关于Wnt路径的结构性质,其稳定状态及其非关联的交换代数的一些结果

The gene encoding the main signaling molecules of the Wnt signaling pathways (the Wnt proteins) was discovered almost four decades ago by Nüsslein-Volhard and Wieschaus. They identified and originally named the gene "wingless" (wg) after a phenotype discovered during their landmark genetic screen in Drosophila for body pattern defects. At around the same time, another researcher named Harold Varmus found that a murine tumor virus activates the mammalian wg homolog, Int-1, which...

Wnt is a zygotic effect gene that is expressed during very early embryonic development. It regulates various processes in animals starting from early development through the adult stage, such as organogenesis in the embryo and maintenance of neuronal and blood stem cells. Wnt proteins can induce a wide variety of intracellular pathways depending upon the specific abilities of different Wnt ligands to form a complex with shared and cognate receptors in the presence of different co-receptors. The...

Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:

A linear circuit is characterized by its output having a direct proportionality to its input, adhering to the linearity property, which encompasses the principles of homogeneity (scaling) and additivity. Homogeneity dictates that when the input, also referred to as the excitation, is multiplied by a constant factor, the output, known as the response, is correspondingly scaled by the same constant factor. For instance, if the current is multiplied by a constant 'k,' the voltage likewise...

In Signal Flow Graph (SFG) algebra, the value a node represents is determined by the sum of all signals entering that node. This summed value is then transmitted through every branch leaving the node, making the SFG a powerful tool for visualizing and analyzing control systems.
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...