Antagonistic activity of one-joint muscles in three-dimensions using non-linear optimisation.

Non-linear optimisation, such as the type presented by R.D. Crowninshield and R.A. Brand [The prediction of forces in joint structures: Distribution of intersegmental resultants, Exercise Sports Sci. Rev. 9 (1981) 159], has been frequently used to obtain a unique set of muscle forces during human or animal movements. In the past, analytical solutions of this optimisation problem have been presented for single degree-of-freedom models, and planar models with a specific number of muscles and a defined musculoskeletal geometry. Results of these studies have been generalised to three-dimensional problems and for general formulations of the musculoskeletal geometry without corresponding proofs. Here, we extend the general solution of the above non-linear, constrained, planar optimisation problem to three-dimensional systems of arbitrary geometry. We show that there always exists a set of intersegmental moments for which the given static optimisation formulation will predict co-contraction of a pair of antagonistic muscles unless they are exact antagonists. Furthermore, we provide, for a given three-dimensional system consisting of single joint muscles, a method that describes all the possible joint moments that give co-contraction for a given pair of antagonistic muscles.

Analysis of the force-sharing problem using an optimization model.

In biomechanics, one frequently used approach for finding a unique set of muscle forces in the 'force-sharing problem' is to formulate and solve a non-linear optimization problem of the form: min phi(f)= summation operator (f(i)/omega(i))(alpha) subject to Af = b and f > or = 0. Solutions to this problem have typically been obtained numerically for complex models, or analytically for specific musculoskeletal geometries. Here, we present simple geometrical methods for analyzing the solution to this family of optimization problems for a general n-degrees-of-freedom musculoskeletal system. For example, it is shown that the moment-arm vectors of active (f(i) > 0) and passive (f(i) = 0) muscles are separated by a hyperplane through the origin of the moment-arm vector space. For the special case of a system with two degrees-of-freedom, solutions can be readily represented in graphical form. This allows for powerful interpretations of force-sharing calculated using optimization.

LL-Z1271alpha: an interleukin-1beta production inhibitor.

LL-Z1271alpha, a fungal metabolite, dose-dependently inhibited interleukin-1beta (IL-1beta) production in lipopolysaccharide (LPS)-stimulated human whole blood. Oral administration of LL-Z1271alpha to LPS-challenged mice caused significant lowering in the IL-1beta levels in peritoneal cavity. Data presented suggest that LL-Z1271alpha inhibits IL-1beta production by a novel mechanism as the inhibitory activity was not due to effects on caspase-1 (IL-1beta converting enzyme), the ATP-induced release mechanism or a lysosomotrophic effect.

Analytic analysis of the force sharing among synergistic muscles in one- and two-degree-of-freedom models.

Mathematical optimization of specific cost functions has been used in theoretical models to calculate individual muscle forces. Measurements of individual muscle forces and force sharing among individual muscles show an intensity-dependent, non-linear behavior. It has been demonstrated that the force sharing between the cat Gastrocnemius, Plantaris and Soleus shows distinct loops that change orientation systematically depending on the intensity of the movement. The purpose of this study was to prove whether or not static, non-linear optimization could inherently predict force sharing loops between agonistic muscles. Using joint moment data from a step cycle of cat locomotion, the forces in three cat ankle plantar flexors (Gastrocnemius, Plantaris and Soleus) were calculated using two popular optimization algorithms and two musculo-skeletal models. The two musculo-skeletal models included a one-degree-of-freedom model that considered the ankle joint exclusively and a two-degree-of-freedom model that included the ankle and the knee joint. The main conclusion of this study was that solutions of the one-degree-of-freedom model do not guarantee force-sharing loops, but the two-degree-of-freedom model predicts force-sharing loops independent of the specific values of the input parameters for the muscles and the musculo-skeletal geometry. The predicted force-sharing loops were found to be a direct result of the loops formed by the knee and ankle moments in a moment-moment graph.

Theoretical considerations on cocontraction of sets of agonistic and antagonistic muscles.

It is well known that static, non-linear minimization of the sum of the stress in muscles to a certain power cannot predict cocontraction of pairs of one-joint antagonistic muscles. In this report, we prove that for a single joint either all agonistic muscles cocontract or all are silent. For two-joint muscles, we show that lengthening and shortening of muscles corresponds closely to zero force and non-zero force states, respectively. This gives a new physiological interpretation of situations in which cocontraction of pairs of two-joint antagonistic muscles is predicted by these static non-linear optimization approaches.

Refolding and purification of a urokinase plasminogen activator fragment by chromatography.

A fragment of recombinant urokinase plasminogen activator (u-PA), was expressed in E. coli in the form of inclusion bodies. Purification and renaturation was achieved in a three-stage process. Capture of the inclusion bodies was achieved by coupling wash steps in Triton X-100 and urea with centrifugation. Solubilised inclusion bodies were then renatured by buffer exchange performed by size-exclusion chromatography (SEPROS). Use of size-exclusion media with higher fractionation ranges resulted in an increase in the recovery of u-PA activity, to a maximum fractionation range of Mr 10000-1500000 after which recovery is reduced, due to a low resolution between the refolded u-PA and denaturant. Fractions of refolded u-PA were concentrated using cation ion-exchange chromatography, which selectively binds correctly folded u-PA. The result is concentrated, active, homogeneous u-PA.

Cocontraction of pairs of antagonistic muscles: analytical solution for planar static nonlinear optimization approaches.

It has been stated in the literature that static, nonlinear optimization approaches cannot predict coactivation of pairs of antagonistic muscles; however, numerical solutions of such approaches have predicted coactivation of pairs of one-joint and multijoint antagonists. Analytical support for either finding is not available in the literature for systems containing more than one degree of freedom. The purpose of this study was to investigate analytically the possibility of cocontraction of pairs of antagonistic muscles using a static nonlinear optimization approach for a multidegree-of-freedom, two-dimensional system. Analytical solutions were found using the Karush-Kuhn-Tucker conditions, which were necessary and sufficient for optimality in this problem. The results show that cocontraction of pairs of one-joint antagonistic muscles is not possible, whereas cocontraction of pairs of multijoint antagonists is. These findings suggest that cocontraction of pairs of antagonistic muscles may be an "efficient" way to accomplish many movement tasks.

Predictions of antagonistic muscular activity using nonlinear optimization.

Optimization theory is used more often than any other method to predict individual muscle forces in human movement. One of the limitations frequently associated with optimization algorithms based on efficiency criteria is that they are thought to not provide solutions containing antagonistic muscular forces; however, it is well known that such forces exist. Since analytical solutions of nonlinear optimization algorithms involving multi-degree-of-freedom models containing multijoint muscles are not available, antagonistic behavior in such models is not well understood. The purpose of this investigation was to study antagonistic behavior of muscles analytically, using a three-degree-of-freedom model containing six one-joint and four two-joint muscles. We found that there is a set of general solutions for a nonlinear optimal design based on a minimal cost stress function that requires antagonistic muscular force to reach the optimal solution. This result depends on a system description involving multijoint muscles and contradicts earlier claims made in the biomechanics, physiology, and motor learning literature that consider antagonistic muscular activities inefficient.