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Foreign body reaction reflects the integration between biomaterials and host cells. At the implantation microenvironment, macrophages usually fuse into multinuclear cells, also known as foreign body giant cells, to respond to the biomaterial implants.

To understand the biomaterial-induced macrophage fusion, we examined whether biomaterial alone can initiate and control the fusion rate without exogenous cytokines and chemicals. We introduced a collagen-based 3D matrix to embed Raw We found the biomaterial-stimuli interacted regional macrophages and altered the overall fusogenic protein expressions to regulate the macrophage fusion rate.

The fusion rate could be altered by modulating the cell-matrix and cell-cell adhesions. The fused macrophage morphologies, the nuclei number in the fused macrophage, and the fusion rates were matrix dependent.

These results suggest that the biomaterial-derived stimuli exert similar functions as cytokines to alter the competency of macrophage fusion as well as their drug sensitivity in the biomaterial implanted tissue environment. Furthermore, this in vitro 3D-matrix model has the potential to serve as a toolbox to predict the host tissue response on implanted biomaterials. Macrophages are the main players in the foreign body reaction. Three critical macrophage responses have been identified in host-material interactions: adhesion, activation, and fusion 1.

Macrophages perform adhesion on the material surfaces via adhesion ligand-receptor interactions. Due to biomaterial physiochemical properties i. These cell-material interactions can trigger intracellular signals to promote macrophage activation. The adherent macrophages perform activation and fusion to form different subtypes of macrophages or multinucleated cells MNC.

MNC cells are the most distinctive features surrounding biomaterials and are considered to perform more enhanced functions than macrophages 3.

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Different from the MNCs observed in the skeletal muscle, placentas, and bones in certain healthy tissues 45they are part of the innate immune system to battle with foreign pathogens and intrusive materials.

Similar MNCs are also observed in the pathological lesions such tuberculosis, atherosclerosis, and cancer. These stimuli convert macrophage into fusion-competent macrophages. These cells adhere to each other and rearrange their cytoskeletons F-actin via integrins for fusion 12 Finally, the arrangement of cytoskeleton regulates the interchanges of intracellular and membrane content, and leads to multinucleation This macrophage fusion model implied that the macrophage fusion competency requires chemical fusogenic stimuli such as cytokines to regulate integrins expression during the process.

However, integrins also function as mechanical sensor to respond to the physical property of biomaterial Hence, this chemicals-induced macrophage fusion model is not sufficient to explain biomaterials-induced macrophage fusion. Although implanted-biomaterials are the main cause of MNCs formation during the foreign body reaction, the mechanism of the biomaterial-induced fusogenic stimuli remains unclear.

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Many researchers consider cytokines from macrophages or chemical properties from biomaterials as the major source of fusogenic stimuli. Even though studies were attempted to emphasize the alteration of biomaterial mechanical properties, cytokines were still included in the culture medium to promote the macrophage fusion.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

It only takes a minute to sign up. I'm interested in possibly wide classification of fusions of real matrix properties. I'll start from the example. In this case fusion of two properties leads to the interesting property on his own, which has even a distinct name.

Question: what are the other known cases of fusions of matrix properties which lead to a property which is enough interesting to give it a new name? Are there other similar cases? Can they always probably not be easily proved as in the case above?

Edit after two days Does nobody have any idea? The example listed by me is the solely example for theory of matrices and their properties? It would be interesting to have such a list to see clearly connections which not always are visible at the first sight Sign up to join this community.

The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Fusion of matrix properties Ask Question. Asked 3 years, 11 months ago.

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Email Required, but never shown. Featured on Meta. Responding to the Lavender Letter and commitments moving forward. Related 4. Hot Network Questions. Question feed. Mathematics Stack Exchange works best with JavaScript enabled.We consider the fusion algebras arising in e.

Wess—Zumino—Witten conformal field theories, affine Kac—Moody algebras at positive integer level, and quantum groups at roots of unity. Using properties of the modular matrix Swe find small sets of primary fields equivalently, sets of highest weights which can be identified with the variables of a polynomial realization of the A r fusion algebra at level k. We prove that for many choices of rank r and level kthe number of these variables is the minimum possible, and we conjecture that it is in fact minimal for most r and k.

We also find new, systematic sources of zeros in the modular matrix S. In addition, we obtain a formula relating the entries of S at fixed points, to entries of S at smaller ranks and levels. Finally, we identify the number fields generated over the rationals by the entries of Sand by the fusion Verlinde eigenvalues.

This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. E-mail: m. Reprints and Permissions. Gannon, T. On Fusion Algebras and Modular Matrices. Comm Math Phys1—22 Download citation. Issue Date : September Search SpringerLink Search.

fusion algebra and fusing matrices

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Wess—Zumino—Witten conformal field theories, affine Kac—Moody algebras at positive integer level, and quantum groups at roots of unity.

Using properties of the modular matrix S, we find small sets of primary fields equivalently, sets of highest weights which can be identified with the variables of a polynomial realization of the A r fusion algebra at level k. We prove that for many choices of rank r and level k, the number of these variables is the minimum possible, and we conjecture that it is in fact minimal for most r and k.

We also find new, systematic sources of zeros in the modular matrix S. In addition, we obtain a formula relating the entries of S at fixed points, to entries of S at smaller ranks and levels.

Finally, we identify the number fields generated over the rationals by the entries of S, and by the fusion Verlinde eigenvalues. Communications in Mathematical Physics — Springer Journals. Enjoy affordable access to over 18 million articles from more than 15, peer-reviewed journals.

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On Fusion Algebras and Modular Matrices

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fusion algebra and fusing matrices

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