Martijn J. Moné

Systems biology towards life in silico: mathematics of the control of living cells

Systems Biology is the science that aims to understand how biological function absent from macromolecules in isolation, arises when they are components of their system. Dedicated to the memory of Reinhart Heinrich, this paper discusses the origin and evolution of the new part of systems biology that relates to metabolic and signal-transduction pathways and extends mathematical biology so as to address postgenomic experimental reality. Various approaches to modeling the dynamics generated by metabolic and signal-transduction pathways are compared. The silicon cell approach aims to describe the intracellular network of interest precisely, by numerically integrating the precise rate equations that characterize the ways macromolecules’ interact with each other. The non-equilibrium thermodynamic or ‘lin–log’ approach approximates the enzyme rate equations in terms of linear functions of the logarithms of the concentrations. Biochemical Systems Analysis approximates in terms of power laws. Importantly all these approaches link system behavior to molecular interaction properties. The latter two do this less precisely but enable analytical solutions. By limiting the questions asked, to optimal flux patterns, or to control of fluxes and concentrations around the (patho)physiological state, Flux Balance Analysis and Metabolic/Hierarchical Control Analysis again enable analytical solutions. Both the silicon cell approach and Metabolic/Hierarchical Control Analysis are able to highlight where and how system function derives from molecular interactions. The latter approach has also discovered a set of fundamental principles underlying the control of biological systems. The new law that relates concentration control to control by time is illustrated for an important signal transduction pathway, i.e. nuclear hormone receptor signaling such as relevant to bone formation. It is envisaged that there is much more Mathematical Biology to be discovered in the area between molecules and Life.

Population-Level Transcription Cycles Derive from Stochastic Timing of Single-Cell Transcription

Eukaryotic transcription is a dynamic process relying on a large number of proteins. By measuring the cycling expression of the pyruvate dehydrogenase kinase 4 gene in human cells, we constructed a detailed stochastic model for single-gene transcription at the molecular level using realistic kinetics for diffusion and protein complex dynamics. We observed that gene induction caused an approximate 60 min periodicity of several transcription related processes: first, the covalent histone modifications and presence of many regulatory proteins at the transcription start site; second, RNA polymerase II activity; third, chromatin loop formation; and fourth, mRNA accumulation. Our model can predict the precise timing of single-gene activity leading to transcriptional cycling on the cell population level when we take into account the sequential and irreversible multistep nature of transcriptional initiation. We propose that the cyclic nature of population gene expression is primarily based on the intrinsic periodicity of the transcription process itself.

Design principles of nuclear receptor signaling: how complex networking improves signal transduction

The topology of nuclear receptor (NR) signaling is captured in a systems biological graphical notation. This enables us to identify a number of ‘design’ aspects of the topology of these networks that might appear unnecessarily complex or even functionally paradoxical. In realistic kinetic models of increasing complexity, calculations show how these features correspond to potentially important design principles, e.g.: (i) cytosolic ‘nuclear’ receptor may shuttle signal molecules to the nucleus, (ii) the active export of NRs may ensure that there is sufficient receptor protein to capture ligand at the cytoplasmic membrane, (iii) a three conveyor belts design dissipating GTP‐free energy, greatly aids response, (iv) the active export of importins may prevent sequestration of NRs by importins in the nucleus and (v) the unspecific nature of the nuclear pore may ensure signal‐flux robustness. In addition, the models developed are suitable for implementation in specific cases of NR‐mediated signaling, to predict individual receptor functions and differential sensitivity toward physiological and pharmacological ligands.

Multiplex Eukaryotic Transcription (In)activation: Timing, Bursting and Cycling of a Ratchet Clock Mechanism

Activation of eukaryotic transcription is an intricate process that relies on a multitude of regulatory proteins forming complexes on chromatin. Chromatin modifications appear to play a guiding role in protein-complex assembly on chromatin. Together, these processes give rise to stochastic, often bursting, transcriptional activity. Here we present a model of eukaryotic transcription that aims to integrate those mechanisms. We use stochastic and ordinary-differential-equation modeling frameworks to examine various possible mechanisms of gene regulation by multiple transcription factors. We find that the assembly of large transcription factor complexes on chromatin via equilibrium-binding mechanisms is highly inefficient and insensitive to concentration changes of single regulatory proteins. An alternative model that lacks these limitations is a cyclic ratchet mechanism. In this mechanism, small protein complexes assemble sequentially on the promoter. Chromatin modifications mark the completion of a protein complex assembly, and sensitize the local chromatin for the assembly of the next protein complex. In this manner, a strict order of protein complex assemblies is attained. Even though the individual assembly steps are highly stochastic in duration, a sequence of them gives rise to a remarkable precision of the transcription cycle duration. This mechanism explains how transcription activation cycles, lasting for tens of minutes, derive from regulatory proteins residing on chromatin for only tens of seconds. Transcriptional bursts are an inherent feature of such transcription activation cycles. Bursting transcription can cause individual cells to remain in synchrony transiently, offering an explanation of transcriptional cycling as observed in cell populations, both on promoter chromatin status and mRNA levels.

Systems Biology: Towards Realistic and Useful Models of Molecular Networks

Molecular biology is shifting focus from single molecules to networks of molecules. This development has changed our way of doing research and is challenging our thinking about cells. Cells turn out be complicated molecular systems displaying multivariate dynamics that can rarely be understood in terms of single molecules. One way to appreciate this complexity is to make mathematical models of signaling, gene, and metabolic network to assess the systemic consequences of specific molecular perturbations. This chapter gives a brief overview of some of the approach in mathematical modeling of molecular networks. We choose to keep the mathematical detail minimal and highlight a number of concepts and approaches that are emerging in the analysis of molecular networks.