Narrow Results

The study of diseases such as cancer requires the modeling of gene regulations and the loss of control associated with it. Prior work has shown that the genetic alterations in the system can be suitably modeled using different fault models (like stuck-at faults) in the Boolean Network paradigm. By studying the dynamics of the original and the faulty BN, it is possible to design intervention strategies which could drive the system from a diseased state to a less harmful one. In this paper, the method of detecting faults along with the intervention design demonstrated on a couple of real biological pathways (DNA damage pathways and osmotic stress response pathways).

Many tissues undergo a steady turnover, where cell divisions are on average balanced with cell deaths. Cell fate decisions such as stem cell (SC) differentiations, proliferations, or differentiated cell (DC) deaths, may be controlled by cell populations through cell-to-cell signaling. Here, we examine a class of mathematical models of turnover in SC lineages to understand engineering design principles of control (feedback) loops, that may operate in such systems. By using ordinary differential equations that describe the co-dynamics of SCs and DCs, we study the effect of different types of mutations that interfere with feedback present within cellular networks. For instance, we find that mutants that do not participate in feedback are less dangerous in the sense that they will not rise from low numbers, whereas mutants that do not respond to feedback signals could rise and replace the wild-type population. Additionally, we asked if different feedback networks can have different degrees of resilience against such mutations. We found that all minimal networks, that is networks consisting of exactly one feedback loop that is sufficient for homeostatic stability of the wild-type population, are equally vulnerable. Mutants with a weakened/eliminated feedback parameter might expand from lower numbers and either enter unlimited growth or reach an equilibrium with an increased number of SCs and DCs. Therefore, from an evolutionary viewpoint, it appears advantageous to combine feedback loops, creating redundant feedback networks. Interestingly, from an engineering prospective, not all such redundant systems are equally resilient. For some of them, any mutation that weakens/eliminates one of the loops will lead to a population growth of SCs. For others, the population of SCs can actually shrink as a result of “cutting” one of the loops, thus slowing down further unwanted transformations.

A closed-loop drug delivery system is constructed in which external negative feedback is used to regulate the dynamics of a time-delayed negative feedback mechanism which regulates hormone concentration. This results in a control system composed of two time-delayed negative feedback loops arranged in parallel. Stability regions in parameter space and the location of steady states are determined for the cases when the time delays are equal and when they are unequal. The advantage of this paradigm for drug delivery is that both the steady states and stability of the multiple loop feedback system can be influenced in a precisely controllable manner.

Biological systems are complex systems with feedback. Very often the scales for the dynamics of the system and the dynamics of the feedback are very different. The mathematical tool used to deal with this different time scales is Tikhonov's theorem which permits to reduce the complexity of the system through suitable approximations. This paper presents a theory of two time scales feedback systems phrased in the language of Nonstandard Analysis (NSA), introduced in the sixties by A. Robinson. Our opinion is that this presentation is more understandable for a non-mathematicaly trained reader than the classical one. Th paper is entirely self contained. A short but comprehensive tutorial on NSA is provided and precise definitions for concepts from systems theory are given.