Backward Cycle Research Articles

Waiting Cycle Times and Generalized Haldane Equality in the Steady-State Cycle Kinetics of Single Enzymes

Enzyme kinetics are cyclic. A more realistic reversible three-step mechanism of the Michaelis-Menten kinetics is investigated in detail, and three kinds of waiting cycle times T, T+, T- are defined. It is shown that the mean waiting cycle times T, T+, and T- are the reciprocal of the steady-state cycle flux Jss, the forward steady-state cycle flux Jss+ and the backward steady-state cycle flux Jss, respectively. We also show that the distribution of T+ conditioned on T+<T- is identical to the distribution of T- conditioned on T-< T+, which is referred to as the generalized Haldane equality. Consequently, the mean waiting cycle time of T+ conditioned on T+<T- (T+|T+<T-) and the one of T- conditioned on T-<T+ (T-|T-<T+) are both just the same as T. In addition, the forward and backward stepping probabilities p+ and p- are also defined and discussed, especially their relationship with the cycle fluxes and waiting cycle times. Furthermore, we extend the same results to the n-step cycle, and finally, experimental and theoretically based evidence are also included.

Generalized Haldane equation and fluctuation theorem in the steady-state cycle kinetics of single enzymes

Enzyme kinetics are cyclic. We study a Markov renewal process model of single-enzyme turnover in nonequilibrium steady state (NESS) with sustained concentrations for substrates and products. We show that the forward and backward cycle times have identical nonexponential distributions: Theta + (t)=Theta_(t). This equation generalizes the Haldane relation in reversible enzyme kinetics. In terms of the probabilities for the forward (p+) and backward (p-) cycles, kBT ln(p+/p-) is shown to be the chemical driving force of the NESS, Delta mu. More interestingly, the moment generating function of the stochastic number of substrate cycle v(t), <e-lambda v(t)> , follows the fluctuation theorem in the form of Kurchan-Lebowitz-Spohn-type symmetry. When lambda=delta mu/kBT, we obtain the Jarzynski-Hatano-Sasa-type equality <e-v(t)Delta mu/kBT> identical with 1 for all t, where v Delta mu is the fluctuating chemical work done for sustaining the NESS. This theory suggests possible methods to experimentally determine the nonequilibrium driving force in situ from turnover data via single-molecule enzymology.

Optimal Multiple Trait Selection for Multiple Linked Quantitative Trait Loci

Abstract A method was developed to optimize selection on multiple traits with multiple quantitative trait loci (QTLs) over multiple generations. The basis of the method was to replace in the objective function the genotypic value of a single trait with an aggregate genotypic value of multiple traits weighted by their corresponding economic weight, and to maximize the weighted sum of the selection response in the planning horizon. The optimization was formulated as a multiple stage optimal control problem and solved by a forward and backward iteration cycle. The practical utility of this method was illustrated in an example of pig breeding population, in which the number born alive (NBA) and days to 100 kg (D100) were used as parameters. The selection response of this method was compared with standard QTL selection and regular best linear unbiased prediction (BLUP) selection. Results showed that optimal selection achieved greater selection response than either standard QTL or regular BLUP selections. The influence of economic weight to optimal selection was significant, and the optimization was better as the economic weight of D100 increased. Optimal selection increased the total selection response by two ways: 1) it sacrificed some QTL responses during early generations and 2) it put more emphasis on D100. Optimal cumulative discounted selection gave more weight to D100 than optimal terminal selection in the longer generations.

On the Potential Role of the Corticospinal Tract in the Control and Progressive Adaptation of the Soleus H-Reflex During Backward Walking

When untrained subjects walk backward on a treadmill, an unexpectedly large amplitude soleus H-reflex occurs in the midswing phase of backward walking. We hypothesized that activity in the corticospinal tract (CST) during midswing depolarizes the soleus alpha-motoneurons subliminally and thus brings them closer to threshold. To test this hypothesis, transcranial magnetic stimulation (TMS) was applied to the leg area of the motor cortex (MCx) during backward walking. Motor-evoked potentials (MEPs) were recorded from the soleus and tibialis anterior (TA) muscles in untrained subjects at different phases of the backward walking cycle. We reasoned that if soleus MEPs could be elicited in midswing, while the soleus is inactive, this would be strong evidence for increased postsynaptic excitability of the alpha-motoneurons. In the event, we found that in untrained subjects, despite the presence of an unexpectedly large H-reflex in midswing, no soleus MEPs were observed at that time. The soleus MEPs were in phase with the soleus electromyographic (EMG) activity during backward walking. Soleus MEPs increased more rapidly as a function of the EMG activity during voluntary activity than during backward walking. Furthermore, a conditioning stimulus to the motor cortex facilitated the soleus H-reflex at rest and during voluntary plantarflexion but not in the midswing phase of backward walking. With daily training at walking backward, the time at which the H-reflex began to increase was progressively delayed until it coincided with the onset of soleus EMG activity, and its amplitude was considerably reduced compared with its value on the first experimental day. By contrast, no changes were observed in the timing or amplitude of soleus MEPs with training. Taken together, these observations make it unlikely that the motor cortex via the CST is involved in control of the H-reflex during the backward step cycle of untrained subjects nor in its progressive adaptation with training. Our observations raise the possibility that the large amplitude of H-reflex in untrained subjects and its adaptation with training are mainly due to control of presynaptic inhibition of Ia-afferents by other descending tracts.

Reactions of dimethylsulfoxide reductase in the presence of dimethyl sulfide and the structure of the dimethyl sulfide-modified enzyme.

The bis-molybdopterin enzyme dimethylsulfoxide reductase (DMSOR) from Rhodobacter capsulatus catalyzes the conversion of dimethyl sulfoxide (DMSO) to dimethyl sulfide (DMS), reversibly, in the presence of suitable e(-)-donors or e(-)-acceptors. The catalytically significant intermediate formed by reaction of DMSOR with DMS ('the DMS species') and a damaged enzyme form derived by reaction of the latter with O(2) (DMS-modified enzyme, DMSOR(mod)D) have been investigated. Evidence is presented that Mo in the DMS species is not, as widely assumed, Mo(IV). Formation of the DMS species is reversed on removing DMS or by addition of an excess of DMSO. Equilibrium constants for the competing reactions of DMS and DMSO with the oxidized enzyme (K(d) = 0.07 +/- 0.01 and 21 +/- 5 mM, respectively) that control these processes indicate formation of the DMS species occurs at a redox potential that is 80 mV higher than that required, according to the literature, for reduction of Mo(VI) to Mo(IV) in the free enzyme. Specificity studies show that with dimethyl selenide, DMSOR yields a species analogous to the DMS species but with the 550 nm peak blue-shifted by 27 nm. It is concluded from published redox potential data that this band is due to metal-to-ligand charge transfer from Mo(V) to the chalcogenide. Since the DMS species gives no EPR signal in the normal or parallel mode, a free radical is presumed to be in close proximity to the metal, most likely on the S. The species is thus formulated as Mo(V)-O-S(*)Me(2). Existing X-ray crystallographic and Raman data are consistent with this structure. Furthermore, 1e(-) oxidation of the DMS species with phenazine ethosulfate yields a Mo(V) form without an -OH ligand, since its EPR signal shows no proton splittings. This form presumably arises via dissociation of DMSO. The structure of DMSOR(mod)D has been determined by X-ray crystallography. All four thiolate ligands and Ogamma of serine-147 remain coordinated to Mo, but there are no terminal oxygen ligands and Mo is Mo(VI). Thus, it is a dead-end species, neither oxo group acceptance nor e(-)-donation being possible. O(2)-dependent formation of DMSOR(mod)D represents noncatalytic breakdown of the DMS species by a pathway alternative to that in turnover, with oxidation to Mo(VI) presumably preceding product release. Steps in the forward and backward catalytic cycles are discussed in relation to earlier stopped-flow data. The finding that in the back-assay the Mo(IV) state may at least in part be by-passed via two successive 1e(-) reactions of the DMS species with the e(-)-acceptor, may have implications in relation to the existence of separate molybdopterin enzymes catalyzing DMSO reduction and DMS oxidation, respectively.

Extraction of yeast alcohol dehydrogenase using reversed micelles formed with CTAB

A large molecular weight protein, alcohol dehydrogenase (ADH, 141 kDa), has been purified from baker's yeast using reversed micelles formed with a cationic surfactant (cetyltrimethylammonium bromide, CTAB) using the phase transfer method. Various parameters, such as pH, ionic strength and contact time of the two phases in ADH forward and backward transfer were studied. The active ADH was successfully recovered after a full forward and backward extraction cycle. The recovery of ADH activity obtained was ∼90% and the purification factor was 3.1 for the overall process. © 2000 Society of Chemical Industry

Electromyographic timing analysis of forward and backward cycling

Backward walking to running progressions are becoming a popular, nontraditional component of functional knee rehabilitation programs. The purpose of this electromyographic (EMG) and motion analysis study was to compare the activation duration of the vastus medialis, vastus lateralis, rectus femoris, medial hamstrings, lateral hamstring, tibialis anterior, and gastrocnemius muscles during forward and backward cycling. We hypothesized that the hamstrings would demonstrate greater activation duration during backward cycling. The right lower extremity of 12 healthy subjects (6 male and 6 female) was instrumented with surface EMG electrodes and retroreflective markers to confirm lower extremity kinematic consistency between conditions. Statistical analysis of hip, knee, and ankle kinematics (200 Hz sampling rate) and gender failed to reveal significant differences between conditions (P > 0.05). Quadrant analysis of muscle activation duration with Bonferroni corrections for multiple comparisons revealed that medial and lateral hamstring activation duration was greater during the early recovery phase (quadrant III) of backward cycling than forward cycling (P < 0.00156). Rectus femoris activation duration was greater in the early propulsive phase of backward cycling (quadrant 1) (P < 0.00156) and in the early recovery phase of forward cycling (quadrant III) (P < 0.00156). These findings lend support for the use of backward cycling during the early recovery phase (quadrant III) to achieve a selective hamstring muscle response of relatively decreased patellofemoral stress and anterior cruciate ligament strain.

Separation of alpha-amylase by reversed micellar extraction. Effect of solvent type and cosolvent concentration on the transfer process.

The recovery of alpha-amylase from the crude enzyme preparation by the reversed micellar liquid-liquid extraction was investigated. The reversed micellar solution was formed by dissolving a cationic surfactant Aliquat 336 in six different alkanes (cyclohexane, n-hexane, isooctane, n-octane, n-decane, and n-dodecane) respectively with addition of a cosolvent n-octanol. It was found that a minimal quantity of n-octanol was needed for Aliquat 336 to dissolve in apolar solvent and form reversed micelles. Furthermore, this minimal amount of n-octanol needed was found to be different when Aliquat 336 was dissolved in different alkanes. It tended to increase with the number of carbon atoms in alkane and also depended on the solvent structure. During the forward extraction process, it was revealed that a high value of solubilization of protein in Aliquat 336 reversed micelles could be achieved when four out of the six alkanes (cyclohexane, n-hexane, isooctane, n-octane) were used as the solvent for Aliquat 336. After a full forward and backward extraction cycle, however, a high recovery of both the protein mass and alpha-amylase activity in the stripping solution could be obtained only when two out of the six alkanes (n-hexane and isooctane) were used as the solvent for Aliquat 336. When n-hexane and isooctane were used as the solvent for Aliquat 336, up to 80% of the total alpha-amylase activity in the crude enzyme preparation could be recovered at the end of extraction cycle, meanwhile alpha-amylase could be concentrated about 1.4-fold. In the cases of other four alkanes (cyclohexane, n-octane, n-decane, and n-dodecane) as solvent, most of the alpha-amylase activity in the crude enzyme preparation would be denatured after an extraction cycle.

Effect of the cosolvent type on the extraction of α-amylase with reversed micelles: Circular dichroism study

Both the activity and conformational properties of α-amylase during the reversed micellar liquid-liquid extraction were investigated by the measurement of enzyme activity and circular dichroism (CD) probe analysis, respectively. The measurement of α-amylase activity indicated that only n-butanol, among the six n-alcohols ( n-butanol, n-pentanol, n-hexanol, n-heptanol, n-octanol, and n-decanol), was the most suitable cosolvent for Aliquat 336 reversed micelles to extract and recover α-amylase in a full reversed micellar extraction cycle. In this case, as high as 80% of the total activity of α-amylase in the initial aqueous phase could be recovered after the forward and backward extraction cycle. For the other five n-alcohols, however, the recovery of enzyme activity was relatively low. Meanwhile, the CD spectra analysis during the same extraction processes revealed some similar behaviors on the conformational change of α-amylase. In the case of n-butanol as the cosolvent, it was found that the conformation of α-amylase in the stripping solution could be restored almost completely to its native state after an extraction cycle; this implied that most of the enzyme activity would be recovered under this condition. For the other five cosolvents, it was found that the conformation of α-amylase could be restored partly to its native state after the full extraction cycle which demonstrated the fact obtained from the activity measurement experiments that only small parts of the total activity of α-amylase in the initial aqueous solution could be recovered at the end of an extraction cycle. Both the measurement of enzyme activity and CD spectra analysis proved that n-butanol was the most suitable cosolvent for Aliquat 336 reversed micelles to extract α-amylase. This observation may be helpful in developing a more effective method to monitor the process of protein reversed micellar extraction.

Liquid-liquid reversed micellar extraction for isolating enzymes: Studies on the purification of α-amylase

The purification of α-amylase from a crude enzyme preparation was carried out be liquid-liquid reversed micellar extraction. After a full forward and backward extraction cycle, the α-amylase was purified about 1·5-fold with 85% recovery. Most of the contaminating neutral protease in the crude enzyme preparation could be removed at the end of an extraction cycle. The separation factor of α-amylase to neutral protease reached about 10.

Selective recovery of two enzymes fromBacillus subtilis using aliquat 336 reversed micelles

Selective separation and purification of two enzymes from Bacillus subtilis (alpha-amylase and neutral protease) by liquid-liquid extraction using Aliquat 336/isooctane reversed micelles were investigated. After a full forward and backward extraction cycle, alpha-amylase was separated and purified in the stripping solution, and neutral protease was recovered in the raffinate.

Purification of industrial αamylase by reversed micellar extraction

The purification of industrial alpha-amylase by liquid-liquid extraction with Aliquat 336 reversed micellar solution as the extractant was studied. Seven kinds of Aliquat 336 reversed micellar solution, formed by using seven kinds of straight chain alkyl alcohols as cosolvent, have been utilized to extract industrial a-amylase. It was found that these seven kinds of reversed micellar solution can all achieve a high protein transfer efficiency in the forward extraction process. After a full forward and backward extraction cycle, however, only the reversed micelles with n-butanol as the cosolvent was found to be able to maintain the activity of alpha-amylase in the stripping solution. By using the reversed micelles of Aliquat 336/isooctane/1% (v/v) n-butanol to perform a full extraction cycle, it was found that 85% of the total activity of alpha-amylase in the industrial a-amylase could be recovered at the end of an extraction cycle and the specific activity of alpha-amylase could be concentrated about 1.5-fold; meanwhile, most of the neutral protease in the industrial a-amylase could be removed. The separation factor of alpha-amylase to neutral protease at the end of an extraction cycle can reach about 10. (c) 1995 John Wiley & Sons, Inc.