Stochasticity is inherent in biochemical systems. Noise can come from internal sources
such as the random motion and reactions of molecules, and external sources such as
environmental fluctuations. The main purpose of this thesis is to study how fluctuations
propagate in biological systems.
First, we focus on how a signaling molecule called a ligand searches for and binds
to its target (receptor). There exist membrane proteins that can bind to the ligand
molecule and localize it near receptors, affecting the association between it and the
receptor. Our analysis shows that although the membrane protein can concentrate
the ligand molecule near the receptor surface, the membrane protein has to pass the
localized ligand molecule to the receptor fast enough, in order to enhance signaling.
Otherwise, the membrane protein inhibits signaling. Moreover, we also study the effect
of localization on signal specificity. In particular, we discuss how the membrane proteins
bind to ligand molecules and distribute them to different downstream signaling
Upon ligand binding to receptors, bound receptors can initiate the downstream
network, which may finally lead to gene expression. We then study how the noise from
the initiation step of transcription propagates in the elongation step. Elongation can
be interrupted by the pauses of the transcription complex on the DNA sequence. We
give a condition under which the pause of the transcription complex can cause bursts
of mRNA production.
Finally, we use stochastic simulations to study dorsal-ventral patterning in Drosophila
numerically. Our results indicate that a feedback loop can stabilize the determination
of the amnioserosa boundary. We then propose a detailed single cell system for the
downstream network in nuclei. Our analysis of time scales of reactions and molecular
transport shows the phosphorylation of Mad and transport of mRNA across the nuclear
membrane are the major limiting steps in the signal transduction pathway. Simulations
results show noises are amplified at these limiting steps.