Cell locomotion forces versus cell contraction forces for collagen lattice contraction: an in vitro model of wound contraction

Cultured human dermal fibroblasts suspended in a rapidly polymerizing collagen matrix produce a fibroblast-populated collagen lattice. With time, this lattice will undergo a reduction in size referred to as lattice contraction. During this process, two distinct cell populations develop. At the periphery of the lattice, highly oriented sheets of cells, morphologically identifiable as myofibroblasts, show cell-to-cell contacts and thick, actin-rich staining cytoplasmic stress fibers. It is proposed that these cells undergoing cell contraction produce a multicellular contractile unit which reorients the collagen fibrils associated with them. The cells in the central region, referred to as fibroblasts, are randomly oriented, with few cell-to-cell contacts and faintly staining actin cytoplasmic filaments. In contrast it is proposed that cells working as single units use cell locomotion forces to reorient the collagen fibrils associated with them. Using this model, we sought to determine which of these two mechanisms, cell contraction or cell locomotion, is responsible for the force that contracts collagen lattices. Our experiments showed that fibroblasts produce this contractile force, and that the mechanism for lattice contraction appears to be related to cell locomotion. This is in contrast to a myofibroblast; where the mechanism for contraction is based upon cell contractions. Fibroblasts attempting to move within the collagen matrix reorganize the surrounding collagen fibrils; when these collagen fibrils can be organized no further and cell-to-cell contacts develop, which occurs at the periphery of the lattice first, these cells can no longer participate in the dynamic aspects of lattice contraction.     

Muscle contraction: viscous-like frictional forces and the impulsive model

Apart from a few experimental studies muscle viscosity has not received much recent analytical attention as a determinant of the contractile process. This is surprising, since any muscle cell is 80% water, and may undergo large shape changes during its working cycle. Intuitively one might expect the viscosity of the solvent to be an important determinant of the physiological activity of muscle tissue. This was apparent to pioneers of the study of muscle contraction such as Hill and his contemporaries, whose putative theoretical formulations contained terms related to muscle viscosity. More recently, though, a hydrodynamic calculation by Huxley, using a solvent viscosity close to that of water, has been held to demonstrate that viscous forces are negligible in muscle contraction. We have re-examined the role of viscosity in contraction, postulating impulsive acto-myosin forces that are opposed by a viscous resistance between the filaments. The viscous force required, 10⁴ times the hydrodynamic estimate, is close to recent experimental measurements, themselves 10²–10³ times the hydrodynamic estimate. This also agrees with contemporary measurements of cytoplasmic viscosity in other biological cells using magnetic bead micro-rheometry. These are several orders of magnitude greater than the viscosity of water. In the course of the analysis we have derived the force-velocity equation for an isolated half-sarcomere containing a single actin filament for the first time, and from first principles. We conclude that muscle viscosity is indeed important for the contractile process, and that it has been too readily discounted.     

Muscle contraction: viscous-like frictional forces and the impulsive model

The thermal denaturation of yeast enolase 1 was studied by differential scanning calorimetry (DSC) under conditions of subunit association/dissociation, enzymatic activity or substrate binding without turnover and substrate analogue binding. Subunit association stabilizes the enzyme, that is, the enzyme dissociates before denaturing. The conformational change produced by conformational metal ion binding increases thermal stability by reducing subunit dissociation. 'Substrate' or analogue binding additionally stabilizes the enzyme, irrespective of whether turnover is occurring, perhaps in part by the same mechanism. More strongly bound metal ions also stabilize the enzyme more, which we interpret as consistent with metal ion loss before denaturation, though possibly the denaturation pathway is different in the absence of metal ion. We suggest that some of the stabilization by 'substrate' and analogue binding is owing to the closure of moveable polypeptide loops about the active site, producing a more 'closed' and hence thermostable conformation.     

A simple Hill element-nonlinear spring model of muscle contraction biomechanics

The purpose of this study was to develop a model to predict the mechanical response of muscles during isometric tetanic, afterloaded isotonic and isovelocity shortening contractions. Two versions of the model were developed. Both incorporated a contractile element that obeyed a Hill force-velocity relationship and a series elastic element. In a quadratic spring version, the series elastic element force was represented as proportional to the square of the stretch; in a cubic spring version, it was represented as proportional to the cube of the stretch. Both versions provided closed-form equations for response predictions that involved four independent parameters. Once the four parameters were chosen, each of these responses could be predicted. Model validity was established by comparing predicted and observed responses in slow and fast hindlimb muscles of rodents. Significant model-predicted responses seldom differed by more than 15% from experimental values. The model can provide insights into how changes in individual properties affect the overall mechanical behavior of muscles in a variety of circumstances and reduce the need for collection of experimental data.     

A modified distance variable for the Hill formalism for kinetic models of muscle contraction

The distance variable of the Hill formalism for kinetic models of muscle contraction is compared to a modified distance variable. Instead of measuring the distance from a fixed point on the myosin filament to a neighboring actin, the modified variable measures the deviation of the myosin cross-bridge from its equilibrium position. Although for attached cross-bridges the two definitions are equivalent, the new variable is an index of cross-bridge conformation for cross-bridges of all states. The modified variable may be used to complement the use of the Hill variable, or to replace it. The utility of the modified variable is illustrated by an example which matches cross-bridge structures to biochemical kinetic data and to the free energy functions necessary for the design of a kinetic model.     

Analysis of the exponential decay model of the neuron showing frequency threshold effects

The exponential decay model of a neuron has been analyzed using the “random walk” approach of stochastic processes and an “absorbing barrier” solution is obtained forg ^T (s)—the Laplace transform of the output pulse interval density function. An expression for the mean output frequency is derived from this and a variety of input-output curves plotted which show frequency threshold effects in single neurons. Our results are compared with those of other authors obtained by computer simulation techniques, and the significance of these results discussed with reference to the possible behavior of networks constructed of such neuron units.     

Craniofacial shortening by contraction osteogenesis: an experimental model

Application of gradual external forces to correct craniofacial deformities challenges many procedures in conventional craniomaxillofacial surgery. Distraction osteogenesis is replacing traditional osteotomies for correction of patients with craniomaxillofacial deficiencies. However, the reverse concept, contraction osteogenesis, has yet to be established for patients with craniomaxillofacial excesses. The purpose of this investigation is to demonstrate the contraction osteogenesis phenomenon applied in a controlled animal model during the craniofacial growth period. Twenty-six 26-day-old rabbits were assigned to one of four groups: 0, control; 1, pin control (pin insertion); 2, no contraction (pins and contraction device application, without active contraction); and 3, contraction (pin insertion, contraction device application, and active contraction). An external fixator was placed across the incisive-maxillary suture, and the effects after 4.5 weeks of contraction at a rate of 0.5 mm twice a week were compared with control groups. The results were assessed by craniometric and cephalometric measurements and by histologic examination. Gross alterations were evident in the contraction group, characterized by midface anteroposterior shortening, maxillary regression, snout deviation, and anterior crossbite. Histologic examination of the contraction group demonstrated a significant increase in osteoblastic activity. Contraction osteogenesis is a new treatment concept in craniofacial development and may offer therapeutic opportunities for shortening skeletal structures without the need of osteotomies, thus taking advantage of the potential of craniofacial growth and remodeling.     

Muscle contraction: a mechanism of energy transduction

A mechanism of muscle contraction is presented in which energy from the hydrolysis of MgATP is transferred directly to conformational strain in a flexible segment of the myosin head. That segment is proximal to both the active site and the subfragment 1—subfragment 2 hinge (the portion of the myosin molecule that connects each of its two enzymatically active globular heads to the long thin helical body). This proximity allows configurational changes at the active site, which are an intrinsic part of the enzymatic mechanism, to impose a localized strain, or distortion, near the hinge. The energy, trapped in the protein this way, is subsequently used for mechanical work when other enzymatically-induced conformational changes free the strained segment of the myosin head to unbend. As this happens, the head rotates and the distal end (opposite the hinge) attaches to the actin filament and pulls on it. In this mechanism, actin interacts with myosin in two different ways: (1) at the active site where it activates a step in the hydrolysis of MgATP that frees the head to rotate; (2) at the distal end of myosin, where it forms the grip through which the rotating head pulls on the actin filament. The first interaction allows actin to initiate primary movement of the myosin head; the second directs the force and allows the movement of the head to be used for the sliding motion of the actin and myosin filaments during contraction. In this model, there are also two different energy transfers: one occurs in the transduction process itself when energy from hydrolysis is trapped as conformational distortion in the hinge region; the other occurs, reversibly, when actin and myosin form and then break the distal grip; in this second transfer there is no net energy change in the course of a cycle. A chemical mechanism is suggested to explain actin-activation of hydrolysis at the active site-hinge region.     

光响应曲线的指数改进模型与常用模型比较

光响应曲线的参数是研究植物生理状态的重要指标, 常用的光响应曲线模型无法准确地计算出光饱和点和最大净光合速率。该文利用光响应曲线新模型——指数改进模型、直角双曲线模型、直角双曲线修正模型、非直角双曲线模型和指数模型, 拟合高粱(Sorghum bicolor)、苋(Amaranthus tricolor)、大麦(Hordeum vulgare)和半夏(Pinellia ternata)的光响应曲线, 并随机选取部分数据进行检验, 得到了各模型计算出的主要生理参数, 并对这些数据进行了比较分析, 讨论了各模型之间的优缺点和准确性, 描述了C₃、C₄植物光响应的适宜性。结果表明, 基于C₃植物得到的指数改进模型和直角双曲线修正模型能较准确地计算出C₃、C₄植物饱和光强和最大净光合速率, 并在描述光响应曲线时比另外3个模型具有更高的精确性和适宜性。实验结果可为光响应曲线模型在C₃和C₄光合途径植物中的应用提供参考。     

Analysis of Hill slopes predicted by the four-ligand exponential model for a regulatory enzyme.

The four-ligand exponential model for a regulatory enzyme is described as it is applied to kinetic studies of yeast pyruvate kinase in which the concentrations of four ligands are systematically varied. The Hill slopes predicted by this model are calculated for the two situations in which the fourth ligand is either a substrate or an effector. It is shown that the individual terms that make up the expression for the Hill slope assist the interpretation of the observed behaviour in terms of the constants employed by the model.     

指数改进模型在大麦光合-CO2响应曲线中的适用性

光合-CO₂响应曲线是研究植物对CO₂响应的重要工具。常用的光合-CO₂响应曲线模型, 除直角双曲线修正模型外, 均无法准确地计算出CO₂饱和点和光合能力。该文利用新的指数改进模型拟合大麦(Hordeum vulgare)光合-CO₂响应曲线, 与直角双曲线修正模型、直角双曲线模型、指数模型、非直角双曲线模型进行比较, 并随机选取部分数据进行检验, 同时得到了各个光合-CO₂响应曲线模型的主要生理参数, 对这些数据进行了比较分析, 讨论了各模型之间的优缺点和准确合理性。结果表明, 指数改进模型在5个模型中具有最好的精确度和合理性, 能准确地描述出大麦的光合-CO₂响应曲线, 计算出CO₂饱和点为484 μmol∙mol^-1, 光合能力为25.9 μmol CO₂∙m^-2∙s^-1。     

Theoretical kinetic studies of models for binding myosin subfragment-1 to regulated actin: Hill model versus Geeves model

It was previously shown that a one-dimensional Ising model could successfully simulate the equilibrium binding of myosin S1 to regulated actin filaments (T. L. Hill, E. Eisenberg and L. Greene, Proc. Natl. Acad. Sci. U.S.A. 77:3186-3190, 1980). However, the time course of myosin S1 binding to regulated actin was thought to be incompatible with this model, and a three-state model was subsequently developed (D. F. McKillop and M. A. Geeves, Biophys. J. 65:693-701, 1993). A quantitative analysis of the predicted time course of myosin S1 binding to regulated actin, however, was never done for either model. Here we present the procedure for the theoretical evaluation of the time course of myosin S1 binding for both models and then show that 1) the Hill model can predict the "lag" in the binding of myosin S1 to regulated actin that is observed in the absence of Ca++ when S1 is in excess of actin, and 2) both models generate very similar families of binding curves when [S1]/[actin] is varied. This result shows that, just based on the equilibrium and pre-steady-state kinetic binding data alone, it is not possible to differentiate between the two models. Thus, the model of Hill et al. cannot be ruled out on the basis of existing pre-steady-state and equilibrium binding data. Physical mechanisms underlying the generation of the lag in the Hill model are discussed.     

Evaluation of a Hill based muscle model for the energy cost and efficiency of muscular contraction

The purpose of this study was to evaluate a Hill-based mathematical model of muscle energetics and to disclose inconsistencies in existing experimental data. For this purpose, we simulated iso-velocity contractions of mouse fast twitch EDL and slow twitch SOL fibers, and we compared the outcome to experimental results. The experimental results were extracted from two studies published in the literature, which were based on the same methodology but yielded different outcomes (B96 and B93). In the model, energy cost was modeled as the sum of heat and work. Parameters used to model heat rate were entirely independent of the experimental data-sets. Parameters describing the mechanical behavior were derived from both experimental studies. The model was found to accurately predict the muscle energetics and mechanical efficiency of data-set B96. The model could not, however, replicate the energetics and efficiency of SOL and EDL that were found in data-set B93. The model overestimated the shortening heat rate of EDL but, surprisingly, also the mechanical work rate for both muscles. This was surprising since mechanical characteristics of the model were derived directly from the experimental data. It was demonstrated that the inconsistencies in data-set B93 must have been due to some unexplained confounding artifact. It was concluded that the presented model of muscle energetics is valid for iso-velocity contractions of mammalian muscle since it accurately predicts experimental results of an independent data-set (B96). In addition, the model appeared to be helpful in revealing inconsistencies in a second data-set (B93).     

Simulating uterine contraction by using an electro-chemo-mechanical model

Contractions of uterine smooth muscle cells consist of a chain of physiological processes. These contractions provide the required force to expel the fetus from the uterus. The inclusion of these physiological processes is, therefore, imperative when studying uterine contractions. In this study, an electro-chemo-mechanical model to replicate the excitation, activation, and contraction of uterine smooth muscle cells is developed. The presented modeling strategy enables efficient integration of knowledge about physiological processes at the cellular level to the organ level. The model is implemented in a three-dimensional finite element setting to simulate uterus contraction during labor in response to electrical discharges generated by pacemaker cells and propagated within the myometrium via gap junctions. Important clinical factors, such as uterine electrical activity and intrauterine pressure, are predicted using this simulation. The predictions are in agreement with clinically measured data reported in the literature. A parameter study is also carried out to investigate the impact of physiologically related parameters on the uterine contractility.     

Analysis of exponential decay curves: a three-step scheme for computing exponents

A study of four techniques is examined to determine which method has the greater overall utility. An iterative least-squares error minimization method provides the greatest accuracy, while a linear algebraic method is accurate only for two-exponential data with small error. Consequently, a three-method sequential identification scheme is devised utilizing a graphical method, a transform method, and an iterative method. This scheme is successfully applied to physiological data containing three and four exponents.     

Cell versus protoplasm: revisionist history

Recent investigations give reason to question anew the historical status of the 'cell theory' as the ultimate driving force in the development of our understanding of life's processes at the most fundamental level. A revisitation of critical research papers and commentaries from the 19th Century shows that the disregarded (and historically maligned) 'protoplasmic theory of life' played a more deterministic role in the early advancement of knowledge on cell structure and function.     

A model for neuron firing with exponential decay of potential resulting in diffusion equations for probability density

A neuron is assumed to receive synaptic input of both excitatory and inhibitory natures from a large number of neighboring neurons; it is also assumed that a large number of such impulses are required to raise the neuron’s transmembrane potential to its threshold potential, at which it “fires” or “spikes”. The model is similar to one of Gerstein and Mandelbrot, except that in the absence of input an exponential decay of potential toward a resting level is introduced. Computational methods of determining the spike timeinterval distribution are discussed, along with the inverse problem of estimating the parameters of the system from observed spike time-interval data.