Development and validation of a novel food exchange system for Chinese pregnant women.

BACKGROUND: The dietary nutritional status of pregnant women is critical for maintaining the health of both mothers and infants. Food exchange systems have been employed in the nutritional guidance of patients in China, although their application in the dietary guidance of healthy pregnant women is quite limited. This study aimed to develop a novel food exchange system for Chinese pregnant women (NFES-CPW) and evaluate the relative validation of its application. METHODS: NFES-CPW covers approximately 500 types of food from ten categories and has more elaborate food portion sizes. It established a recommendation index for guiding food selection and used energy, water content, and protein as the exchange basis to balance the supply of energy and important nutrients throughout pregnancy. Furthermore, dietitians used the NFES-CPW and traditional food exchange system to generate new recipes based on the sample recipe. There were 40 derived recipes for each of the two food exchange methods. The food consumption, energy, and key nutrients of each recipe were calculated, and the differences between the two food exchange systems were compared using the Wilcoxon rank sum test or the Chi-square test. RESULTS: The results revealed that compared to those derived from traditional food exchange system, the NFES-CPW derived recipes had a better dietary structure, as evidenced by the intakes of whole-grain cereals, beans excluding soybeans, potatoes, fruits, fish, shrimp and shellfish, as well as eggs (P < 0.05), which were more conducive to reaching the recommended range of balanced dietary pagoda. After calculating energy and nutrients, although these two food exchange systems have similar effects on the dietary energy and macronutrient intake of pregnant women, the intake of micronutrients in NFES-CPW derived recipes was significantly higher than that from the traditional food exchange system, which was more conducive to meeting the dietary requirements of pregnant women. The outstanding improvement are primarily vitamin A, vitamin B2, folic acid, vitamin B12, vitamin C, calcium, iron, and iodine (P < 0.05). Moreover, when compared to recipes obtained from the traditional food exchange system, the error ranges of energy and most nutrients were significantly reduced after employing the NFES-CPW. CONCLUSIONS: Therefore, NFES-CPW is an appropriate tool that adheres to Chinese dietary characteristics and can provide suitable dietary guidance to pregnant women.

Global Sensitivity Analysis with Mixtures: A Generalized Functional ANOVA Approach.

This work investigates aspects of the global sensitivity analysis of computer codes when alternative plausible distributions for the model inputs are available to the analyst. Analysts may decide to explore results under each distribution or to aggregate the distributions, assigning, for instance, a mixture. In the first case, we lose uniqueness of the sensitivity measures, and in the second case, we lose independence even if the model inputs are independent under each of the assigned distributions. Removing the unique distribution assumption impacts the mathematical properties at the basis of variance-based sensitivity analysis and has consequences on result interpretation as well. We analyze in detail the technical aspects. From this investigation, we derive corresponding recommendations for the risk analyst. We show that an approach based on the generalized functional ANOVA expansion remains theoretically grounded in the presence of a mixture distribution. Numerically, we base the construction of the generalized function ANOVA effects on the diffeomorphic modulation under observable response preserving homotopy regression. Our application addresses the calculation of variance-based sensitivity measures for the well-known Nordhaus' DICE model, when its inputs are assigned a mixture distribution. A discussion of implications for the risk analyst and future research perspectives closes the work.

Experimental Design of Formulations Utilizing High Dimensional Model Representation.

Many applications involve formulations or mixtures where large numbers of components are possible to choose from, but a final composition with only a few components is sought. Finding suitable binary or ternary mixtures from all the permissible components often relies on simplex-lattice sampling in traditional design of experiments (DoE), which requires performing a large number of experiments even for just tens of permissible components. The effect rises very rapidly with increasing numbers of components and can readily become impractical. This paper proposes constructing a single model for a mixture containing all permissible components from just a modest number of experiments. Yet the model is capable of satisfactorily predicting the performance for full as well as all possible binary and ternary component mixtures. To achieve this goal, we utilize biased random sampling combined with high dimensional model representation (HDMR) to replace DoE simplex-lattice design. Compared with DoE, the required number of experiments is significantly reduced, especially when the number of permissible components is large. This study is illustrated with a solubility model for solvent mixture screening.

Valorizing Arthrospira cell residues into polysaccharides: Characterization and application in yogurt.

This study aimed to extract and characterize polysaccharides from Arthrospira cell residue and evaluate their application in yogurt. Four Arthrospira polysaccharides (APP-50, APP-60, APP-70, and APP-80) were obtained by different ethanol concentrations. With the increase in ethanol concentration, the component peaks of polysaccharide became less and the components were simpler. The results showed that APP-60 had the highest neutral sugar content and the densest spherical structure. APP-50 had the highest protein content, the strongest antioxidant capacity, the porous structure, and the structure was incomplete. The addition of polysaccharides increased the viscosity, storage modulus, loss modulus, and particle size of yogurt, and improved the stability of yogurt during long-term storage. The microstructure of yogurt with added polysaccharides was tighter and more orderly than that of the control yogurt. This study demonstrated that Arthrospira polysaccharides could be used as functional ingredients to enhance the quality and nutritional value of yogurt.

V-type granular starches prepared by maize starches with different amylose contents: An investigation in structure, physicochemical properties and digestibility.

V-type granular starches (VGSs) were prepared via an ethanol-alkaline (EA) method using maize starch with different amylose contents, specifically, high amylose (HAM), normal maize starch (MS), and waxy maize starch (WS). The X-ray diffraction pattern of the native starch was completely transformed into a V-type pattern after the EA treatment, indicating a structural change in the starch granules. The VGSs prepared by HAM had highest relative crystallinity (31.8°), while the VGSs prepared by WS showed amorphous diffraction pattern. Excessive NaOH, however, would disrupt the formation of V-type structures and cause granular shape rupture. The quantity of double-helical structures, particularly those formed by amylopectin at the starch granules' periphery, significantly decreased. Conversely, single-helical structures formed by amylose increased. A notable rise in the relative crystallinity of V crystals. Four VGS samples, characterized by granular integrity, were chosen for the next investigation of physicochemical and digestive properties. VGS prepared from HAM exhibited higher granular integrity, lower cold-water swelling extent (59.0 and 161.0 cP), improved thermal stability (the value of breakdown as lower as 57.67 and 186.67 cP), and higher resistance to digestion (RS content was up to 10.38 % and 9.00 % higher than 5.86 % and 5.66 % of VGS prepared from WS and MS). The results confirmed that amylose content has a substantial impact on the microstructural and physicochemical properties of VGSs.

Rapidly molded sodium alginate/soy protein adhesive hydrogel with 808-nm laser inhibition of infected wounds.

Infected wounds produce pus and heal slowly. To address this issue, we developed a rapid-setting SP/SA@BP-C hydrogel by combining sodium alginate (SA) and soy protein (SP) with black phosphorus (BP) grafted with clarithromycin (Cla) and incorporating Ca2+ for chelation. This hydrogel dressing exhibits excellent photothermal (PT) and photodynamic (PD) bacteriostatic effects without biotoxicity, making it suitable for treating infected wounds. Characterization confirmed its successful fabrication, and the bacteriostatic effect demonstrated over 99 % efficacy through the synergistic effects of PT, PD, and Cla. Cellular studies indicated nontoxicity and a promoting effect on cell proliferation (121.6 %). In the mouse-infected wound model, the hydrogel led to complete healing in 12 days, with good recovery of the skin's superficial dermal layer and appendages. Consequently, SP/SA@BP-C is a natural hydrogel dressing with promising properties.

Effects of dynamic zero COVID-19 policy on anxiety status and lifestyle changes of pregnant women in rural South China: a survey-based analysis by propensity score matching method.

Introduction: The coronavirus disease 2019 (COVID-19) pandemic triggered a global public health crisis and has brought an unprecedented impact on pregnant women. The problems faced by pregnant women in the rural areas of China during the epidemic are different from those in urban areas. Although the epidemic situation in China has gradually improved, studying the impact of the previous dynamic zero COVID-19 policy on the anxiety status and lifestyle of pregnant women in rural areas of China, is still necessary. Methods: A cross-sectional survey of pregnant women in rural South China was conducted from September 2021 to June 2022.Using questionnaires, sociodemographic characteristics, anxiety status, physical activity, sleep quality, and dietary status of the population were collected. Using the propensity score matching method, the effect of the dynamic zero COVID-19 strategy on the anxiety status and lifestyle of pregnant women was analyzed. Results: Among the pregnant women in the policy group (n = 136) and the control group (n = 680), 25.7 and 22.4% had anxiety disorders, 83.1 and 84.7% had low or medium levels of physical activity, and 28.7 and 29.1% had sleep disorders, respectively. However, no significant difference (p > 0.05) was observed between the two groups. Compared with control group, the intake of fruit in the policy group increased significantly (p = 0.019), whereas that of aquatic products and eggs decreased significantly (p = 0.027). Both groups exhibited an unreasonable dietary structure and poor compliance with the Chinese dietary guidelines for pregnant women (p > 0.05). The proportion of pregnant women in the policy group, whose intake of stable food (p = 0.002), soybean, and nuts (p = 0.004) was less than the recommended amount, was significantly higher than that in the control group. Discussion: The dynamic zero COVID-19 strategy had little impact on the anxiety status, physical activity, and sleep disorders of pregnant women in the rural areas of South China. However, it affected their intake of certain food groups. Improving corresponding food supply and organized nutritional support should be addressed as a strategic approach to improve the health of pregnant women in rural South China during the pandemic.

Correlation of lifestyle behaviors during pregnancy with postpartum depression status of puerpera in the rural areas of South China.

Background: Postpartum depression (PPD) is among the most common postpartum complications. Its prevalence is associated with strong regional variability. Women in rural areas of China have a high risk of PPD. The aim of this study was to investigate the PPD status of women in rural South China and explore the effects of modifiable lifestyle behaviors during pregnancy on their PPD status, thereby providing a scientific basis for the prevention and intervention of PPD in rural China. Methods: A cohort study was conducted on 261 women from four maternal health institutions situated in rural areas of Guangdong Province and the Guangxi Zhuang Autonomous Region from October 2021 to December 2022. The questionnaires were administered to these women to obtain data about sociodemographic characteristics, health literacy, physical activity during pregnancy, and sleep and dietary status during pregnancy, as well as depression status on the 42nd day after delivery. The lifestyle behaviors during pregnancy and the PPD status of the study population were analyzed. Multiple linear regression models were used to determine the correlation between lifestyle behaviors and PPD status. Path analysis was performed to explore the interaction between various lifestyle behaviors. Results: A total of 14.6% of women had a PPD status. Women who continued to work during pregnancy had an Edinburgh Postpartum Depression Scale (EPDS) score of 1.386 points higher than that of women who did not (В = 1.386, ß = 0.141, p = 0.029). For every 1-point increase in the infant feeding-related knowledge score and pregnancy diet diversity score, the EPDS score decreased by 0.188 and 0.484 points, respectively, and for every 1-point increase in the Pittsburgh sleep quality index score, the EPDS score increased by 0.288 points. Age was related to infant feeding-related knowledge (indirect path coefficient = 0.023). During pregnancy, sedentary time was correlated with sleep quality (indirect path coefficient = 0.031) and employment status (indirect path coefficient = 0.043). Conclusion: Employment status, infant feeding-related knowledge, sleep quality, and diet diversity during pregnancy directly influenced the PPD status, while age and sedentary time during pregnancy indirectly influenced the PPD status. Promoting healthy lifestyle behaviors, including reducing sedentary time, improving sleep quality, and increasing dietary diversity, may be effective in reducing PPD occurrence.

Water Intake and Hydration Status among Pregnant Women in the Second Trimester in China: A Three-Day Metabolic Trial.

Adequate water intake and optimal hydration status during pregnancy are crucial for maternal and infant health. However, research on water intake by pregnant women in China is very limited. This study mainly aimed to observe the daily total water intake (TWI) of pregnant women and its different sources and to investigate the relationship between their water intake and hydration biomarkers. From October to November 2020, a convenience sample of pregnant women in the second trimester (n = 21) was recruited. Under conditions close to daily life, they undertook a 3-day metabolic trial. Each participant was provided with sufficient bottled water, and the weight of what they drank each time was measured. The intake of other beverages and foods was measured using a combination of weighing and duplicate portion method. Fasting venous blood and 24 h urine samples were collected and analyzed for the hydration biomarkers, including the serum/urine osmolality, urine pH, urine specific gravity, and the concentrations of major electrolytes in urine and serum. The results showed that the mean daily TWI was 3151 mL, of which water from beverages and foods accounted for 60.1% and 39.9%, respectively. The mean total fluid intake (TFI) was 1970 mL, with plain water being the primary contributor (68.7%, r = 0.896). Among the participants, 66.7% (n = 14, Group 1) met the TWI recommendation set by the Chinese Nutrition Society. Further analysis revealed that the TFI, water from beverages and foods, plain water, and milk and milk derivatives (MMDs) were significantly higher in Group 1 than those who did not reach the adequate intake value (Group 2) (p < 0.05). The results of hydration biomarkers showed that the mean 24 h urine volume in Group 1 was significantly higher than that in Group 2 (p < 0.05), while the 24 h urine osmolality, sodium, magnesium, phosphorus, chloride, and creatinine concentrations in Group 1 were significantly lower than those in Group 2 (p < 0.05). However, no significant differences were observed in serum biomarkers. Partial correlation analysis showed that TWI was moderately positively correlated with 24 h urine volume (r = 0.675) and negatively correlated with urine osmolality, sodium, potassium, magnesium, calcium, phosphorus, and chloride concentrations (r = from-0.505 to -0.769), but it was not significantly correlated with serum biomarkers. Therefore, under free-living conditions, increasing the daily intake of plain water and MMDs is beneficial for pregnant women to maintain optimal hydration. The hydration biomarkers in urine are more accurate indicators of water intake and exhibit greater sensitivity compared to serum biomarkers. These findings provide a scientific basis for establishing appropriate water intake and hydration status for pregnant women in China.

Global sensitivity analysis of the regional atmospheric chemical mechanism: an application of random sampling-high dimensional model representation to urban oxidation chemistry.

Chemical mechanisms play a crucial part for the air quality modeling and pollution control decision-making. Parameters in a chemical mechanism have uncertainties, leading to the uncertainties of model predictions. A recently developed global sensitivity analysis (SA) method based on Random Sampling-High Dimensional Model Representation (RS-HDMR) was applied to the Regional Atmospheric Chemical Mechanism (RACM) within a zero-dimensional photochemical model to highlight the main uncertainty sources of atmospheric hydroxyl (OH) and hydroperoxyl (HO(2)) radicals. This global SA approach can be applied as a routine in zero-dimensional photochemical modeling to comprehensively assess model uncertainty and sensitivity under different conditions. It also highlights the parameters to which the model is most sensitive during periods when the model/measurement OH and HO(2) discrepancies are greatest. Uncertainties in 584 model parameters were assigned for measured constituents used to constrain the model, for photolysis and kinetic rate coefficients, and for product yields of the reactions. With simulations performed for the hourly field data of two typical days, modeled and measured OH and HO(2) generally agree better for polluted conditions than for cleaner conditions, except during morning rush hour. Sensitivity analysis shows that the modeled OH and HO(2) depend most critically on the reactions of xylenes and isoprene with OH, NO(2) with OH, NO with HO(2), and internal alkenes with O(3) and suggests that model/measurement discrepancies in OH and HO(2) would benefit from a closer examination of these reactions.

Impact of DHA from Algal Oil on the Breast Milk DHA Levels of Lactating Women: A Randomized Controlled Trial in China.

Population research on the intervention of docosahexaenoic acid (DHA) supplementation in lactating women is in its infancy in China. This study investigated the effect of DHA supplementation on DHA concentrations in the breast milk of lactating women, and the intervention effect, with respect to different dietary patterns. In this trial, 160 healthy lactating women in Nanjing (30−50 days postpartum) were recruited and randomly divided into control (one placebo capsule of similar appearance per day) and supplement (one capsule with 200 mg of DHA from algal oil per day) groups for 8 weeks. Before and after the intervention, all subjects were asked to maintain basic information, maternal anthropometric parameters, breast milk (10−15 mL) sample collection, and a dietary survey using a food frequency questionnaire. The concentrations of DHA and other fatty acids in breast milk were detected using capillary gas chromatography. This study was completed by 137 subjects, with 60 in the control group and 77 in the supplement group. Compared with the DHA concentrations in the breast milk at enrollment, the absolute concentrations of the control group showed a significant decrease at the end of the trial (p = 0.037). In addition, after intervention, the absolute and relative DHA concentrations in the supplement group (10.07 mg/100 mL and 0.40%, respectively) were higher than those in the control group (7.57 mg/100 mL and 0.28%, respectively), being statistically significant (p = 0.012 and p = 0.001). Furthermore, the maternal diet in the supplement group was divided into four dietary patterns. Pattern 1 mainly included fruits and livestock meat. Pattern 2 was dominated by milk and its products, eggs, fish, shrimp and shellfish, and soybeans and its products. Pattern 3 chiefly comprised cereal and beans other than soybeans, potatoes, and nuts. Pattern 4 was high in poultry meat and low in cooking oils. The change in the absolute concentration of DHA in Pattern 3 was lower than that in other patterns (p < 0.05). In conclusion, DHA supplementation in lactating mothers increased breast milk DHA concentrations. The dietary pattern mainly characterized by cereal and beans other than soybeans, potatoes, and nuts may contribute to the poor intervention effect.

Dairy fortification as a good option for dietary nutrition status improvement of 676 preschool children in China: A simulation study based on a cross-sectional diet survey (2018-2019).

Background: Chinese children are deficient in several essential nutrients due to poor dietary choices. Dairy products are a source of many under-consumed nutrients, but preschool children in China consume dairy products significantly less than the recommended level. Methods: From the cross-sectional dietary intake survey of infants and young children aged 0-6 years in China (2018-2019), preschool children (age: 3-6 years) (n = 676) were selected. The four-day dietary data (including 2 working days and 2 weekends) collected through an online diary with reference to the food atlas were used for analysis and simulation. In scenario 1, individual intake of liquid milk equivalents was substituted at a corresponding volume by soymilk, cow's milk, or formulated milk powder for preschool children (FMP-PSC). In scenario 2, the amount of cow's milk or FMP-PSC increased to ensure each child's dairy intake reached the recommended amount (350 g/day). In both scenarios, the simulated nutrient intakes and nutritional inadequacy or surplus were compared to the survey's actual baseline data. Results: It was suggested suggested that replacing dairy foods with FMP-PSC at matching volume is better than replacing them with soymilk or cow's milk to increase the intake of DHA, calcium, iron, zinc, iodine, vitamin A, vitamin B1, vitamin B3, vitamin B12, vitamin C and vitamin D. Moreover, our results suggested that adding FMP-PSC to bring each child's dairy intake to the recommended amount can bring the intakes of dietary fiber, DHA, calcium, iron, zinc, iodine, vitamin A, vitamin B1, vitamin B3, vitamin B9, vitamin B12, vitamin C and vitamin D more in line with the recommendations when compared with cow's milk. Conclusion: Accurate nutrition information should be provided to the parents of preschool children so as to guide their scientific consumption of dairy products and the usage and addition of fortified dairy products can be encouraged as needed.

Global sensitivity analysis for systems with independent and/or correlated inputs.

The objective of a global sensitivity analysis is to rank the importance of the system inputs considering their uncertainty and the influence they have upon the uncertainty of the system output, typically over a large region of input space. This paper introduces a new unified framework of global sensitivity analysis for systems whose input probability distributions are independent and/or correlated. The new treatment is based on covariance decomposition of the unconditional variance of the output. The treatment can be applied to mathematical models, as well as to measured laboratory and field data. When the input probability distribution is correlated, three sensitivity indices give a full description, respectively, of the total, structural (reflecting the system structure) and correlative (reflecting the correlated input probability distribution) contributions for an input or a subset of inputs. The magnitudes of all three indices need to be considered in order to quantitatively determine the relative importance of the inputs acting either independently or collectively. For independent inputs, these indices reduce to a single index consistent with previous variance-based methods. The estimation of the sensitivity indices is based on a meta-modeling approach, specifically on the random sampling-high dimensional model representation (RS-HDMR). This approach is especially useful for the treatment of laboratory and field data where the input sampling is often uncontrolled.

An efficient algorithm to accelerate the discovery of complex material formulations.

The identification of complex multicomponent material formulations that possess specific optimal properties is a challenging task in materials discovery. The high dimensional composition space needs to be adequately sampled and the properties measured with the goal of efficiently identifying effective formulations. This task must also take into account mass fraction and possibly other constraints placed on the material components. Either combinatorial or noncombinatorial sampling of the composition space may be employed in practice. This paper introduces random sampling-high dimensional model representation (RS-HDMR) as an algorithmic tool to facilitate these nonlinear multivariate problems. RS-HDMR serves as a means to accurately interpolate over sampled materials, and simulations of the technique show that it can be very efficient. A variety of simulations is carried out modeling multicomponent-->property relationships, and the results show that the number of sampled materials to attain a given level of accuracy for a predicted property does not significantly depend on the number of components in the formulation. Although RS-HDMR best operates in the laboratory by guided iterative rounds of random sampling of the composition space along with property observation, the technique was tested successfully on two existing databases of a seven component phosphor material and a four component deNO(x) catalyst for reduction of NO with C(3)H(6).

Efficiency of four different dietary preparation methods in extracting functional compounds from dried tangerine peel.

Dried tangerine peel (DTP) is an excellent plant resource that has been used as ingredients for both food and traditional Chinese medicine. In this study, the efficiency of four different dietary preparation methods (i.e. soaking, boiling, steaming, and ethanol extraction) in extraction of functional compounds (i.e. flavonoids and essential oil constituents) from DTP was evaluated systematically for the first time. To conduct a comprehensive evaluation of the extraction of the functional compounds, a synthetic evaluation model based on a weighting method was established. The optimum conditions of each dietary preparation method (e.g., time, temperature, solid-liquid ratio, etc.) were determined by response surface methodology. Ethanol extraction showed the best extraction efficiency, followed by soaking, boiling, and steaming. Additionally, different DTP extracts were shown to be clearly distinguished by electronic eye and electronic tongue. This research provides essential findings for the effective dietary instruction of DTP consumption.

Dissecting enzyme regulation by multiple allosteric effectors: nucleotide regulation of aspartate transcarbamoylase.

The enzyme aspartate transcarbamoylase (ATCase, EC 2.1.3.2 of Escherichia coli), which catalyzes the committed step of pyrimidine biosynthesis, is allosterically regulated by all four ribonucleoside triphosphates (NTPs) in a nonlinear manner. Here, we dissect this regulation using the recently developed approach of random sampling-high-dimensional model representation (RS-HDMR). ATCase activity was measured in vitro at 300 random NTP concentration combinations, each involving (consistent with in vivo conditions) all four NTPs being present. These data were then used to derive a RS-HDMR model of ATCase activity over the full four-dimensional NTP space. The model accounted for 90% of the variance in the experimental data. Its main elements were positive ATCase regulation by ATP and negative by CTP, with the negative effects of CTP dominating the positive ones of ATP when both regulators were abundant (i.e., a negative cooperative effect of ATP x CTP). Strong sensitivity to both ATP and CTP concentrations occurred in their physiological concentration ranges. UTP had only a slight effect, and GTP had almost none. These findings support a predominant role of CTP and ATP in ATCase regulation. The general approach provides a new paradigm for dissecting multifactorial regulation of biological molecules and processes.

High efficiency classification of children with autism spectrum disorder.

Autism spectrum disorder (ASD) is a wide-ranging collection of developmental diseases with varying symptoms and degrees of disability. Currently, ASD is diagnosed mainly with psychometric tools, often unable to provide an early and reliable diagnosis. Recently, biochemical methods are being explored as a means to meet the latter need. For example, an increased predisposition to ASD has been associated with abnormalities of metabolites in folate-dependent one carbon metabolism (FOCM) and transsulfuration (TS). Multiple metabolites in the FOCM/TS pathways have been measured, and statistical analysis tools employed to identify certain metabolites that are closely related to ASD. The prime difficulty in such biochemical studies comes from (i) inefficient determination of which metabolites are most important and (ii) understanding how these metabolites are collectively related to ASD. This paper presents a new method based on scores produced in Support Vector Machine (SVM) modeling combined with High Dimensional Model Representation (HDMR) sensitivity analysis. The new method effectively and efficiently identifies the key causative metabolites in FOCM/TS pathways, ranks their importance, and discovers their independent and correlative action patterns upon ASD. Such information is valuable not only for providing a foundation for a pathological interpretation but also for potentially providing an early, reliable diagnosis ideally leading to a subsequent comprehensive treatment of ASD. With only tens of SVM model runs, the new method can identify the combinations of the most important metabolites in the FOCM/TS pathways that lead to ASD. Previous efforts to find these metabolites required hundreds of thousands of model runs with the same data.

Analysis of gene network robustness based on saturated fixed point attractors.

The analysis of gene network robustness to noise and mutation is important for fundamental and practical reasons. Robustness refers to the stability of the equilibrium expression state of a gene network to variations of the initial expression state and network topology. Numerical simulation of these variations is commonly used for the assessment of robustness. Since there exists a great number of possible gene network topologies and initial states, even millions of simulations may be still too small to give reliable results. When the initial and equilibrium expression states are restricted to being saturated (i.e., their elements can only take values 1 or -1 corresponding to maximum activation and maximum repression of genes), an analytical gene network robustness assessment is possible. We present this analytical treatment based on determination of the saturated fixed point attractors for sigmoidal function models. The analysis can determine (a) for a given network, which and how many saturated equilibrium states exist and which and how many saturated initial states converge to each of these saturated equilibrium states and (b) for a given saturated equilibrium state or a given pair of saturated equilibrium and initial states, which and how many gene networks, referred to as viable, share this saturated equilibrium state or the pair of saturated equilibrium and initial states. We also show that the viable networks sharing a given saturated equilibrium state must follow certain patterns. These capabilities of the analytical treatment make it possible to properly define and accurately determine robustness to noise and mutation for gene networks. Previous network research conclusions drawn from performing millions of simulations follow directly from the results of our analytical treatment. Furthermore, the analytical results provide criteria for the identification of model validity and suggest modified models of gene network dynamics. The yeast cell-cycle network is used as an illustration of the practical application of this analytical treatment.

Identifying biological network structure, predicting network behavior, and classifying network state with High Dimensional Model Representation (HDMR).

This work presents an adapted Random Sampling - High Dimensional Model Representation (RS-HDMR) algorithm for synergistically addressing three key problems in network biology: (1) identifying the structure of biological networks from multivariate data, (2) predicting network response under previously unsampled conditions, and (3) inferring experimental perturbations based on the observed network state. RS-HDMR is a multivariate regression method that decomposes network interactions into a hierarchy of non-linear component functions. Sensitivity analysis based on these functions provides a clear physical and statistical interpretation of the underlying network structure. The advantages of RS-HDMR include efficient extraction of nonlinear and cooperative network relationships without resorting to discretization, prediction of network behavior without mechanistic modeling, robustness to data noise, and favorable scalability of the sampling requirement with respect to network size. As a proof-of-principle study, RS-HDMR was applied to experimental data measuring the single-cell response of a protein-protein signaling network to various experimental perturbations. A comparison to network structure identified in the literature and through other inference methods, including Bayesian and mutual-information based algorithms, suggests that RS-HDMR can successfully reveal a network structure with a low false positive rate while still capturing non-linear and cooperative interactions. RS-HDMR identified several higher-order network interactions that correspond to known feedback regulations among multiple network species and that were unidentified by other network inference methods. Furthermore, RS-HDMR has a better ability to predict network response under unsampled conditions in this application than the best statistical inference algorithm presented in the recent DREAM3 signaling-prediction competition. RS-HDMR can discern and predict differences in network state that arise from sources ranging from intrinsic cell-cell variability to altered experimental conditions, such as when drug perturbations are introduced. This ability ultimately allows RS-HDMR to accurately classify the experimental conditions of a given sample based on its observed network state.

Nonlinear bionetwork structure inference using the random sampling-high dimensional model representation (RS-HDMR) algorithm.

This work presents the random sampling - high dimensional model representation (RS-HDMR) algorithm for identifying complex bionetwork structures from multivariate data. RS-HDMR describes network interactions through a hierarchy of input-output (IO) functions of increasing dimensionality. Sensitivity analysis based on the calculated RS-HDMR component functions provides a statistically interpretable measure of network interaction strength, and can be used to efficiently infer network structure. Advantages of RS-HDMR include the ability to capture nonlinear and cooperative realtionships among network components, the ability to handle both continuous and discrete relationships, the ability to be used as a high-dimensional IO model for quantitative property prediction, and favorable scalability with respect to the number of variables. To demonstrate, RS-HDMR was applied to experimental data measuring the single-cell response of a protein-protein signaling network to various perturbations. The resultant analysis identified the network structure comparable to that reported in the literature and to the results from a previous Bayesian network (BN) analysis. The IO model also revealed several nonlinear feedback and cooperative mechanisms that were unidentified through BN analysis.