Is the future biology Shakespearean or Newtonian?

The effect of coupled stochastic processes in a two-state biochemical switch

Cell signaling pathways consist of multiple connections of different types of gene, mRNA and protein networks. It is not a trivial task to follow the signals flowing through these networks. The difficulty comes from considering the entire biological structure as a single network without breaking it into connected modules. The study of these networks simplifies if the complex system is reduced to a hierarchy of interconnected modules. Out of many potential modules, a specific one, namely the Goldbeter-Koshland switch, was encountered by the authors during their study of the Mammalian Heat Shock Response Network (MHSRN) where the switch acts as a stress sensor. Usually, only the steady state behavior of the switch is studied, in which the phosphorylated protein is given as a function of the enzyme concentration. Experimental results show that the heat shock response is still present 20 h after the temperature stress had ended. Thus, it is useful to analyze the transient behavior of the switch that couples the environment to the MHSRN. A stochastic model for the switch is proposed using the Master Equation which is subsequently transformed into an equation for the factorial cumulant generating function. This generating function can be easily read from a graphical representation of the stochastic switch. The second order approximation of the equation for the factorial cumulant generating function is solved and the time dependence of the transient regime of the mean and standard deviation is readily obtained. Using the mean and standard deviation of the switch's output as a function of the stochastic input signals that represent the environment, we classify the switches according to different criteria. The switches differ by the numerical values of the parameters that characterize the switch's chemical reactions. The classifying criteria will distinguish the switches by the levels of the response for a given transition time and by the sensitivity of the response to the enzyme levels. It is also found that the environment can drastically change the response of the switch, which has important biological consequences.

Heat shock response in CHO mammalian cells is controlled by a nonlinear stochastic process

In many biological systems, the interactions that describe the coupling between different units in a genetic network are nonlinear and stochastic. We study the interplay between stochasticity and nonlinearity using the responses of Chinese hamster ovary (CHO) mammalian cells to different temperature shocks. The experimental data show that the mean value response of a cell population can be described by a mathematical expression (empirical law) which is valid for a large range of heat shock conditions. A nonlinear stochastic theoretical model was developed that explains the empirical law for the mean response. Moreover, the theoretical model predicts a specific biological probability distribution of responses for a cell population. The prediction was experimentally confirmed by measurements at the single-cell level. The computational approach can be used to study other nonlinear stochastic biological phenomena.

The structure of an unknown biological system is uncovered by experimentally perturbing the system with a series of input signals. The response to these perturbations is measured as output signals. Then, the mathematical relation between the input and the output signals constitutes a model for the system. As a result, a classification of biological molecular networks can be devised using their input–output functional relation. This article studies the input–output functional form for the response to heat shocks in mammalian cells. The Chinese hamster ovary (CHO) mammalian cells were perturbed with a series of heat pulses of precise duration and temperature. The experimental data, taken at the single-cell level, revealed a simple and precise mathematical law for the time evolution of the heat shock response. Parameters of the mathematical law can be experimentally measured and can be used by heat shock biologists to classify the heat shock response in different experimental conditions. Since the response to heat shock is the outcome of a transcriptional factor control, it is highly probable that the empirical law is valid for other biological systems. The mathematical model explains not only the mean value of the response but also the time evolution of its probability distribution in a cell population.