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Knowing chemical soil properties might be determinant in crop management and total yield production. Traditional soil properties estimation approaches are time-consuming and require complex lab setups, refraining farmers from promptly taking steps towards optimal practices in their crops. Soil properties estimation from its spectral signals, vis-NIRS, emerged as a low-cost, non-invasive, and non-destructive alternative. Current approaches use mathematical and statistical techniques, avoiding machine learning frameworks. This proposal uses vis-NIRS in sugarcane soils and machine learning techniques such as three regression and six classification methods. The scope is to assess performance in predicting and inferring categories of common soil properties (pH, soil organic matter OM, Ca, Na, K, and Mg), evaluated by the most common metrics. We use regression to estimate properties and classification to assess soil property status. In both cases, we achieved comparable performance on similar setups reported in the literature for property estimation for pH($R^2$=0.8, $\rho$=0.89), OM($R^2$=0.37, $\rho$=0.63), Ca($R^2$=0.54, $\rho$=0.74), Mg($R^2$=0.44, $\rho$=0.66) in the validation set.

Recent experiments have supported the Adder model for E. coli division control. This model posits that bacteria grow, on average, a fixed size before division. It also predicts decorrelation between the noise in the added size and the size at birth. Here we use new experiments and a theoretical approach based on continuous rate models to explore deviations from the adder strategy, specifically, the division control of E. coli growing with glycerol as carbon source. In this medium, the division strategy is sizer-like, which means that the added size decreases with the size at birth. We found that in a sizer-like strategy the mean added size decreases with the size at birth while the noise in added size increases. We discuss possible molecular mechanisms underlying this strategy, and propose a general model that encompasses the different division strategies.

In the stochastic formulation of chemical kinetics, the stationary moments of the population count of species can be described via a set of linear equations. However, except for some specific cases such as systems with linear reaction propensities, the moment equations are underdetermined as a lower order moment might depend upon a higher order moment. Here, we propose a method to find lower, and upper bounds on stationary moments of molecular counts in a chemical reaction system. The method exploits the fact that statistical moments of any positive-valued random variable must satisfy some constraints. Such constraints can be expressed as nonlinear inequalities on moments in terms of their lower order moments, and solving them in conjugation with the stationary moment equations results in bounds on the moments. Using two examples of biochemical systems, we illustrate that not only one obtains upper and lower bounds on a given stationary moment, but these bounds also improve as one uses more moment equations and utilizes the inequalities for the corresponding higher order moments. Our results provide avenues for development of moment approximations that provide explicit bounds on moment dynamics for systems whose dynamics are otherwise intractable.

A ubiquitous feature of living cells is their growth over time followed by division into daughter cells. How isogenic cell populations maintain size homeostasis, i.e., a narrow distribution of cell size, is an intriguing fundamental problem. We model cell size using a stochastic hybrid system, where a cell grows exponentially in size (volume) over time and probabilistic division events are triggered at discrete time intervals. Moreover, whenever division events occur, size is randomly partitioned among daughter cells. We first consider a scenario, where a timer (i.e., cell-cycle clock) that measures the time since the last division event regulates both the cellular growth and division rates. Analysis reveals that such a timer-controlled system cannot achieve size homeostasis, in the sense that, the cell-to-cell size variation grows unboundedly with time. To explore biologically meaningful mechanisms for controlling size we consider two classes of regulation: a size-dependent growth rate and a size-dependent division rate. Our results show that these strategies can provide bounded intercellular variation in cell size, and exact mathematical conditions on the form of regulation needed for size homeostasis are derived. Different known forms of size control strategies, such as, the adder and the sizer are shown to be consistent with these results. Interestingly, for timer-based division mechanisms, the mean cell size depends on the noise in the cell-cycle duration but independent of errors incurred in partitioning of volume among daughter cells. In contrast, the mean cell size decreases with increasing partitioning errors for size-based division mechanisms. Finally, we discuss how organisms ranging from bacteria to mammalian cells have adopted different control approaches for maintaining size homeostasis.

How exponentially growing cells maintain size homeostasis is an important fundamental problem. Recent single-cell studies in prokaryotes have uncovered the adder principle, where cells on average, add a fixed size (volume) from birth to division. Interestingly, this added volume differs considerably among genetically-identical newborn cells with similar sizes suggesting a stochastic component in the timing of cell-division. To mechanistically explain the adder principle, we consider a time-keeper protein that begins to get stochastically expressed after cell birth at a rate proportional to the volume. Cell-division time is formulated as the first-passage time for protein copy numbers to hit a fixed threshold. Consistent with data, the model predicts that while the mean cell-division time decreases with increasing size of newborns, the noise in timing increases with size at birth. Intriguingly, our results show that the distribution of the volume added between successive cell-division events is independent of the newborn cell size. This was dramatically seen in experimental studies, where histograms of the added volume corresponding to different newborn sizes collapsed on top of each other. The model provides further insights consistent with experimental observations: the distributions of the added volume and the cell-division time when scaled by their respective means become invariant of the growth rate. Finally, we discuss various modifications to the proposed model that lead to deviations from the adder principle. In summary, our simple yet elegant model explains key experimental findings and suggests a mechanism for regulating both the mean and fluctuations in cell-division timing for size control.

Inside individual cells, expression of genes is inherently stochastic and manifests as cell-to-cell variability or noise in protein copy numbers. Since proteins half-lives can be comparable to the cell-cycle length, randomness in cell-division times generates additional intercellular variability in protein levels. Moreover, as many mRNA/protein species are expressed at low-copy numbers, errors incurred in partitioning of molecules between the mother and daughter cells are significant. We derive analytical formulas for the total noise in protein levels for a general class of cell-division time and partitioning error distributions. Using a novel hybrid approach the total noise is decomposed into components arising from i) stochastic expression; ii) partitioning errors at the time of cell-division and iii) random cell-division events. These formulas reveal that random cell-division times not only generate additional extrinsic noise but also critically affect the mean protein copy numbers and intrinsic noise components. Counter intuitively, in some parameter regimes noise in protein levels can decrease as cell-division times become more stochastic. Computations are extended to consider genome duplication, where the gene dosage is increased by two-fold at a random point in the cell-cycle. We systematically investigate how the timing of genome duplication influences different protein noise components. Intriguingly, results show that noise contribution from stochastic expression is minimized at an optimal genome duplication time. Our theoretical results motivate new experimental methods for decomposing protein noise levels from single-cell expression data. Characterizing the contributions of individual noise mechanisms will lead to precise estimates of gene expression parameters and techniques for altering stochasticity to change phenotype of individual cells., Comment: 40 pages, 10 figures