Amyloid fibrils are aggregates of misfolded proteins.  Under most circumstances, misfolded proteins are either refolded by chaperone proteins or degraded by the proteasome. However, in the case of a mutation or a disease, these proteins can accumulate to form large clusters and often further assemble to form elongated fibers, called fibrils. 
Amyloid deposits were observed as early as 1639 in the liver and the spleen.   In 1854, Rudolph Virchow performed iodine staining,...

If acceleration as a function of time is known, then velocity and position functions can be derived using integral calculus. For constant acceleration, the integral equations refer to the first and second kinematic equations for velocity and position functions, respectively.
Consider an example to calculate the velocity and position from the acceleration function. A motorboat is traveling at a constant velocity of 5.0 m/s when it starts to decelerate to arrive at the dock. Its acceleration is...

Fibril-associated collagens are a type of collagens present in the extracellular matrix with interrupted triple helices or FACIT (Fibril-associated collagens interrupted triple-helices). FACIT help connect and attach the collagen fibrils with each other as well as with other proteins of the extracellular matrix.
For example, the type II collagen fibrils in cartilage have covalently bound type IX fibril-associated collagens at regular intervals. Other types of fibril-associated collagens are...

Integration by parts is a fundamental technique in calculus for evaluating integrals involving the product of two functions. It is particularly useful when direct integration is not feasible. The method is based on the product rule for differentiation, which states that the derivative of a product equals the derivative of the first function times the second, plus the first function times the derivative of the second. By integrating this identity and rearranging terms, the integration by parts...

Definite integrals involving the product of two functions over a fixed interval can be evaluated using integration by parts. This method rewrites the integral as the difference of a product evaluated at the endpoints and a remaining definite integral that is often simpler to compute.A representative example is the definite integral of the inverse tangent function. Since there is no direct integration formula for arctan ⁡x, the integrand is rewritten as a product of arctan⁡ x and the...