# Mathematical Modeling to Estimate Photosynthesis: A State of the Art
In the morning, when the water supply is abundant and solar radiation favors photosynthetic activity, the demand for CO\({}_{2}\) inside the leaf is big and the stomatal pores are wide open, reducing the stomatal resistance to the diffusion of the CO\({}_{2}\)[8]. Plants have developed three photosynthetic systems, C\({}_{3}\), C\({}_{4}\), and CAM (Crassulacean acid metabolism), with different anatomical and chemical characteristics [9], the C\({}_{3}\) type being the most common [10; 11]. The main difference between the types of photosynthesis lies in the way CO\({}_{2}\) is synthesized. The first step in the Calvin cycle is carbon dioxide fixation by rubisco. Plants that use only this \"standard\" carbon fixation mechanism are called C\({}_{3}\) plants because of the three-carbon compound (3-PGA) that they produce during this part of the photosynthetic process. In C\({}_{4}\) plants, the light-dependent reactions and the Calvin cycle are physically separated: the light-dependent reactions occur in the cells of the mesophyll (spongy tissue in the center of the leaf) and the Calvin cycle occurs in special cells around the veins of the leaf. These cells are called vascular bundle cells. Some plants adapted to dry environments use the crassulaceae acid metabolism (CAM) pathway to minimize photorespiration. Instead of separating the light-dependent reactions and the use of CO\({}_{2}\) in the Calvin cycle, the temporary separation of photosynthetic processes in CAM plants causes carbon assimilation to take place at night. At night, they open their stomata so that the CO\({}_{2}\) diffuses into the leaves. This CO\({}_{2}\) is fixed to oxaloacetate by PEP carboxylase (the same step that C\({}_{4}\) plants use), which is then converted into malate or another organic acid [8]. The organic acid is stored inside vacuoles until the next day. During the day, CAM plants do not open their stomata, but they can still carry out photosynthesis. Because organic acids are transported out of vacuoles and broken down to release CO\({}_{2}\), which enters the Calvin cycle. This controlled cycle maintains a high concentration of CO\({}_{2}\) around rubisco [4]. The ability to represent the three photosynthetic types (C\({}_{3}\), C\({}_{4}\), and CAM) has important implications for studying natural ecosystems and agroecosystems [12]. The described complex process of photosynthesis must work, integrally and efficiently, in an environment where there is an enormous natural variability of factors that affect the rate of photosynthesis. For instance, light, environment temperature, air humidity,availability of water, and mineral nutrients in the soil, among others. Carbon dioxide (CO\({}_{2}\)) can also be considered as part of this list of relevant factors due to global climate change [13]. The photosynthesis rate of a leaf is conditioned by one of more than 50 individual reactions, each presenting its response to each environmental variable. This photosynthetic rate can widely vary between days and also throughout seasons, due to environmental factors such as light and temperature. It can also vary in the longer term during the coming decades as a response to increasing atmospheric CO\({}_{2}\) levels. The increase in CO\({}_{2}\) and other greenhouse gases in the atmosphere can cause global climate change. As can be understood, each of the aforementioned environmental factors affects the photosynthesis rate in a different way, depending on the time scale [8]. Photosynthesis is important for many reasons. From humanity's point of view, it produces food and oxygen; therefore, it is often studied in its end products. However, these are secondary aspects of an integral process. The most important aspects are capturing and transforming light [14]. A critical component of crop production is the ability to produce more biomass [15]. Photosynthesis at the ecosystem scale, also known as the gross primary productivity (GPP), is the first step of CO\({}_{2}\) entering the biosphere from the atmosphere.