[Topics for basic research regarding osteoclasts and Wnt signals in ASBMR 2018.]

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...

Basic signal operations include time reversal, time scaling, time shifting, and amplitude transformations. These operations are fundamental in signal processing and analysis.
Time Reversal mirrors a continuous-time signal about the vertical axis at t=0. This is achieved by substituting t with −t. For example, if a signal x(t) is considered, the time-reversed signal is x(−t). This operation can be graphically represented, showing the mirrored signal.

Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...

The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...

The Fourier Transform is a pivotal mathematical tool in signal processing, enabling the transformation of time-domain signals into their frequency-domain representations. Among the numerous elements within this domain, certain functions like the sinc function, delta function, and exponential signals hold significant importance due to their unique properties and implications.
The sinc function, defined as sinc(x) = sin(πx)/(πx), is particularly notable for its symmetry and behavior at...