Zuyi Huang

Mathematical Model of Dynamic Behavior of Microbial Desalination Cells for Simultaneous Wastewater Treatment and Water Desalination

Microbial desalination cells (MDCs) are an emerging concept for simultaneous wastewater treatment and water desalination. This work presents a mathematical model to simulate dynamic behavior of MDCs for the first time through evaluating multiple factors such as organic supply, salt loading, and current generation. Ordinary differential equations were applied to describe the substrate as well as bacterial concentrations in the anode compartment. Local sensitivity analysis was employed to select model parameters that needed to be re-estimated from the previous studies. This model was validated by experimental data from both a bench- and a large-scale MDC system. It could fit current generation fairly well and simulate the change of salt concentration. It was able to predict the response of the MDC with time under various conditions, and also provide information for analyzing the effects of different operating conditions. Furthermore, optimal operating conditions for the MDC used in this study were estimated to have an acetate flow rate of 0.8 mL·min(-1), influent salt concentration of 15 g·L(-1) and salt solution flow rate of 0.04 mL·min(-1), and to be operated with an external resistor less than 30 Ω. The MDC model will be helpful with determining operational parameters to achieve optimal desalination in MDCs.

Integrated experimental investigation and mathematical modeling of brackish water desalination and wastewater treatment in microbial desalination cells.

Desalination of brackish water can provide freshwater for potable use or non potable applications such as agricultural irrigation. Brackish water desalination is especially attractive to microbial desalination cells (MDCs) because of its low salinity, but this has not been well studied before. Herein, three brackish waters prepared according to the compositions of actual brackish water in three locations in Israel were examined with domestic wastewater as an electron source in a bench-scale MDC. All three brackish waters could be effectively desalinated with simultaneous wastewater treatment. The MDC achieved the highest salt removal rate of 1.2 g L(-1) d(-1) with an initial salinity of 5.9 g L(-1) and a hydraulic retention time (HRT) of 0.8 d. The desalinated brackish water could meet the irrigation standard of both salinity (450 mg L(-1) TDS) and the concentrations of major ionic species, given a sufficient HRT. The MDC also accomplished nearly 70% removal of organic compounds in wastewater with Coulombic efficiency varied between 5 and 10%. A previously developed MDC model was improved for brackish water desalination, and could well predict salinity variation and the concentrations of individual ions. The model also simulated a staged operation mode with improved desalination performance. This integrated experiment and mathematical modeling approach provides an effective method to understand the key factors in brackish water desalination by MDCs towards further system development.

Investigation of IL-6 and IL-10 signalling via mathematical modelling

Steatosis, i.e., the accumulation of fat in hepatocytes, plays an important role in the progression of non-alcoholic fatty liver disease (NAFLD). It has been shown that STAT3 activation is involved in a decrease of lipid accumulation while C∕EBP is correlated with an increase of fat content and steatosis. It is known that STAT3 and C∕EBP are activated by IL-6 and that IL-6 signalling is also affected by IL-10, even though the exact mechanism is unclear. This paper develops a model for IL-6 and IL-10 signal transduction and then investigates the effect that stimulation with these cytokines has on the transcription factor dynamics. In an initial step, some parameters of a previously developed IL-6 signalling model are re-estimated based upon newly developed experimental data for the Jak-STAT pathway. Furthermore, the Erk-C∕EBP pathway model is extended to also include the activated transcription factor C∕EBP in the nucleus. Since IL-10 signals through the Jak-STAT but not the Erk-C∕EBP pathway, a model was developed which includes interaction between IL-6 and IL-10 signalling as both mechanisms share signal transduction through the Jak-STAT pathway. Based upon the model, the activity ratio of Jak-STAT and Erk-C∕EBP was investigated for different stimulation levels of IL-6 and IL-10.

Integrated modeling and experimental approach for determining transcription factor profiles from fluorescent reporter data

BackgroundThe development of quantitative models of signal transduction, as well as parameter estimation to improve existing models, depends on the ability to obtain quantitative information about various proteins that are part of the signaling pathway. However, commonly-used measurement techniques such as Western blots and mobility shift assays provide only qualitative or semi-quantitative data which cannot be used for estimating parameters. Thus there is a clear need for techniques that enable quantitative determination of signal transduction intermediates.ResultsThis paper presents an integrated modeling and experimental approach for quantitatively determining transcription factor profiles from green fluorescent protein (GFP) reporter data. The technique consists of three steps: (1) creating data sets for green fluorescent reporter systems upon stimulation, (2) analyzing the fluorescence images to determine fluorescence intensity profiles using principal component analysis (PCA) and K-means clustering, and (3) computing the transcription factor concentration from the fluorescence intensity profiles by inverting a model describing transcription, translation, and activation of green fluorescent proteins.We have used this technique to quantitatively characterize activation of the transcription factor NF-κB by the cytokine TNF-α. In addition, we have applied the quantitative NF-κB profiles obtained from our technique to develop a model for TNF-α signal transduction where the parameters were estimated from the obtained data.ConclusionThe technique presented here for computing transcription factor profiles from fluorescence microscopy images of reporter cells generated quantitative data on the magnitude and dynamics of NF-κB activation by TNF-α. The obtained results are in good agreement with qualitative descriptions of NF-κB activation as well as semi-quantitative experimental data from the literature. The profiles computed from the experimental data have been used to re-estimate parameters for a NF-κB model and the results of additional experiments are predicted very well by the model with the new parameter values. While the presented approach has been applied to NF-κB and TNF-α signaling, it can be used to determine the profile of any transcription factor as long as GFP reporter fluorescent profiles are available.

A kinematic model coupling stress fiber dynamics with JNK activation in response to matrix stretching

The role of the actin cytoskeleton in regulating mechanotransduction in response to external forces is complex and incompletely understood. Here, we develop a mathematical model coupling the dynamic disassembly and reassembly of actin stress fibers and associated focal adhesions to the activation of c-jun N-terminal kinase (JNK) in cells attached to deformable matrices. The model is based on the assumptions that stress fibers are pre-extended to a preferred level under static conditions and that perturbations from this preferred level destabilize the stress fibers. The subsequent reassembly of fibers upregulates the rate of JNK activation as a result of the formation of new integrin bonds within the associated focal adhesions. Numerical solutions of the model equations predict that different patterns of matrix stretch result in distinct temporal patterns in JNK activation that compare well with published experimental results. In the case of cyclic uniaxial stretching, stretch-induced JNK activation slowly subsides as stress fibers gradually reorient perpendicular to the stretch direction. In contrast, JNK activation is chronically elevated in response to cyclic equibiaxial stretch. A step change in either uniaxial or equibiaxial stretch results in a short, transient upregulation in JNK that quickly returns to the basal level as overly stretched stress fibers disassemble and are replaced by fibers assembled at the preferred level of stretch. In summary, the model describes a mechanism by which the dynamic properties of the actin cytoskeleton allow cells to adapt to applied forces through turnover and reorganization to modulate intracellular signaling.

An Integrated Modeling and Experimental Approach to Study the Influence of Environmental Nutrients on Biofilm Formation of Pseudomonas aeruginosa

The availability of nutrient components in the environment was identified as a critical regulator of virulence and biofilm formation in Pseudomonas aeruginosa. This work proposes the first systems-biology approach to quantify microbial biofilm formation upon the change of nutrient availability in the environment. Specifically, the change of fluxes of metabolic reactions that were positively associated with P. aeruginosa biofilm formation was used to monitor the trend for P. aeruginosa to form a biofilm. The uptake rates of nutrient components were changed according to the change of the nutrient availability. We found that adding each of the eleven amino acids (Arg, Tyr, Phe, His, Iso, Orn, Pro, Glu, Leu, Val, and Asp) to minimal medium promoted P. aeruginosa biofilm formation. Both modeling and experimental approaches were further developed to quantify P. aeruginosa biofilm formation for four different availability levels for each of the three ions that include ferrous ions, sulfate, and phosphate. The developed modeling approach correctly predicted the amount of biofilm formation. By comparing reaction flux change upon the change of nutrient concentrations, metabolic reactions used by P. aeruginosa to regulate its biofilm formation are mainly involved in arginine metabolism, glutamate production, magnesium transport, acetate metabolism, and the TCA cycle.

Using a two species competitive binding model to predict expanded bed breakthrough of a recombinant protein expressed in a high cell density fermentation

Expanded Bed experiments were conducted using a mixed mode (MM) resin to capture and purify a recombinant protein produced in yeast fermentation. Expanded bed breakthrough profiles show an overshoot in column effluent concentration of the target protein in the presence of cells and other broth proteins, similar to that seen by other researchers when loading two competing species onto packed beds. In this research, a numerical model assuming negligible axial dispersion is developed and first validated for columns loads that contain only the target protein. This model is solved by finite differences in a unique way that uses an embedded analytical-solution to increase solution speed and stability. To model expanded bed breakthrough of the target protein in the actual cell broth, it was assumed that the other non-product proteins in the broth compete for MM resin binding sites and might be represented as a second “average” species via a traditional two-component competitive Langmuir isotherm. Estimates of the Langmuir constant and broth concentration of this second species were then calculated from batch adsorption data. Using these parameters for the second species, and other batch-derived parameters for the target protein with this resin, this unique numerical modeling approach provided results that compare favorably to experimental breakthrough data at various flow rates. Finally, the model was employed for a parameter sensitivity analysis that shows which process variables are most important in determining breakthrough time and the shape and magnitude of the concentration overshoot.

Using the Tet-On system to develop a procedure for extracting transcription factor activation dynamics

The regulation of gene expression by transcription factors through different expression and activation dynamics is an important aspect of genomics and systems biology. Reporter systems using green fluorescent protein (GFP) or luciferase are often used to infer transcription factor dynamics. We recently used an inverse problem solution of GFP reporter profiles to demonstrate that the activation dynamics of a model transcription actor (NF-kappaB) can be reconstructed from GFP data. This approach assumes that the general nature of the transcription factor dynamics is known; however, it is non-trivial to determine the exact nature of the transcription factor dynamics as it often depends upon the cell type and the stimulus used to activate the transcription factor. This, in turn, limits the determination of accurate transcription factor dynamics from reporter data, especially since the model used for solution of an inverse problem needs to be verified. To address this point, we developed a reporter cell line for expressing GFP using an inducible, artificial transcription factor (tTA) and minimal promoter system. The artificial transcription factor can be activated independent of the cellular regulatory machinery through addition of doxycycline. This allows us to directly control the dynamics of the artificial transcription factor, and thereby, develop a model describing its activation dynamics from reporter data. Our experimental data and model predictions are in good agreement, and illustrate the utility of our approach. Future work will focus on using the developed approach, i.e. solution of an inverse problem involving the model describing expression of GFP, to extract the dynamics of transcription factors that are currently uncharacterized.

Fuzzy Modeling of Signal Transduction Networks

Abstract This work proposes a fuzzy modeling–based approach for describing signal transduction networks. Many key steps in signal transduction mechanisms have been investigated qualitatively in the literature, however, only little quantitative information is available. Fuzzy models can make use of this situation as fuzzy rules can be based upon the qualitative information that is found in the literature whereas training of the model can be performed with data that is available. This combination of a fuzzy rule set based upon qualitative information with parameters to be determined from data can result in models where fewer parameters need to be estimated than if fundamental or black-box models were used. This work investigates the use of fuzzy modeling to describe an IL-6 signal transduction mechanism as it plays a key role in the bodys response to inflammation. The resulting model is capable of capturing the dynamics of key components of the IL-6 signal transduction pathway.

Generalisation of a procedure for computing transcription factor profiles

The limited amount of quantitative experimental data generated from life-science experiments poses a major challenge in systems biology. The reason for this is that many systems approaches, such as parameter estimation, simulation and sensitivity analysis make use of models or analyse quantitative data. However, these techniques are only of limited use if only qualitative or semi-quantitative information is available about a system. Therefore procedures that generate quantitative data from experiments in the life sciences can greatly expand the use of systems approaches to biological problems. This study addresses this issue as it introduces a procedure that computes quantitative transcription factor profiles from fluorescent microscopy data collected from green fluorescent protein (GFP) reporter cells. This technique forms a generalisation of a method that has recently been introduced for monitoring NF-B profiles. The contribution made in this work is that the assumption that the transcription factor profile exhibits damped oscillations is relaxed, as transcription factors, other than the previously investigated NF-B, may exhibit different profiles. This is achieved by investigating a variety of potential profiles and solving the inverse problem for the model describing transcription, translation and activation of GFP for each one. The transcription factor profile that results in the best fit among the potential candidates, for the measured fluorescent intensity data, is then chosen as the most likely concentration profile. The technique is illustrated in two detailed case studies, where one case study involves simulation data whereas the other one uses experimentally derived fluorescent intensity data.