PeerJ:Mathematical Biologyhttps://peerj.com/articles/index.atom?journal=peerj&subject=1900Mathematical Biology articles published in PeerJComparing enzyme activity modifier equations through the development of global data fitting templates in Excelhttps://peerj.com/articles/60822018-12-142018-12-14Ryan Walsh
The classical way of defining enzyme inhibition has obscured the distinction between inhibitory effect and the inhibitor binding constant. This article examines the relationship between the simple binding curve used to define biomolecular interactions and the standard inhibitory term (1 + ([I]∕Ki)). By understanding how this term relates to binding curves which are ubiquitously used to describe biological processes, a modifier equation which distinguishes between inhibitor binding and the inhibitory effect, is examined. This modifier equation which can describe both activation and inhibition is compared to standard inhibitory equations with the development of global data fitting templates in Excel and via the global fitting of these equations to simulated and previously published datasets. In both cases, this modifier equation was able to match or outperform the other equations by providing superior fits to the datasets. The ability of this single equation to outperform the other equations suggests an over-complication of the field. This equation and the template developed in this article should prove to be useful tools in the study of enzyme inhibition and activation.
The classical way of defining enzyme inhibition has obscured the distinction between inhibitory effect and the inhibitor binding constant. This article examines the relationship between the simple binding curve used to define biomolecular interactions and the standard inhibitory term (1 + ([I]∕Ki)). By understanding how this term relates to binding curves which are ubiquitously used to describe biological processes, a modifier equation which distinguishes between inhibitor binding and the inhibitory effect, is examined. This modifier equation which can describe both activation and inhibition is compared to standard inhibitory equations with the development of global data fitting templates in Excel and via the global fitting of these equations to simulated and previously published datasets. In both cases, this modifier equation was able to match or outperform the other equations by providing superior fits to the datasets. The ability of this single equation to outperform the other equations suggests an over-complication of the field. This equation and the template developed in this article should prove to be useful tools in the study of enzyme inhibition and activation.Modelling of the SDF-1/CXCR4 regulated in vivo homing of therapeutic mesenchymal stem/stromal cells in micehttps://peerj.com/articles/60722018-12-062018-12-06Wang JinXiaowen LiangAnastasia BrooksKathryn FutregaXin LiuMichael R. DoranMatthew J. SimpsonMichael S. RobertsHaolu Wang
Background
Mesenchymal stem/stromal cells (MSCs) are a promising tool for cell-based therapies in the treatment of tissue injury. The stromal cell-derived factor-1 (SDF-1)/CXC chemokine receptor 4 (CXCR4) axis plays a significant role in directing MSC homing to sites of injury. However in vivo MSC distribution following intravenous transplantation remains poorly understood, potentially hampering the precise prediction and evaluation of therapeutic efficacy.
Methods
A murine model of partial ischemia/reperfusion (I/R) is used to induce liver injury, increase the hepatic levels of SDF-1, and study in vivo MSC distribution. Hypoxia-preconditioning increases the expression of CXCR4 in human bone marrow-derived MSCs. Quantitative assays for human DNA using droplet digital PCR (ddPCR) allow us to examine the in vivo kinetics of intravenously infused human MSCs in mouse blood and liver. A mathematical model-based system is developed to characterize in vivo homing of human MSCs in mouse models with SDF-1 levels in liver and CXCR4 expression on the transfused MSCs. The model is calibrated to experimental data to provide novel estimates of relevant parameter values.
Results
Images of immunohistochemistry for SDF-1 in the mouse liver with I/R injury show a significantly higher SDF-1 level in the I/R injured liver than that in the control. Correspondingly, the ddPCR results illustrate a higher MSC concentration in the I/R injured liver than the normal liver. CXCR4 is overexpressed in hypoxia-preconditioned MSCs. An increased number of hypoxia-preconditioned MSCs in the I/R injured liver is observed from the ddPCR results. The model simulations align with the experimental data of control and hypoxia-preconditioned human MSC distribution in normal and injured mouse livers, and accurately predict the experimental outcomes with different MSC doses.
Discussion
The modelling results suggest that SDF-1 in organs is an effective in vivo attractant for MSCs through the SDF-1/CXCR4 axis and reveal the significance of the SDF-1/CXCR4 chemotaxis on in vivo homing of MSCs. This in vivo modelling approach allows qualitative characterization and prediction of the MSC homing to normal and injured organs on the basis of clinically accessible variables, such as the MSC dose and SDF-1 concentration in blood. This model could also be adapted to abnormal conditions and/or other types of circulating cells to predict in vivo homing patterns.
Background
Mesenchymal stem/stromal cells (MSCs) are a promising tool for cell-based therapies in the treatment of tissue injury. The stromal cell-derived factor-1 (SDF-1)/CXC chemokine receptor 4 (CXCR4) axis plays a significant role in directing MSC homing to sites of injury. However in vivo MSC distribution following intravenous transplantation remains poorly understood, potentially hampering the precise prediction and evaluation of therapeutic efficacy.
Methods
A murine model of partial ischemia/reperfusion (I/R) is used to induce liver injury, increase the hepatic levels of SDF-1, and study in vivo MSC distribution. Hypoxia-preconditioning increases the expression of CXCR4 in human bone marrow-derived MSCs. Quantitative assays for human DNA using droplet digital PCR (ddPCR) allow us to examine the in vivo kinetics of intravenously infused human MSCs in mouse blood and liver. A mathematical model-based system is developed to characterize in vivo homing of human MSCs in mouse models with SDF-1 levels in liver and CXCR4 expression on the transfused MSCs. The model is calibrated to experimental data to provide novel estimates of relevant parameter values.
Results
Images of immunohistochemistry for SDF-1 in the mouse liver with I/R injury show a significantly higher SDF-1 level in the I/R injured liver than that in the control. Correspondingly, the ddPCR results illustrate a higher MSC concentration in the I/R injured liver than the normal liver. CXCR4 is overexpressed in hypoxia-preconditioned MSCs. An increased number of hypoxia-preconditioned MSCs in the I/R injured liver is observed from the ddPCR results. The model simulations align with the experimental data of control and hypoxia-preconditioned human MSC distribution in normal and injured mouse livers, and accurately predict the experimental outcomes with different MSC doses.
Discussion
The modelling results suggest that SDF-1 in organs is an effective in vivo attractant for MSCs through the SDF-1/CXCR4 axis and reveal the significance of the SDF-1/CXCR4 chemotaxis on in vivo homing of MSCs. This in vivo modelling approach allows qualitative characterization and prediction of the MSC homing to normal and injured organs on the basis of clinically accessible variables, such as the MSC dose and SDF-1 concentration in blood. This model could also be adapted to abnormal conditions and/or other types of circulating cells to predict in vivo homing patterns.Shielding effects of myelin sheath on axolemma depolarization under transverse electric field stimulationhttps://peerj.com/articles/60202018-12-032018-12-03Hui YeJeffrey Ng
Axonal stimulation with electric currents is an effective method for controlling neural activity. An electric field parallel to the axon is widely accepted as the predominant component in the activation of an axon. However, recent studies indicate that the transverse component to the axolemma is also effective in depolarizing the axon. To quantitatively investigate the amount of axolemma polarization induced by a transverse electric field, we computed the transmembrane potential (Vm) for a conductive body that represents an unmyelinated axon (or the bare axon between the myelin sheath in a myelinated axon). We also computed the transmembrane potential of the sheath-covered axonal segment in a myelinated axon. We then systematically analyzed the biophysical factors that affect axonal polarization under transverse electric stimulation for both the bare and sheath-covered axons. Geometrical patterns of polarization of both axon types were dependent on field properties (magnitude and field orientation to the axon). Polarization of both axons was also dependent on their axolemma radii and electrical conductivities. The myelin provided a significant “shielding effect” against the transverse electric fields, preventing excessive axolemma depolarization. Demyelination could allow for prominent axolemma depolarization in the transverse electric field, via a significant increase in myelin conductivity. This shifts the voltage drop of the myelin sheath to the axolemma. Pathological changes at a cellular level should be considered when electric fields are used for the treatment of demyelination diseases. The calculated term for membrane polarization (Vm) could be used to modify the current cable equation that describes axon excitation by an external electric field to account for the activating effects of both parallel and transverse fields surrounding the target axon.
Axonal stimulation with electric currents is an effective method for controlling neural activity. An electric field parallel to the axon is widely accepted as the predominant component in the activation of an axon. However, recent studies indicate that the transverse component to the axolemma is also effective in depolarizing the axon. To quantitatively investigate the amount of axolemma polarization induced by a transverse electric field, we computed the transmembrane potential (Vm) for a conductive body that represents an unmyelinated axon (or the bare axon between the myelin sheath in a myelinated axon). We also computed the transmembrane potential of the sheath-covered axonal segment in a myelinated axon. We then systematically analyzed the biophysical factors that affect axonal polarization under transverse electric stimulation for both the bare and sheath-covered axons. Geometrical patterns of polarization of both axon types were dependent on field properties (magnitude and field orientation to the axon). Polarization of both axons was also dependent on their axolemma radii and electrical conductivities. The myelin provided a significant “shielding effect” against the transverse electric fields, preventing excessive axolemma depolarization. Demyelination could allow for prominent axolemma depolarization in the transverse electric field, via a significant increase in myelin conductivity. This shifts the voltage drop of the myelin sheath to the axolemma. Pathological changes at a cellular level should be considered when electric fields are used for the treatment of demyelination diseases. The calculated term for membrane polarization (Vm) could be used to modify the current cable equation that describes axon excitation by an external electric field to account for the activating effects of both parallel and transverse fields surrounding the target axon.Cochlear impulse responses resolved into sets of gammatones: the case for beating of closely spaced local resonanceshttps://peerj.com/articles/60162018-11-272018-11-27Andrew BellHero P. Wit
Gammatones have had a long history in auditory studies, and recent theoretical work suggests they may play an important role in cochlear mechanics as well. Following this lead, the present paper takes five examples of basilar membrane impulse responses and uses a curve-fitting algorithm to decompose them into a number of discrete gammatones. The limits of this ‘sum of gammatones’ (SOG) method to accurately represent the impulse response waveforms were tested and it was found that at least two and up to six gammatones could be isolated from each example. Their frequencies were stable and largely independent of stimulus parameters. The gammatones typically formed a regular series in which the frequency ratio between successive members was about 1.1. Adding together the first few gammatones in a set produced beating-like waveforms which mimicked waxing and waning, and the instantaneous frequencies of the waveforms were also well reproduced, providing an explanation for frequency glides. Consideration was also given to the impulse response of a pair of elastically coupled masses—the basis of two-degree-of-freedom models comprised of coupled basilar and tectorial membranes—and the resulting waveform was similar to a pair of beating gammatones, perhaps explaining why the SOG method seems to work well in describing cochlear impulse responses. A major limitation of the SOG method is that it cannot distinguish a waveform resulting from an actual physical resonance from one derived from overfitting, but taken together the method points to the presence of a series of closely spaced local resonances in the cochlea.
Gammatones have had a long history in auditory studies, and recent theoretical work suggests they may play an important role in cochlear mechanics as well. Following this lead, the present paper takes five examples of basilar membrane impulse responses and uses a curve-fitting algorithm to decompose them into a number of discrete gammatones. The limits of this ‘sum of gammatones’ (SOG) method to accurately represent the impulse response waveforms were tested and it was found that at least two and up to six gammatones could be isolated from each example. Their frequencies were stable and largely independent of stimulus parameters. The gammatones typically formed a regular series in which the frequency ratio between successive members was about 1.1. Adding together the first few gammatones in a set produced beating-like waveforms which mimicked waxing and waning, and the instantaneous frequencies of the waveforms were also well reproduced, providing an explanation for frequency glides. Consideration was also given to the impulse response of a pair of elastically coupled masses—the basis of two-degree-of-freedom models comprised of coupled basilar and tectorial membranes—and the resulting waveform was similar to a pair of beating gammatones, perhaps explaining why the SOG method seems to work well in describing cochlear impulse responses. A major limitation of the SOG method is that it cannot distinguish a waveform resulting from an actual physical resonance from one derived from overfitting, but taken together the method points to the presence of a series of closely spaced local resonances in the cochlea.Optimal and near-optimal exponent-pairs for the Bertalanffy-Pütter growth modelhttps://peerj.com/articles/59732018-11-232018-11-23Katharina Renner-MartinNorbert BrunnerManfred KühleitnerWerner-Georg NowakKlaus Scheicher
The Bertalanffy–Pütter growth model describes mass m at age t by means of the differential equation dm/dt = p * ma − q * mb. The special case using the von Bertalanffy exponent-pair a = 2/3 and b = 1 is most common (it corresponds to the von Bertalanffy growth function VBGF for length in fishery literature). Fitting VBGF to size-at-age data requires the optimization of three model parameters (the constants p, q, and an initial value for the differential equation). For the general Bertalanffy–Pütter model, two more model parameters are optimized (the pair a < b of non-negative exponents). While this reduces bias in growth estimates, it increases model complexity and more advanced optimization methods are needed, such as the Nelder–Mead amoeba method, interior point methods, or simulated annealing. Is the improved performance worth these efforts? For the case, where the exponent b = 1 remains fixed, it is known that for most fish data any exponent a < 1 could be used to model growth without affecting the fit to the data significantly (when the other parameters were optimized). We hypothesized that the optimization of both exponents would result in a significantly better fit of the optimal growth function to the data and we tested this conjecture for a data set (20,166 fish) about the mass-growth of Walleye (Sander vitreus), a fish from Lake Erie, USA. To this end, we assessed the fit on a grid of 14,281 exponent-pairs (a, b) and identified the best fitting model curve on the boundary a = b of the grid (a = b = 0.686); it corresponds to the generalized Gompertz equation dm/dt = p * ma − q * ln(m) * ma. Using the Akaike information criterion for model selection, the answer to the conjecture was no: The von Bertalanffy exponent-pair model (but not the logistic model) remained parsimonious. However, the bias reduction attained by the optimal exponent-pair may be worth the tradeoff with complexity in some situations where predictive power is solely preferred. Therefore, we recommend the use of the Bertalanffy–Pütter model (and of its limit case, the generalized Gompertz model) in natural resources management (such as in fishery stock assessments), as it relies on careful quantitative assessments to recommend policies for sustainable resource usage.
The Bertalanffy–Pütter growth model describes mass m at age t by means of the differential equation dm/dt = p * ma − q * mb. The special case using the von Bertalanffy exponent-pair a = 2/3 and b = 1 is most common (it corresponds to the von Bertalanffy growth function VBGF for length in fishery literature). Fitting VBGF to size-at-age data requires the optimization of three model parameters (the constants p, q, and an initial value for the differential equation). For the general Bertalanffy–Pütter model, two more model parameters are optimized (the pair a < b of non-negative exponents). While this reduces bias in growth estimates, it increases model complexity and more advanced optimization methods are needed, such as the Nelder–Mead amoeba method, interior point methods, or simulated annealing. Is the improved performance worth these efforts? For the case, where the exponent b = 1 remains fixed, it is known that for most fish data any exponent a < 1 could be used to model growth without affecting the fit to the data significantly (when the other parameters were optimized). We hypothesized that the optimization of both exponents would result in a significantly better fit of the optimal growth function to the data and we tested this conjecture for a data set (20,166 fish) about the mass-growth of Walleye (Sander vitreus), a fish from Lake Erie, USA. To this end, we assessed the fit on a grid of 14,281 exponent-pairs (a, b) and identified the best fitting model curve on the boundary a = b of the grid (a = b = 0.686); it corresponds to the generalized Gompertz equation dm/dt = p * ma − q * ln(m) * ma. Using the Akaike information criterion for model selection, the answer to the conjecture was no: The von Bertalanffy exponent-pair model (but not the logistic model) remained parsimonious. However, the bias reduction attained by the optimal exponent-pair may be worth the tradeoff with complexity in some situations where predictive power is solely preferred. Therefore, we recommend the use of the Bertalanffy–Pütter model (and of its limit case, the generalized Gompertz model) in natural resources management (such as in fishery stock assessments), as it relies on careful quantitative assessments to recommend policies for sustainable resource usage.The BackMAP Python module: how a simpler Ramachandran number can simplify the life of a protein simulatorhttps://peerj.com/articles/57452018-10-162018-10-16Ranjan Mannige
Protein backbones occupy diverse conformations, but compact metrics to describe such conformations and transitions between them have been missing. This report re-introduces the Ramachandran number (ℛ) as a residue-level structural metric that could simply the life of anyone contending with large numbers of protein backbone conformations (e.g., ensembles from NMR and trajectories from simulations). Previously, the Ramachandran number (ℛ) was introduced using a complicated closed form, which made the Ramachandran number difficult to implement. This report discusses a much simpler closed form of ℛ that makes it much easier to calculate, thereby making it easy to implement. Additionally, this report discusses how ℛ dramatically reduces the dimensionality of the protein backbone, thereby making it ideal for simultaneously interrogating large numbers of protein structures. For example, 200 distinct conformations can easily be described in one graphic using ℛ (rather than 200 distinct Ramachandran plots). Finally, a new Python-based backbone analysis tool—BackMAP—is introduced, which reiterates how ℛ can be used as a simple and succinct descriptor of protein backbones and their dynamics.
Protein backbones occupy diverse conformations, but compact metrics to describe such conformations and transitions between them have been missing. This report re-introduces the Ramachandran number (ℛ) as a residue-level structural metric that could simply the life of anyone contending with large numbers of protein backbone conformations (e.g., ensembles from NMR and trajectories from simulations). Previously, the Ramachandran number (ℛ) was introduced using a complicated closed form, which made the Ramachandran number difficult to implement. This report discusses a much simpler closed form of ℛ that makes it much easier to calculate, thereby making it easy to implement. Additionally, this report discusses how ℛ dramatically reduces the dimensionality of the protein backbone, thereby making it ideal for simultaneously interrogating large numbers of protein structures. For example, 200 distinct conformations can easily be described in one graphic using ℛ (rather than 200 distinct Ramachandran plots). Finally, a new Python-based backbone analysis tool—BackMAP—is introduced, which reiterates how ℛ can be used as a simple and succinct descriptor of protein backbones and their dynamics.Resource availability and adjustment of social behaviour influence patterns of inequality and productivity across societieshttps://peerj.com/articles/54882018-10-022018-10-02António M.M. Rodrigues
Animal societies vary widely in the diversity of social behaviour and the distribution of reproductive shares among their group members. It has been shown that individual condition can lead to divergent social roles and that social specialisation can cause an exacerbation or a mitigation of the inequality among group members within a society. This work, however, has not investigated cases in which resource availability varies between different societies, a factor that is thought to explain variation in the level of cooperation and the disparities in reproductive shares within each social group. In this study, I focus on how resource availability mediates the expression of social behaviour and how this, in turn, mediates inequality both within and between groups. I find that when differences in resource availability between societies persist over time, resource-rich societies become more egalitarian. Because lower inequality improves the productivity of a society, the inequality between resource-rich and resource-poor societies rises. When resource availability fluctuates over time, resource-rich societies tend to become more unequal. Because inequality hinders the productivity of a society, the inequality between resource-rich and resource-poor societies falls. From the evolutionary standpoint, my results show that spatial and temporal variation in resource availability may exert a strong influence on the level of inequality both within and between societies.
Animal societies vary widely in the diversity of social behaviour and the distribution of reproductive shares among their group members. It has been shown that individual condition can lead to divergent social roles and that social specialisation can cause an exacerbation or a mitigation of the inequality among group members within a society. This work, however, has not investigated cases in which resource availability varies between different societies, a factor that is thought to explain variation in the level of cooperation and the disparities in reproductive shares within each social group. In this study, I focus on how resource availability mediates the expression of social behaviour and how this, in turn, mediates inequality both within and between groups. I find that when differences in resource availability between societies persist over time, resource-rich societies become more egalitarian. Because lower inequality improves the productivity of a society, the inequality between resource-rich and resource-poor societies rises. When resource availability fluctuates over time, resource-rich societies tend to become more unequal. Because inequality hinders the productivity of a society, the inequality between resource-rich and resource-poor societies falls. From the evolutionary standpoint, my results show that spatial and temporal variation in resource availability may exert a strong influence on the level of inequality both within and between societies.Analysis of relative abundances with zeros on environmental gradients: a multinomial regression modelhttps://peerj.com/articles/56432018-09-272018-09-27Fiona ChongMatthew Spencer
Ecologists often analyze relative abundances, which are an example of compositional data. However, they have made surprisingly little use of recent advances in the field of compositional data analysis. Compositions form a vector space in which addition and scalar multiplication are replaced by operations known as perturbation and powering. This algebraic structure makes it easy to understand how relative abundances change along environmental gradients. We illustrate this with an analysis of changes in hard-substrate marine communities along a depth gradient. We fit a quadratic multivariate regression model with multinomial observations to point count data obtained from video transects. As well as being an appropriate observation model in this case, the multinomial deals with the problem of zeros, which often makes compositional data analysis difficult. We show how the algebra of compositions can be used to understand patterns in dissimilarity. We use the calculus of simplex-valued functions to estimate rates of change, and to summarize the structure of the community over a vertical slice. We discuss the benefits of the compositional approach in the interpretation and visualization of relative abundance data.
Ecologists often analyze relative abundances, which are an example of compositional data. However, they have made surprisingly little use of recent advances in the field of compositional data analysis. Compositions form a vector space in which addition and scalar multiplication are replaced by operations known as perturbation and powering. This algebraic structure makes it easy to understand how relative abundances change along environmental gradients. We illustrate this with an analysis of changes in hard-substrate marine communities along a depth gradient. We fit a quadratic multivariate regression model with multinomial observations to point count data obtained from video transects. As well as being an appropriate observation model in this case, the multinomial deals with the problem of zeros, which often makes compositional data analysis difficult. We show how the algebra of compositions can be used to understand patterns in dissimilarity. We use the calculus of simplex-valued functions to estimate rates of change, and to summarize the structure of the community over a vertical slice. We discuss the benefits of the compositional approach in the interpretation and visualization of relative abundance data.Estimating the frequency of multiplets in single-cell RNA sequencing from cell-mixing experimentshttps://peerj.com/articles/55782018-09-032018-09-03Jesse D. Bloom
In single-cell RNA-sequencing, it is important to know the frequency at which the sequenced transcriptomes actually derive from multiple cells. A common method to estimate this multiplet frequency is to mix two different types of cells (e.g., human and mouse), and then determine how often the transcriptomes contain transcripts from both cell types. When the two cell types are mixed in equal proportion, the calculation of the multiplet frequency from the frequency of mixed transcriptomes is straightforward. But surprisingly, there are no published descriptions of how to calculate the multiplet frequency in the general case when the cell types are mixed unequally. Here, I derive equations to analytically calculate the multiplet frequency from the numbers of observed pure and mixed transcriptomes when two cell types are mixed in arbitrary proportions, under the assumption that the loading of cells into droplets or wells is Poisson.
In single-cell RNA-sequencing, it is important to know the frequency at which the sequenced transcriptomes actually derive from multiple cells. A common method to estimate this multiplet frequency is to mix two different types of cells (e.g., human and mouse), and then determine how often the transcriptomes contain transcripts from both cell types. When the two cell types are mixed in equal proportion, the calculation of the multiplet frequency from the frequency of mixed transcriptomes is straightforward. But surprisingly, there are no published descriptions of how to calculate the multiplet frequency in the general case when the cell types are mixed unequally. Here, I derive equations to analytically calculate the multiplet frequency from the numbers of observed pure and mixed transcriptomes when two cell types are mixed in arbitrary proportions, under the assumption that the loading of cells into droplets or wells is Poisson.Analysis of the light intensity dependence of the growth of Synechocystis and of the light distribution in a photobioreactor energized by 635 nm lighthttps://peerj.com/articles/52562018-07-272018-07-27Alessandro CordaraAngela ReCristina PaglianoPascal Van AlphenRaffaele PironeGuido SaraccoFilipe Branco dos SantosKlaas HellingwerfNicolò Vasile
Synechocystis gathered momentum in modelling studies and biotechnological applications owing to multiple factors like fast growth, ability to fix carbon dioxide into valuable products, and the relative ease of genetic manipulation. Synechocystis physiology and metabolism, and consequently, the productivity of Synechocystis-based photobioreactors (PBRs), are heavily light modulated. Here, we set up a turbidostat-controlled lab-scale cultivation system in order to study the influence of varying orange–red light intensities on Synechocystis growth characteristics and photosynthetic activity. Synechocystis growth and photosynthetic activity were found to raise as supplied light intensity increased up to 500 μmol photons m−2 s−1 and to enter the photoinhibition state only at 800 μmol photons m−2 s−1. Interestingly, reverting the light to a non-photo-inhibiting intensity unveiled Synechocystis to be able to promptly recover. Furthermore, our characterization displayed a clear correlation between variations in growth rate and cell size, extending a phenomenon previously observed in other cyanobacteria. Further, we applied a modelling approach to simulate the effects produced by varying the incident light intensity on its local distribution within the PBR vessel. Our model simulations suggested that the photosynthetic activity of Synechocystis could be enhanced by finely regulating the intensity of the light incident on the PBR in order to prevent cells from experiencing light-induced stress and induce their exploitation of areas of different local light intensity formed in the vessel. In the latter case, the heterogeneous distribution of the local light intensity would allow Synechocystis for an optimized usage of light.
Synechocystis gathered momentum in modelling studies and biotechnological applications owing to multiple factors like fast growth, ability to fix carbon dioxide into valuable products, and the relative ease of genetic manipulation. Synechocystis physiology and metabolism, and consequently, the productivity of Synechocystis-based photobioreactors (PBRs), are heavily light modulated. Here, we set up a turbidostat-controlled lab-scale cultivation system in order to study the influence of varying orange–red light intensities on Synechocystis growth characteristics and photosynthetic activity. Synechocystis growth and photosynthetic activity were found to raise as supplied light intensity increased up to 500 μmol photons m−2 s−1 and to enter the photoinhibition state only at 800 μmol photons m−2 s−1. Interestingly, reverting the light to a non-photo-inhibiting intensity unveiled Synechocystis to be able to promptly recover. Furthermore, our characterization displayed a clear correlation between variations in growth rate and cell size, extending a phenomenon previously observed in other cyanobacteria. Further, we applied a modelling approach to simulate the effects produced by varying the incident light intensity on its local distribution within the PBR vessel. Our model simulations suggested that the photosynthetic activity of Synechocystis could be enhanced by finely regulating the intensity of the light incident on the PBR in order to prevent cells from experiencing light-induced stress and induce their exploitation of areas of different local light intensity formed in the vessel. In the latter case, the heterogeneous distribution of the local light intensity would allow Synechocystis for an optimized usage of light.