Tatiana T. Marquez-Lago

A tunable synthetic mammalian oscillator

Autonomous and self-sustained oscillator circuits mediating the periodic induction of specific target genes are minimal genetic time-keeping devices found in the central and peripheral circadian clocks. They have attracted significant attention because of their intriguing dynamics and their importance in controlling critical repair, metabolic and signalling pathways. The precise molecular mechanism and expression dynamics of this mammalian circadian clock are still not fully understood. Here we describe a synthetic mammalian oscillator based on an auto-regulated sense–antisense transcription control circuit encoding a positive and a time-delayed negative feedback loop, enabling autonomous, self-sustained and tunable oscillatory gene expression. After detailed systems design with experimental analyses and mathematical modelling, we monitored oscillating concentrations of green fluorescent protein with tunable frequency and amplitude by time-lapse microscopy in real time in individual Chinese hamster ovary cells. The synthetic mammalian clock may provide an insight into the dynamics of natural periodic processes and foster advances in the design of prosthetic networks in future gene and cell therapies.

Binomial tau-leap spatial stochastic simulation algorithm for applications in chemical kinetics

In cell biology, cell signaling pathway problems are often tackled with deterministic temporal models, well mixed stochastic simulators, and/or hybrid methods. But, in fact, three dimensional stochastic spatial modeling of reactions happening inside the cell is needed in order to fully understand these cell signaling pathways. This is because noise effects, low molecular concentrations, and spatial heterogeneity can all affect the cellular dynamics. However, there are ways in which important effects can be accounted without going to the extent of using highly resolved spatial simulators (such as single-particle software), hence reducing the overall computation time significantly. We present a new coarse grained modified version of the next subvolume method that allows the user to consider both diffusion and reaction events in relatively long simulation time spans as compared with the original method and other commonly used fully stochastic computational methods. Benchmarking of the simulation algorithm was performed through comparison with the next subvolume method and well mixed models (MATLAB), as well as stochastic particle reaction and transport simulations (CHEMCELL, Sandia National Laboratories). Additionally, we construct a model based on a set of chemical reactions in the epidermal growth factor receptor pathway. For this particular application and a bistable chemical system example, we analyze and outline the advantages of our presented binomial tau-leap spatial stochastic simulation algorithm, in terms of efficiency and accuracy, in scenarios of both molecular homogeneity and heterogeneity.

Generalized binomial τ-leap method for biochemical kinetics incorporating both delay and intrinsic noise

The delay stochastic simulation algorithm (DSSA) by Barrio et al. [Plos Comput. Biol. 2, 117(E) (2006)] was developed to simulate delayed processes in cell biology in the presence of intrinsic noise, that is, when there are small-to-moderate numbers of certain key molecules present in a chemical reaction system. These delayed processes can faithfully represent complex interactions and mechanisms that imply a number of spatiotemporal processes often not explicitly modeled such as transcription and translation, basic in the modeling of cell signaling pathways. However, for systems with widely varying reaction rate constants or large numbers of molecules, the simulation time steps of both the stochastic simulation algorithm (SSA) and the DSSA can become very small causing considerable computational overheads. In order to overcome the limit of small step sizes, various tau-leap strategies have been suggested for improving computational performance of the SSA. In this paper, we present a binomial tau-DSSA method that extends the tau-leap idea to the delay setting and avoids drawing insufficient numbers of reactions, a common shortcoming of existing binomial tau-leap methods that becomes evident when dealing with complex chemical interactions. The resulting inaccuracies are most evident in the delayed case, even when considering reaction products as potential reactants within the same time step in which they are produced. Moreover, we extend the framework to account for multicellular systems with different degrees of intercellular communication. We apply these ideas to two important genetic regulatory models, namely, the hes1 gene, implicated as a molecular clock, and a Her1/Her 7 model for coupled oscillating cells.

Counter-Intuitive Stochastic Behavior of Simple Gene Circuits with Negative Feedback

It has often been taken for granted that negative feedback loops in gene regulation work as homeostatic control mechanisms. If one increases the regulation strength a less noisy signal is to be expected. However, recent theoretical studies have reported the exact contrary, counter-intuitive observation, which has left a question mark over the relationship between negative feedback loops and noise. We explore and systematically analyze several minimal models of gene regulation, where a transcriptional repressor negatively regulates its own expression. For models including a quasi-steady-state assumption, we identify processes that buffer noise change (RNA polymerase binding) or accentuate it (repressor dimerization) alongside increasing feedback strength. Moreover, we show that lumping together transcription and translation in simplified models clearly underestimates the impact of negative feedback strength on the systems noise. In contrast, in systems without a quasi-steady-state assumption, noise always increases with negative feedback strength. Hence, subtle mathematical properties and model assumptions yield different types of noise profiles and, by consequence, previous studies have simultaneously reported decrease, increase or persistence of noise levels with increasing feedback. We discuss our findings in terms of separation of timescales and time correlations between molecular species distributions, extending current theoretical findings on the topic and allowing us to propose what we believe new ways to better characterize noise.

POSSUM: a bioinformatics toolkit for generating numerical sequence feature descriptors based on PSSM profiles

Summary: Evolutionary information in the form of a Position‐Specific Scoring Matrix (PSSM) is a widely used and highly informative representation of protein sequences. Accordingly, PSSM‐based feature descriptors have been successfully applied to improve the performance of various predictors of protein attributes. Even though a number of algorithms have been proposed in previous studies, there is currently no universal web server or toolkit available for generating this wide variety of descriptors. Here, we present POSSUM (Position‐Specific Scoring matrix‐based feature generator for machine learning), a versatile toolkit with an online web server that can generate 21 types of PSSM‐based feature descriptors, thereby addressing a crucial need for bioinformaticians and computational biologists. We envisage that this comprehensive toolkit will be widely used as a powerful tool to facilitate feature extraction, selection, and benchmarking of machine learning‐based models, thereby contributing to a more effective analysis and modeling pipeline for bioinformatics research. Availability and implementation: http://possum.erc.monash.edu/. Contact: trevor.lithgow@monash.edu or jiangning.song@monash.edu Supplementary information: Supplementary data are available at Bioinformatics online.

Integrative physical oncology

Cancer is arguably the ultimate complex biological system. Solid tumors are microstructured soft matter that evolves as a consequence of spatio‐temporal events at the intracellular (e.g., signaling pathways, macromolecular trafficking), intercellular (e.g., cell–cell adhesion/communication), and tissue (e.g., cell–extracellular matrix interactions, mechanical forces) scales. To gain insight, tumor and developmental biologists have gathered a wealth of molecular, cellular, and genetic data, including immunohistochemical measurements of cell type‐specific division and death rates, lineage tracing, and gain‐of‐function/loss‐of‐function mutational analyses. These data are empirically extrapolated to a diagnosis/prognosis of tissue‐scale behavior, e.g., for clinical decision. Integrative physical oncology (IPO) is the science that develops physically consistent mathematical approaches to address the significant challenge of bridging the nano (nm)–micro (µm) to macro (mm, cm) scales with respect to tumor development and progression. In the current literature, such approaches are referred to as multiscale modeling. In the present article, we attempt to assess recent modeling approaches on each separate scale and critically evaluate the current ‘hybrid‐multiscale’ models used to investigate tumor growth in the context of brain and breast cancers. Finally, we provide our perspective on the further development and the impact of IPO. WIREs Syst Biol Med 2012, 4:1–14. doi: 10.1002/wsbm.158

Stochastic Simulation for Spatial Modelling of Dynamic Processes in a Living Cell

One of the fundamental motivations underlying computational cell biology is to gain insight into the complicated dynamical processes taking place, for example, on the plasma membrane or in the cytosol of a cell. These processes are often so complicated that purely temporal mathematical models cannot adequately capture the complex chemical kinetics and transport processes of, for example, proteins or vesicles. On the other hand, spatial models such as Monte Carlo approaches can have very large computational overheads. This chapter gives an overview of the state of the art in the development of stochastic simulation techniques for the spatial modelling of dynamic processes in a living cell.

Anomalous diffusion and multifractional Brownian motion: simulating molecular crowding and physical obstacles in systems biology

There have been many recent studies from both experimental and simulation perspectives in order to understand the effects of spatial crowding in molecular biology. These effects manifest themselves in protein organisation on the plasma membrane, on chemical signalling within the cell and in gene regulation. Simulations are usually done with lattice- or meshless-based random walks but insights can also be gained through the computation of the underlying probability density functions of these stochastic processes. Until recently much of the focus had been on continuous time random walks, but some very recent work has suggested that fractional Brownian motion may be a good descriptor of spatial crowding effects in some cases. The study compares both fractional Brownian motion and continuous time random walks and highlights how well they can represent different types of spatial crowding and physical obstacles. Simulated spatial data, mimicking experimental data, was first generated by using the package Smoldyn. We then attempted to characterise this data through continuous time anomalously diffusing random walks and multifractional Brownian motion (MFBM) by obtaining MFBM paths that match the statistical properties of our sample data. Although diffusion around immovable obstacles can be reasonably characterised by a single Hurst exponent, we find that diffusion in a crowded environment seems to exhibit multifractional properties in the form of a different short- and long-time behaviour.

Dynamic regulation of T follicular regulatory cell responses by interleukin 2 during influenza infection

Interleukin 2 (IL-2) promotes Foxp3+ regulatory T (Treg) cell responses, but inhibits T follicular helper (TFH) cell development. However, it is not clear how IL-2 affects T follicular regulatory (TFR) cells, a cell type with properties of both Treg and TFH cells. Using an influenza infection model, we found that high IL-2 concentrations at the peak of the infection prevented TFR cell development by a Blimp-1-dependent mechanism. However, once the immune response resolved, some Treg cells downregulated CD25, upregulated Bcl-6 and differentiated into TFR cells, which then migrated into the B cell follicles to prevent the expansion of self-reactive B cell clones. Thus, unlike its effects on conventional Treg cells, IL-2 inhibits TFR cell responses.

Probability distributed time delays: integrating spatial effects into temporal models

BackgroundIn order to provide insights into the complex biochemical processes inside a cell, modelling approaches must find a balance between achieving an adequate representation of the physical phenomena and keeping the associated computational cost within reasonable limits. This issue is particularly stressed when spatial inhomogeneities have a significant effect on systems behaviour. In such cases, a spatially-resolved stochastic method can better portray the biological reality, but the corresponding computer simulations can in turn be prohibitively expensive.ResultsWe present a method that incorporates spatial information by means of tailored, probability distributed time-delays. These distributions can be directly obtained by single in silico or a suitable set of in vitro experiments and are subsequently fed into a delay stochastic simulation algorithm (DSSA), achieving a good compromise between computational costs and a much more accurate representation of spatial processes such as molecular diffusion and translocation between cell compartments. Additionally, we present a novel alternative approach based on delay differential equations (DDE) that can be used in scenarios of high molecular concentrations and low noise propagation.ConclusionsOur proposed methodologies accurately capture and incorporate certain spatial processes into temporal stochastic and deterministic simulations, increasing their accuracy at low computational costs. This is of particular importance given that time spans of cellular processes are generally larger (possibly by several orders of magnitude) than those achievable by current spatially-resolved stochastic simulators. Hence, our methodology allows users to explore cellular scenarios under the effects of diffusion and stochasticity in time spans that were, until now, simply unfeasible. Our methodologies are supported by theoretical considerations on the different modelling regimes, i.e. spatial vs. delay-temporal, as indicated by the corresponding Master Equations and presented elsewhere.