The communication within a cell is taken care of by an intriguing system of ‘messages in molecular bottles’ known as intracellular signaling. This signaling system is coupled to other biochemical reaction systems that regulate specific intracellular processes. For a good understanding of the biochemical reaction networks involved in signaling and regulation, molecular biological techniques are essential. These techniques provide valuable information about the individual chemical reactions and interactions that constitute the reaction network. However, even with this knowledge, the complex interplay between those reactions cannot fully be understood. Therefore, there is an increasing demand for mathematical modeling and simulations to help to unravel the secrets of intracellular signaling and regulation. The most commonly used methods for mathematical modeling of biochemical reaction systems are deterministic. In such methods, differential equations are used to describe the average behavior of a reaction system. These methods are suitable for relatively large systems. However, of some types of molecules that are involved in intracellular signaling and regulation, only several hundred or a few thousand copies are present in a cell. In those cases, random events (intrinsic noise) may play an important role and so-called stochastic modeling methods may provide a better description of the behavior of the reaction network. Such stochastic methods take into account that from an initial state various other states can be visited subsequently. In this dissertation, we investigate biochemical reaction systems for which both deterministic and stochastic models are constructed. For those systems, we study how the behavior of the stochastic model depends on the total number of molecules. In addition, we relate this dependency to the behavior of the corresponding deterministic model. Depending on the topology of the reaction system, we use an analytical or a numerical approach to study the stochastic model. In our analytical approach, we introduce a novel framework, based on a potential function, similar to potential functions in thermodynamics. This function does not only provide more information about the stochastic model; it also provides a means for a straightforward comparison between the stochastic and the deterministic model. This provides more insight into the applicability of both models under different circumstances. In particular, we can determine how the behavior of the stochastic model depends on the number of molecules in the system. In general, with an increasing numbers of molecules, the behavior of the stochastic model tends to that of the deterministic model. The rate at which the former tends to the latter depends on the potential function for the reaction network. For various properties of interest we can find an analytical expression for this rate. Although the analytical approach provides more detailed information, our numerical approach can be applied to a broader class of reaction systems. In this approach, we explicitly compute the probability to find the system in a given state, as a function of time. With increasing numbers of molecules, also the total number of states grows. This causes an increase in computation time. However, by using a parallel computer cluster the computation time can be reduced. In this dissertation, we introduce a program that can perform such parallel computation. This program also deals efficiently with the limited number of possible state transitions in biochemical reaction networks. As a result, our program can compute the stochastic dynamics of relatively large reaction systems. Both our approaches provide novel tools to obtain insight into the behavior of intracellular signaling and regulation. In this dissertation we apply our methods on both conceptual and real-life reaction systems. We deal with three types of systems: closed elementary systems, oscillatory systems and bistable (or multistable) systems. In this context, the notion closed systems is used for elementary systems that do not exchange materials with their surroundings. For such a system, the potential function has only one local minimum. The corresponding deterministic model predicts that the system converges to the state with the lowest potential. On the other hand, if the number of molecules is small, the stochastic model predicts that there is still a reasonable chance to find the system in states with a higher potential. Oscillatory systems are examples of systems for which the potential function cannot be defined. Nevertheless, we can still apply our numerical methods on such systems. As an example, we have studied a MAPK-network. For this network, both the deterministic and the stochastic model predict a sustained oscillation. However, there is a clear difference if we would apply those models to predict the behavior of the MAPK-network in a group of uncoupled cells. If, initially, all cells oscillate in phase, the deterministic model predicts that they willremain oscillating in a synchronous fashion. On the other hand, the stochastic model predicts that they will move out of phase. Such a desynchronization is indeed known to occur in vitro for some oscillatory systems. The bistable reaction systems that are dealt with in this dissertation allow the formulation of a potential function. In those cases, the potential function has two local minima. According to the predictions of the deterministic model, the system converges to the nearest local minimum. Contrastingly, the stochastic model predicts that the system can move to either local minimum of the potential function. Moreover, in the stochastic model, there is still a possibility to switch from one ‘stable’ state (i.e., a state with a local minimum of the potential function) to the other. In a biological context, such switching events are often unwanted. However, the occurrence of such events can be limited by increasing the number of molecules at the cost of cellular resources. With our methods it is possible to study how the number of molecules is optimized in specific real-life networks.
|Qualification||Doctor of Philosophy|
|Award date||14 Apr 2010|
|Place of Publication||Eindhoven|
|Publication status||Published - 2010|