detail the mechanisms through which the training-induced increase in OXPHOS activity and likely decrease in Pi peak determine the increases in • VO 2max and CP and decrease in t 0.63 .Previous in silico studies [29,33,45] demonstrated that the rise in OXPHOS activity led to rises in • VO 2max and CP and a fall in t 0.63 , while the decrease in Pi peak diminishes the increases in • VO 2max and CP.However, the detailed mechanism underlying this effect was not explicated.Additionally, previous studies did not address the effect of the OXPHOS activity and peak P i on exercise duration until exhaustion.
The present article demonstrates that the effect of the training-induced increase in

OXPHOS activity on
• VO 2max , CP and t 0.63 and of the decrease in Pi peak on • VO 2max and CP is mediated through the attenuation (decrease and delay) of the P i increase after the onset of exercise.This attenuation is caused by the increase in OXPHOS activity and is possibly partly compensated for (diminished) by the Pi peak decrease.
The details of the mechanism of the impact of the elevated OXPHOS activity on • VO 2max , CP and t 0.63 are presented in Figures 2-4 and are summarized in Figure 7. ) and reaching of Pipeak by Pi are attenuated; VȮ2 can increase more at a given Pi, and thus, VȮ2 at Pipeak, that is VȮ2max, is elevated; 2. At a given work intensity (ATP usage activity, AUT), the new steady state of primary phase II of metabolites (ADP, Pi, PCr, H + ) on-kinetics is reached in a shorter time, OXPHOS is stimulated faster by increases in ADP and Pi, and therefore, the transition time t0.63 of the VȮ2 on-kinetics is shortened; 3. The steady state of Pi concentration (not reached for PO greater than CP, that is, for AUT greater than AUTcrit) can fall, for a given AUT, from greater than to less than Pipeak so that the system passes from the very heavy/severe to heavy, or even moderate exercise intensity domain, and thus, AUTcrit (CP) is elevated.
The training-induced increase in the total OXPHOS activity can occur through an increase in the "default" OXPHOS activity kOX (see Introduction), an increase in the "work-induced" OXPHOS activity (ESA intensity, AOX) [13] or both.The present study focuses on the former, but the general reasoning would be very similar for the latter.
The training-induced rise in OXPHOS activity leads to attenuation (decrease and delay) of changes in the bioenergetic system metabolites (e.g., increases in ADP, Pi, Cr and H + and decrease in PCr) during the rest-to-work transition at a given power output.In particular, this change concerns the increase in Pi: it rises at a slower pace and to a smaller extent at a given VȮ2 (Figure 2).During the rest-to-work transition, OXPHOS with the default (resting) activity (kOX) is very quickly (in a few seconds) stimulated by ESA (workinduced OXPHOS activity, AOX) and then more slowly (tens of seconds to minutes) by increases in ADP and Pi.In the result of the training-induced rise in the total OXPHOS activity (kOX and/or AOX), Pi (and ADP) does not have to increase as much to stimulate OXPHOS (oxidative ATP supply to match the elevated ATP usage), as its activity is already elevated by training.As a result, in trained muscle, Pi increases at a slower pace and reaches Pipeak (during very heavy and severe exercise), and exercise is terminated because of fatigue after a longer time and at a higher VȮ2 than in untrained muscle.Because of the elevated OXPHOS activity, the Pi increase is delayed in relation to the VȮ2 increase, or alternatively, VȮ2 increases more at a given Pi increase until Pi reaches Pipeak.Consequently, the exercise duration until exhaustion timeend is lengthened, and VȮ2max is elevated.The system remains in the very heavy exercise-intensity domain.• VO 2 can increase more at a given P i , and thus, • VO 2 at Pi peak , that is • VO 2max , is elevated; 2. At a given work intensity (ATP usage activity, A UT ), the new steady state of primary phase II of metabolites (ADP, P i , PCr, H + ) on-kinetics is reached in a shorter time, OXPHOS is stimulated faster by increases in ADP and P i , and therefore, the transition time t 0.63 of the • VO 2 on-kinetics is shortened; 3. The steady state of P i concentration (not reached for PO greater than CP, that is, for A UT greater than A UTcrit ) can fall, for a given A UT , from greater than to less than Pi peak so that the system passes from the very heavy/severe to heavy, or even moderate exercise intensity domain, and thus, A UTcrit (CP) is elevated.
The training-induced increase in the total OXPHOS activity can occur through an increase in the "default" OXPHOS activity k OX (see Introduction), an increase in the "workinduced" OXPHOS activity (ESA intensity, A OX ) [13] or both.The present study focuses on the former, but the general reasoning would be very similar for the latter.
The training-induced rise in OXPHOS activity leads to attenuation (decrease and delay) of changes in the bioenergetic system metabolites (e.g., increases in ADP, P i , Cr and H + and decrease in PCr) during the rest-to-work transition at a given power output.In particular, this change concerns the increase in P i : it rises at a slower pace and to a smaller extent at a given • VO 2 (Figure 2).During the rest-to-work transition, OXPHOS with the default (resting) activity (k OX ) is very quickly (in a few seconds) stimulated by ESA (work-induced OXPHOS activity, A OX ) and then more slowly (tens of seconds to minutes) by increases in ADP and P i .In the result of the training-induced rise in the total OXPHOS activity (k OX and/or A OX ), P i (and ADP) does not have to increase as much to stimulate OXPHOS (oxidative ATP supply to match the elevated ATP usage), as its activity is already elevated by training.As a result, in trained muscle, P i increases at a slower pace and reaches Pi peak (during very heavy and severe exercise), and exercise is terminated because of fatigue after a longer time and at a higher • VO 2 increases more at a given P i increase until P i reaches Pi peak .Consequently, the exercise duration until exhaustion time end is lengthened, and • VO 2max is elevated.The system remains in the very heavy exercise-intensity domain.
The training-induced slowed and decreased P i increase during exercise (due to augmented OXPHOS activity) can cause, at a given power output (PO), the steady-state P i value to decrease: P i ultimately stabilizes at a steady-state value less than Pi peak , and exercise continues potentially ad infinitum, instead of rising unceasingly until reaching Pi peak and causing exercise termination.This outcome is demonstrated in Figures 3 and 7.In other words, muscle training causes the PO value, which was greater than CP (critical power) before training, to be smaller than CP after training.Consequently, exercise of a given intensity passes from the very heavy to heavy, or even moderate, domain.
The decreased magnitude of the P i increase during exercise of a given intensity also leads to a shortening of the transition time of primary phase II of the • VO 2 on-kinetics: t 0.63 .Easterby [48] showed in an abstract and general way that the time of the transition between steady states in a metabolic system is proportional to the changes in metabolite concentrations during this transition.It was demonstrated in the concrete case of the skeletal muscle bioenergetic system that t 0.63 of the • VO 2 on-kinetics depends near-linearly on the changes in, first of all, PCr, Cr and P i (anyway, related to each other) during the rest-to-work transition at the same PO [49] (ADP and its changes are in the micromolar range and therefore contribute little to the general effect, while ATP is essentially constant in the absence of AMP deamination).At a given metabolic flux, the smaller that the changes in metabolites are, the faster that the new steady-state is reached, and consequently the shorter that the transition time is.The effect of the smaller P i increase on t 0.63 is demonstrated in Figure 4 (and summarized in Figure 7) regarding the example of moderate exercise, where the additional ATP usage and slow component of the At some lower PO values, the decrease in Pi peak can lead to a transition from the heavy to very heavy exercise-intensity domain.The P i concentration, which did not reach (unchanged) Pi peak in the absence of the Pi peak decrease, can be greater than (lowered) Pi peak in the presence of the Pi peak decrease.Therefore, while in the former case, exercise could be continued potentially ad infinitum, in the latter case, it is terminated after some time because of fatigue.This outcome is demonstrated in Figure 6 and is equivalent to a CP decrease.Therefore, a given PO can be less than CP in the absence of the Pi peak fall and greater than CP in the presence of this fall.
As mentioned above, as Pi peak does not affect the reaching of a steady state of P i and • VO 2 in primary phase II of the • VO 2 and P i on-kinetics, changes in Pi peak have no effect on t 0.63 .
Summing up, the training-induced increase in the "default" OXPHOS activity and possibly "work-induced" OXPHOS activity (ESA intensity) acts through a decrease and delay in metabolite (ADP, P i , PCr, H + , AMP, IMP, NH 3 ) changes, especially the P i increase during the rest-to-work transition (improvement in metabolite homeostasis, at least at a given time and • VO 2 ).This outcome in turn leads to an increase in • VO 2max , increase in CP and shortening of t 0.63 (Figure 7).The effect on • VO 2max and CP can be diminished by a training-induced decrease in Pi peak , which is associated with improved end-exercise metabolite homeostasis.

General Discussion
The present article addresses the training-induced changes in • VO 2max , CP (A UTcrit ) and t 0.63 at the muscle level.However, the kinetic properties of the system at the whole-body, including the pulmonary, level can to a certain degree differ from their counterparts at the muscle level.First, the pulmonary and muscle • VO 2 kinetics can somewhat dissociate, for instance, during very intense exercise or off-transient.This outcome can be caused by some delays in oxygen transport by the circulatory system from working muscles to the lungs, buffering of the O 2 level by oxygen stores in tissues, blood and lungs or contributions of oxygen consumption by auxiliary tissues (heart, respiratory muscle, posture-maintaining muscles) to the pulmonary oxygen consumption [45].Second, it is possible that the moderate/heavy exercise border at the whole-body level (lactate threshold, LT, ventilatory threshold, VT) appears earlier (in time and at a lower PO) than at the working muscle level (A UTadd , ATP usage activity at which the additional ATP usage, underlying the • VO 2 and metabolites' slow component, is initiated) Previous in silico studies [29,33] demonstrated that the training-induced increase in OXPHOS activity and/or ESA intensity not only elevates the critical ATP usage activity (A UTcrit , analogous to CP) but shifts the whole power-duration dependence upward (toward higher values of A UTcrit /PO).At the same time, depending on detailed parameter values (particularly changes in k OX and Pi peak ), the curvature constant W' of the power-duration relationship (equivalent to the slope of the linear A UT -1/time relationship) remains essentially unaffected by training or somewhat decreases.Both cases were encountered in experimental studies [3][4][5].Of course, this effect can be explained in terms of the impact on the P i increase kinetics during the rest-to-work transition, which affects both CP and duration of exercise, as demonstrated above.
Only the effect of Pi peak on the training-induced changes in the kinetic properties of the skeletal muscle bioenergetic system elicited through OXPHOS activity enhancement and attenuation of the P i increase during exercise was analyzed in the present study.However, it cannot be excluded that other parameters, for example, Pi crit (critical P i , above which the additional ATP usage, underlying the  [29,46].It also reduces the slow component of  [29,46].Of course, it enlarges the slow component intensity.The mechanism of the potential action of Pi crit and k add will be discussed and explained in detail when evidence for/reasons to believe in training-induced changes in these parameters appear.The • VO 2 on-kinetics (t 0.63 and/or O 2 deficit) was proposed recently [50] to determine CP.However, • VO 2 and its kinetics are emergent properties of the system and can only be correlated with, but they do not bring about (determine) anything within the system.On the contrary, t 0.63 and CP result from system parameters, such as OXPHOS activity and Pi peak , acting through the P i on-kinetics, as demonstrated in the present in silico study.The inverse correlation between t 0.63 and CP encountered in experimental studies results from, e.g., OXPHOS activity changing t 0.63 and CP (A UTcrit ) in the opposite directions [46].Additionally, it was postulated [50] that t 0.63 determines metabolite changes during the rest-to-work transition.However, in reality, the relation is just the opposite: this is changes in the metabolites (especially PCr, Cr and P i ) that determine t 0.63 at a given work intensity (see above [45,49]).
Of course, the possibility of a training-induced Pi peak decrease can be tested experimentally, for example, by measuring the end-exercise P i concentration in very heavy exercise before and after training.

Study Limitations
Every computer model of a complex biochemical/cellular/physiological system constitutes at best only a simplification and approximation of the reality.Of course, this fact also concerns the dynamic model of the skeletal muscle bioenergetic system used in the present study.
The model describes only one compartment corresponding to working muscles and does not distinguish particular working (power-generating) muscles (including the gluteus, quadriceps, biceps femoris, gastrocnemius and soleus, the kinetic/metabolic properties of which can differ to a certain extent) and different muscle fiber types within muscles (type I, IIa and IIx fibers and their various sub-types), and it involves parameters and variables (rate constants, activities, fluxes, metabolite concentrations) that are averaged over the entire working muscles group and particular muscles.Nevertheless, the model is compared with experimental data concerning muscle (or pulmonary) • VO 2 and muscle PCr, P i , ADP, ATP and H + concentrations averaged over the entire muscle.Even then, the model can generate, at least semi-quantitatively, a surprisingly broad set of dynamic properties of the modeled system.
Only the total P i concentration as the main fatigue factor is considered explicitly by the "P i double-threshold" mechanism.It was postulated as a major fatigue-related factor in peripheral fatigue [51].Nevertheless, other metabolites, such as H + , ADP, NH 4 + , IMP and AMP, can also contribute to peripheral muscle fatigue [51].On the other hand, the levels of these metabolites (at least H + and ADP) change together with P i during exercise [28,29].Therefore, P i can be regarded as a "representative" of various metabolites causing muscle fatigue.Some authors [28,52] have proposed that rather than H 2 PO 4 − , a deprotonated form of P i , and not P i itself, is the most important fatigue-related factor.H 2 PO 4 − seems to be an attractive candidate, as its relative increase during the rest-to-work transition is greater than that of P i [45], and it represents the increase in both P i and H + (pH decrease increases the fraction of P i in the form of H 2 PO 4 − ), regarded as the two most important fatigue factors [51].A substitution within the computer model of P i by H 2 PO 4 − as the fatigue factor provided similar general results.Moreover, altered Ca 2+ sensitivity was postulated to contribute to peripheral fatigue generation [51,53].However, P i can cause Ca 2+ precipitation in sarcoplasmic reticulum [53].Additionally, one can speculate that P i (and other related metabolites) can be potentially involved in central fatigue, as the central nervous system can detect the metabolic state of working muscle cells, for instance, through type III/IV afferents [30].Moreover, one could speculate that, for example, mental fatigue, sleepiness or illness can co-determine the Pi peak and/or Pi crit fixed by the brain.Therefore, P i as the main, or at least representative, fatigue-related factor seems to be quite a satisfactory approximation, as it leads to astonishingly good agreement of computer simulations with various experimental data and can account for different, seemingly unrelated, features of the system.

Conclusions
The training-induced increase in • VO 2max , increase in critical power (CP) and acceleration of • VO 2 on-kinetics (decrease in t 0.63 ) in the skeletal muscle bioenergetic system caused by a rise in OXPHOS activity are mediated by attenuation (delay and decrease) of the rise in P i (inorganic phosphate) after the onset exercise.This outcome delays the reaching of Pi peak (peak P i ) by P i and termination of exercise because of fatigue, and it lowers P i at a given • VO 2 , causing a higher • VO 2 to be reached at the end of exercise, when P i reaches Pi peak .This outcome is equivalent to the increase in the duration of exercise of a given power output and elevation of • VO 2max .Additionally, the decrease/delay in trained muscle of the P i increase during exercise of a given power output (PO) can lead to stabilization of P i at a steady state less than Pi peak and continuation of exercise potentially ad infinitum, while in untrained muscle, P i reaches Pi peak after a certain time, and exercise terminates because of fatigue.Therefore, PO that was greater than critical power (CP) before training is less than CP after training.In other words, the system transitions from the very heavy exercise domain to the heavy exercise domain.Finally, the decreased rise in P i (and changes in other metabolites) in moderate exercise of a given power output (or in primary phase II of the P i on-kinetics in exercises of higher intensity) leads to faster reaching by P i and ADP (both stimulate OXPHOS during rest-to-work transition) of the working steady state, faster reaching by • VO 2max and CP (but not t 0.63 ).At a lowered Pi peak , P i reaches Pi peak faster, • VO 2 has less time to increase, and thus, the exercise duration is shortened, and • VO 2max falls.The steady-state P i value for a given PO at an unchanged Pi peak can become greater than Pi peak at a diminished Pi peak ; as a consequence, P i would reach Pi peak instead of stabilizing at a steady state less than Pi peak , exercise would be terminated because of fatigue instead of continuing potentially ad infinitum, CP would become less than PO, and the system would pass from the heavy exercise-intensity domain to very heavy exercise-intensity domain.

•
VO 2max and lengthens the duration of exercise in very heavy exercise.This outcome is demonstrated if Figure 2. It occurs through attenuation (delay and decrease in relation of • VO 2 ) of the P i rise during exercise.As a result, in trained muscle, P i reaches Pi peak , and exercise is terminated because of fatigue after a longer time and at a higher • VO 2 ( • VO 2max ) than in untrained muscle.Thus, at a given work intensity (regular ATP usage activity),

Figure 2 . 18 Figure 2 .
Figure 2. Simulated effect of training-induced increase in OXPHOS activity on

Figure 3 .
Figure 3. Simulated effect of training-induced increase in OXPHOS activity on CP (AUTcrit).Time courses of muscle VȮ2 and Pi in untrained and trained muscle are shown.VȮ2max and end-exercise time before training are indicated.After training, Pi reaches a steady state less than Pipeak, VȮ2 reaches a steady state less than VȮ2max, and exercise is not terminated because of fatigue: the system passes from the very heavy to heavy exercise intensity domain (AUT = 82 is greater than AUTcrit before training and less than AUTcrit after training).The additional ATP usage, underlying the slow component of the VȮ2 and Pi slow component, is initiated when Pi exceeds Picrit, and exercise is terminated because of fatigue when Pi reaches Pipeak.The elevated OXPHOS activity as the result of training shortens the transition time of primary phase II of the VȮ2 on-kinetics t0.63, which is best seen in the moderate exerciseintensity domain, where the VȮ2 slow component and the additional ATP usage

Figure 3 .
Figure 3. Simulated effect of training-induced increase in OXPHOS activity on CP (A UTcrit ).Time courses of muscle

Figure 4 .
Figure 4. Simulated effect of training-induced increase in OXPHOS activity on t0.63.Time courses of muscle VȮ2 and Pi in untrained and trained muscle are shown.t0.63 before and after training is shown.The system remains in the moderate exercise intensity domain (AUT = 50 is less than AUTadd, AUT at which Pi exceeds Picrit ,and the additional ATP usage, underlying the slow component of the VȮ2 and Pi slow component, is launched, both before and after training).

Figure 4 . 18 Figure 5 .
Figure 4. Simulated effect of training-induced increase in OXPHOS activity on t 0.63 .Time courses of muscle

Figure 5 .
Figure 5. Simulated effect of training-induced decrease in Pi peak (Pi peak decr.) on

Figure 6 .
Figure 6.Simulated effect of training-induced decrease in Pipeak (Pipeak decr.) on CP (AUTcrit).OXPHOS activity is increased as the result of training, as in Figure 3.Time courses of muscle VȮ2 and Pi in trained muscle without and with Pipeak decreases are shown.The lines representing VȮ2 and Pi overlap at the moment when exercise is terminated at lowered Pipeak.The Pipeak decrease lowers AUTcrit, causing AUT = 82 to be greater than AUTcrit, Pi reaches (decreased) Pipeak, VȮ2 reaches (decreased) VȮ2max and the system passes from the heavy to very heavy exercise-intensity domain.Exercise is terminated because of fatigue when Pi reaches (lowered) Pipeak.

Figure 6 .•
Figure 6.Simulated effect of training-induced decrease in Pi peak (Pi peak decr.) on CP (A UTcrit ).OXPHOS activity is increased as the result of training, as in Figure 3.Time courses of muscle

• VO 2
on-kinetics does not depend on Pi peak .4. Discussion 4.1.Mechanism of the Impact of Training-Induced Increase in OXPHOS Activity and Decrease in Pi peak on • VO 2max , CP and t 0.63

Figure 7 .
Figure 7. Mechanism of the training-induced increases in VȮ2max, CP and t0.63.Muscle training causes an increase in total (default and/or work-induced) OXPHOS activity, leading to smaller changes in metabolites (ADP, Pi, PCr, H + ) at a given time after the onset of exercise (delay/attenuation of metabolite changes).As a result: 1.The increase in Pi with time (especially in relation to the increase in VȮ2) and reaching of Pipeak by Pi are attenuated; VȮ2 can increase more at a given Pi, and thus, VȮ2 at Pipeak, that is VȮ2max, is elevated; 2. At a given work intensity (ATP usage activity, AUT), the new steady state of primary phase II of metabolites (ADP, Pi, PCr, H + ) on-kinetics is reached in a shorter time, OXPHOS is stimulated faster by increases in ADP and Pi, and therefore, the transition time t0.63 of the VȮ2 on-kinetics is shortened; 3. The steady state of Pi concentration (not reached for PO greater than CP, that is, for AUT greater than AUTcrit) can fall, for a given AUT, from greater than to less than Pipeak so that the system passes from the very heavy/severe to heavy, or even moderate exercise intensity domain, and thus, AUTcrit (CP) is elevated.

Figure 7 .
Figure 7. Mechanism of the training-induced increases in

• VO 2
than in untrained muscle.Because of the elevated OXPHOS activity, the P i increase is delayed in relation to the • VO 2 increase, or alternatively,

•
VO 2 on-kinetics are absent, facilitating a clear presentation.The possible training-induced decrease in Pi peak counterbalances to a certain extent the effect of elevated OXPHOS activity.In the presence of a lowered Pi peak , P i reaches Pi peak in a shorter time and at a lower • VO 2 , than at unaltered Pi peak , leading to the shortening of exercise duration and a fall in • VO 2max .This outcome is demonstrated in Figure5.This effect takes place within the very heavy exercise-intensity domain.

• VO 2
of the active steady state and thus shortening of the • VO 2 on-kinetics transition time: t 0.63 .A possible training-induced decrease in Pi peak diminishes the effect of the elevated OXPHOS activity on

•
VO 2max and CP) and faster reaching of a new steady state (the effect of elevated OXPHOS activity on t 0.63 ) through an accelerated reaching of Pi peak by P i (the effect of lowered Pi peak on • VO 2max and CP).It is clearly demonstrated and explicated exactly how this mechanism works.

•
VO 2 and metabolites' slow component, is initiated) or k add (the activity or "rate constant" of the additional ATP usage), are affected by muscle training.It was demonstrated that an increase in Pi crit elevates