Erika Tatiana Camacho

• PhD
• Professor at Arizona State University

Pavlovian conditioning tasks have been used to identify the neural systems involved with learning cue-outcome relationships. In delay conditioning, the conditioned stimulus (CS) overlaps or co-terminates with the delivery of the unconditioned stimulus (US). Prior studies demonstrate that dopamine in the nucleus accumbens (NAc) regulates behavioral...

We report an improved measurement of the valence u and d quark distributions from the forward-backward asymmetry in the Drell-Yan process using 8.6 fb − 1 of data collected with the D0 detector in p p ¯ collisions at s = 1.96 . This analysis provides the values of new structure parameters that are directly related to the valence up and down quark d...

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. Aero...

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 th...

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 expres...

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...

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 productio...

Cell degeneration, including that resulting in retinal diseases, is linked to metabolic issues. In the retina, photoreceptor degeneration can result from imbalance in lactate production and consumption as well as disturbances to pyruvate and glucose levels. To identify the key mechanisms in metabolism that may be culprits of this degeneration, we u...

Cell degeneration, including that resulting in retinal diseases, is linked to metabolic issues. In the retina, photoreceptor degeneration can result from imbalance in lactate production and consumption as well as disturbances to pyruvate and glucose levels. To identify the key mechanisms in metabolism that may be culprits of this degeneration, we u...

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, un...

Patients affected by retinitis pigmentosa, an inherited retinal disease, experience a decline in vision due to photoreceptor degeneration leading to irreversible blindness. Rod-derived cone viability factor (RdCVF) is the most promising mutation-independent treatment today. To identify pathologic processes leading to secondary cone photoreceptor dy...

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...

This work examines bistability and multistability within a Recurrent Neural Network model (RNN) for a 2-node and 3-node system under many different regulation scenarios. We determine parameter regions where there is bistability, multistability, or other stable modes in the expression states of the systems described by this network model. Our result...

Drell-Yan lepton pairs produced in the process pp¯→ℓ+ℓ−+X through an intermediate γ*/Z boson have an asymmetry in their angular distribution related to the spontaneous symmetry breaking of the electroweak force and the associated mixing of its neutral gauge bosons. The CDF and D0 experiments have measured the effective-leptonic electroweak mixing p...

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...

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 eco...

Retinitis Pigmentosa (RP) is the term used to describe a diverse set of degenerative eye diseases affecting the photoreceptors (rods and cones) in the retina. This work builds on an existing mathematical model of RP that focused on the interaction of the rods and cones. We non-dimensionalize the model and examine the stability of the equilibria. We...

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 transc...

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 diff...

This chapter describes how sustained mentoring together with rigorous collaborative learning and community building contributed to successful mathematical research and individual growth in the Applied Mathematical Sciences Summer Institute (AMSSI), a program that focused on women, underrepresented minorities, and individuals from small teaching ins...

Melanopsin is an unusual vertebrate photopigment that, in mammals, is expressed in a small subset of intrinsically photosensitive retinal ganglion cells (ipRGCs), whose signaling has been implicated in non-image forming vision, regulating such functions as circadian rhythms, pupillary light reflex, and sleep. The biochemical cascade underlying the...

Numerous therapies have been implemented in an effort to minimize the debilitating effects of the degenerative eye disease Retinitis Pigmentosa (RP), yet none have provided satisfactory long-term solution. To date there is no treatment that can halt the degeneration of photoreceptors. The recent discovery of the RdCVF protein has provided researche...

Through the mathematical study of two models we quantify some of the theories of co-development and co-existence of focused groups in the social sciences. This work attempts to develop the mathematical framework behind the social sciences of community formation. By using well developed theories and concepts from ecology and epidemiology we hope to...

This article details the history, logistical operations, and design philosophy of the Mathematical and Theoretical Biology Institute (MTBI), a nationally recognized research program with an 18-year history of mentoring researchers at every level from high school through university faculty, increasing the number of researchers from historically unde...

This study compares the effects of two types of metering (periodic resetting and periodic increments) on one variable in a dynamical system, relative to the behavior of the corresponding system with an equivalent level of constant recruitment (influx). While the level of the target population in the constant-influx system generally remains between...

Vicodin is the most commonly prescribed pain reliever in the United States. Research indicates that there are two million people who are currently abusing Vicodin, and the majority of those who abuse Vicodin were initially exposed to it via prescription. Our goal is to determine the most effective strategies for reducing the overall population of V...

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...

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...

In this paper, we investigate the positive influence dominating set (PIDS) which has applications in social networks. We prove that PIDS is APX-hard and propose a greedy algorithm with an approximation ratio of H(δ) where H is the harmonic function and δ is the maximum vertex degree of the graph representing a social network.

In this work we mathematically explore the biological consequences of the effect of overnutrition, fat accumulation, and β-cell function in a model of the progression of Type 2 diabetes (T2D). More specifically, we focus on the effects of fat mass in the liver and the mechanism underlying the initiation and progression of β-cell failure. This mathe...

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 abund...

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-aw...

Focusing on highly-skilled labor populations in science, technology, engineering, and mathematics (STEM) fields, we offer a conceptual schema and approach to capture the complex dimensions and dynamics of labor migration and mobility relative to processes of brain drain, brain gain, brain circulation, and brain waste in the world today. Combining i...

There are many natural, physical, and biological systems that exhibit multiple time scales. For example, the dynamics of a population of ticks can be described in continuous time during their individual life cycle yet discrete time is used to describe the generation of offspring. These characteristics cause the population levels to be reset periodi...

Online social network has developed significantly in recent years as a medium of communicating, sharing and disseminating information and spreading influence. Most of current research has been on understanding the property of online social network and utilizing it to spread information and ideas. In this paper, we explored the problem of how to ut...

An SIS=SAS model of gonorrhea transmission in a men-seeking-men (MSM) system is presented in this paper to study the impact of education on the dynamics of gonorrhea prevalence. Education affects behaviors that may fall into two categoriesprevention and disease status awareness. Stability conditions for the disease free equilibrium and endemic equi...

The FitzHugh-Nagumo equations have been used as a caricature of the Hodgkin-Huxley equations of neuron firing and to capture, qualitatively, the general properties of an excitable membrane. In this paper, we utilize a modified version of the FitzHugh-Nagumo equations to model the spatial propagation of neuron firing; we assume that this propagation...

Neurons are responsible for transmitting messages throughout the body via long-distance electrical signals known as action potentials. These depend on the active transport of sodium and potassium ions across the neuron cell membrane. The effect of various drugs on the process of neuron firing is a current research interest. The Hodgkin-Huxley equat...

The Fitzhugh-Nagumo equations have been used as a caricature of the Hodgkin-Huxley equations of neuron firing to better understand the essential dynamics of the interaction of the membrane potential and the restoring force and to capture, qualitatively, the general properties of an excitable membrane. Even though its simplicity allows very valuable...

In this work we study a system of two van der Pol oscillators, x and y, coupled via a “bath” z:We investigate the existence and stability of the in-phase and out-of-phase modes for parameters ϵ>0 and k>0. To this end we use Floquet theory and numerical integration. Surprisingly, our results show that the out-of-phase mode exists and is stable for a...

The retina is arguably the single most important component in the vision process. Via its photoreceptors it is responsible for converting electromagnetic radiation into a chemical signal understandable by the brain. The interactions between rod and cones in the retina have been the focus of innumerable experimental and theoretical biological studie...

Antiviral drugs have been known to prolong the lives of HIV infected patients. However, it is still uncertain if antiviral drugs affect the rate of virion clearance, the loss of target cells, or both. In this study, we used mathematical models to measure the effects of a protease inhibitor on three infected patients. After analysis of this data, we...

Abstract Drinking on college campuses, especially binge drinking, contributes to numerous unintentional injuries, sexual assaults, and poor performance in classes. We are inter- ested in modeling college drinking in order to guide policymakers in the creation of laws that will help decrease college binge drinking and its efiects. In order to model...

We study a reaction-diffusion model of a hypothetical chemical reaction presented in [1] by Pearson. We perform bifurcation and linear stability analysis of the coupled non-linear system of PDE's as well as numerical simulations of chemical pattern formation [2–6].