Modulation of differentiation in vitro. I. Influence of the attachment surface on myogenesis

Myogenic cells of the L6 line proliferate and fuse in culture to form myotubes that actively synthesize muscle-specific proteins such as myosin. We show that the expression of the differentiated phenotype can be influenced by the electrical charges of the substratum on which the cells were grown. Negatively charged surfaces did not influence the developmental program of the cells although positively charged ones interfered with myogenesis. The interaction operates primarily by interfering with the mitotic cycle, which is slowed down, with fusion which is blocked, and with myosin synthesis, which is reduced. Our results show that growth of the cells on positively charged surfaces prevents the switching of a large fraction of the population from a proliferative state to a differentiating program. We postulate that this interference might operate through the slowdown in DNA replication. The cell culture method described represents a good model for studying the different steps involved in the differentiation of L6 cells.     

Commitment,fusion and biochemical differentiation of a myogenic cell line in the absence of DNA synthesis

L₆E₉ rat myoblasts derived from the L₆ cell line can be induced to differentiate to a very high percentage by manipulating the culture conditions. Under standard differentiating conditions, L₆E₉ cells divide an average of 2.5 times before differentiating and >99% of them incorporate ³H-TdR before fusing. By inhibiting DNA replication by a variety of means, data have been obtained which demonstrate that this DNa synthesis is not required to switch from growth to differentiation. After every cell division, L₆E₉ cells have the option either to fuse or to proliferate without intervening DNA synthesis.Cell cloning and DNA labeling experiments show a direct correlation between the time of culture in differentiating medium and a progressive loss of proliferative capacity of mononucleated L₆E₉ cells, demonstrating that these cells become irreversibly committed to differentiation and withdraw from the cell cycle prior to and not as a consequence of cell fusion. The commitment step occurs during the G1 phase prior to fusion. This G1 phase has a latent period during which no irreversible step toward differentiation occurs and the cells remain ambivalent toward growth or differentiation. Under proper conditions, this period is followed by an irreversible commitment toward differentiation and a loss of proliferative capacity. The kinetics of this commitment step strongly suggest that L₆E₉ cells become irreversibly committed in a stochastic manner. Once the cells have become committed, with or without DNA synthesis, they will fuse to form myotubes and biochemically differentiate in a deterministic fashion.The data presented are consistent with a stochastic model of differentiation for L₆E₉ cells and demonstrate that the switch from a proliferating to a differentiating genetic program can occur in the absence of DNA synthesis.     

N‐isopropylacrylamide‐based thermoresponsive polyelectrolyte multilayer films for human mesenchymal stem cell expansion

Human mesenchymal stem cells (hMSCs) are colony‐forming unit fibroblasts (CFU‐F) derived from adult bone marrow and have significant potential for many cell‐based tissue‐engineering applications. Their therapeutic potential, however, is restricted by their diminishing plasticity as they are expanded in culture. In this study, we used N‐isopropylacrylamide (NIPAM)‐based thermoresponsive polyelectrolyte multilayer (N‐PEMU) films as culture substrates to support hMSC expansion and evaluated their effects on cell properties. The N‐PEMU films were made via layer‐by‐layer adsorption of thermoresponsive monomers copolymerized with charged monomers, positively charged allylamine hydrochloride (PAH), or negatively charged styrene sulfonic acid (PSS) and compared to fetal bovine serum (FBS) coated surfaces. Surface charges were shown to alter the extracellular matrix (ECM) structure and subsequently regulate hMSC responses including adhesion, proliferation, integrin expression, detachment, and colony forming ability. The positively charged thermal responsive surfaces improved cell adhesion and growth in a range comparable to control surfaces while maintaining significantly higher CFU‐F forming ability. Immunostaining and Western blot results indicate that the improved cell adhesion and growth on the positively charged surfaces resulted from the elevated adhesion of ECM proteins such as fibronectin on the positively charge surfaces. These results demonstrate that the layer‐by‐layer approach is an efficient way to form PNIPAM‐based thermal responsive surfaces for hMSC growth and removal without enzymatic treatment. The results also show that surface charge regulates ECM adhesion, which in turn influences not only cell adhesion but also CFU‐forming ability and their multi‐lineage differentiation potential. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

The Role of Negative Charge in the Delivery of Quantum Dots to Neurons

Despite our extensive knowledge of the structure of negatively charged cell surface proteoglycans and sialoglycoconjugates in the brain, we have little understanding of how their negative charge contributes to brain function. We have previously shown that intensely photoluminescent 9-nm diameter quantum dots (QDs) with a CdSe core, a ZnS shell, and a negatively charged compact molecular ligand coating (CL4) selectively target neurons rather than glia. We now provide an explanation for this selective neuronal delivery. In this study, we compared three zwitterionic QD coatings differing only in their regions of positive or negative charge, as well as a positively charged (NH₂) polyethylene glycol (PEG) coat, for their ability to deliver the cell-membrane-penetrating chaperone lipopeptide JB577 (WG(Palmitoyl)VKIKKP₉G₂H₆) to individual cells in neonatal rat hippocampal slices. We confirm both that preferential uptake in neurons, and the lack of uptake in glia, is strongly associated with having a region of greater negative charge on the QD coating. In addition, the role of negatively charged chondroitin sulfate of the extracellular matrix (ECM) in restricting uptake was further suggested by digesting neonatal rat hippocampal slices with chondroitinase ABC and showing increased uptake of QDs by oligodendrocytes. Treatment still did not affect uptake in astrocytes or microglia. Finally, the future potential of using QDs as vehicles for trafficking proteins into cells continues to show promise, as we show that by administering a histidine-tagged green fluorescent protein (eGFP-His₆) to hippocampal slices, we can observe neuronal uptake of GFP.     

The physico-chemical characterization of casein-modified surfaces and their influence on the adhesion of spores from a Geobacillus species

To gain a better understanding of the factors influencing spore adhesion in dairy manufacturing plants, casein-modified glass surfaces were prepared and characterized and their effect on the adhesion kinetics of spores from a Geobacillus sp., isolated from a dairy manufacturing plant (DMP) was assessed using a flow chamber. Surfaces were produced by initially silanizing glass using (3-glycidyloxypropyl) trimethoxysilane (GPS) or (3-aminopropyl) triethoxysilane to form epoxy-functionalized (G-GPS) or amino-functionalized glass (G-NH₂) substrata. Casein was grafted to the G-GPS directly by its primary amino groups (G-GPS-casein) or to G-NH₂ by employing glutaraldehyde as a linking agent (G-NH₂-glutar-casein). The surfaces were characterised using streaming potential measurements, contact angle goniometry, infrared spectroscopy and scanning electron microscopy. The attachment rate of spores suspended in 0.1 M KCl at pH 6.8, was highest on the positively charged (+14 mV) G-NH₂ surface (333 spores cm^?2 s^?1) compared to the negatively charged glass (?22 mV), G-GPS (?20 mV) or G-GPS-casein (?21 mV) surfaces (162, 17 or 6 spores cm^?2 s^?1 respectively). Whilst there was a clear decrease in attachment rate to negatively charged casein-modified surfaces compared to the positively charged amine surface, there was no clear relationship between surface hydrophobicity and spore attachment rate.     

Effect of surfaces on amyloid fibril formation

Using atomic force microscopy (AFM) we investigated the interaction of amyloid beta (Aβ) (1–42) peptide with chemically modified surfaces in order to better understand the mechanism of amyloid toxicity, which involves interaction of amyloid with cell membrane surfaces. We compared the structure and density of Aβ fibrils on positively and negatively charged as well as hydrophobic chemically-modified surfaces at physiologically relevant conditions. We report that due to the complex distribution of charge and hydrophobicity amyloid oligomers bind to all types of surfaces investigated (CH₃, COOH, and NH₂) although the charge and hydrophobicity of surfaces affected the structure and size of amyloid deposits as well as surface coverage. Hydrophobic surfaces promote formation of spherical amorphous clusters, while charged surfaces promote protofibril formation. We used the nonlinear Poisson-Boltzmann equation (PBE) approach to analyze the electrostatic interactions of amyloid monomers and oligomers with modified surfaces to complement our AFM data.     

Two-Dimensional Crystallization of Brush Border Myosin I

Brush border myosin-I (BBMI) is a single-headed unconventional myosin found in the microvilli of intestinal epithelial cells, where it links the core bundle of actin filaments to the plasma membrane. An association of BBMI with anionic phospholipids has been shown to be mediated by a carboxy-terminal domain which is rich in basic amino acids. We have exploited this natural affinity of BBMI for negatively charged lipids to form two-dimensional (2D) crystals of this protein which are suitable for structural analysis by electron crystallographic techniques. The 2D crystals which we have obtained belong to one of two space groups, p22₁2₁or p2. We present here projection maps calculated from images of negatively stained crystals for each of these crystal types to a resolution of 20 Å and show that the asymmetric unit is the same in both crystal types.     

Transient induction of poly(A)-short myosin heavy chain messenger RNA during terminal differentiation of L6E9 myoblasts

The rat myoblast L₆E₉ cell line under appropriate culture conditions is a uniform population of cycling cells which can be induced to differentiate into a pure population of myotubes. The pattern and kinetics of myogenic differentiation of this cell line are similar to those of primary skeletal muscle myoblasts. We have used this cell line to investigate the controls regulating the synthesis and accumulation of myosin heavy chain during myogenic development. From pulse labeling studies of total cellular protein synthesis, we observed that activation of MHC⁴ synthesis is temporally correlated with cell fusion and myotube formation. MHC synthesis is transiently induced from <1% up to 25% of the total protein synthesized. After MHC has accumulated to the steady-state level characteristic of fully differentiated myotubes, MHC synthesis decreases very rapidly to almost basal levels. To determine whether this transient induction of MHC synthesis was due to parallel changes in MHC messenger RNA levels, the accumulation and compartmentalization of MHC mRNA during L₆E₉ cell differentiation was followed by complementary DNA/RNA hybridization using cDNA prepared against MHC mRNA purified from L₆E₉ cells. We demonstrate that the level of MHC synthesis closely parallels the level of cytoplasmic MHC mRNA. The induction of MHC mRNA accumulation is initiated at least 36 hours prior to cell fusion and at a time when all cells in the population are still uncommitted to terminal differentiation as tested by cell cloning. The level of cytoplasmic MHC mRNA is increased from ~200 molecules per cell in the growing state to ~50,000 molecules at the peak of induction (day 6 after plating). Subsequently the levels of MHC mRNA decrease very rapidly and at day 10 after plating there are only ~3000 molecules per myotube nucleus. A striking feature of this regulation is the behavior of MHC mRNA on oligo(dT) columns. Most (~90%) of the MHC mRNA transiently induced during differentiation has a very short poly(A) tail (<20 nucleotides). We conclude that the striking induction followed by deinduction of MHC synthesis is controlled primarily by the induction and deinduction of cytoplasmic MHC mRNA accumulation. The relationship of our observations to muscle physiology is discussed.     

Electrostatic engineering of the interface between heavy and light chains promotes antibody Fab fragment production

Monoclonal antibodies and antibody fragments are used for diverse diagnostic and therapeutic applications. We have investigated the secretory production of Fab fragments from insect cells cotransfected with plasmid vectors carrying heavy- and light-chain genes. In the present study, to promote the formation of the disulfide bond between the heavy and light chains, some positively charged amino acid residues were introduced near the cysteine residue for the disulfide bond at the C-terminus of C_L, while some negatively charged amino acid residues were added near the cysteine residue for the disulfide bond at the C-terminus of C_H1. This electrostatic steering led to an increase in Fab secretions from insect cells.     

Differentiation markers of mouse C2C12 and rat L6 myogenic cell lines and the effect of the differentiation medium

Summary The differentiation grade of cells in culture is dependent on the composition of the culture medium. Two commonly used myogenic cell lines, mouse C₂C₁₂ and rat L₆, usually differentiate at a low concentration of horse serum. In this study we compared the effect of horse serum with a medium containing a low percentage of Ultroser G and rat brain extract. The maturation grade was evaluated on the basis of various biochemical, (immuno)histochemical and cell-physiological parameters. Substitution of horse serum by Ultroser G and rat brain extract during the differentiation phase resulted in a higher maturation grade of the myotubes of both cell lines, on the basis of creatine kinase activity and the diameter of the myotubes. In addition, the C₂C₁₂ myotubes display cross-striation, contain a higher percentage of creatine kinase muscle-specific isoenzyme MM, show a ninefold increase in acetylcholine receptor (AChR) clusters, form a continuous basement membrane, and have a lower resting cytosolic Ca²⁺ concentration. L₆ myotubes show a fivefold increase in AChR clusters and a twofold increase in the expression of the mRNA of the ɛ-subunit of AChR. C₂C₁₂ cells show spontaneous contraction and response of cytosolic Ca²⁺ to various stimulants in contrast to L₆ cells which do not. These studies established that the Ultroser G/brain extract medium leads to a higher differentiation grade of both cell lines, but parameters appropriate for use as differentiation markers appear to differ between both cell lines.     

Androgens Exert a Cysticidal Effect upon Taenia crassiceps by Disrupting Flame Cell Morphology and Function

The effects of testosterone (T₄) and dihydrotestosterone (DHT) on the survival of the helminth cestode parasite Taenia crassiceps, as well as their effects on actin, tubulin and myosin expression and their assembly into the excretory system of flame cells are described in this paper. In vitro evaluations on parasite viability, flow cytometry, confocal microscopy, video-microscopy of live flame cells, and docking experiments of androgens interacting with actin, tubulin, and myosin were conducted. Our results show that T₄ and DHT reduce T. crassiceps viability in a dose- and time-dependent fashion, reaching 90% of mortality at the highest dose used (40 ng/ml) and time exposed (10 days) in culture. Androgen treatment does not induce differences in the specific expression pattern of actin, tubulin, and myosin isoforms as compared with control parasites. Confocal microscopy demonstrated a strong disruption of the parasite tegument, with reduced assembly, shape, and motion of flame cells. Docking experiments show that androgens are capable of affecting parasite survival and flame cell morphology by directly interacting with actin, tubulin and myosin without altering their protein expression pattern. We show that both T₄ and DHT are able to bind actin, tubulin, and myosin affecting their assembly and causing parasite intoxication due to impairment of flame cell function. Live flame cell video microscopy showing a reduced motion as well changes in the shape of flame cells are also shown. In summary, T₄ and DHT directly act on T. crassiceps cysticerci through altering parasite survival as well as the assembly and function of flame cells.     

Alterations of the carrier-mediated transport of an anionic solute,methotrexate, by charged liposomes in Ehrlich ascites tumor cells

Summary Interaction of positively charged liposomes with Ehrlich ascites tumor cells increases the bidirectional transmembrane fluxes of the anionic folic acid analog, methotrexate. Negative liposomes reduce methotrexate influx. Stimulation of methotrexate influx by positively charged liposomes is time and concentration dependent, requiring at least a 5-min incubation with 2.5mm phosphatidylcholine containing 20% stearylamine for maximum effect. Stimulation is not appreciably reversed by washing the cells. Similar increases are observed for influx and efflux so that there is no change in the steady-state methotrexate electrochemical-potential difference across the cell membrane. The increase in influx appears to be a stimulation of the carrier-mediated transport process for methotrexate since both control and stimulated influx are abolished by the competitive inhibitor, 5-formyltetrahydrofolate or the sulfhydryl group inhibitor,p-chloromercuriphenylsulfonic acid and the Q₁₀ of the system remains unchanged. Influx of 5-methyltetrahydrofolate, which shares the same transport carrier as methotrexate, is also stimulated. However, the transport of folic acid, which is structurally similar to methotrexate but does not utilize the carrier, is unaffected. The kinetic change induced by positively charged liposomes is an increase in theV _ma ⁱⁿ , while theK _t ⁱⁿ remains unchanged. Trans-stimulation of methotrexate influx by 5-formyltetrahydrofolate occurs to the same extent in the presence or absence of positively charged liposomes. The liposomes have no apparent effect on the intracellular water, the extracellular space, or the chloride distribution ratio. The data suggest that interaction of positively charged liposomes with Ehrlich ascites tumor cells accelerates the rate of transposition of the membrane carrier system for methotrexate, altering the kinetics of transport without a change in transport thermodynamics.     

Phosphate and ADP Differently Inhibit Coordinated Smooth Muscle Myosin Groups

Actin filaments propelled in vitro by groups of skeletal muscle myosin motors exhibit distinct phases of active sliding or arrest, whose occurrence depends on actin length (L) within a range of up to 1.0 μm. Smooth muscle myosin filaments are exponentially distributed with ≈150 nm average length in vivo—suggesting relevance of the L-dependence of myosin group kinetics. Here, we found L-dependent actin arrest and sliding in in vitro motility assays of smooth muscle myosin. We perturbed individual myosin kinetics with varying, physiological concentrations of phosphate (P_i, release associated with main power stroke) and adenosine diphosphate (ADP, release associated with minor mechanical step). Adenosine triphosphate was kept constant at physiological concentration. Increasing [P_i] lowered the fraction of time for which actin was actively sliding, reflected in reduced average sliding velocity (ν) and motile fraction (f_mot, fraction of time that filaments are moving); increasing [ADP] increased the fraction of time actively sliding and reduced the velocity while sliding, reflected in reduced ν and increased f_mot. We introduced specific P_i and ADP effects on individual myosin kinetics into our recently developed mathematical model of actin propulsion by myosin groups. Simulations matched our experimental observations and described the inhibition of myosin group kinetics. At low [P_i] and [ADP], actin arrest and sliding were reflected by two distinct chemical states of the myosin group. Upon [P_i] increase, the probability of the active state decreased; upon [ADP] increase, the probability of the active state increased, but the active state became increasingly similar to the arrested state.     

The Positively Charged Region of the Myosin IIC Non-helical Tailpiece Promotes Filament Assembly

The motor protein, non-muscle myosin II (NMII), must undergo dynamic oligomerization into filaments to participate in cellular processes such as cell migration and cytokinesis. A small non-helical region at the tail of the long coiled-coil region (tailpiece) is a common feature of all dynamically assembling myosin II proteins. In this study, we investigated the role of the tailpiece in NMII-C self-assembly. We show that the tailpiece is natively unfolded, as seen by circular dichroism and NMR experiments, and is divided into two regions of opposite charge. The positively charged region (Tailpiece_1946–1967) starts at residue 1946 and is extended by seven amino acids at its N terminus from the traditional coiled-coil ending proline (Tailpiece_1953–1967). Pull-down and sedimentation assays showed that the positive Tailpiece_1946–1967 binds to assembly incompetent NMII-C fragments inducing filament assembly. The negative region, residues 1968–2000, is responsible for NMII paracrystal morphology as determined by chimeras in which the negative region was swapped between the NMII isoforms. Mixing the positive and negative peptides had no effect on the ability of the positive peptide to bind and induce filament assembly. This study provides molecular insight into the role of the structurally disordered tailpiece of NMII-C in shifting the oligomeric equilibrium of NMII-C toward filament assembly and determining its morphology.     

Studies on cell adhesion in tissue culture : XV. Some effects of cycloheximide on cell detachment

Attempts were made to identify positively charged groups at the surfaces of Ehrlich ascites tumour (EAT) cells, and particles of polystyrene polymer which had adsorbed proteins after incubation in serum-containing culture medium. The cells and particles were treated with 2,4,6-trinitrobenzene sulphonic acid (TNBS) or 2,3-dimethylmaleic anhydride (DMA), which react with amino and other cationic groups. The increases in cell and particle anodic electrophoretic mobility were consistent with approx. 5% of the total surface charge of each, being due to positively charged groups. The effects of DMA or TNBS treatment of the cells and/or polystyrene surfaces, on the rates of cell adhesion to these surfaces were then determined. The significantly slower rates of adhesion after some modes of treatment suggest that positively charged groups at the surfaces of EAT cells play a part in their initial contact with and adhesion to, protein-coated plastic surfaces. However, quantitatively the role of cationic groups is a minor one in this part of the adhesion process.     

Modulation of differentiation in vitro. II. Influence of cell spreading and surface events on myogenesis

Summary We examined the influence of attachment and spreading on myogenesis by adding polylysine-covered beads at different times after plating the cells on a plastic substratum. We show that polylysine per se acting on the cell surface can modulate myogenesis independently of cell spreading. Thus cell shape would not be the limiting factor for the division and differentiation of L₆ myoblasts. Multinucleation of the cells was found to be first enhanced by the addition of polylysine-covered beads to replicating myoblasts, although the final percentage of fusion attained by these cultures was lower than in the controls. A similar phenomenon was observed concerning myosin synthesis. No such effect could be observed when the beads were added to a nonfusing mutant or to fibroblasts. Our results show that this phenomenon is specific. We postulate that some of the surface molecules necessary for this process appear on myoblasts shortly before they fuse. This work was supported by the American Dystrophy Association and by the Association pour la Recherche sur le Cancer (ARC) (Contract no 3050).     

Dexamethasone inhibits apoptosis in C6 glioma cells through increased expression of Bcl-XL

The glucocorticoid dexamethasone (Dex) has been reported to modulate a number of signaling pathways and physiological processes, including apoptosis. This study was carried out to investigate the cytoprotective mechanism of Dex in C6 glioma cells. Pre-treatment of cells with Dex inhibited apoptosis induced by staurosporine, etoposide and thapsigargin. Apoptosis inhibition correlated with blockade of mitochondrial cytochrome c release, abolition of caspase-3 activity along with inhibition of caspase-9 and PARP cleavage. Dex-mediated cytoprotection coincided with the induction of the anti-apoptotic protein, Bcl-X_L. The specific glucocorticoid receptor antagonist, RU486, reversed the anti-apoptotic effect of Dex and prevented Bcl-X_L induction. Here, we show for the first time that knockdown of Bcl-X_L expression with siRNA reversed the protective effects of the glucocorticoid in glioma cells. We conclude that Dex-mediated inhibition of apoptosis in C6 glioma cells is through induction of Bcl-X_L.     

Arrangement of type IV collagen on NH2 and COOH functionalized surfaces

Apart from the paradigm that cell–biomaterials interaction depends on the adsorption of soluble adhesive proteins we anticipate that upon distinct conditions also other, less soluble ECM proteins such as collagens, associate with the biomaterials interface with consequences for cellular response that might be of significant bioengineering interest. Using atomic force microscopy (AFM) we seek to follow the nanoscale behavior of adsorbed type IV collagen (Col IV)—a unique multifunctional matrix protein involved in the organization of basement membranes (BMs) including vascular ones. We have previously shown that substratum wettability significantly affects Col IV adsorption pattern, and in turn alters endothelial cells interaction. Here we introduce two new model surfaces based on self‐assembled monolayers (SAMs), a positively charged –NH₂, and negatively charged –COOH surface, to learn more about their particular effect on Col IV behavior. AFM studies revealed distinct pattern of Col IV assembly onto the two SAMs resembling different aspects of network‐like structure or aggregates (suggesting altered protein conformation). Moreover, the amount of adsorbed FITC‐labeled Col IV was quantified and showed about twice more protein on NH₂ substrata. Human umbilical vein endothelial cells attached less efficiently to Col IV adsorbed on negatively charged COOH surface judged by altered cell spreading, focal adhesions formation, and actin cytoskeleton development. Immunofluorescence studies also revealed better Col IV recognition by both α₁ and α₂ integrins on positively charged NH₂ substrata resulting in higher phosphorylated focal adhesion kinase recruitment in the focal adhesion complexes. On COOH surface, no integrin clustering was observed. Taken altogether these results, point to the possibility that combined NH₂ and Col IV functionalization may support endothelization of cardiovascular implants. Biotechnol. Bioeng. 2011;108: 3009–3018. © 2011 Wiley Periodicals, Inc.     

Pre-power-stroke cross-bridges contribute to force transients during imposed shortening in isolated muscle fibers

When skeletal muscles are activated and mechanically shortened, the force that is produced by the muscle fibers decreases in two phases, marked by two changes in slope (P₁ and P₂) that happen at specific lengths (L₁ and L₂). We tested the hypothesis that these force transients are determined by the amount of myosin cross-bridges attached to actin and by changes in cross-bridge strain due to a changing fraction of cross-bridges in the pre-power-stroke state. Three separate experiments were performed, using skinned muscle fibers that were isolated and subsequently (i) activated at different Ca²⁺ concentrations (pCa²⁺ 4.5, 5.0, 5.5, 6.0) (n = 13), (ii) activated in the presence of blebbistatin (n = 16), and (iii) activated in the presence of blebbistatin at varying velocities (n = 5). In all experiments, a ramp shortening was imposed (amplitude 10%L_o, velocity 1 L_o•sarcomere length (SL)•s⁻¹), from an initial SL of 2.5 µm (except by the third group, in which velocities ranged from 0.125 to 2.0 L_o•s⁻¹). The values of P₁, P₂, L₁, and L₂ did not change with Ca²⁺ concentrations. Blebbistatin decreased P₁, and it did not alter P₂, L₁, and L₂. We developed a mathematical cross-bridge model comprising a load-dependent power-stroke transition and a pre-power-stroke cross-bridge state. The P₁ and P₂ critical points as well as the critical lengths L₁ and L₂ were explained qualitatively by the model, and the effects of blebbistatin inhibition on P₁ were also predicted. Furthermore, the results of the model suggest that the mechanism by which blebbistatin inhibits force is by interfering with the closing of the myosin upper binding cleft, biasing cross-bridges into a pre-power-stroke state.