a b s t r a c t A simple kinetic model structure for chlorophyll fluorescence (ChlF) from Photosy... more a b s t r a c t A simple kinetic model structure for chlorophyll fluorescence (ChlF) from Photosystem II (PSII) offers practical usefulness in quantitative analysis and extraction of information from measured ChlF. In this work, the major PSII phototransduction kinetics was represented with only five state variables. Parameters were estimated through a least-squares algorithm. The developed model structure could produce the well-known OJIP pattern and fit measured ChlF. Influences of PQ pool size, active Q B sites, and Q A reduction rate on ChlF emission were simulated and discussed in light of the existing literature.
In the photosynthesis process, part of the absorbed photon energy in photosystem II (PSII) may be... more In the photosynthesis process, part of the absorbed photon energy in photosystem II (PSII) may be reemitted as chlorophyll a fluorescence (ChlF). Environmental and plant physiological changes affect the emission of ChlF, which makes ChlF a potentially useful tool to sense these changes. Volumes of research on ChlF are published each year and some published work has been controversial. To facilitate the application of ChlF, it is important to have a holistic picture of the field. This review summarizes ChlF applications published in the last 10 years.
Retinal damage can occur in normal ambient lighting conditions. Infants are particularly vulnerab... more Retinal damage can occur in normal ambient lighting conditions. Infants are particularly vulnerable to retinal damage, and thousands of preterm infants sustain vision damage each year. The size of the ocular fundus affects retinal light absorption, but there is a lack of understanding of this effect for infants. In this work, retinal light absorption is simulated for different ocular fundus sizes, wavelengths, and pigment concentrations by using the Monte Carlo method. The results indicate that the neural retina light absorption per volume for infants can be two or more times that for adults.
Physiologically-based drought stress evaluation is very desirable for sustainable plant productio... more Physiologically-based drought stress evaluation is very desirable for sustainable plant production, but effective measures and technologies are lacking. Drought stress limits photons utilized for photosynthetic reactions and delayed fluorescence (DF) generated by photosystem II (PSII). In this research, DF is measured as an output variable of the PSII phototransduction system and its dependence on photon utilization rate as affected by water status is modeled and analyzed. This yields an effective way to define and measure plant water status or deficiency (drought stress) according to PSII photon utilization rate. Water deficiency is determined by the deficit from the maximum photon utilization rate achievable through rehydration. The method was validated experimentally with drought-stressed plant samples. Analysis and experiments show that this drought-dependent deficit in photon utilization rate can be effectively evaluated from measured DF emissions and it varies with drought severity.
Many systems can be represented as linear time-invariant (LTI) systems in state space with ordina... more Many systems can be represented as linear time-invariant (LTI) systems in state space with ordinary di erential equations (ODE). Forced responses are often used for model parameter estimation; however, some models are not uniquely identi able from the data of forced responses, or experiments with pure forced response may not be the optimal design. It is thus meaningful to look for other types of data for model parameter estimation through redesigning experiments. In this work, we compare the in uence of forced and initial condition responses on the deterministic identi ability of LTI systems in state space with ODEs as model structure. It is clearly demonstrated that one initial condition vector is equivalent to one column vector of the control matrix for constraining system eigenvectors. The combination of forced and initial condition responses can improve the identi ability of models that are not identi able only from forced responses. Explicit formulations and an algorithm are derived to identify model parameters from the combined data of forced and initial condition responses.
Kinetic Monte Carlo (KMC) simulation is employed to represent the photochemical reactions involve... more Kinetic Monte Carlo (KMC) simulation is employed to represent the photochemical reactions involved in the initial phases of chlorophyll fluorescence (ChlF) emission from photosystem II (PSII). Comparison with a differential equation representation reveals similarities and differences. Both KMC and differential equation models can describe the kinetic variations and show the main characteristics of ChlF emission. Differential equation models are simpler to implement but have limitations that warrant future improvements.
We developed a Monte Carlo model to calculate light absorption in human and mouse retinas. The re... more We developed a Monte Carlo model to calculate light absorption in human and mouse retinas. The retina was modeled as a five-layer spherical structure. The effects of melanin concentrations in the retinal pigment epithelium (RPE) and choroid layer were studied. Variations of blood content in choroid were also considered in the simulation. Our simulation results indicated that light absorption in neural retina was at least 20% higher in albino subjects than in pigmented subjects under both photobleaching and dark-adapted conditions. It can be four times higher at optical wavelengths corresponding to minimal hemoglobin absorption. The elevated absorption at neural retina was attributed to the light backscattered from the choroid and sclera layers. This simulation model may provide useful information in studying light-induced retina damage.
Forced responses are commonly used for system identification, but only initial condition response... more Forced responses are commonly used for system identification, but only initial condition responses may be available when a system has no controllable inputs or forced responses cannot be practically measured. It is therefore meaningful to analyse whether initial condition responses can be used to estimate the system matrix. In this work, the identifiability of the nth order (n41) linear timeinvariant systems from initial condition responses is analysed. Systems with only one measurable state (OMS systems) and those with n measurable states (NMS systems) are considered. Analysis indicates that one initial condition response is not sufficient to uniquely determine the system matrix of an OMS system and n initial condition responses are necessary. The identifiability of an OMS system with data from n independent initial condition responses is equivalent to that of an NMS system with only one initial condition response. Explicit formulations and a non-iterative algorithm are developed for both OMS and NMS systems.
In this research, we demonstrated that the plastoquinone-related electron-transport kinetics in p... more In this research, we demonstrated that the plastoquinone-related electron-transport kinetics in photosynthesis could be sufficiently described with as few as three state variables, Q A − , Q B − , and Q B 2− . A third-order kinetic model structure was developed with delayed fluorescence as the measurable output. Delayed fluorescence emissions from drought-stressed, DCMU [3-(3,4-dichlorophenyl)-1,1-dimethylurea] treated, or healthy plants were measured with a photon-counting system and used to verify the model structure through nonlinear least-squares optimization. While there were no visible differences between the healthy and the stressed plants, the model showed an obvious decrease of Q A reduction rate in the drought-stressed samples and a clear decline of functional Q A Q B pairs in the DCMU-treated samples. The changes were consistent with the known mechanisms by which water and DCMU affect electron transport in photosynthetic plants. The results proved that the three-state formulation was a compact and practically useful model structure for describing delayed fluorescence from plants.
Discrete Fourier Transform (DFT) is frequently used to determine parameters like frequency, ampli... more Discrete Fourier Transform (DFT) is frequently used to determine parameters like frequency, amplitude, and phase; however, the finite length of data being used often leads to errors. Modeling a signal process in time-domain and estimating model parameters from observed data will provide a prediction about the data outside the sampled window and thus may lead to a better estimation of the signal spectrum. Many models were developed in literature for this purpose. While these models can provide better spectrum estimation than DFT, they may not be the best option because the parameter estimation is only suboptimal of least squares or the methods have very narrow convergence area. In this paper, the traditional nonlinear separable estimation has been modified and a new time-domain least-squares method was developed for the identification of multi-frequency signal parameters. Algorithm convergence was analyzed and improved through segmentation of data. Simulations and an experiment were provided to validate the effectiveness of the developed method.
Delayed fluorescence (DF) from photosystem II (PSII) of plants can be potentially used as a biose... more Delayed fluorescence (DF) from photosystem II (PSII) of plants can be potentially used as a biosensor for the detection of plant physiological status and environmental changes. It has been analyzed mainly in the time domain. Frequency-domain analysis through Fourier transform allows viewing a signal from another angle, but the usefulness of DF spectra has not been well studied. In this work, experiments were conducted to show the differences and similarities in DF spectra of different plants with short pulse excitation. The DF spectra show low-pass characteristics with first-order attenuation of high frequencies. The results also show that the low-frequency components differ while the high-frequency components are similar. These may imply the potential usefulness of Fourier spectra of DF to analyze photoelectron transport in plants and classify samples.
While photosystem II (PSII) of plants utilizes light for photosynthesis, part of the absorbed ene... more While photosystem II (PSII) of plants utilizes light for photosynthesis, part of the absorbed energy may be reverted back and dissipated as long-term fluorescence (delayed fluorescence or DF). Because the generation of DF is coupled with the processes of forward photosynthetic activities, DF contains the information about plant physiological states and plant-environment interactions. This makes DF a potentially powerful biosensing mechanism to measure plant photosynthetic activities and environmental conditions. While DF has attracted the interest of many researchers, some aspects of it are still unknown because of the complexity of photosynthetic system. In order to provide a holistic picture about the usefulness of DF, it is meaningful to summarize the research on DF applications. In this short review, available literature on applications of DF from PSII is summarized.
Herbicide application incurs water contamination and thus effective herbicide detection methods a... more Herbicide application incurs water contamination and thus effective herbicide detection methods are needed. In this research, a kinetic model was developed to describe the processes of herbicide diffusion into plant tissues and binding to the active sites. DCMU [3-(3,4-dichlorophenyl)-1,1-dimethylurea], a commonly used herbicide, was used as a test chemical and its diffusion into plant leaves and binding to plastoquinone B (Q B ) sites were analyzed by using the model. The dependency of delayed fluorescence (DF) emission on unbound Q B sites was first derived theoretically and then observed experimentally. This yields a biophotonic method to measure the concentrations of DCMU and other herbicides that function by a similar mechanism. Experiments were performed to validate the developed method.
Pulse is often used to excite biological systems. The inputs such as irrigation, therapy, and tre... more Pulse is often used to excite biological systems. The inputs such as irrigation, therapy, and treatments to biological systems are also equivalent to pulses. This makes the biological system behave as switched models under the function of the input. To reduce difficulty in model parameter estimation, the system could be represented as a switched linear model under the pulse excitation. In this research, we studied the identification of a class of switched linear biological models with single input and the system matrix dependent on the intensity of excitation. System identifiability and identification were discussed. A recurrent-pulse excitation method was devised to provide necessary constraints for parameter estimation. The recurrent-pulse technique allowed determination of model parameters that would otherwise be difficult to determine uniquely. The usefulness of the method was demonstrated by examples including delayed fluorescence from photosystem II, which was well known as a versatile tool for sensing plant physiological status and environmental changes in the literature.
Attempts to account for the variations in photosystem II (PSII) under general conditions result i... more Attempts to account for the variations in photosystem II (PSII) under general conditions result in non-linear and cumbersome models that are difficult to validate and render few insights about the system kinetics. In this research, the authors experimentally show that under certain conditions, linear-system techniques could be applied to advantage for probing some basic kinetic characteristics of the plastoquinones (PQs). The PQ redox states of the reaction centres were represented in a conditionally linear model structure with delayed fluorescence (DF) as a measurable output. DF data were acquired for different plant samples and conditions. After least-squares parameter optimisation, not only could the model closely describe the measured DF, but more significantly, the estimated parameters correctly reflected the expected changes induced by drought or [3-(3,4-dichlorophenyl)-1,1dimethylurea] (DCMU) stress. Analysis showed that for short-pulse illumination, the PQ kinetic states of the reaction centres in an initially dark-adapted plant leaf can be represented as a time-invariant bilinear system in a five-dimensional state space. The system becomes linear for constant illuminations, but the system matrix and the kinetic behaviour are illumination dependent. In particular, the system behaves differently between lights-on and lights-off conditions. The simplicity of the model structure, nonetheless, permits observation and analysis of the PQ kinetics of PSII reaction centres from DF measurements by using linear-system techniques.
Wavelet transform is used to analyze PAM chlorophyll a fluorescence for the first time. Wavelet-b... more Wavelet transform is used to analyze PAM chlorophyll a fluorescence for the first time. Wavelet-based features showed promising effectiveness in revealing plant stresses. The work demonstrates how chlorophyll a fluorescence may be analyzed in the time-frequency domain.
First attempt to use delayed fluorescence (DF) to sense herbicides in frequency domain. A quantit... more First attempt to use delayed fluorescence (DF) to sense herbicides in frequency domain. A quantitative method to measure herbicides was derived based on DF spectrum. Experiments clearly validated the developed method. The work serves as an example to use DF in frequency domain for other applications.
a b s t r a c t A simple kinetic model structure for chlorophyll fluorescence (ChlF) from Photosy... more a b s t r a c t A simple kinetic model structure for chlorophyll fluorescence (ChlF) from Photosystem II (PSII) offers practical usefulness in quantitative analysis and extraction of information from measured ChlF. In this work, the major PSII phototransduction kinetics was represented with only five state variables. Parameters were estimated through a least-squares algorithm. The developed model structure could produce the well-known OJIP pattern and fit measured ChlF. Influences of PQ pool size, active Q B sites, and Q A reduction rate on ChlF emission were simulated and discussed in light of the existing literature.
In the photosynthesis process, part of the absorbed photon energy in photosystem II (PSII) may be... more In the photosynthesis process, part of the absorbed photon energy in photosystem II (PSII) may be reemitted as chlorophyll a fluorescence (ChlF). Environmental and plant physiological changes affect the emission of ChlF, which makes ChlF a potentially useful tool to sense these changes. Volumes of research on ChlF are published each year and some published work has been controversial. To facilitate the application of ChlF, it is important to have a holistic picture of the field. This review summarizes ChlF applications published in the last 10 years.
Retinal damage can occur in normal ambient lighting conditions. Infants are particularly vulnerab... more Retinal damage can occur in normal ambient lighting conditions. Infants are particularly vulnerable to retinal damage, and thousands of preterm infants sustain vision damage each year. The size of the ocular fundus affects retinal light absorption, but there is a lack of understanding of this effect for infants. In this work, retinal light absorption is simulated for different ocular fundus sizes, wavelengths, and pigment concentrations by using the Monte Carlo method. The results indicate that the neural retina light absorption per volume for infants can be two or more times that for adults.
Physiologically-based drought stress evaluation is very desirable for sustainable plant productio... more Physiologically-based drought stress evaluation is very desirable for sustainable plant production, but effective measures and technologies are lacking. Drought stress limits photons utilized for photosynthetic reactions and delayed fluorescence (DF) generated by photosystem II (PSII). In this research, DF is measured as an output variable of the PSII phototransduction system and its dependence on photon utilization rate as affected by water status is modeled and analyzed. This yields an effective way to define and measure plant water status or deficiency (drought stress) according to PSII photon utilization rate. Water deficiency is determined by the deficit from the maximum photon utilization rate achievable through rehydration. The method was validated experimentally with drought-stressed plant samples. Analysis and experiments show that this drought-dependent deficit in photon utilization rate can be effectively evaluated from measured DF emissions and it varies with drought severity.
Many systems can be represented as linear time-invariant (LTI) systems in state space with ordina... more Many systems can be represented as linear time-invariant (LTI) systems in state space with ordinary di erential equations (ODE). Forced responses are often used for model parameter estimation; however, some models are not uniquely identi able from the data of forced responses, or experiments with pure forced response may not be the optimal design. It is thus meaningful to look for other types of data for model parameter estimation through redesigning experiments. In this work, we compare the in uence of forced and initial condition responses on the deterministic identi ability of LTI systems in state space with ODEs as model structure. It is clearly demonstrated that one initial condition vector is equivalent to one column vector of the control matrix for constraining system eigenvectors. The combination of forced and initial condition responses can improve the identi ability of models that are not identi able only from forced responses. Explicit formulations and an algorithm are derived to identify model parameters from the combined data of forced and initial condition responses.
Kinetic Monte Carlo (KMC) simulation is employed to represent the photochemical reactions involve... more Kinetic Monte Carlo (KMC) simulation is employed to represent the photochemical reactions involved in the initial phases of chlorophyll fluorescence (ChlF) emission from photosystem II (PSII). Comparison with a differential equation representation reveals similarities and differences. Both KMC and differential equation models can describe the kinetic variations and show the main characteristics of ChlF emission. Differential equation models are simpler to implement but have limitations that warrant future improvements.
We developed a Monte Carlo model to calculate light absorption in human and mouse retinas. The re... more We developed a Monte Carlo model to calculate light absorption in human and mouse retinas. The retina was modeled as a five-layer spherical structure. The effects of melanin concentrations in the retinal pigment epithelium (RPE) and choroid layer were studied. Variations of blood content in choroid were also considered in the simulation. Our simulation results indicated that light absorption in neural retina was at least 20% higher in albino subjects than in pigmented subjects under both photobleaching and dark-adapted conditions. It can be four times higher at optical wavelengths corresponding to minimal hemoglobin absorption. The elevated absorption at neural retina was attributed to the light backscattered from the choroid and sclera layers. This simulation model may provide useful information in studying light-induced retina damage.
Forced responses are commonly used for system identification, but only initial condition response... more Forced responses are commonly used for system identification, but only initial condition responses may be available when a system has no controllable inputs or forced responses cannot be practically measured. It is therefore meaningful to analyse whether initial condition responses can be used to estimate the system matrix. In this work, the identifiability of the nth order (n41) linear timeinvariant systems from initial condition responses is analysed. Systems with only one measurable state (OMS systems) and those with n measurable states (NMS systems) are considered. Analysis indicates that one initial condition response is not sufficient to uniquely determine the system matrix of an OMS system and n initial condition responses are necessary. The identifiability of an OMS system with data from n independent initial condition responses is equivalent to that of an NMS system with only one initial condition response. Explicit formulations and a non-iterative algorithm are developed for both OMS and NMS systems.
In this research, we demonstrated that the plastoquinone-related electron-transport kinetics in p... more In this research, we demonstrated that the plastoquinone-related electron-transport kinetics in photosynthesis could be sufficiently described with as few as three state variables, Q A − , Q B − , and Q B 2− . A third-order kinetic model structure was developed with delayed fluorescence as the measurable output. Delayed fluorescence emissions from drought-stressed, DCMU [3-(3,4-dichlorophenyl)-1,1-dimethylurea] treated, or healthy plants were measured with a photon-counting system and used to verify the model structure through nonlinear least-squares optimization. While there were no visible differences between the healthy and the stressed plants, the model showed an obvious decrease of Q A reduction rate in the drought-stressed samples and a clear decline of functional Q A Q B pairs in the DCMU-treated samples. The changes were consistent with the known mechanisms by which water and DCMU affect electron transport in photosynthetic plants. The results proved that the three-state formulation was a compact and practically useful model structure for describing delayed fluorescence from plants.
Discrete Fourier Transform (DFT) is frequently used to determine parameters like frequency, ampli... more Discrete Fourier Transform (DFT) is frequently used to determine parameters like frequency, amplitude, and phase; however, the finite length of data being used often leads to errors. Modeling a signal process in time-domain and estimating model parameters from observed data will provide a prediction about the data outside the sampled window and thus may lead to a better estimation of the signal spectrum. Many models were developed in literature for this purpose. While these models can provide better spectrum estimation than DFT, they may not be the best option because the parameter estimation is only suboptimal of least squares or the methods have very narrow convergence area. In this paper, the traditional nonlinear separable estimation has been modified and a new time-domain least-squares method was developed for the identification of multi-frequency signal parameters. Algorithm convergence was analyzed and improved through segmentation of data. Simulations and an experiment were provided to validate the effectiveness of the developed method.
Delayed fluorescence (DF) from photosystem II (PSII) of plants can be potentially used as a biose... more Delayed fluorescence (DF) from photosystem II (PSII) of plants can be potentially used as a biosensor for the detection of plant physiological status and environmental changes. It has been analyzed mainly in the time domain. Frequency-domain analysis through Fourier transform allows viewing a signal from another angle, but the usefulness of DF spectra has not been well studied. In this work, experiments were conducted to show the differences and similarities in DF spectra of different plants with short pulse excitation. The DF spectra show low-pass characteristics with first-order attenuation of high frequencies. The results also show that the low-frequency components differ while the high-frequency components are similar. These may imply the potential usefulness of Fourier spectra of DF to analyze photoelectron transport in plants and classify samples.
While photosystem II (PSII) of plants utilizes light for photosynthesis, part of the absorbed ene... more While photosystem II (PSII) of plants utilizes light for photosynthesis, part of the absorbed energy may be reverted back and dissipated as long-term fluorescence (delayed fluorescence or DF). Because the generation of DF is coupled with the processes of forward photosynthetic activities, DF contains the information about plant physiological states and plant-environment interactions. This makes DF a potentially powerful biosensing mechanism to measure plant photosynthetic activities and environmental conditions. While DF has attracted the interest of many researchers, some aspects of it are still unknown because of the complexity of photosynthetic system. In order to provide a holistic picture about the usefulness of DF, it is meaningful to summarize the research on DF applications. In this short review, available literature on applications of DF from PSII is summarized.
Herbicide application incurs water contamination and thus effective herbicide detection methods a... more Herbicide application incurs water contamination and thus effective herbicide detection methods are needed. In this research, a kinetic model was developed to describe the processes of herbicide diffusion into plant tissues and binding to the active sites. DCMU [3-(3,4-dichlorophenyl)-1,1-dimethylurea], a commonly used herbicide, was used as a test chemical and its diffusion into plant leaves and binding to plastoquinone B (Q B ) sites were analyzed by using the model. The dependency of delayed fluorescence (DF) emission on unbound Q B sites was first derived theoretically and then observed experimentally. This yields a biophotonic method to measure the concentrations of DCMU and other herbicides that function by a similar mechanism. Experiments were performed to validate the developed method.
Pulse is often used to excite biological systems. The inputs such as irrigation, therapy, and tre... more Pulse is often used to excite biological systems. The inputs such as irrigation, therapy, and treatments to biological systems are also equivalent to pulses. This makes the biological system behave as switched models under the function of the input. To reduce difficulty in model parameter estimation, the system could be represented as a switched linear model under the pulse excitation. In this research, we studied the identification of a class of switched linear biological models with single input and the system matrix dependent on the intensity of excitation. System identifiability and identification were discussed. A recurrent-pulse excitation method was devised to provide necessary constraints for parameter estimation. The recurrent-pulse technique allowed determination of model parameters that would otherwise be difficult to determine uniquely. The usefulness of the method was demonstrated by examples including delayed fluorescence from photosystem II, which was well known as a versatile tool for sensing plant physiological status and environmental changes in the literature.
Attempts to account for the variations in photosystem II (PSII) under general conditions result i... more Attempts to account for the variations in photosystem II (PSII) under general conditions result in non-linear and cumbersome models that are difficult to validate and render few insights about the system kinetics. In this research, the authors experimentally show that under certain conditions, linear-system techniques could be applied to advantage for probing some basic kinetic characteristics of the plastoquinones (PQs). The PQ redox states of the reaction centres were represented in a conditionally linear model structure with delayed fluorescence (DF) as a measurable output. DF data were acquired for different plant samples and conditions. After least-squares parameter optimisation, not only could the model closely describe the measured DF, but more significantly, the estimated parameters correctly reflected the expected changes induced by drought or [3-(3,4-dichlorophenyl)-1,1dimethylurea] (DCMU) stress. Analysis showed that for short-pulse illumination, the PQ kinetic states of the reaction centres in an initially dark-adapted plant leaf can be represented as a time-invariant bilinear system in a five-dimensional state space. The system becomes linear for constant illuminations, but the system matrix and the kinetic behaviour are illumination dependent. In particular, the system behaves differently between lights-on and lights-off conditions. The simplicity of the model structure, nonetheless, permits observation and analysis of the PQ kinetics of PSII reaction centres from DF measurements by using linear-system techniques.
Wavelet transform is used to analyze PAM chlorophyll a fluorescence for the first time. Wavelet-b... more Wavelet transform is used to analyze PAM chlorophyll a fluorescence for the first time. Wavelet-based features showed promising effectiveness in revealing plant stresses. The work demonstrates how chlorophyll a fluorescence may be analyzed in the time-frequency domain.
First attempt to use delayed fluorescence (DF) to sense herbicides in frequency domain. A quantit... more First attempt to use delayed fluorescence (DF) to sense herbicides in frequency domain. A quantitative method to measure herbicides was derived based on DF spectrum. Experiments clearly validated the developed method. The work serves as an example to use DF in frequency domain for other applications.
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