Optimal Control with RdCVFL for Degenerating Photoreceptors.

Both the rod and cone photoreceptors, along with the retinal pigment epithelium have been experimentally and mathematically shown to work interdependently to maintain vision. Further, the theoredoxin-like rod-derived cone viability factor (RdCVF) and its long form (RdCVFL) have proven to increase photoreceptor survival in experimental results. Aerobic glycolysis is the primary source of energy production for photoreceptors and RdCVF accelerates the intake of glucose into the cones. RdCVFL helps mitigate the negative effects of reactive oxidative species and has shown promise in slowing the death of cones in mouse studies. However, this potential treatment and its effects have never been studied in mathematical models. In this work, we examine an optimal control with the treatment of RdCVFL. We mathematically illustrate the potential this treatment might have for treating degenerative retinal diseases such as retinitis pigmentosa, as well as compare this to the results of an updated control model with RdCVF.

The role of RdCVFL in a mathematical model of photoreceptor interactions.

Recent experimental and mathematical work has shown the interdependence of the rod and cone photoreceptors with the retinal pigment epithelium in maintaining sight. Accelerated intake of glucose into the cones via the theoredoxin-like rod-derived cone viability factor (RdCVF) is needed as aerobic glycolysis is the primary source of energy production. Reactive oxidative species (ROS) result from the rod and cone metabolism and recent experimental work has shown that the long form of RdCVF (RdCVFL) helps mitigate the negative effects of ROS. In this work we investigate the role of RdCVFL in maintaining the health of the photoreceptors. The results of our mathematical model show the necessity of RdCVFL and also demonstrate additional stable modes that are present in this system. The sensitivity analysis shows the importance of glucose uptake, nutrient levels, and ROS mitigation in maintaining rod and cone health in light-damaged mouse models. Together, these suggests areas on which to focus treatment in order to prolong the photoreceptors, especially in situations where ROS is a contributing factor to their death such as retinitis pigmentosa.

Site mutation of residues in a loop surrounding the active site of a PI snake venom metalloproteinase abrogates its hemorrhagic activity.

Abrogation of the hemorrhagic activity of BaP1, a PI Snake Venom Metalloproteinase (SVMP) from the venom of Bothrops asper, was achieved by the substitution of residues in the first part of the Ω loop surrounding the active site by the corresponding residues of a structurally-similar non-hemorrhagic PI SVMP from a related venom. Previous studies by molecular dynamic simulation showed higher flexibility in the first part of the loop in hemorrhagic SVMPs, as compared to non-hemorrhagic SVMPs. It has been suggested that the Ω loop is critical for protein-protein interface and may be involved in the interaction with extracellular matrix proteins, hence influencing the ability of the toxin to bind and hydrolyze basement membrane components. The SVMP with the site mutation completely lost hemorrhagic activity, and only had a partial reduction of proteolytic activity, indicating that this region in the loop plays a key role in the ability to induce hemorrhage. Our findings demonstrate a key structural determinant of the hemorrhagic capacity of PI SVMPs.

The Vicodin abuse problem: A mathematical approach.

The prescription drug epidemic in the United States has gained attention in recent years. Vicodin, along with its generic version, is the country's mostly widely prescribed pain reliever, and it contains a narcotic component that can lead to physical and chemical dependency. The majority of Vicodin abusers were first introduced via prescription, unlike other drugs which are often experienced for the first time due to experimentation. Most abusers report obtaining their supply from a prescription, either their own or someone else's. Although the problem with prescription drug abuse is well known, there is no standard method of addressing the problem. To better understand how to do this, we develop and analyze a mathematical model of Vicodin use and abuse, considering only those patients who were initially prescribed the drug. Through global sensitivity analysis, we show that focusing efforts on abuse prevention rather than treatment has greater success at reducing the population of Vicodin abusers. Our results demonstrate that relying solely on rehabilitation and other treatment programs is not enough to combat the prescription drug problem in the United States. We anticipate that implementing preventative measures in both prescribers and patients will reduce the number of Vicodin abusers.

Quantifying the metabolic contribution to photoreceptor death in retinitis pigmentosa via a mathematical model.

Retinitis pigmentosa (RP) is a family of inherited retinal degenerative diseases that leads to blindness. In many cases the disease-causing allele encodes for a gene exclusively expressed in the night active rod photoreceptors. However, because rod death always leads to cone death affected individuals eventually lose their sight. Many theories have been proposed to explain the secondary loss of cones in RP; however, most fail to fully explain the different pathological transition stages seen in humans. Incorporating experimental data of rod and cone death kinetics from two mouse models of RP, we use a mathematical model to investigate the interplay and role of energy consumption and uptake of the photoreceptors as well as nutrient availability supplied through the retinal pigment epithelium (RPE) throughout the progression of RP. Our data driven mathematical model predicts that the system requires a total reduction of approximately 27-31% in nutrients available to result in the complete demise of all cones. Simulations utilizing retinal degeneration 1 (rd1) mouse cell count data in which cone death was delayed by altering cell metabolism in cones show that preventing a 1-2% decrease in nutrients available can permanently halt cone death even when 90% have already died. Our results also indicate that the ratio of energy consumption to uptake of cones, Dc, is mainly disrupted during the death wave of the rods with negligible changes thereafter and that the subsequent nutrient decrease is mainly responsible for the demise of the cones. The change in this ratio Dc highlights the compensation that the cones must undergo during rod death to meet the high metabolic demands of the entire photoreceptor population. Global sensitivity analysis confirms the results and suggests areas of focus for halting RP, even at later stages of the disease, through feasible therapeutic interventions.

Mathematical Model of the Role of RdCVF in the Coexistence of Rods and Cones in a Healthy Eye.

Understanding the essential components and processes for coexistence of rods and cones is at the forefront of retinal research. The recent discovery on RdCVF's mechanism and mode of action for enhancing cone survival brings us a step closer to unraveling key questions of coexistence and codependence of these neurons. In this work, we build from ecological and enzyme kinetic work on functional response kinetics and present a mathematical model that allows us to investigate the role of RdCVF and its contribution to glucose intake. Our model results and analysis predict a dual role of RdCVF for enhancing and repressing the healthy coexistence of the rods and cones. Our results show that maintaining RdCVF above a threshold value allows for coexistence. However, a significant increase above this value threatens the existence of rods as the cones become extremely efficient at uptaking glucose and begin to take most of it for themselves. We investigate the role of natural glucose intake and that due to RdCVF in both high and low nutrient levels. Our analysis reveals that under low nutrient levels coexistence is not possible regardless of the amount of RdCVF present. With high nutrient levels coexistence can be achieved with a relative small increase in glucose uptake. By understanding the contributions of rods to cones survival via RdCVF in a non-diseased retina, we hope to shed light on degenerative diseases such as retinitis pigmentosa.

Mathematical modeling of fungal infection in immune compromised individuals: The effect of back mutation on drug treatment.

We present a mathematical model that describes treatment of a fungal infection in an immune compromised patient in which both susceptible and resistant strains are present with a mutation allowing the susceptible strain to become resistant as well as a back mutation allowing resistant fungus to again become susceptible. The resulting nonlinear differential equations model the biological outcome, in terms of strain growth and cell number, when an individual is treated with a fungicidal or fungistatic drug. The model demonstrates that under any levels of the drug both strains will be in stable co-existence and high levels of treatment will never completely eradicate the susceptible strain. A modified model is then described in which the drug is changed to one in which both strains are susceptible, and subsequently, at the appropriate level of treatment, complete eradication of both fungal strains ensues. We discuss the model and implications for treatment options within the context of an immune compromised patient.

Parameter Estimation for Gene Regulatory Networks from Microarray Data: Cold Shock Response in Saccharomyces cerevisiae.

We investigated the dynamics of a gene regulatory network controlling the cold shock response in budding yeast, Saccharomyces cerevisiae. The medium-scale network, derived from published genome-wide location data, consists of 21 transcription factors that regulate one another through 31 directed edges. The expression levels of the individual transcription factors were modeled using mass balance ordinary differential equations with a sigmoidal production function. Each equation includes a production rate, a degradation rate, weights that denote the magnitude and type of influence of the connected transcription factors (activation or repression), and a threshold of expression. The inverse problem of determining model parameters from observed data is our primary interest. We fit the differential equation model to published microarray data using a penalized nonlinear least squares approach. Model predictions fit the experimental data well, within the 95% confidence interval. Tests of the model using randomized initial guesses and model-generated data also lend confidence to the fit. The results have revealed activation and repression relationships between the transcription factors. Sensitivity analysis indicates that the model is most sensitive to changes in the production rate parameters, weights, and thresholds of Yap1, Rox1, and Yap6, which form a densely connected core in the network. The modeling results newly suggest that Rap1, Fhl1, Msn4, Rph1, and Hsf1 play an important role in regulating the early response to cold shock in yeast. Our results demonstrate that estimation for a large number of parameters can be successfully performed for nonlinear dynamic gene regulatory networks using sparse, noisy microarray data.

Tracing the progression of retinitis pigmentosa via photoreceptor interactions.

Retinitis pigmentosa (RP) is a group of inherited degenerative eye diseases characterized by mutations in the genetic structure of the photoreceptors that leads to the premature death of both rod and cone photoreceptors. Defects in particular genes encoding proteins that are involved in either the photoreceptor structure, phototransduction cascades, or visual cycle are expressed in the rods but ultimately affect both types of cells. RP is "typically" manifested by a steady death of rods followed by a period of stability in which cones survive initially and then inevitably die too. In some RP cases, rods and cones die off simultaneously or even cone death precedes rod death (reverse RP). The mechanisms and factors involved in the development of the different types of RP are not well understood nor have researchers been able to provide more than a limited number of short-term therapies. In this work we trace the progression of RP to complete blindness through each subtype via bifurcation theory. We show that the evolution of RP from one stage to another often requires the failure of multiple components. Our results indicate that a delicate balance between the availability of nutrients and the rates of shedding and renewal of photoreceptors is needed at every stage of RP to halt its progression. This work provides a framework for future physiological investigations potentially leading to long-term targeted multi-facet interventions and therapies dependent on the particular stage and subtype of RP under consideration. The results of this mathematical model may also give insight into the progression of many other degenerative eye diseases involving genetic mutations or secondary photoreceptor death and potential ways to circumvent these diseases.

Mathematical model for glutathione dynamics in the retina.

The retina is highly susceptible to the generation of toxic reactive oxygen species (ROS) that disrupt the normal operations of retinal cells. The glutathione (GSH) antioxidant system plays an important role in mitigating ROS. To perform its protective functions, GSH depends on nicotinamide adenine dinucleotide phosphate (NADPH) produced through the pentose phosphate pathway. This work develops the first mathematical model for the GSH antioxidant system in the outer retina, capturing the most essential components for formation of ROS, GSH production, its oxidation in detoxifying ROS, and subsequent reduction by NADPH. We calibrate and validate the model using experimental measurements, at different postnatal days up to PN28, from control mice and from the rd1 mouse model for the disease retinitis pigmentosa (RP). Global sensitivity analysis is then applied to examine the model behavior and identify the pathways with the greatest impact in control compared to RP conditions. The findings underscore the importance of GSH and NADPH production in dealing with oxidative stress during retinal development, especially after peak rod degeneration occurs in RP, leading to increased oxygen tension. This suggests that stimulation of GSH and NADPH synthesis could be a potential intervention strategy in degenerative mouse retinas with RP.

Neutralization, by a polyspecific antivenom, of the coagulopathy induced by the venom of Bothrops asper: Assessment by standard coagulation tests and rotational thromboelastometry in a murine model.

Venom-induced consumption coagulopathy and thrombocytopenia are common and potentially severe manifestations of viperid snakebite envenoming since they contribute to local and systemic hemorrhage. Therefore, the assessment of the efficacy of antivenoms to neutralize coagulopathic and thrombocytopenic toxins should be part of the preclinical evaluation of these drugs. To evaluate the efficacy of the polyvalent (Crotalinae) antivenom produced in Costa Rica, in this study we have used a mouse model of coagulopathy and thrombocytopenia induced by the venom of Bothrops asper, based on the bolus intravenous (i.v.) injection of venom. When venom and antivenom were incubated before injection, or when antivenom was administered i.v. immediately after venom injection, venom-induced hemostatic alterations were largely abrogated. We also studied the recovery rate of clotting parameters in conditions where antivenom was administered when mice were coagulopathic. Some parameters recovered more rapidly in antivenom-treated mice than in control envenomed animals, but others showed a spontaneous recovery without antivenom. This is due to a rapid clearance of plasma venom levels in these experimental conditions. This implies that models based on the bolus i.v. injection of venom have limitations for assessing the effect of antivenom in the recovery of clotting alterations once coagulopathy has developed. It is suggested that alternative models should be developed based on a slower systemic absorption of venom. Overall, our findings provide a protocol for the preclinical evaluation of antivenoms and demonstrate that the polyvalent antivenom is effective in neutralizing the toxins of B. asper venom responsible for coagulopathy and thrombocytopenia.

A mathematical model of GLUT1 modulation in rods and RPE and its differential impact in cell metabolism.

We present a mathematical model of key glucose metabolic pathways in two cells of the human retina: the rods and the retinal pigmented epithelium (RPE). Computational simulations of glucose transporter 1 (GLUT1) inhibition in the model accurately reproduce experimental data from conditional knockout mice and reveal that modification of GLUT1 expression levels of both cells differentially impacts their metabolism. We hypothesize that, under glucose scarcity, the RPE's energy producing pathways are altered in order to preserve its functionality, impacting the photoreceptors' outer segment renewal. On the other hand, when glucose is limited in the rods, aerobic glycolysis is preserved, which maintains the lactate contribution to the RPE.

Insights into pathological mechanisms and interventions revealed by analyzing a mathematical model for cone metabolism.

This work analyzes a mathematical model for the metabolic dynamics of a cone photoreceptor, which is the first model to account for energy generation from fatty acids oxidation of shed photoreceptor outer segments (POS). Multiple parameter bifurcation analysis shows that joint variations in external glucose, the efficiency of glucose transporter 1 (GLUT1), lipid utilization for POS renewal, and oxidation of fatty acids affect the cone's metabolic vitality and its capability to adapt under glucose-deficient conditions. The analysis further reveals that when glucose is scarce, cone viability cannot be sustained by only fueling energy production in the mitochondria, but it also requires supporting anabolic processes to create lipids necessary for cell maintenance and repair. In silico experiments are used to investigate how the duration of glucose deprivation impacts the cell without and with a potential GLUT1 or oxidation of fatty acids intervention as well as a dual intervention. The results show that for prolonged duration of glucose deprivation, the cone metabolic system does not recover with higher oxidation of fatty acids and requires greater effectiveness of GLUT1 to recover. Finally, time-varying global sensitivity analysis (GSA) is applied to assess the sensitivity of the model outputs of interest to changes and uncertainty in the parameters at specific times. The results reveal a critical temporal window where there would be more flexibility for interventions to rescue a cone cell from the detrimental consequences of glucose shortage.

Mathematical modeling of fungal infection in immune compromised individuals: implications for drug treatment.

We present a mathematical model that describes treatment of a fungal infection in an immune compromised patient in which both susceptible and resistant strains are present. The resulting nonlinear differential equations model the biological outcome, in terms of strain growth and cell number, when an individual, who has both a susceptible and a resistant population of fungus, is treated with a fungicidal or fungistatic drug. The model demonstrates that when the drug is only successful at treating the susceptible strain, low levels of the drug cause both strains to be in stable co-existence and high levels eradicate the susceptible strain while allowing the resistant strain to persist or to multiply unchecked. A modified model is then described in which the drug is changed to one in which both strains are susceptible, and subsequently, at the appropriate level of treatment, complete eradication of both fungal strains ensues. We discuss the model and implications for treatment options within the context of an immune compromised patient.

Whole Genome Sequencing Links Mycobacterium bovis From Cattle, Cheese and Humans in Baja California, Mexico.

Mycobacterium bovis causes tuberculosis (TB) in cattle, which in turn can transmit the pathogen to humans. Tuberculosis in dairy cattle is of particular concern where the consumption of raw milk and dairy products is customary. Baja California (BCA), Mexico, presents high prevalence of TB in both cattle and humans, making it important to investigate the molecular epidemiology of the disease in the region. A long-term study was undertaken to fully characterize the diversity of M. bovis genotypes circulating in dairy cattle, cheese and humans in BCA by whole-genome sequencing (WGS). During a 2-year period, 412 granulomatous tissue samples were collected from local abattoirs and 314 cheese samples were purchased from local stores and vendors in BCA and sent to the laboratory for mycobacterial culture, histology, direct PCR and WGS. For tissue samples M. bovis was recovered from 86.8%, direct PCR detected 90% and histology confirmed 85.9% as mycobacteriosis-compatible. For cheese, M. bovis was recovered from 2.5% and direct PCR detected 6% of the samples. There was good agreement between diagnostic tests. Subsequently, a total of 345 whole-genome SNP sequences were obtained. Phylogenetic analysis grouped these isolates into 10 major clades. SNP analysis revealed putative transmission clusters where the pairwise SNP distance between isolates from different dairies was ≤3 SNP. Also, human and/or cheese isolates were within 8.45 (range 0-17) and 5.8 SNP (range 0-15), respectively, from cattle isolates. Finally, a comparison between the genotypes obtained in this study and those reported previously suggests that the genetic diversity of M. bovis in BCA is well-characterized, and can be used to determine if BCA is the likely source of M. bovis in humans and cattle in routine epidemiologic investigations and future studies. In conclusion, WGS provided evidence of ongoing local transmission of M. bovis among the dairies in this high-TB burden region of BCA, as well as show close relationships between isolates recovered from humans, cheese, and cattle. This confirms the need for a coordinated One Health approach in addressing the elimination of TB in animals and humans. Overall, the study contributes to the knowledge of the molecular epidemiology of M. bovis in BCA, providing insight into the pathogen's dynamics in a high prevalence setting.

Static behavioral effects on gonorrhea transmission dynamics in a MSM population.

An SIS/SAS model of gonorrhea transmission in a population of highly active men-having-sex-with-men (MSM) is presented in this paper to study the impact of safe behavior on the dynamics of gonorrhea prevalence. Safe behaviors may fall into two categories-prevention and self-awareness. Prevention will be modeled via consistent condom use and self-awareness via STD testing frequency. Stability conditions for the disease free equilibrium and endemic equilibrium are determined along with a complete analysis of global dynamics. The control reproductive number is used as a means for measuring the effect of changes to model parameters on the prevalence of the disease. We also find that appropriate intervention would be in the form of a multifaceted approach at overall risk reduction rather than tackling one specific control individually.

A mathematical model for photoreceptor interactions.

The interactions between rods and cones in the retina have been the focus of innumerable experimental and theoretical biological studies in previous decades yet the understanding of these interactions is still incomplete primarily due to the lack of a unified concept of cone photoreceptor organization and its role in retinal diseases. The low abundance of cones in many of the non-primate mammalian models that have been studied make conclusions about the human retina difficult. A more complete knowledge of the human retina is crucial for counteracting the events that lead to certain degenerative diseases, in particular those associated with photoreceptor cell death (e.g., retinitis pigmentosa). In an attempt to gain important insight into the role and interactions of the rods and the cones we develop and analyze a set of mathematical equations that model a system of photoreceptors and incorporate a direct rod-cone interaction. Our results show that the system can exhibit stable oscillations, which correspond to the rhythmic renewal and shedding of the photoreceptors. In addition, our results show the mathematical necessity of this rod-cone direct interaction for survival of both and gives insight into this mechanism.

Analysis of wound exudates reveals differences in the patterns of tissue damage and inflammation induced by the venoms of Daboia russelii and Bothrops asper in mice.

Clinical manifestations of envenomings by bites of the viperid snakes Bothrops asper and Daboia russelii show marked differences. Both venoms elicit the typical effects induced by viperid venoms (local tissue damage, bleeding, coagulopathies, shock). In addition, envenomings by D. russelii are characterized by a high incidence of acute kidney injury and by systemic capillary leak syndrome. The present investigation aimed to compare the local pathological and inflammatory events induced by the intramuscular injection of these venoms in a mouse model. B. asper venom induced stronger local hemorrhage, whereas D. russelii venom caused a higher extent of myonecrosis, and both venoms induced inflammation. Exudates collected from the site of tissue damage showed higher proteolytic activity in the case of samples from B. asper venom-treated mice. This activity was abrogated by antivenoms, indicating that it is the result of the action of venom proteinases. In addition, an increase in matrix metalloproteinases (MMPs) over time was detected in exudates induced by both venoms. Proteome analysis of exudates revealed higher abundance of extracellular matrix (ECM)-derived protein fragments in samples collected from B. asper venom-injected mice, whereas those from D. russelii venom-injected animals had higher amounts of intracellular proteins. Analysis of the subproteome of inflammatory mediators in exudates showed various patterns of change over time. Some mediators peaked at 180 min and decreased afterwards, whereas others increased and remained elevated during the 360 min observation period. Interestingly, various mediators (MIP-1α, MIP-1ß, KC, MIP-2, GM-CSF, VEGF, and LIX) increased and then decreased in the case of B. asper venom, while they remained elevated at 360 min in the case of D. russelii venom. Our findings show that these venoms induce a different pattern of local tissue damage and suggest that the venom of D. russelii induces a more sustained inflammatory reaction, an observation that may have implications for the pathophysiology of envenomings.

Optimal control with MANF treatment of photoreceptor degeneration.

People afflicted with diseases such as retinitis pigmentosa and age-related macular degeneration experience a decline in vision due to photoreceptor degeneration, which is currently unstoppable and irreversible. Currently there is no cure for diseases linked to photoreceptor degeneration. Recent experimental work showed that mesencephalic astrocyte-derived neurotrophic factor (MANF) can reduce neuron death and, in particular, photoreceptor death by reducing the number of cells that undergo apoptosis. In this work, we build on an existing system of ordinary differential equations that represent photoreceptor interactions and incorporate MANF treatment for three experimental mouse models having undergone varying degrees of photoreceptor degeneration. Using MANF treatment levels as controls, we investigate optimal control results in the three mouse models. In addition, our numerical solutions match the experimentally observed surviving percentage of photoreceptors and our uncertainty and sensitivity analysis identifies significant parameters in the math model both with and without MANF treatment.

Snake venomics, experimental toxic activities and clinical characteristics of human envenomation by Bothrocophias myersi (Serpentes: Viperidae) from Colombia.

Venoms of the viperid genus Bothrocophias, restricted to Colombia and Ecuador, are poorly known. Only a proteomic analysis of B. campbelli venom has been described. In this work we present a proteomic study of B. myersi venom, its biological activities, and describe the clinical characteristics of a patient bitten by this species. B. myersi venom mainly consists of phospholipases A2 (54.0%) and metalloproteinases (21.5%), among proteins of twelve different families. This venom exhibited proteolytic, phospholipase A2, myotoxic, edema-forming, and lethal activities. Enzymatic activities did not show statistically significant differences in comparison to Bothrops asper venom, but B. myersi venom displayed weaker hemorrhagic and coagulant activities. Polyvalent Viperidae antivenoms produced in Costa Rica and Colombia cross-recognized B. myersi venom by ELISA, however only the latter neutralized its lethal activity in mice when tested at a ratio of 3 mg venom/mL antivenom, suggesting it should be useful to treat envenomings inflicted by this species. A patient bitten by B. myersi developed edema and myotoxicity, evidenced by an increased creatine kinase activity in plasma. A good correlation was found between experimental biological activities of Bothrocophias myersi venom and the clinical features of an envenoming provoked by this species. SIGNIFICANCE: The proteomic characterization, toxicity, immunorecognition and neutralization of Bothrocophias myersi venom have been determined for the first time. The distribution of this pit viper is restricted to Colombia and Ecuador, and its venom contains a high proportion of phospholipases A2 and metalloproteinases. The polyvalent antivenom produced in Colombia neutralized the lethal activity of this venom in vivo, and therefore should be effective in the treatment of envenomings by this snake.