Relative entropy: free energy associated with equilibrium fluctuations and nonequilibrium deviations

Using a one-dimensional macromolecule in aqueous solution as an illustration, we demonstrate that the relative entropy from information theory, Sigma(k)p(k) ln(p(k)/p(*)(k)), has a natural role in the energetics of equilibrium and nonequilibrium conformational fluctuations of the single molecule. It is identified as the free energy difference associated with a fluctuating density in equilibrium, and is associated with the distribution deviate from the equilibrium in nonequilibrium relaxation. This result can be generalized to any other isothermal macromolecular system using the mathematical theories of large deviations and Markov processes, and at the same time provides the well-known mathematical results with interesting physical interpretations.

Protein and DNA oxidation in spinal injury: neurofilaments--an oxidation target

This study measured the time courses of protein and DNA oxidation following spinal cord injury (SCI) in rats and characterized oxidative degradation of proteins. Protein carbonyl content-a marker of protein oxidation-significantly increased at 3-9 h postinjury and the ratio 8-hydroxy-2-deoxyguanosine/deoxyguanosine-an indicator of DNA oxidation-was significantly higher at 3-6 h postinjury in the injured cords than in the sham controls. This suggests that oxidative modification of proteins and DNA contributes to secondary damage in SCI. Densities of selected bands on coomassie-stained gels indicated that most proteins were degraded. Neurofilament protein (NFP) was particularly evaluated immunohistochemically; its light chain (NFP-68) was gradually degraded in nerve fibers, neuron bodies, and large dendrites following SCI. A mixture of Mn (III) tetrakis (4-benzoic acid) porphyrin (10 mg/kg)-a novel SOD mimetic-and nitro-L-arginine (1 mg/kg)-an inhibitor of nitric oxide synthase-injected intraperitoneally, increased NFP-68 immunoreactivity and the numbers of NFP-positive nerve fibers post-SCI, correlating NFP degradation in SCI to free radical-triggered oxidative damage for the first time. Therefore, blockage of protein and DNA oxidation in the secondary injury stage may improve long-term recovery-important information for development of the SCI therapies.

Responses of small- and large-field bipolar cells to GABA and glycine

Morphologically distinct subtypes of retinal bipolar cells transmit information along parallel pathways to convey different aspects of the visual scene, but the synaptic mechanisms that regulate signal transmission are largely unknown. The all-rod retina of skate provides a comparatively simple system in which to correlate bipolar cell morphology with responses to the inhibitory neurotransmitters GABA and glycine. Two subtypes of bipolar cells can be identified when isolated in culture: large-field bipolar cells with extensive dendritic arbors, and small-field bipolar cells with one or two dendritic branches. Under voltage-clamp, glycine elicited significant current responses from small-field cells, but not from large-field bipolar cells. Although all bipolar cells displayed GABA-activated chloride currents mediated by both GABA(A) and GABA(C) receptors, the small-field bipolar cells showed a significantly greater contribution from GABA(A) receptors. The results of the present study reveal for the first time that the relative expression of the two classes of GABA receptor on each bipolar cell type correlates with cell morphology and the presence of the glycine receptor.

[Studies on the manufacture and immunogenicity of purified rabies vaccines on humans Vero cell]

OBJECTIVE

Using Vero cell as basic cultural material to improve the quality of rabies vaccines and to produce rabies vaccines for humans.

METHODS

CTN-1V10 strain were used for production. Vero cell of 150th generation were used for cultivation. Rotating cultivatal method with rotating bottle was used. Fluids with virus were collected at different time. Puritied rabies vaccine was produced on Vero cell after clarification, condensation, purification and extermination. A batch of vaccines made by this techniques were used for immunological observation. Sixty-three people were injected with this rabies vaccine according to the procedure of time of exposure. Thirty of them were injected with vaccines made in France (Verorab) while the others were injected with vaccines to be tested. Side effect and neutralizing antibody were recorded.

RESULTS

The quality of this newly developed rabies vaccines has met the quality set by WHO. After all dosages of injection, the rates of positive antibody were both 100% in two groups. The neutralizing antibody among testing group was 11.94 IU/ml comparing with control as 11.69 IU/ml.

CONCLUSION

Purified rabies vaccines on Vero cell for humans had reasonable manufacture technique and less little effect with good technological imnunogenicity.

p27-p16 Chimera: a superior antiproliferative for the prevention of neointimal hyperplasia

Cyclin-dependent kinase inhibitors (CDKi's) may be useful to treat hyperproliferative vascular disorders, such as restenosis induced following angioplasty or vein engraftment. We have shown that a novel fusion protein of the CDKi's p27 and p16, named W9, significantly reduces proliferation of human coronary smooth muscle cells in vitro, by blocking cell proliferation without inducing apoptosis. We have now evaluated the efficacy of adenovirus-mediated gene transfer of W9 (AV-W9) in a balloon-injury model, in the carotid arteries of cholesterol-fed rabbits. We observed that intravascular delivery of 2 x 10(11) viral particles of AV-W9 3 days following balloon injury inhibited intimal hyperplasia by 60% compared to a control virus (P > 0.001). PCNA expression in the AV-W9-treated vessels, a marker of injury-induced cell proliferation, was also reduced compared to the control virus-treated vessels. Direct comparison of the efficacy of AV-W9 and AV-p16 and AV-p27 in this model indicated that delivery of either of the parental genes was significantly less effective in inhibiting intimal thickening compared to the AV-W9 treatment. We conclude that combining the activities of multiple cell cycle regulatory proteins greatly increases the potency of cytostatic gene therapy in the treatment of balloon injury-induced intimal hyperplasia and represents a promising potential approach to preventing postangioplasty restenosis.

Dietary boron supplementation enhanced the action of estrogen, but not that of parathyroid hormone, to improve trabecular bone quality in ovariectomized rats

This study investigated whether boron would enhance the ability of 17beta-estradiol (E2) or parathyroid hormone (PTH) to improve bone quality in ovariectomized OVX rats. Adult OVX rats were treated for 5 wk with vehicle, boron (5 ppm as boric acid), E2 (30 microg/kg/d, sc), PTH (60 microg/kg/d, sc), or a combination of boron and E2 or PTH, respectively. The E2 treatment corrected many adverse effects of OVX on bone quality, increased bone Ca, P, and Mg contents, and decreased trabecular plate separation. Dietary boron supplementation had no effects on these bone parameters in OVX rats. When OVX rats were treated with boron and E2 together, trabecular bone volume (Tb.BS/TV) and plate density were increased significantly more than that caused by E2 alone. The boron and E2 combination also increased trabecular bone surface (Tb.BV/TV) and decreased trabecular plate separation in OVX rats. In contrast, whereas daily PTH injection also increased bone Ca, Mg, and P contents, Tb.BV/TV, Tb.BS/TV, trabecular plate density and thickness, and decreased trabecular plate separation in OVX rats, the combination of boron and PTH had no additional improvement in bone quality over that achieved by PTH alone. In summary, this study shows for the first time that boron enhanced the action of E2, but not that of PTH, to improve trabecular bone quality in OVX rats.

[The effect of whole pleural cavity irradiation with combined 60Co and electron beam plus local biological agents on malignant pleural effusion]

BACKGROUND

To study the effect and complications of combined 60Co γ ray and electron beam irradiation to malignant pleural effusion.

METHODS

From January,1996 to December,1998,55 patients with malignant pleural effusion (unilateral; 49 cases of primary lung cancer,4 breast cancer and 2 thymic tumor) received whole pleural cavity irradiation of 60Co γ ray with centrally placed lead blocks to protect the vital organs and normal lung tissue,and the electron beam irradiation at the area which was covered by lead blocks in 60Co γ ray irradiation.The pleural effusion was completely drained before radiotherapy,and dose distribution of middle level was calculated by TPS using EXT 2.4 version software (Multidata Co.USA).The 100% isodose curve was 2Gy,15 fractions were given and another 20Gy/10Fx irradiation was added to the visible tumor.All patients received sequential chemotherapy for 3-6 cycles (cisplatin-based regimens for lung cancer and thymic tumor,cyclophosphamide and adriamycin and fluoracil for breast cancer).Kaplan-Meier curve was used to evaluate the pleural effusion control rate and survival rate of patients.

RESULTS

Complete remission of the malignant pleural effusion was seen in 9 patients and partial in 46 when treatment completed.The 6-,12-,18-month pleural effusion control rate and survival rate of the patients were 76%,53%,44% and 64%,34%,26%,respectively.The median control time of effusion and survival time were 14 months (2-32 months) and 9 months (4-32 months) respectively.We did not find any abnormality in liver function as well as in kidney function before and after treatment.Myelosuppression was the main side effect after combined chemotherapy and radiotherapy.Nineteen patients suffered from acute oesophagitis in grade 1-2,and 3 serious pleural fibrosis.There was no acute irradiation pneumonitis.

CONCLUSIONS

The treatment for malignant pleural effusion with combined 60Co γ ray and electron beam irradiation is tolerable and effective in clinical use.

[Phase I clinical trial of dose escalation on three dimensional conformal radiation therapy for non-small cell lung cancer]

BACKGROUND

To establish the technique of 3-dimensional conformal radiation therapy (3DCRT) for non-small cell lung cancer (NSCLC) in stage II-IIIB,and to assess its acute side-effects and to obtain the maximum tolerance dose (MTD).

METHODS

From June,1999 to June,2000,38 cases of NSCLC in stage II-IIIB were enrolled in this study.MTD was identified by dose escalation study.After 42Gy/21Fx/4.2wks by conventional fractionated irradiation through AP/PA fields,which covered the primary tumor and lymph nodes,the technique of 3DCRT was used as boost.The boost fields encompassed the clinical lesions showed on chest CT.The planning of total dose escalation depended on the percentage,i.e.,<25%,25%-37%,and >37% of normal lung volume irradiated to over 20Gy.The scheduled dose escalation ranged from 69 to 81Gy.The criteria for stopping dose escalation was grade III or more worse radiation pneumonitis (RTOG).The boost doses were delivered with 3Gy/fraction,once a day,5 fractions a week.

RESULTS

Thirty-three cases had completed their treatments and could be evaluated by now.Acute radiation pneumonitis occurred in 26% of patients with grade I-II and 3% with grade III,and acute radiation esophagitis in 61% with grade I-II and 9% with grade III,and the hematopoietic toxicity in 58% with grade I-II and 9% with grade III.The current doses implemented were 78,78,and 75Gy respectively for patients with <25%,25%-37%,and >37% of normal lung volume irradiated.The overall immediate response rate of tumors was 88%(29/33).

CONCLUSIONS

Dose escalation in a volume-dependent organ as the lungs is acceptable and applicable.The immediate response is encouraging.MTD is to be determined.The long-term follow-up is needed to observe late complications and treatment efficacy.

[Chemotherapy combined with chest radiation therapy in the treatment of 95 patients with limited stage small cell lung cancer]

BACKGROUND

To analyse retrospectively the results and prognostic factors of 95 patients with limited stage small cell lung cancer treated with chemotherapy plus chest radiation therapy.

METHODS

Ninety-five patients with limited stage small cell lung cancer were treated with combination chemotherapy plus chest radiation therapy from December,1989 to June,1997.There were 84 males and 11 females with median age of 58 years (32-75 years).The P-TNM stages of the disease were as follows:stage I disease,3 patients; stage II disease,7 patients; stage IIIA disease,49 patients and stage IIIB disease,36 patients.Chemotherapy regimens were CAP (cyclophosphamide,doxorubicin,cisplatin),EP(etoposide,cisplatin),TP(Teniposide,cisplatin),or IEP (ifosphamide,etoposide,cisplatin).Median cycles were 6 (1-10).After one cycle of chemotherapy,patients received chest radiation therapy with median total tumor dose of 59.1Gy(43.8-76.9Gy)/31fx(22-64fx) for 48 days(30-73days).The radiation fields covered tumors with 1.5-2.0cm margins.Supraclavicular region and brain did not receive prophylactic irradiation.

RESULTS

Of the ninety-five patients,55(58%) had a complete response,36(38%) had a partial response,three had a stable disease and one had a disease progression.The median survival time was 28 months.The 1-,2-,3- and 5-year survival rates were 85%,62%,31% and 13%,respectively.The 1-,2-,3-,and 5-year local control rates were 95%,86%,77% and 64%,respectively.The 1-,2-,3- and 5-year distant metastasis rates were 23%,52%,73%,and 83%,respectively.From multivariate regression analyses,KPS≥70 and complete response and partial response could be the favorable predictors.

CONCLUSIONS

Chemotherapy combined with chest irradiation in limited stage small cell lung cancer can get better survival and local control and less distant metastases.KPS≥70 and complete response and partial response might be the favorable predictors.

Integrin-like proteins in the pollen tube: detection, localization and function

The distribution of integrin-like proteins in the pollen tube was examined by immunofluorescent labeling and western blotting techniques using antibodies against human placenta integrin vitronectin receptor (VnR), and alpha(v), beta3 and beta1 integrin subunits. Pseudocolor-coded confocal images showed intense immunostaining within 10 and 5 microm of the tip of the pollen tube in Lilium davidii and Nicotiana tabacum respectively. In both segments the site near the plasma membrane was labeled. Western blotting analyses revealed cross-reaction of anti-beta3, anti-alpha(v) and anti-VnR with the proteins in the plasma membrane preparation of L. davidii and Hemerocallis citrina pollen tube. These studies provide evidence for the first time that the integrin-like protein is present in pollen tubes, and it may be mainly composed of alpha(v) and beta3 subunits in lily pollen tubes. In a functional assay, neither anti-VnR antibody nor the Arg-Gly-Asp-Ser tetrapeptide inhibited pollen tube growth of N. tabacum in vitro, but both of them depressed tube growth on the stigma and in style under quasi in vivo culture conditions. The integrin-like proteins localized in the tip and periphery of the pollen tube appeared to play roles in growth of the pollen tube tip and interaction with the extracellular matrix of the style.

A mathematical analysis for the Brownian dynamics of a DNA tether

In the single-particle tracking experiment, the internal motion of a single DNA or polymer molecule whose one end is attached to a microsphere (optical marker) and the other end is anchored to a substratum is studied (Finzi and Gelles, 1995). The stochastic Brownian dynamics of the sphere reflect the spontaneous fluctuations, thus the physical characteristics, of the DNA or polymer molecule (Qian and Elson, 1999, Qian, 2000). In this paper, two continuous models of polymer molecules, a flexible elastic string and a weakly bendable elastic rod, are analyzed. Both models are cast mathematically in terms of linear stochastic differential equations. Based on Fourier analyses, we calculate the mean square displacement (MSD) of the particle motion, the key observable in the experiment. We obtain for both models the short-time asymptomatics for the MSD, as well as the long-time behavior in terms of the smallest non-zero eigenvalues. It is shown that: (i) the long-time dynamics of continuous elastic string model quantitatively agree with that of the discrete bead-spring model. (ii) The short-time MSD of both models are controlled by the tethered particle, with linear dependence on t. (iii) The two models show characteristic difference for long-time behavior: The longest relaxation time is proportional to L2 for long elastic string and to L for short elastic string, but is proportional to L4 for both long and short weakly bendable rod.

Large-scale processes and the Asian bias in species diversity of temperate plants

An important issue in the study of biodiversity is the extent to which global patterns of species richness reflect large-scale processes and historical contingencies. Ecological interactions in local assemblages may constrain the number of species that can coexist, but differences in diversity in similar habitats within different regions (diversity anomalies) suggest that this limit is not firm. Variation in rate of species production could influence regional and perhaps local diversity independently of the ecological capacity of an area to support coexisting species, thereby creating diversity anomalies. Temperate Zone genera of plants that are disjunct between similar environments in eastern Asia and eastern North America (EAS-ENA) have twice as many species in Asia as in North America. Because lineages of these genera in Asia and North America are mostly sister pairs, they share a common history of adaptation and ecological relationship before disjunction. Thus, the diversity anomaly in EAS-ENA genera is not an artefact of taxon or habitat sampling but reflects differences in the net diversification (speciation-extinction) of the lineages in each of the continents. Here we propose that the most probable cause of the EAS-ENA anomaly in diversity is the extreme physiographical heterogeneity of temperate eastern Asia, especially compared with eastern North America, which in conjunction with climate and sea-level change has provided abundant opportunities for evolutionary radiation through allopatric speciation.

Experimental validation of a finite element model of light-activated polymerization shrinkage

An important consideration in improving the longevity of dental resin composite restorations is how to minimize the stresses that develop between resin composites and the wall of the preparation as the resin shrinks during polymerization. If the stress is too great, failure of the bonded interface occurs and microleakage results, with possible margin failure, staining, and secondary caries. This present project was performed to validate a previously developed FEM approach for investigating polymerization shrinkage. Light-cured resin composite was condensed into a cylindrical cavity preparation, which contained a centrally located wire. A profilometer stylus was positioned on the end of the wire to detect the initial surface displacement as the wire moved with the superficial layer of composite resin. The plots of the experimentally derived data were compared to the data plot from the FEM. The initial segments of the experimental plots matched the calculated plot very closely in shape, thus validating the FEM approach.

Nitric oxide synthase in atherosclerosis and vascular injury: insights from experimental gene therapy

Gene therapy aims to intervene in a disease process by transfer and expression of specific genes in a target tissue or organ. Cardiovascular gene therapy in humans remains in its infancy, but in the last decade, experimental gene transfer has emerged as a powerful biological tool to investigate the function of specific genes in vascular disease pathobiology. Nitric oxide synthases, the enzymes that produce nitric oxide, have received considerable attention as potential candidates for vascular gene therapy because nitric oxide has pleiotropic antiatherogenic actions in the vessel wall, and abnormalities in nitric oxide biology are apparent very early in the atherogenic process. In this article, we review the use of nitric oxide synthases in experimental vascular gene therapy and assess the utility of these approaches for investigating the role of nitric oxide in atherosclerosis and their potential for human gene therapy.

A class of flow bifurcation models with lognormal distribution and fractal dispersion

We report a quantitative analysis of a simple dichotomous branching tree model for blood flow in vascular networks. Using the method of moment-generating function and geometric Brownian motion from stochastic mathematics, our analysis shows that a vascular network with asymmetric branching and random variation at each bifurcating point gives rise to an asymptotic lognormal flow distribution with a positive skewness. The model exhibits a fractal scaling in the dispersion of the regional flow in the branches. Experimentally measurable fractal dimension of the relative dispersion in regional flow is analytically calculated in terms of the asymmetry and the variance at local bifurcation; hence the model suggests a powerful method to obtain the physiological information on local flow bifurcation in terms of flow dispersion analysis. Both the fractal behavior and the lognormal distribution are intimately related to the fact that it is the logarithm of flow, rather than flow itself, which is the natural variable in the tree models. The kinetics of tracer washout is also discussed in terms of the lognormal distribution.

Single-particle tracking: Brownian dynamics of viscoelastic materials

A unifying theoretical framework for analyzing stochastic data from single-particle tracking (SPT) in viscoelastic materials is presented. A generalization of the bead-spring model for linear polymers is developed from a molecular point of view and from the standpoint of phenomenological linear viscoelasticity. The hydrodynamic interaction in the former is identified as the dashpots in the latter. In elementary terms, the intimate correspondence between time-correlation of the fluctuation measurements and transient relaxation kinetics after perturbation is discussed, and the central role of the fluctuation-dissipation relation is emphasized. The work presented here provides a bridge between the microscopic and the macroscopic views of linear viscoelastic biological materials, and is applicable to membrane protein diffusion, linear DNA chain dynamics, and mechanics of intracellular cytoskeletal networks.

The impact of overall treatment time on outcomes in radiation therapy for non-small cell lung cancer

PURPOSE

A retrospective study was carried out to evaluate the impact of overall treatment time (OTT) on the results of radiation therapy for non-small cell lung cancer (NSCLC).

MATERIALS AND METHODS

From Jan. 1990 to Dec. 1996, 256 patients with stages I-IIIb NSCLC entered this analysis. All patients received definitive radiotherapy. Biologically effective dose (BED) was used to standardize the irradiation effects. The correlation between OTT and local progression-free survival was analyzed by linear-regression and Cox proportional hazard models. The prognostic variables for survival and distant metastasis were also briefly studied.

RESULTS

OTT had been shortened in 64 patients because of an accelerated hyperfractioned irradiation, while OTT was prolonged i n 114 patients due to interruptions of irradiation courses. The main ca uses of interruption were machine breakdown or delayed preparations of c errobend block for boost fields (55%), holidays (11%) and treatment toxi city and side effects (34%). Patients tre ated with prolonged OTT (> 45 days) had significant poorer local progression-free survival than whom with OTT of </=45 days, 1, 3 and 5 year actuarial local progression-free survivals being 49, 17 and 15% for the former, and 74, 35 and 25% for the latter, respectively (P<0.001). BED-T that contained the factor of OTT correlated directly to local controls, which implied that BED-T represented radiobiological effects accurately, in other words, OTT had played a role in determining the radiobiological effects. Linear-regression on 103 cases treated with BED of 80-85 Gy(10) showed that 3 year local progression-free survival decreased by 9% per week with prolongation of OTT, or vice versa it increased by 9% per week with shortening OTT in an OTT range of 30-76 days. Cox multivariate analyses confirmed that OTT was an independent prognostic factor for local controls.

CONCLUSION

OTT may have played an important role in determining local controls in radiotherapy for NSCLC. One should always keep in mind to make the OTT as short as possible, provided the patients can tolerate it, and to reduce irradiation interruptions for whatever reasons to a minimum.

Pumped biochemical reactions, nonequilibrium circulation, and stochastic resonance

Based on a master equation formalism for mesoscopic, unimolecular biochemical reactions, we show the periodic oscillation arising from severe nonequilibrium pumping is intimately related to the periodic motion in recently studied stochastic resonance (SR). The white noise in SR is naturally identified with the temperature in the biochemical reactions; the drift in the SR is associated with the circular flux in nonequilibrium steady state (NESS). As in SR, an optimal temperature for biochemical oscillation is shown to exist. A unifying framework for Hill's theory of NESS and the SR without periodic forcing is presented. The new formalism provides an analytically solvable model for SR.

[Effect of protein expression on antisense c-myc and PCNA for vascular smooth muscle cells]

OBJECTIVE

To study the methods of inhibiting proliferation of vascular smooth muscle cells (VSMCs), we observed the change of protein expression after using antisense c-myc, PCNA for VSMCs.

METHODS

The sense, antisense, and mismatched oligomers for c-myc or PCNA were individually delivered to the cultured VSMCs. Using Western blot, immunohistochemistry assay and image analysis system, we observed the change of c-myc and PCNA protein expression in the VSMCs.

RESULTS

Antisense c-myc, PCNA at concentration of 10 micromol/L can successfully inhibit the expression of c-myc, PCNA protein in the VSMCs (P < 0.05), but the sense and the mismatched do not have this effect (P > 0.05).

CONCLUSION

The data suggested that the antisense c-myc, PCNA could attenuate the protein expression of c-myc, PCNA, and it is an effective method for the inhibition of VSMCs hyperplasia.

Agonist-induced phosphorylation of the angiotensin II (AT(1A)) receptor requires generation of a conformation that is distinct from the inositol phosphate-signaling state

G protein-coupled receptors are thought to isomerize between distinct inactive and active conformations, an idea supported by receptor mutations that induce constitutive (agonist-independent) activation. The agonist-promoted active state initiates signaling and, presumably, is then phosphorylated and internalized to terminate the signal. In this study, we examined the phosphorylation and internalization of wild type and constitutively active mutants (N111A and N111G) of the type 1 (AT(1A)) angiotensin II receptor. Cells expressing these receptors were stimulated with angiotensin II (AngII) and [Sar(1),Ile(4),Ile(8)]AngII, an analog that only activates signaling through the constitutive receptors. Wild type AT(1A) receptors displayed a basal level of phosphorylation, which was stimulated by AngII. Unexpectedly, the constitutively active AT(1A) receptors did not exhibit an increase in basal phosphorylation nor was phosphorylation enhanced by AngII stimulation. Phosphorylation of the constitutively active receptors was unaffected by pretreatment with the non-peptide AT(1) receptor inverse agonist, EXP3174, and was not stimulated by the selective ligand, [Sar(1),Ile(4),Ile(8)]AngII. Paradoxically, [Sar(1),Ile(4), Ile(8)]AngII produced a robust ( approximately 85% of AngII), dose-dependent phosphorylation of the wild type AT(1A) receptor at sites in the carboxyl terminus similar to those phosphorylated by AngII. Moreover, internalization of both wild type and constitutive receptors was induced by AngII, but not [Sar(1),Ile(4),Ile(8)]AngII, providing a differentiation between the phosphorylated and internalized states. These data suggest that the AT(1A) receptor can attain a conformation for phosphorylation without going through the conformation required for inositol phosphate signaling and provide evidence for a transition of the receptor through multiple states, each associated with separate stages of receptor activation and regulation. Separate transition states may be a common paradigm for G protein-coupled receptors.

A simple theory of motor protein kinetics and energetics. II

A three-state stochastic model of motor protein [Qian, Biophys. Chem. 67 (1997) pp. 263-267] is further developed to illustrate the relationship between the external load on an individual motor protein in aqueous solution with various ATP concentrations and its steady-state velocity. A wide variety of dynamic motor behavior are obtained from this simple model. For the particular case of free-load translocation being the most unfavorable step within the hydrolysis cycle, the load-velocity curve is quasi-linear, V/Vmax = (cF/Fmax-c)/(1-c), in contrast to the hyperbolic relationship proposed by A.V. Hill for macroscopic muscle. Significant deviation from the linearity is expected when the velocity is less than 10% of its maximal (free-load) value--a situation under which the processivity of motor diminishes and experimental observations are less certain. We then investigate the dependence of load-velocity curve on ATP (ADP) concentration. It is shown that the free load Vmax exhibits a Michaelis-Menten like behavior, and the isometric Fmax increases linearly with ln([ATP]/[ADP]). However, the quasi-linear region is independent of the ATP concentration, yielding an apparently ATP-independent maximal force below the true isometric force. Finally, the heat production as a function of ATP concentration and external load are calculated. In simple terms and solved with elementary algebra, the present model provides an integrated picture of biochemical kinetics and mechanical energetics of motor proteins.