A deterministic oscillatory model of microtubule growth and shrinkage for differential actions of short chain fatty acids.

Short chain fatty acids (SCFA), principally acetate, propionate, butyrate and valerate, are produced in pharmacologically relevant concentrations by the gut microbiome. Investigations indicate that they exert beneficial effects on colon epithelia. There is increasing interest in whether different SCFAs have distinct functions which may be exploited for prevention or treatment of colonic diseases including colorectal cancer (CRC), inflammatory bowel disease and obesity. Based on experimental evidence, we hypothesised that odd-chain SCFAs may possess anti-mitotic capabilities in colon cancer cells by disrupting microtubule (MT) structural integrity via dysregulation of ß-tubulin isotypes. MT dynamic instability is an essential characteristic of MT cellular activity. We report a minimal deterministic model that takes a novel approach to explore the hypothesised pathway by triggering spontaneous oscillations to represent MT dynamic behaviour. The dynamicity parameters in silico were compared to those reported in vitro. Simulations of untreated and butyrate (even-chain length) treated cells reflected MT behaviour in interphase or untreated control cells. The propionate and valerate (odd-chain length) simulations displayed increased catastrophe frequencies and longer periods of MT-fibre shrinkage. Their enhanced dynamicity was dissimilar to that observed in mitotic cells, but parallel to that induced by MT-destabilisation treatments. Antimicrotubule drugs act through upward or downward modulation of MT dynamic instability. Our computational modelling suggests that metabolic engineering of the microbiome may facilitate managing CRC risk by predicting outcomes of SCFA treatments in combination with AMDs.

Mathematical modelling of metabolic regulation in aging.

The underlying cellular mechanisms that characterize aging are complex and multifaceted. However, it is emerging that aging could be regulated by two distinct metabolic hubs. These hubs are the pathway defined by the mammalian target of rapamycin (mTOR) and that defined by the NAD+-dependent deacetylase enzyme, SIRT1. Recent experimental evidence suggests that there is crosstalk between these two important pathways; however, the mechanisms underpinning their interaction(s) remains poorly understood. In this review, we propose using computational modelling in tandem with experimentation to delineate the mechanism(s). We briefly discuss the main modelling frameworks that could be used to disentangle this relationship and present a reduced reaction pathway that could be modelled. We conclude by outlining the limitations of computational modelling and by discussing opportunities for future progress in this area.

Scaling-up ultrasound standing wave enhanced sedimentation filters.

Particle concentration and filtration is a key stage in a wide range of processing industries and also one that can be present challenges for high throughput, continuous operation. Here we demonstrate some features which increase the efficiency of ultrasound enhanced sedimentation and could enable the technology the potential to be scaled up. In this work, 20 mm piezoelectric plates were used to drive 100 mm high chambers formed from single structural elements. The coherent structural resonances were able to drive particles (yeast cells) in the water to nodes throughout the chamber. Ultrasound enhanced sedimentation was used to demonstrate the efficiency of the system (>99% particle clearance). Sub-wavelength pin protrusions were used for the contacts between the resonant chamber and other elements. The pins provided support and transferred power, replacing glue which is inefficient for power transfer. Filtration energies of ∼4 J/ml of suspension were measured. A calculation of thermal convection indicates that the circulation could disrupt cell alignment in ducts >35 mm high when a 1K temperature gradient is present; we predict higher efficiencies when this maximum height is observed. For the acoustic design, although modelling was minimal before construction, the very simple construction allowed us to form 3D models of the nodal patterns in the fluid and the duct structure. The models were compared with visual observations of particle movement, Chladni figures and scanning laser vibrometer mapping. This demonstrates that nodal planes in the fluid can be controlled by the position of clamping points and that the contacts could be positioned to increase the efficiency and reliability of particle manipulations in standing waves.

Model-directed engineering of "difficult-to-express" monoclonal antibody production by Chinese hamster ovary cells.

Despite improvements in volumetric titer for monoclonal antibody (MAb) production processes using Chinese hamster ovary (CHO) cells, some "difficult-to-express" (DTE) MAbs inexplicably reach much lower process titers. These DTE MAbs require intensive cell line and process development activity, rendering them more costly or even unsuitable to manufacture. To rapidly and rationally identify an optimal strategy to improve production of DTE MAbs, we have developed an engineering design platform combining high-yielding transient production, empirical modeling of MAb synthesis incorporating an unfolded protein response (UPR) regulatory loop with directed expression and cell engineering approaches. Utilizing a panel of eight IgG1 λ MAbs varying >4-fold in volumetric titer, we showed that MAb-specific limitations on folding and assembly rate functioned to induce a proportionate UPR in host CHO cells with a corresponding reduction in cell growth rate. Derived from comparative empirical modeling of cellular constraints on the production of each MAb we employed two strategies to increase production of DTE MAbs designed to avoid UPR induction through an improvement in the rate/cellular capacity for MAb folding and assembly reactions. Firstly, we altered the transfected LC:HC gene ratio and secondly, we co-expressed a variety of molecular chaperones, foldases or UPR transactivators (BiP, CypB, PDI, and active forms of ATF6 and XBP1) with recombinant MAbs. DTE MAb production was significantly improved by both strategies, although the mode of action was dependent upon the approach employed. Increased LC:HC ratio or CypB co-expression improved cell growth with no effect on qP. In contrast, BiP, ATF6c and XBP1s co-expression increased qP and reduced cell growth. This study demonstrates that expression-engineering strategies to improve production of DTE proteins in mammalian cells should be product specific, and based on rapid predictive tools to assess the relative impact of different engineering interventions.

Impact of gene vector design on the control of recombinant monoclonal antibody production by Chinese hamster ovary cells.

In this study, we systematically compare two vector design strategies for recombinant monoclonal antibody (Mab) synthesis by Chinese hamster ovary (CHO) cells; a dual open reading frame (ORF) expression vector utilizing separate cytomegalovirus (CMV) promoters to drive heavy chain (HC) and light chain (LC) expression independently, and a single ORF vector design employing a single CMV promoter to drive HC and LC polypeptide expression joined by a foot and mouth disease virus F2A polypeptide self-cleaving linker sequence. Initial analysis of stable transfectants showed that transfectants utilizing the single ORF vector designs exhibited significantly reduced Mab production. We employed an empirical modeling strategy to quantitatively describe the cellular constraints on recombinant Mab synthesis in all stable transfectants. In all transfectants, an intracellular molar excess of LC polypeptide over HC polypeptide was observed. For CHO cells transfected with the single ORF vectors, model-predicted, and empirical intracellular intermediate levels could only be reconciled by inclusion of nascent HC polypeptide degradation. Whilst a local sensitivity analysis showed that qMab of all transfectants was primarily constrained by recombinant mRNA translation rate, our data indicated that all single ORF transfectants exhibited a reduced level of recombinant gene transcription and that Mab folding and assembly reactions generically exerted greater control over qMab. We infer that the productivity of single ORF transfectants is limited by ER processing/degradation "capacity" which sets a limit on transcriptional input. We conclude that gene vector design for oligomeric recombinant proteins should be based on an understanding of protein-specific synthetic kinetics rather than polypeptide stoichiometry.

An empirical modeling platform to evaluate the relative control discrete CHO cell synthetic processes exert over recombinant monoclonal antibody production process titer.

In this study we have combined empirically derived mathematical models of intracellular Mab synthesis to quantitatively compare the degree to which individual cellular processes limit recombinant IgG(4) monoclonal antibody production by GS-CHO cells throughout a state-of-the-art industrial fed-batch culture process. Based on the calculation of a production process control coefficient for each stage of the intracellular Mab synthesis and secretion pathway, we identified the major cellular restrictions on Mab production throughout the entire culture process to be recombinant heavy chain gene transcription and heavy chain mRNA translation. Surprisingly, despite a substantial decline in the rate of cellular biomass synthesis during culture, with a concomitant decline in the calculated rate constants for energy-intensive Mab synthetic processes (Mab folding/assembly and secretion), these did not exert significant control of Mab synthesis at any stage of production. Instead, cell-specific Mab production was maintained by increased Mab gene transcription which offset the decline in cellular biosynthetic rates. Importantly, this study shows that application of this whole-process predictive modeling strategy should rationally precede and inform cell engineering approaches to increase production of a recombinant protein by a mammalian host cell--where control of productivity is inherently protein product and cell line specific.

Modelling the microtubule: towards a better understanding of short-chain fatty acid molecular pharmacology.

Systems biology combines experimental data with computational modelling to describe complex biological mechanisms and pathways. Short-chain fatty acids (SCFAs-chemopreventive compounds produced in the colon lumen) impair microtubule (MT) function in colon cancer cells by altering the relative expression of ß-tubulin isotypes. The ß-tubulin isotype composition along MT fibres is believed to contribute to a "tubulin code" defining which microtubule-associated proteins (MAPs) and kinesins are recruited and the arrangement of tubulin post-transcriptional modifications (PTMs) along the fibre, which in turn dictate many critical cellular functions. SCFAs drive acetylation of many proteins by virtue of being histone deacetylase inhibitors (HDACi's). Known acetyl-proteins include transcription factors and cytoplasmic cytoskeletal keratins as well as histones. Disruption of the MT cytoskeleton is a prime target of many cancer therapies including anti-microtubule drugs (AMD). This review focuses on SCFAs as HDACi's and how they might affect tubulin dynamics, modifications and isotypes. It discusses the evolution of mechanistic models that have helped improve understanding of tubulin-MT structure and dynamics and how to develop these models, combined with those describing transcription and the cell cycle, could provide hypotheses for how SCFAs disrupt cytoskeletal function. The review demonstrates how systems biology could offer potentially novel ideas for therapies in the prevention and treatment of cancers through the continued development and elaboration of such models.

Cell line-specific control of recombinant monoclonal antibody production by CHO cells.

In this study we compare the cellular control of recombinant human IgG(4) monoclonal antibody (Mab) synthesis in different CHO cell lines. Based on comprehensive empirical analyses of mRNA and polypeptide synthetic intermediates we constructed cell line-specific mathematical models of recombinant Mab manufacture in seven GS-CHO cell lines varying in specific production rate (qMab) over 350-fold. This comparative analysis revealed that control of qMab involved both genetic construct and cell line-specific factors. With respect to the former, all cell lines exhibited excess production of light chain (LC) mRNA and polypeptide relative to heavy chain (HC) mediated by more rapid LC transcription and enhanced LC mRNA stability. Downstream of this, cell lines differed markedly in their relative rates of recombinant mRNA translation, Mab assembly and secretion although HC mRNA abundance and the rate of HC translation generally exerted most control over qMab--the latter being directly proportional to qMab. This study shows that (i) cell lines capable of high qMab exceed a threshold functional competency in all synthetic processes, (ii) the majority of cells in parental and transfected cell populations are functionally limited and (iii) cell engineering strategies to increase Mab production should be cell line specific.

Properties of the proximate parameter tuning regularization algorithm.

An important aspect of systems biology research is the so-called "reverse engineering" of cellular metabolic dynamics from measured input-output data. This allows researchers to estimate and validate both the pathway's structure as well as the kinetic constants. In this paper, the recently published 'Proximate Parameter Tuning' (PPT) method for the identification of biochemical networks is analysed. In particular, it is shown that the described PPT algorithm is essentially equivalent to a sequential linear programming implementation of a constrained optimization problem. The corresponding objective function consists of two parts, the first emphasises the data fitting where a residual 1-norm is used, and the second emphasises the proximity of the calculated parameters to the specified nominal values, using an infinity-norm. The optimality properties of PPT algorithm solution as well as its geometric interpretation are analyzed. The concept of optimal parameter locus is applied for the exploration of the entire family of optimal solutions. An efficient implementation of the parameter locus is also developed. Parallels are drawn with 1-norm parameter deviation regularization which attempt to fit the data with a minimal number of parameters. Finally, a small example is used to illustrate all of these properties.

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.

Control of translation initiation: a model-based analysis from limited experimental data.

We have built a detailed kinetic model of translation initiation in yeast and have used a novel approach to determine the flux controlling steps based on limited experimental data. An efficient parameter estimation method was adapted in order to fit the most uncertain parameters (rate constants) to in vivo measurements in yeast. However, it was found that there were many other sets of plausible parameter values that also gave a good fit of the model to the data. We therefore used random sampling of this uncertain parameter space to generate a large number of diverse fitted parameter sets. A compact characterization of these parameter sets was provided by considering flux control. In particular, we suggest that the rate of translation initiation is most strongly influenced by one of two reactions: either the guanine nucleotide exchange reaction involving initiation factors eIF2 and eIF2B or the assembly of the multifactor complex from its constituent protein/tRNA containing complexes. It is hoped that the approach presented in this paper will add to our understanding of translation initiation pathway and can be used to identify key system-level properties of other biochemical processes.

Proximate parameter tuning for biochemical networks with uncertain kinetic parameters.

It is commonly the case in biochemical modelling that we have knowledge of the qualitative 'structure' of a model and some measurements of the time series of the variables of interest (concentrations and fluxes), but little or no knowledge of the model's parameters. This is, then, a system identification problem, that is commonly addressed by running a model with estimated parameters and assessing how far the model's behaviour is from the 'target' behaviour of the variables, and adjusting parameters iteratively until a good fit is achieved. The issue is that most of these problems are grossly underdetermined, such that many combinations of parameters can be used to fit a given set of variables. We introduce the constraint that the estimated parameters should be within given bounds and as close as possible to stated nominal values. This deterministic 'proximate parameter tuning' algorithm turns out to be exceptionally effective, and we illustrate its utility for models of p38 signalling, of yeast glycolysis and for a benchmark dataset describing the thermal isomerisation of alpha-pinene.

Bridging the gap between in silico and cell-based analysis of the nuclear factor-kappaB signaling pathway by in vitro studies of IKK2.

Previously, we have shown by sensitivity analysis, that the oscillatory behavior of nuclear factor (NF-kappaB) is coupled to free IkappaB kinase-2 (IKK2) and IkappaBalpha(IkappaBalpha), and that the phosphorylation of IkappaBalpha by IKK influences the amplitude of NF-kappaB oscillations. We have performed further analyses of the behavior of NF-kappaB and its signal transduction network to understand the dynamics of this system. A time lapse study of NF-kappaB translocation in 10,000 cells showed discernible oscillations in levels of nuclear NF-kappaB amongst cells when stimulated with interleukin (IL-1alpha), which suggests a small degree of synchronization amongst the cell population. When the kinetics for the phosphorylation of IkappaBalpha by IKK were measured, we found that the values for the affinity and catalytic efficiency of IKK2 for IkappaBalpha were dependent on assay conditions. The application of these kinetic parameters in our computational model of the NF-kappaB pathway resulted in significant differences in the oscillatory patterns of NF-kappaB depending on the rate constant value used. Hence, interpretation of in silico models should be made in the context of this uncertainty.