Abstract
Then, two different parameter identification techniques are presented for the proposed models. One is based on a least squares procedure, which treats the signals provided by a high gain observer; the other one is based on a Mixed Extended Kalman Filter. Prior to the estimation phase, identifiability and sensitivity analyses are used to determine which parameters can be and/or should be estimated. The procedures are tested and compared by means of data obtained by in silico experiments.
TopBackground
When in 1953 James Watson and Francis Crick described the DNA double helix, its structure seemed so solid and stable that research on notions such as DNA damage and repair was initially hindered (Friedberg, 2003). Actually, DNA is continuously exposed to several types of damage. The most relevant kind of DNA damage is helix-distorting lesions throughout the genome. These lesions are generated by different causes, including the formation of DNA adducts after administration of common drugs used in cancer therapy (Fayad et al., 2009), such as cisplatin and other platinum-based compounds. Another type of damage occurs when internal or environmental factors, such as exposition to radiation, cause breakages in both strands of the DNA helix. This event, called double strand breaks (DSB) can be lethal to the whole organism if not properly treated, since they can induce cancer and hereditary diseases (Bolderson et al., 2009).
Cells react to DNA damage in three basic ways. If the damage level is very low it is tolerated: the cell has specific structures to operate DNA replication and transcription even in presence of lesions. If the damage is more serious, it is repaired: the cellular growth is arrested (cell cycle arrest) and one of the several repair mechanisms available is started. If the damage level is too high to be effectively treated, apoptosis is started: this is a programmed death through which the cell eliminates itself from a population that might otherwise suffer the serious pathological consequences of the transmission of disrupted genetic material (Letai et al., 2008).
Sensing DNA damages is a very complex process, which involves a large number of pathways. A genetic network built upon the p53 gene and protein plays a key role in this process. First discovered in 1979, the actual tumor suppressing function of p53 was clarified only twenty years later (Vogelstein et al., 2000). The fact that DSBs induce an increase in p53 levels which, in turn, induce apoptosis has been demonstrated for the first time by Yonish-Rouach et al. (1991), and it is now generally accepted (Meek, 2009).
Among a number of different mechanisms for DNA repair, in this chapter, we consider nucleotide excision repair (NER). It is a versatile DNA repair mechanism that enables cells to eliminate helix-distorting lesions throughout the genome (Cleaver et al., 2009).
DNA damage is investigated by means of dynamic mathematical modeling, in the framework of systems biology. Mathematical modeling of biological systems often require the judicious choice of parameters and variables, which remains a challenging problem.
Key Terms in this Chapter
DNA Repair: Refers to a collection of processes by which a cell identifies and corrects damage to the DNA molecules that encode its genome. DNA repair process is constantly active as it responds to damage in the DNA structure. When normal repair processes fail, and when cellular apoptosis does not take effect, “Irreparable DNA Damage” can occur, including double-strand breaks and DNA cross linkages
State Observer: In control theory, is a system that models a real system in order to provide an estimate of its internal state, given measurements of the input and output of the real system. An asymptotic observer is an observer that converges to the internal state of the system for time that goes to infinity.
Ordinary Differential Equation (ODE): A relation that contains functions of only one independent variable, and one or more of its derivatives with respect to that variable.
Extended Kalman Filter: An efficient recursive filter that estimates the state of a non linear dynamic system from a series of noisy measurements.
State Estimation: Concerns the problem of estimating the time behavior of the internal state of a process which is not directly measurable or accessible.
Identifiability Analysis: Concerned with whether the unknown parameters can be uniquely determined from perfect, noise-free, and continuous data.
Nucleotide Excision Repair (NER): A DNA repair mechanism by cell can prevent unwanted mutations by removing the vast majority of UV-induced DNA damage (mostly in the form of thymine dimers and 6-4-photoproducts).
Sensitivity analysis: The study of how uncertainty in the output of a model (numerical or otherwise) can be apportioned to different sources of uncertainty in the model input.
Hybrid Model: In control theory, is a dynamical system with interacting continuous-time dynamics (modeled, for example, by differential equations) and discrete-event dynamics (modeled, for example, by automata).