Muscle is a hierarchical composite material, and that architecture is the key to the new framework. At the smallest level sit myofibrils, the contractile protein threads built from repeating sarcomeres, each containing Z-disks, A-bands, and H-bands. Myofibrils bundle together into muscle fibers, wrapped in a thin collagenous sheath called the endomysium. Fibers in turn group into bundles encased in a thicker connective tissue layer, the perimysium. Connective tissues form a continuous network that reinforces the muscle and transmits force between fibers and bundles. Because each level contributes to the whole, the team hypothesized that macroscopic texture could be quantitatively predicted if the mechanical properties of the microscopic components and their volume fractions were known.

Testing that hypothesis required measuring mechanics at scales where no conventional test can operate. The researchers turned to atomic force microscopy, or AFM, a technique in which an ultrasharp silicon nitride tip, with a radius of just a few nanometers, is pressed against a sample while the force of contact is recorded. Fitting the resulting force-indentation curves with the Derjaguin-Muller-Toporov contact model, which accounts for both elastic deformation and van der Waals adhesion, yields the local Young’s modulus. The team applied this to myofibrils isolated from pork tenderloin, beef tenderloin, and chicken breast, as well as to extracted endomysium and perimysium, measuring both dried and hydrated samples. Hydration mattered enormously: dried myofibrils showed moduli in the gigapascal range, while wet samples dropped by one to two orders of magnitude into the tens of megapascals, a reminder that data from dried biological materials can have limited relevance to real food.

The nanoscale maps revealed striking patterns. In raw myofibrils, stiffness followed a consistent spatial order across all three species: the Z-disk was stiffest, the A-band intermediate, and the H-band softest, echoing earlier AFM studies on rabbit and rat muscle. Species differences were also clear. In the hydrated raw state, pork myofibrils were the stiffest at roughly 50 megapascals, beef followed at about 47, and chicken was softest at around 34. Cooking reshuffled the dried-state landscape, erasing the species-specific sarcomere structures as proteins denatured and aggregated, but the wet cooked myofibrils preserved the same hierarchy, with pork highest at about 75 megapascals and chicken lowest at about 45. The collagenous membranes told their own story: the perimysium was consistently slightly stiffer than the endomysium, and both stiffened after cooking, likely through heat-induced collagen denaturation and aggregation.

With the microscopic inputs in hand, the team built a two-level analytical model based on the classical Reuss series scheme from composite mechanics. Under transverse compression, a single muscle fiber was treated as myofibrils embedded in an endomysium matrix, and a fiber bundle as equivalent fibers in series with the perimysium. The effective modulus of each level is the volume-fraction-weighted combination of its phases, with the phase fractions measured from scanning electron microscope images of fiber cross-sections. Running the numbers, the model predicted bundle moduli that ranked pork highest, beef intermediate, and chicken lowest, and predicted a significant increase after cooking, trends that mirror the myofibril data feeding into it. Notably, the predicted bundle modulus correlated strongly with the myofibril and endomysium moduli but not with the perimysium modulus, suggesting that in this low-connective-tissue muscle system, the bundle stiffness is governed primarily by the fibers themselves.

The validation step came from macroscopic compression tests on cubes of raw and cooked meat using a texture analyzer, with the compression axis carefully aligned perpendicular to the muscle fibers to match the orientation of the nanoscale measurements. The stress-strain curves were strongly nonlinear, stiffening as strain increased, so the team fitted them with two constitutive models. A combined logarithmic-polynomial hyperelastic model, originally developed for liver tissue, captured the general shape but showed systematic deviations, particularly for chicken. A logistic model, adapted from work on passive spinal muscle mechanics, performed far better, with coefficients of determination above 0.997 for every sample. Its parameters carried clear physical meaning: an initial modulus reflecting the relaxed response of the microscopic components, a hardening increment describing nonlinear stiffening, a hardening rate, and a critical strain at which stiffening accelerates.

The correlation analysis tied the scales together. The logistic model’s initial modulus correlated strongly with the linear modulus measured from the first five percent of strain, and both correlated with the multiscale model’s predicted bundle modulus and, through it, with the myofibril and endomysium properties. In other words, the initial stiffness of a piece of meat is largely written into its myofibrils. The nonlinear parameters told a different story. Beef showed the largest hardening increment, which the authors attribute to its denser network of mature collagen crosslinks and the pronounced nonlinear hardening behavior of the perimysium observed in the AFM force curves, potentially explaining why beef is chewier than pork or chicken. Bound water content correlated positively with the initial stiffness parameters, while free water correlated negatively with the hardening rate, hinting that water acts as a lubricant that smooths the structural response under compression.

The authors are careful about scope. The AFM-derived moduli of the isolated connective tissues represent effective properties of collagen-rich fractions rather than absolute in situ values, and the constitutive models describe rate-independent behavior at a single loading speed rather than the full viscoelastic response of muscle. Validation was performed on three relatively lean, low-connective-tissue muscles, so extending the framework to collagen-rich cuts such as tendon-laden muscles remains future work. The link between micro- and macroscale is also framed as a parametric correlation rather than a direct numerical equivalence, with microscopic stiffness serving as the physical foundation for macroscopic structural stiffness rather than substituting for it one-to-one.

Even with those caveats, the implications are broad. The study delivers a quantitative, bottom-up route from nanoscale protein mechanics to the texture a consumer actually perceives, clarifying which hierarchical structures dominate which aspects of the mechanical response. For the booming plant-based meat industry, where replicating the fibrous architecture and anisotropic mechanics of real muscle remains the central challenge, the framework offers something like a design blueprint: a way to specify the stiffness and volume fraction of the protein and matrix phases needed to hit a target bite. More broadly, it demonstrates that with enough care at the nanoscale, even something as familiar and complex as the texture of dinner can be reduced to physics you can measure, model, and ultimately engineer.

Subject of Research: Multiscale mechanical modeling linking AFM nanomechanics of myofibrils and connective tissue to the macroscopic compressive texture of meat

Article Title: Predicting the compression mechanical properties of muscle from microscale indentation mechanics using multiscale mechanical models

Article References: Zhao, C., Jiang, R., Zhang, Z., Jia, J., Nishinari, K., & Yang, N. (2026). Predicting the compression mechanical properties of muscle from microscale indentation mechanics using multiscale mechanical models. Current Research in Food Science, Article 101577. https://doi.org/10.1016/j.crfs.2026.101577

Image Credits: AI Generated

DOI: 10.1016/j.crfs.2026.101577

Keywords: meat texture, atomic force microscopy, myofibrils, multiscale modeling, connective tissue, food science, compression mechanics, plant-based meat, collagen, constitutive models, Reuss model, nanoindentation