Jujube fruit cracking has become a major concern in jujube production. It can affect fruit quality and yield and crop productivity, resulting in significant economic loss. Fruit cracking occurs at the maturation period when favorable environmental conditions such as rainfalls are present. Changes in environment factors, and fertilizer input as well as changes in plant physiological metabolism contribute to the development of fruit cracking, resulting in fruit surface cracking, flesh exertion and acidifying decay (Figure 1 and Figure 2). Fruit cracking currently poses severe challenges to jujube producers.

The development and the adoption of a systemic modeling approach that help to understand the functions of external and internal factors are one of the solutions to the successful management of jujube fruit cracking. Recent advances in our understanding of plant physiology from the molecular to the whole-plant levels and behavior and functional relationships between multiple elements in the whole system or organism make it possible towards this goal [1] -[3] . The emergence of bioinformatics has facilitated the analysis of complicated networks and assisted in identifying novel components and biological pathways [4] . Mathematical modeling of these pathways helps to generate new hypotheses and experimental designs, improving our understanding of biochemical processes in plants [5] [6] . In the context of computational systems biology, modeling can be used to identify connections between elements in a network and to predict the spatio-temporal dynamics of a system through simulations of model variables [7] . Kinetic modeling on the use of lipase for the hydrolysis of fats and oils, and the prediction of the hydrolysis rate, although they are still lacking, can offer advantages over conventional chemical reactions. A Ping-Pong Bi Bi model with substrate inhibition by water has been used to describe the reaction mechanism and kinetic characteristics of lipase-catalyzed hydrolysis of palm olein [8] . Modeling studies do not necessarily end at the model development stage. New information can also be generated from analyzing performance and behavior of the model itself [4] . In this article, we present some salient examples of modeling studies in plant systems. Comprehensive reviews of plant morphogenesis and growth modeling have been published [9] [10] . Stockle et al. (2003) developed CropSyst, a multi-year, multi-crop, daily time step cropping systems simulation model, which can serve as an analytical tool to study the effects of climate, soil, and management on cropping systems productivity. CropSyst is able to better simulate soil, water and nitrogen budgets, crop growth and development, crop yield, residue production and decomposition, soil erosion by water, and salinity [11] . More recently, functional-structural plant models, which stem from early plant architectural models, have emerged to incorporate with the effects of shoot structure on light interception to better understand the availability of biomass for the growth of individual organ and the whole plant [12] -[14] . Grima and Schnell (2008) reviewed four distinct theoretical and simulation frameworks, showing that taking noise and space into account not only improves quantitative prediction accuracy but also may lead to qualitatively different physiological predictions, unaccounted by classical deterministic models [15] . In a stochastic functional-structural model developed by Kang et al. (2008) to simulate plant development and growth, it is clearly indicated that the number of organs (internodes, leaves and fruits) produced by the model is not only a key intermediate variable for biomass production computation, but also an indicator of model complexity [16] . Furthermore, Harrington et al. (2010) developed a new curves modeling on the effectiveness of temperature for chilling and forcing based on their data and published information, which can predict the effectiveness over a wide range of temperatures [17] .

Objective of this article was to develop a novel functional and/or integrated modeling software for jujube fruit cracking that can serve as a viable modeling tool to help our understanding of the jujube plant network structure and their functional mechanisms. The results of this research demonstrate, for the first time, how to use modeling approaches to better manage jujube fruit cracking by manipulating external environment and other inputs and internal physiological metabolism parameters. Some perspectives on the directions of future development of jujube fruit cracking modeling systems were discussed.

There have been increased concerns about the vulnerability of agricultural production to climate change. The potential impacts of climate change on crop production have been widely analyzed and hypothesized by using crop models and climate change scenarios, but little evidence of the observed impacts of climate change on crop production has been reported [18] . Over the past decade there has been an increased interest in developing methodology that can study intracellular reactions, in particular those focusing on the determination of kinetic parameters [19] . Typically, data obtained from experimental assays are input into a mathematical model before it can be interpreted meaningfully. The bulk of these models are based on the macroscopic and deterministic models of classical physical chemistry [20] . A prominent example of this analysis is the characterization of enzymes using the Michaelis-Menten equation [21] . The use of any type of modeling methodology implicitly assumes that a number of physical, chemical or biochemical constraints are satisfied [15] . So external environment and inputs including climate, soil and management as well as internal physiological metabolism parameters are among the most important factors for the development of such plant modeling systems. This article reports the functional and/or integrated modeling software for jujube fruit cracking (Figure 3). The external environment and inputs and internal physiological metabolism parameters (Figures 3(A)-(B)) are presented as follows:

Application of modeling techniques of engineering and physical sciences will help to understand how a suite of different biological, physical, and chemical signals interact and regulate plant growth and development. Indeed, these techniques have been already used in plant modeling such as the description of water, gas, and nutrition transport in the fruit, root, and stem [23] [24] . There is also a potential need to use a modular approach to improve existing models as practiced in climate modeling [25] . Modeling approaches can be applicable to crop research at different levels. Models that integrate genetic, molecular and biochemical information can facilitate our understanding of complex behavior such as pathway integration whereas models that cross scales from the molecular, cellular to whole plant or field level have enormous potential in crop improvement and crop yield forecasting [26] . With the global demand for food projected to increase 70% - 100% by 2050, innovation approaches to enhance crop robustness and yield will play an increasingly important role in meeting the nutritional demands of a growing world population [22] [27] -[29] . We need to look at different examples of models that cover various levels of biological organization, systems and scales. As demonstrated in our study as an example, simulation-based models are useful and viable in identifying new network components and interactions that are not always intuitive from experimental data. This is a good example of how experimental data are required to construct a model, and model prediction can in turn drive new hypotheses for testing in the lab and the field.

In this study, a circadian clock system has been incorporated into our modeling software for jujube fruit cracking. Such clock is a complicated system that can coordinate external stimuli and an internal timing mechanism to optimize the growth and development of jujube fruit. Further investigation into the functions of known clock components and the elucidation of interactions between the clock and input and output pathways will help us to understand how plants thrive in a predictably changing environment. As illustrated by recent studies in crop plants, these insights are likely to have important implications for agricultural improvement.

As illustrated in this study, the development and use of reliable and viable modeling techniques can improve our understanding and management of jujube fruit cracking. To our knowledge, this is the first report to help our understanding of the jujube fruit cracking system.

The systemic modeling software proposed here can provide a novel tool for the effective management of jujube fruit cracking.

We thank China National Forestry Industry Research Special Funds for the Public Welfare (No. 201004041) and Shanxi Province Science and Technology Development Grant Programs (No. 20110311012-4 and 20130311021-2) for providing financial support for this research.

The authors declare no conflict of interest.

YBH conceived and designed the study, and drafted the manuscript. YQS, JL and CFT participated in the design and coordination of the study. XGZ reviewed and revised the design and manuscript, and prepared the final version of the manuscript. LLL supervised the study and provided the key information for design. All authors read and approved the final manuscript.