Stochastic noise reduction upon complexification: positively correlated birth-death type systems

Deciphering noise amplification and reduction in open chemical reaction networks

The impact of fluctuations on the dynamical behaviour of complex biological systems is a longstanding issue, whose understanding would elucidate how evolutionary pressure tends to modulate intrinsic noise. Using the Itō stochastic differential equation formalism, we performed analytic and numerical analyses of model systems containing different molecular species in contact with the environment and interacting with each other through mass-action kinetics. For networks of zero deficiency, which admit a detailed- or complex-balanced steady state, all molecular species are uncorrelated and their Fano factors are Poissonian. Systems of higher deficiency have non-equilibrium steady states and non-zero reaction fluxes flowing between the complexes. When they model homo-oligomerization, the noise on each species is reduced when the flux flows from the oligomers of lowest to highest degree, and amplified otherwise. In the case of hetero-oligomerization systems, only the noise on the highest-degree species shows this behaviour.

Insights into noise modulation in oligomerization systems of increasing complexity

Understanding under which conditions the increase of systems complexity is evolutionarily advantageous, and how this trend is related to the modulation of the intrinsic noise, are fascinating issues of utmost importance for synthetic and systems biology. To get insights into these matters, we analyzed a series of chemical reaction networks with different topologies and complexity, described by mass-action kinetics. We showed, analytically and numerically, that the global level of fluctuations at the steady state, measured by the sum over all species of the Fano factors of the number of molecules, is directly related to the network's deficiency. For zero-deficiency systems, this sum is constant and equal to the rank of the network. For higher deficiencies, additional terms appear in the Fano factor sum, which are proportional to the net reaction fluxes between the molecular complexes. We showed that the system's global intrinsic noise is reduced when all fluxes flow from lower to higher degree oligomers, or equivalently, towards the species of higher complexity, whereas it is amplified when the fluxes are directed towards lower complexity species.

The Interplay between Feedback and Buffering in Cellular Homeostasis

Buffering, the use of reservoirs of molecules to maintain concentrations of key molecular species, and negative feedback are the primary known mechanisms for robust homeostatic regulation. To our knowledge, however, the fundamental principles behind their combined effect have not been elucidated. Here, we study the interplay between buffering and negative feedback in the context of cellular homeostasis. We show that negative feedback counteracts slow-changing disturbances, whereas buffering counteracts fast-changing disturbances. Furthermore, feedback and buffering have limitations that create trade-offs for regulation: instability in the case of feedback and molecular noise in the case of buffering. However, because buffering stabilizes feedback and feedback attenuates noise from slower-acting buffering, their combined effect on homeostasis can be synergistic. These effects can be explained within a traditional control theory framework and are consistent with experimental observations of both ATP homeostasis and pH regulation in vivo. These principles are critical for studying robustness and homeostasis in biology and biotechnology.

Is the Cell Nucleus a Necessary Component in Precise Temporal Patterning?

One of the functions of the cell nucleus is to help regulate gene expression by controlling molecular traffic across the nuclear envelope. Here we investigate, via stochastic simulation, what effects, if any, does segregation of a system into the nuclear and cytoplasmic compartments have on the stochastic properties of a motif with a negative feedback. One of the effects of the nuclear barrier is to delay the nuclear protein concentration, allowing it to behave in a switch-like manner. We found that this delay, defined as the time for the nuclear protein concentration to reach a certain threshold, has an extremely narrow distribution. To show this, we considered two models. In the first one, the proteins could diffuse freely from cytoplasm to nucleus (simple model); and in the second one, the proteins required assistance from a special class of proteins called importins. For each model, we generated fifty parameter sets, chosen such that the temporal profiles they effectuated were very similar, and whose average threshold time was approximately 150 minutes. The standard deviation of the threshold times computed over one hundred realizations were found to be between 1.8 and 7.16 minutes across both models. To see whether a genetic motif in a prokaryotic cell can achieve this degree of precision, we also simulated five variations on the coherent feed-forward motif (CFFM), three of which contained a negative feedback. We found that the performance of these motifs was nowhere near as impressive as the one found in the eukaryotic cell; the best standard deviation was 6.6 minutes. We argue that the significance of these results, the fact and necessity of spatio-temporal precision in the developmental stages of eukaryotes, and the absence of such a precision in prokaryotes, all suggest that the nucleus has evolved, in part, under the selective pressure to achieve highly predictable phenotypes.