Lactate's behavioral switch in the brain: An in-silico model

Emerging evidence emphasizes lactate's involvement in both physiological processes (energy metabolism, memory, etc.) and disease (traumatic brain injury, epilepsy, etc.). Furthermore, the usefulness of mathematical modeling in deciphering underlying dynamics of the brain to investigate lactate roles and mechanisms of action has been well established. Here, we analyze a novel mathematical model of brain lactate exchanges between four compartments: neurons, astrocytes, capillaries, and extracellular space. A system of four ordinary differential equations is proposed to explain interactions between these compartments. We first optimize and analyze the model's parameters under normal, resting state conditions, and then use it to simulate changes linked to elevated arterial lactate. Our results show that even though increased arterial lactate results in increased uptake by astrocytes and release to the extracellular space, it cannot strongly recover the initial drop in neuronal lactate concentration. Also, we show that the direction of lactate transport between the compartments is influenced by the maximum astrocyte production rate and the transport rate between astrocytes and extracellular space.

Theoretical Considerations and Empirical Predictions of the Pharmaco- and Population Dynamics of Heteroresistance

Antibiotics are considered one of the most important contributions to clinical medicine in the last 100 years. Due to the use and overuse of these drugs, there have been increasing frequencies of infections with resistant pathogens. One form of resistance, heteroresistance, is particularly problematic; pathogens appear sensitive to a drug by common susceptibility tests. However, upon exposure to the antibiotic, resistance rapidly ascends, and treatment fails. To quantitatively explore the processes contributing to the emergence and ascent of resistance during treatment and the waning of resistance following cessation of treatment, we develop two distinct mathematical and computer-simulations models of heteroresistance. In our analysis of the properties of these models, we consider the factors that determine the response to antibiotic-mediated selection. In one model, heteroresistance is progressive, with each resistant state sequentially generating a higher resistance level. In the other model, heteroresistance is non-progressive, with a susceptible population directly generating populations with different resistance levels. The conditions where resistance will ascend in the progressive model are narrower than those of the non-progressive model. The rates of reversion from the resistant to the sensitive states are critically dependent on the transition rates and the fitness cost of resistance. Our results demonstrate that the standard test used to identify heteroresistance is insufficient. The predictions of our models are consistent with empirical results. Our results demand a reevaluation of the definition and criteria employed to identify heteroresistance. We recommend the definition of heteroresistance should include a consideration of the rate of return to susceptibility.

Computational modeling of hypercoagulability in COVID-19

Coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has infected more than 100 million people worldwide and claimed millions of lives. While the leading cause of mortality in COVID-19 patients is the hypoxic respiratory failure from acute respiratory distress syndrome, there is accumulating evidence that shows excessive coagulation also increases the fatalities in COVID-19. Thus, there is a pressing demand to understand the association between COVID-19-induced hypercoagulability and the extent of formation of undesired blood clots. Mathematical modeling of coagulation has been used as an important tool to identify novel reaction mechanisms and to identify targets for new drugs. Here, we employ the coagulation factor data of COVID-19 patients reported from published studies as inputs for two mathematical models of coagulation to identify how the concentrations of coagulation factors change in these patients. Our simulation results show that while the levels of many of the abnormal coagulation factors measured in COVID-19 patients promote the generation of thrombin and fibrin, two key components of blood clots, the increased level of fibrinogen and then the reduced level of antithrombin are the factors most responsible for boosting the level of fibrin and thrombin, respectively. Altogether, our study demonstrates the potential of mathematical modeling to identify coagulation factors responsible for the increased clot formation in COVID-19 patients where clinical data is scarce.

Multi-Faceted Analysis of COVID-19 Epidemic in Korea Considering Omicron Variant: Mathematical Modeling-Based Study

BACKGROUND

The most recent variant of concern, omicron (B.1.1.529), has caused numerous cases worldwide including the Republic of Korea due to its fast transmission and reduced vaccine effectiveness.

METHODS

A mathematical model considering age-structure, vaccine, antiviral drugs, and influx of the omicron variant was developed. We estimated transmission rates among age groups using maximum likelihood estimation for the age-structured model. The impact of non-pharmaceutical interventions (NPIs; in community and border), quantified by a parameter μ in the force of infection, and vaccination were examined through a multi-faceted analysis. A theory-based endemic equilibrium study was performed to find the manageable number of cases according to omicron- and healthcare-related factors.

RESULTS

By fitting the model to the available data, the estimated values of μ ranged from 0.31 to 0.73, representing the intensity of NPIs such as social distancing level. If μ < 0.55 and 300,000 booster shots were administered daily from February 3, 2022, the number of severe cases was forecasted to exceed the severe bed capacity. Moreover, the number of daily cases is reduced as the timing of screening measures is delayed. If screening measure was intensified as early as November 24, 2021 and the number of overseas entrant cases was contained to 1 case per 10 days, simulations showed that the daily incidence by February 3, 2022 could have been reduced by 87%. Furthermore, we found that the incidence number in mid-December 2021 exceeded the theory-driven manageable number of daily cases.

CONCLUSION

NPIs, vaccination, and antiviral drugs influence the spread of omicron and number of severe cases in the Republic of Korea. Intensive and early screening measures during the emergence of a new variant is key in controlling the epidemic size. Using the endemic equilibrium of the model, a formula for the manageable daily cases depending on the severity rate and average length of hospital stay was derived so that the number of severe cases does not surpass the severe bed capacity.

Type 2 diabetes epidemic and key risk factors in Qatar: a mathematical modeling analysis

INTRODUCTION

We aimed to characterize and forecast type 2 diabetes mellitus (T2DM) disease burden between 2021 and 2050 in Qatar where 89% of the population comprises expatriates from over 150 countries.

RESEARCH DESIGN AND METHODS

An age-structured mathematical model was used to forecast T2DM burden and the impact of key risk factors (obesity, smoking, and physical inactivity). The model was parametrized using data from T2DM natural history studies, Qatar's 2012 STEPwise survey, the Global Health Observatory, and the International Diabetes Federation Diabetes Atlas, among other data sources.

RESULTS

Between 2021 and 2050, T2DM prevalence increased from 7.0% to 14.0%, the number of people living with T2DM increased from 170 057 to 596 862, and the annual number of new T2DM cases increased from 25 007 to 45 155 among those 20-79 years of age living in Qatar. Obesity prevalence increased from 8.2% to 12.5%, smoking declined from 28.3% to 26.9%, and physical inactivity increased from 23.1% to 26.8%. The proportion of incident T2DM cases attributed to obesity increased from 21.9% to 29.9%, while the contribution of smoking and physical inactivity decreased from 7.1% to 6.0% and from 7.3% to 7.2%, respectively. The results showed substantial variability across various nationality groups residing in Qatar-for example, in Qataris and Egyptians, the T2DM burden was mainly due to obesity, while in other nationality groups, it appeared to be multifactorial.

CONCLUSIONS

T2DM prevalence and incidence in Qatar were forecasted to increase sharply by 2050, highlighting the rapidly growing need of healthcare resources to address the disease burden. T2DM epidemiology varied between nationality groups, stressing the need for prevention and treatment intervention strategies tailored to each nationality.

Modeling strategies for the allocation of SARS-CoV-2 vaccines in the United States

The Advisory Committee on Immunization Practices (ACIP) recommended phased allocation of SARS-CoV-2 vaccines in December 2020. To support the development of this guidance, we used a mathematical model of SARS-CoV-2 transmission to evaluate the relative impact of three vaccine allocation strategies on infections, hospitalizations, and deaths. All three strategies initially prioritized healthcare personnel (HCP) for vaccination. Strategies of subsequently prioritizing adults aged ≥65 years, or a combination of essential workers and adults aged ≥75 years, prevented the most deaths. Meanwhile, prioritizing adults with high-risk medical conditions immediately after HCP prevented the most infections. All three strategies prevented a similar fraction of hospitalizations. While no model is capable of fully capturing the complex social dynamics which shape epidemics, exercises such as this one can be a useful way for policy makers to formalize their assumptions and explore the key features of a problem before making decisions.

A study on the efficiency of the estimation models of COVID-19

Today, the world is fighting against a dangerous epidemic caused by the novel coronavirus, also known as COVID-19. All have been impacted and countries are trying to recover from the social, economic, and health devastations of COVID-19. Recent epidemiology research has concentrated on using different prediction models to estimate the numbers of infected, recovered, and deceased cases around the world. This study is primarily focused on evaluating two common prediction models: Susceptible - Infected - Recovered (SIR) and Susceptible - Exposed - Infected - Recovered (SEIR). The SIR and SEIR models were compared in estimating the outbreak and identifying the better fitting model for forecasting future spread in Kuwait. Based on the results of the comparison, the SEIR model was selected for predicting COVID-19 infected, recovered, and cumulative cases. The data needed for estimation was collected from official sites of the Kuwait Government between 24 February and 1 December 2020. This study presents estimated values for peak dates and expected eradication of COVID-19 in Kuwait. The proposed estimation model is simulated using the Python Programming language on the collected data. The simulation was performed with various basic reproduction numbers (between 5.2 and 3), the initial exposed population, and the incubation rate. The results show that the SEIR model was better suited than the SIR model for predicting both infection and recovery cases with R 0 values ranging from 3 to 4, E 0 = 80 and α = 0.2 .

Mathematical modeling of peripheral blood neutrophil kinetics to predict CLAD after lung transplantation

BACKGROUND

The presence of neutrophils in the lung was identified as a factor associated with CLAD but requires invasive samples. The aim of this study was to assess the kinetics of peripheral blood neutrophils after lung transplantation as early predictor of CLAD.

METHODS

We retrospectively included all recipients transplanted in our center between 2009 and 2014. Kinetics of blood neutrophils were evaluated to predict early CLAD by mathematical modeling using unadjusted and adjusted analyses.

RESULTS

103 patients were included, 80 in the stable group and 23 in the CLAD group. Bacterial infections at 1 year were associated with CLAD occurrence. Neutrophils demonstrated a high increase postoperatively and then a progressive decrease until normal range. Recipients with CLAD had higher neutrophil counts (mixed effect coefficient beta over 3 years = +1.36 G/L, 95% Confidence Interval [0.99-1.92], p < .001). A coefficient of celerity (S for speed) was calculated to model the kinetics of return to the norm before CLAD occurrence. After adjustment, lower values of S (slower decrease of neutrophils) were associated with CLAD (Odds Ratio = 0.26, 95% Confidence Interval [0.08-0.66], p = .01).

CONCLUSION

A slower return to the normal range of blood neutrophils was early associated with CLAD occurrence.

School Opening Delay Effect on Transmission Dynamics of Coronavirus Disease 2019 in Korea: Based on Mathematical Modeling and Simulation Study

BACKGROUND

Nonpharmaceutical intervention strategy is significantly important to mitigate the coronavirus disease 2019 (COVID-19) spread. One of the interventions implemented by the government is a school closure. The Ministry of Education decided to postpone the school opening from March 2 to April 6 to minimize epidemic size. We aimed to quantify the school closure effect on the COVID-19 epidemic.

METHODS

The potential effects of school opening were measured using a mathematical model considering two age groups: children (aged 19 years and younger) and adults (aged over 19). Based on susceptible-exposed-infectious-recovered model, isolation and behavior-changed susceptible individuals are additionally considered. The transmission parameters were estimated from the laboratory confirmed data reported by the Korea Centers for Disease Control and Prevention from February 16 to March 22. The model was extended with estimated parameters and estimated the expected number of confirmed cases as the transmission rate increased after school opening.

RESULTS

Assuming the transmission rate between children group would be increasing 10 fold after the schools open, approximately additional 60 cases are expected to occur from March 2 to March 9, and approximately additional 100 children cases are expected from March 9 to March 23. After March 23, the number of expected cases for children is 28.4 for 7 days and 33.6 for 14 days.

CONCLUSION

The simulation results show that the government could reduce at least 200 cases, with two announcements by the Ministry of education. After March 23, although the possibility of massive transmission in the children's age group is lower, group transmission is possible to occur.

Accurate Estimation of Context-Dependent False Discovery Rates in Top-Down Proteomics

Within the last several years, top-down proteomics has emerged as a high throughput technique for protein and proteoform identification. This technique has the potential to identify and characterize thousands of proteoforms within a single study, but the absence of accurate false discovery rate (FDR) estimation could hinder the adoption and consistency of top-down proteomics in the future. In automated identification and characterization of proteoforms, FDR calculation strongly depends on the context of the search. The context includes MS data quality, the database being interrogated, the search engine, and the parameters of the search. Particular to top-down proteomics-there are four molecular levels of study: proteoform spectral match (PrSM), protein, isoform, and proteoform. Here, a context-dependent framework for calculating an accurate FDR at each level was designed, implemented, and validated against a manually curated training set with 546 confirmed proteoforms. We examined several search contexts and found that an FDR calculated at the PrSM level under-reported the true FDR at the protein level by an average of 24-fold. We present a new open-source tool, the TDCD_FDR_Calculator, which provides a scalable, context-dependent FDR calculation that can be applied post-search to enhance the quality of results in top-down proteomics from any search engine.

Quantifying Homologous Proteins and Proteoforms

Many proteoforms-arising from alternative splicing, post-translational modifications (PTM), or paralogous genes-have distinct biological functions, such as histone PTM proteoforms. However, their quantification by existing bottom-up mass-spectrometry (MS) methods is undermined by peptide-specific biases. To avoid these biases, we developed and implemented a first-principles model (HIquant) for quantifying proteoform stoichiometries. We characterized when MS data allow inferring proteoform stoichiometries by HIquant and derived an algorithm for optimal inference. We applied this algorithm to infer proteoform stoichiometries in two experimental systems that supported rigorous bench-marking: alkylated proteoforms spiked-in at known ratios and endogenous histone 3 PTM proteoforms quantified relative to internal heavy standards. When compared with the benchmarks, the proteoform stoichiometries interfered by HIquant without using external standards had relative error of 5-15% for simple proteoforms and 20-30% for complex proteoforms. A HIquant server is implemented at: https://web.northeastern.edu/slavov/2014HIquant/.

Mathematical Modeling for Scrub Typhus and Its Implications for Disease Control

BACKGROUND

The incidence rate of scrub typhus has been increasing in the Republic of Korea. Previous studies have suggested that this trend may have resulted from the effects of climate change on the transmission dynamics among vectors and hosts, but a clear explanation of the process is still lacking. In this study, we applied mathematical models to explore the potential factors that influence the epidemiology of tsutsugamushi disease.

METHODS

We developed mathematical models of ordinary differential equations including human, rodent and mite groups. Two models, including simple and complex models, were developed, and all parameters employed in the models were adopted from previous articles that represent epidemiological situations in the Republic of Korea.

RESULTS

The simulation results showed that the force of infection at the equilibrium state under the simple model was 0.236 (per 100,000 person-months), and that in the complex model was 26.796 (per 100,000 person-months). Sensitivity analyses indicated that the most influential parameters were rodent and mite populations and contact rate between them for the simple model, and trans-ovarian transmission for the complex model. In both models, contact rate between humans and mites is more influential than morality rate of rodent and mite group.

CONCLUSION

The results indicate that the effect of controlling either rodents or mites could be limited, and reducing the contact rate between humans and mites is more practical and effective strategy. However, the current level of control would be insufficient relative to the growing mite population.

Analysis of Volume Overestimation Artifacts in the Breast Outline Segmentation in Tomosynthesis

In digital breast tomosynthesis (DBT), the reconstruction is calculated from x-ray projection images acquired over a small range of angles. One step in the reconstruction process is to identify the pixels that fall outside the shadow of the breast, to segment the breast from the background (air). In each projection, rays are back-projected from these pixels to the focal spot. All voxels along these rays are identified as air. By combining these results over all projections, a breast outline can be determined for the reconstruction. This paper quantifies the accuracy of this breast segmentation strategy in DBT. In this study, a physical phantom modeling a breast under compression was analyzed with a prototype next-generation tomosynthesis (NGT) system described in previous work. Multiple wires were wrapped around the phantom. Since the wires are thin and high contrast, their exact location can be determined from the reconstruction. Breast parenchyma was portrayed outside the outline defined by the wires. Specifically, the size of the phantom was overestimated along the posteroanterior (PA) direction; i.e., perpendicular to the plane of conventional source motion. To analyze how the acquisition geometry affects the accuracy of the breast outline segmentation, a computational phantom was also simulated. The simulation identified two ways to improve the segmentation accuracy; either by increasing the angular range of source motion laterally or by increasing the range in the PA direction. The latter approach is a unique feature of the NGT design; the advantage of this approach was validated with our prototype system.

A Risk-based Model for Predicting the Impact of using Condoms on the Spread of Sexually Transmitted Infections

We create and analyze a mathematical model to understand the impact of condom-use and sexual behavior on the prevalence and spread of Sexually Transmitted Infections (STIs). STIs remain significant public health challenges globally with a high burden of some Sexually Transmitted Diseases (STDs) in both developed and undeveloped countries. Although condom-use is known to reduce the transmission of STIs, there are a few quantitative population-based studies on the protective role of condom-use in reducing the incidence of STIs. The number of concurrent partners is correlated with their risk of being infectious by an STI such as chlamydia, gonorrhea, or syphilis. We develop a Susceptible-Infectious-Susceptible (SIS) model that stratifies the population based on the number of concurrent partners. The model captures the multi-level heterogeneous mixing through a combination of biased (preferential) and random (proportional) mixing processes between individuals with distinct risk levels, and accounts for differences in condom-use in the low- and high-risk populations. We use sensitivity analysis to assess the relative impact of high-risk people using condom as a prophylactic intervention to reduce their chance of being infectious, or infecting others. The model predicts the STI prevalence as a function of the number of partners of an individual, and quantifies how this distribution of effective partners changes as a function of condom-use. Our results show that when the mixing is random, then increasing the condom-use in the high-risk population is more effective in reducing the prevalence than when many of the partners of high-risk people have high risk. The model quantifies how the risk of being infected increases for people who have more partners, and the need for high-risk people to consistently use condoms to reduce their risk of infection.

Targeting an alcohol intervention cost-effectively to persons living with HIV/AIDS in East Africa

BACKGROUND

In the current report, we ask if targeting a cognitive behavioral therapy (CBT)-based intervention aimed at reducing hazardous alcohol consumption to HIV-infected persons in East Africa would have a favorable value at costs that are feasible for scale-up.

METHODS

Using a computer simulation to inform HIV prevention decisions in East Africa, we compared 4 different strategies for targeting a CBT intervention-(i) all HIV-infected persons attending clinic; (ii) only those patients in the pre-antiretroviral therapy (ART) stages of care; (iii) only those patients receiving ART; and (iv) only those patients with detectable viral loads (VLs) regardless of disease stage. We define targeting as screening for hazardous alcohol consumption (e.g., using the Alcohol Use Disorders Identification Test and offering the CBT intervention to those who screen positive). We compared these targeting strategies to a null strategy (no intervention) or a hypothetical scenario where an alcohol intervention was delivered to all adults regardless of HIV status.

RESULTS

An intervention targeted to HIV-infected patients could prevent 18,000 new infections, add 46,000 quality-adjusted life years (QALYs), and yield an incremental cost-effectiveness ratio of $600/QALY compared to the null scenario. Narrowing the prioritized population to only HIV-infected patients in pre-ART phases of care results in 15,000 infections averted, the addition of 21,000 QALYs and would be cost-saving, while prioritizing based on an unsuppressed HIV-1 VL test results in 8,300 new infections averted, adds 6,000 additional QALYs, and would be cost-saving as well.

CONCLUSIONS

Our results suggest that targeting a cognitive-based treatment aimed at reducing hazardous alcohol consumption to subgroups of HIV-infected patients provides favorable value in comparison with other beneficial strategies for HIV prevention and control in this region. It may even be cost-saving under certain circumstances.

Dynamics of HIV infection in lymphoid tissue network

Human immunodeficiency virus (HIV) is a fast replicating ribonucleic acid virus, which can easily mutate in order to escape the effects of drug administration. Hence, understanding the basic mechanisms underlying HIV persistence in the body is essential in the development of new therapies that could eradicate HIV infection. Lymphoid tissues are the primary sites of HIV infection. Despite the recent progress in real-time monitoring technology, HIV infection dynamics in a whole body is unknown. Mathematical modeling and simulations provide speculations on global behavior of HIV infection in the lymphatic system. We propose a new mathematical model that describes the spread of HIV infection throughout the lymphoid tissue network. In order to represent the volume difference between lymphoid tissues, we propose the proportionality of several kinetic parameters to the lymphoid tissues' volume distribution. Under this assumption, we perform extensive numerical computations in order to simulate the spread of HIV infection in the lymphoid tissue network. Numerical computations simulate single drug treatments of an HIV infection. One of the important biological speculations derived from this study is a drug saturation effect generated by lymphoid network connection. This implies that a portion of reservoir lymphoid tissues to which drug is not sufficiently delivered would inhibit HIV eradication despite of extensive drug injection.

Kinetics of iron import into developing mouse organs determined by a pup-swapping method

The kinetics of dietary iron import into various organs of mice were evaluated using a novel pup-swapping approach. Newborn pups whose bodies primarily contained (56)Fe or (57)Fe were swapped at birth such that each nursed on milk containing the opposite isotope. A pup from each litter was euthanized weekly over a 7-week period. Blood plasma was obtained, and organs were isolated typically after flushing with Ringer's buffer. (56)Fe and (57)Fe concentrations were determined for organs and plasma; organ volumes were also determined. Mössbauer spectra of equivalent (57)Fe-enriched samples were used to quantify residual blood in organs; this fraction was excluded from later analysis. Rates of import into brain, spleen, heart, and kidneys were highest during the first 2 weeks of life. In contrast, half of iron in the newborn liver exited during that time, and influx peaked later. Two mathematical models were developed to analyze the import kinetics. The only model that simulated the data adequately assumed that an iron-containing species enters the plasma and converts into a second species and that both are independently imported into organs. Consistent with this, liquid chromatography with an on-line ICP-MS detector revealed numerous iron species in plasma besides transferrin. Model fitting required that the first species, assigned to non-transferrin-bound iron, imports faster into organs than the second, assigned to transferrin-bound-iron. Non-transferrin-bound iron rather than transferrin-bound-iron appears to play the dominant role in importing iron into organs during early development of healthy mice.

Combination treatment with meropenem plus levofloxacin is synergistic against Pseudomonas aeruginosa infection in a murine model of pneumonia

BACKGROUND

Meropenem plus levofloxacin treatment was shown to be a promising combination in our in vitro hollow fiber infection model. We strove to validate this finding in a murine Pseudomonas pneumonia model.

METHODS

A dose-ranging study with meropenem and levofloxacin alone and in combination against Pseudomonas aeruginosa was performed in a granulocytopenic murine pneumonia model. Meropenem and levofloxacin were administered to partially humanize their pharmacokinetic profiles in mouse serum. Total and resistant bacterial populations were estimated after 24 hours of therapy. Pharmacokinetic profiling of both drugs was performed in plasma and epithelial lining fluid, using a population model.

RESULTS

Meropenem and levofloxacin penetrations into epithelial lining fluid were 39.3% and 64.3%, respectively. Both monotherapies demonstrated good exposure responses. An innovative combination-therapy analytic approach demonstrated that the combination was statistically significantly synergistic (α = 2.475), as was shown in the hollow fiber infection model. Bacterial resistant to levofloxacin and meropenem was seen in the control arm. Levofloxacin monotherapy selected for resistance to itself. No resistant subpopulations were observed in any combination therapy arm.

CONCLUSIONS

The combination of meropenem plus levofloxacin was synergistic, producing good bacterial kill and resistance suppression. Given the track record of safety of each agent, this combination may be worthy of clinical trial.

A single mechanism can explain network-wide insulin resistance in adipocytes from obese patients with type 2 diabetes

The response to insulin is impaired in type 2 diabetes. Much information is available about insulin signaling, but understanding of the cellular mechanisms causing impaired signaling and insulin resistance is hampered by fragmented data, mainly obtained from different cell lines and animals. We have collected quantitative and systems-wide dynamic data on insulin signaling in primary adipocytes and compared cells isolated from healthy and diabetic individuals. Mathematical modeling and experimental verification identified mechanisms of insulin control of the MAPKs ERK1/2. We found that in human adipocytes, insulin stimulates phosphorylation of the ribosomal protein S6 and hence protein synthesis about equally via ERK1/2 and mTORC1. Using mathematical modeling, we examined the signaling network as a whole and show that a single mechanism can explain the insulin resistance of type 2 diabetes throughout the network, involving signaling both through IRS1, PKB, and mTOR and via ERK1/2 to the nuclear transcription factor Elk1. The most important part of the insulin resistance mechanism is an attenuated feedback from the protein kinase mTORC1 to IRS1, which spreads signal attenuation to all parts of the insulin signaling network. Experimental inhibition of mTORC1 using rapamycin in adipocytes from non-diabetic individuals induced and thus confirmed the predicted network-wide insulin resistance.

A fundamental trade-off in covalent switching and its circumvention by enzyme bifunctionality in glucose homeostasis

Covalent modification provides a mechanism for modulating molecular state and regulating physiology. A cycle of competing enzymes that add and remove a single modification can act as a molecular switch between "on" and "off" and has been widely studied as a core motif in systems biology. Here, we exploit the recently developed "linear framework" for time scale separation to determine the general principles of such switches. These methods are not limited to Michaelis-Menten assumptions, and our conclusions hold for enzymes whose mechanisms may be arbitrarily complicated. We show that switching efficiency improves with increasing irreversibility of the enzymes and that the on/off transition occurs when the ratio of enzyme levels reaches a value that depends only on the rate constants. Fluctuations in enzyme levels, which habitually occur due to cellular heterogeneity, can cause flipping back and forth between on and off, leading to incoherent mosaic behavior in tissues, that worsens as switching becomes sharper. This trade-off can be circumvented if enzyme levels are correlated. In particular, if the competing catalytic domains are on the same protein but do not influence each other, the resulting bifunctional enzyme can switch sharply while remaining coherent. In the mammalian liver, the switch between glycolysis and gluconeogenesis is regulated by the bifunctional 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase (PFK-2/FBPase-2). We suggest that bifunctionality of PFK-2/FBPase-2 complements the metabolic zonation of the liver by ensuring coherent switching in response to insulin and glucagon.

Pulsatile hormonal signaling to extracellular signal-regulated kinase: exploring system sensitivity to gonadotropin-releasing hormone pulse frequency and width

Gonadotropin-releasing hormone (GnRH) is secreted in brief pulses that stimulate synthesis and secretion of pituitary gonadotropin hormones and thereby mediate control of reproduction. It acts via G-protein-coupled receptors to stimulate effectors, including ERK. Information could be encoded in GnRH pulse frequency, width, amplitude, or other features of pulse shape, but the relative importance of these features is unknown. Here we examine this using automated fluorescence microscopy and mathematical modeling, focusing on ERK signaling. The simplest scenario is one in which the system is linear, and response dynamics are relatively fast (compared with the signal dynamics). In this case integrated system output (ERK activation or ERK-driven transcription) will be roughly proportional to integrated input, but we find that this is not the case. Notably, we find that relatively slow response kinetics lead to ERK activity beyond the GnRH pulse, and this reduces sensitivity to pulse width. More generally, we show that the slowing of response kinetics through the signaling cascade creates a system that is robust to pulse width. We, therefore, show how various levels of response kinetics synergize to dictate system sensitivity to different features of pulsatile hormone input. We reveal the mathematical and biochemical basis of a dynamic GnRH signaling system that is robust to changes in pulse amplitude and width but is sensitive to changes in receptor occupancy and frequency, precisely the features that are tightly regulated and exploited to exert physiological control in vivo.

Tight control of hypoxia-inducible factor-α transient dynamics is essential for cell survival in hypoxia

Intracellular signaling involving hypoxia-inducible factor (HIF) controls the adaptive responses to hypoxia. There is a growing body of evidence demonstrating that intracellular signals encode temporal information. Thus, the dynamics of protein levels, as well as protein quantity and/or localization, impacts on cell fate. We hypothesized that such temporal encoding has a role in HIF signaling and cell fate decisions triggered by hypoxic conditions. Using live cell imaging in a controlled oxygen environment, we observed transient 3-h pulses of HIF-1α and -2α expression under continuous hypoxia. We postulated that the well described prolyl hydroxylase (PHD) oxygen sensors and HIF negative feedback regulators could be the origin of the pulsatile HIF dynamics. We used iterative mathematical modeling and experimental analysis to scrutinize which parameter of the PHD feedback could control HIF timing and we probed for the functional redundancy between the three main PHD proteins. We identified PHD2 as the main PHD responsible for HIF peak duration. We then demonstrated that this has important consequences, because the transient nature of the HIF pulse prevents cell death by avoiding transcription of p53-dependent pro-apoptotic genes. We have further shown the importance of considering HIF dynamics for coupling mathematical models by using a described HIF-p53 mathematical model. Our results indicate that the tight control of HIF transient dynamics has important functional consequences on the cross-talk with key signaling pathways controlling cell survival, which is likely to impact on HIF targeting strategies for hypoxia-associated diseases such as tumor progression and ischemia.

Scaffold state switching amplifies, accelerates, and insulates protein kinase C signaling

Scaffold proteins localize two or more signaling enzymes in close proximity to their downstream effectors. A-kinase-anchoring proteins (AKAPs) are a canonical family of scaffold proteins known to bind protein kinase A (PKA) and other enzymes. Several AKAPs have been shown to accelerate, amplify, and specify signal transduction to dynamically regulate numerous cellular processes. However, there is little theory available to mechanistically explain how signaling on protein scaffolds differs from solution biochemistry. In our present study, we propose a novel kinetic mechanism for enzymatic reactions on protein scaffolds to explain these phenomena, wherein the enzyme-substrate-scaffold complex undergoes stochastic state switching to reach an active state. This model predicted anchored enzymatic reactions to be accelerated, amplified, and insulated from inhibition compared with those occurring in solution. We exploited a direct interaction between protein kinase C (PKC) and AKAP7α as a model to validate these predictions experimentally. Using a genetically encoded PKC activity reporter, we found that both the strength and speed of substrate phosphorylation were enhanced by AKAP7α. PKC tethered to AKAP7α was less susceptible to inhibition from the ATP-competitive inhibitor Gö6976 and the substrate-competitive inhibitor PKC 20-28, but not the activation-competitive inhibitor calphostin C. Model predictions and experimental validation demonstrated that insulation is a general property of scaffold tethering. Sensitivity analysis indicated that these findings may be applicable to many other scaffolds as well. Collectively, our findings provide theoretical and experimental evidence that scaffold proteins can amplify, accelerate, and insulate signal transduction.

Model of tryptophan metabolism, readily scalable using tissue-specific gene expression data

Tryptophan is utilized in various metabolic routes including protein synthesis, serotonin, and melatonin synthesis and the kynurenine pathway. Perturbations in these pathways have been associated with neurodegenerative diseases and cancer. Here we present a comprehensive kinetic model of the complex network of human tryptophan metabolism based upon existing kinetic data for all enzymatic conversions and transporters. By integrating tissue-specific expression data, modeling tryptophan metabolism in liver and brain returned intermediate metabolite concentrations in the physiological range. Sensitivity and metabolic control analyses identified expected key enzymes to govern fluxes in the branches of the network. Combining tissue-specific models revealed a considerable impact of the kynurenine pathway in liver on the concentrations of neuroactive derivatives in the brain. Moreover, using expression data from a cancer study predicted metabolite changes that resembled the experimental observations. We conclude that the combination of the kinetic model with expression data represents a powerful diagnostic tool to predict alterations in tryptophan metabolism. The model is readily scalable to include more tissues, thereby enabling assessment of organismal tryptophan metabolism in health and disease.

A conserved protein motif is required for full modulatory activity of negative elongation factor subunits NELF-A and NELF-B in modifying glucocorticoid receptor-regulated gene induction properties

NELF-B is a BRCA1-interacting protein and subunit (with NELF-A, -C/D, and -E) of the human negative elongation factor (NELF) complex, which participates in RNA polymerase II pausing shortly after transcription initiation, especially for synchronized gene expression. We now report new activities of NELF-B and other NELF complex subunits, which are to attenuate glucocorticoid receptor (GR)-mediated gene induction, reduce the partial agonist activity of an antagonist, and increase the EC50 of an agonist during nonsynchronized expression of exogenous and endogenous reporters. Stable knockdown of endogenous NELF-B has the opposite effects on an exogenous gene. The GR ligand-binding domain suffices for these biological responses. ChIP assays reveal that NELF-B diminishes GR recruitment to promoter regions of two endogenous genes. Using a new competition assay, NELF-A and NELF-B are each shown to act independently as competitive decelerators at two steps after the site of GR action and before or at the site of reporter gene activity. A common motif in each NELF was identified that is required for full activity of both NELF-A and NELF-B. These studies allow us to position the actions of two new modulators of GR-regulated transactivation, NELF-A and NELF-B, relative to other factors in the overall gene induction sequence.

Exploration of the spontaneous fluctuating activity of single enzyme molecules

Single enzyme molecules display inevitable, stochastic fluctuations in their catalytic activity. In metabolism, for instance, the stochastic activity of individual enzymes is averaged out due to their high copy numbers per single cell. However, many processes inside cells rely on single enzyme activity, such as transcription, replication, translation, and histone modifications. Here we introduce the main theoretical concepts of stochastic single-enzyme activity starting from the Michaelis-Menten enzyme mechanism. Next, we discuss stochasticity of multi-substrate enzymes, of enzymes and receptors with multiple conformational states and finally, how fluctuations in receptor activity arise from fluctuations in signal concentration. This paper aims to introduce the exciting field of single-molecule enzyme kinetics and stochasticity to a wider audience of biochemists and systems biologists.

A mathematical model for scanning and catalysis on single-stranded DNA, illustrated with activation-induced deoxycytidine deaminase

We formulated a master equation-based mathematical model to analyze random scanning and catalysis for enzymes that act on single-stranded DNA (ssDNA) substrates. Catalytic efficiencies and intrinsic scanning distances are deduced from the distribution of positions and gap lengths between a series of catalytic events occurring over time, which are detected as point mutations in a lacZα-based reporter sequence containing enzyme target motifs. Mathematical analysis of the model shows how scanning motions become separable from the catalysis when the proper statistical properties of the mutation pattern are used to interpret the readouts. Two-point correlations between all catalytic events determine intrinsic scanning distances, whereas gap statistics between mutations determine their catalytic efficiencies. Applying this model to activation-induced deoxycytidine deaminase (AID), which catalyzes C→U deaminations processively on ssDNA, we have established that deaminations of AGC hot motifs occur at a low rate, ∼0.03 s(-1), and low efficiency, ∼3%. AID performs random bidirectional movements for an average distance of 6.2 motifs, at a rate of about 15 nucleotides per second, and "dwells" at a motif site for 2.7 s while bound >4 min to the same DNA molecule. These results provide new and important insights on how AID may be optimized for generating mutational diversity in Ig genes, and we discuss how the properties of AID acting freely on a "naked" ssDNA relate to the constrained action of AID during transcription-dependent somatic hypermutation and class-switch recombination.

A physiologically required G protein-coupled receptor (GPCR)-regulator of G protein signaling (RGS) interaction that compartmentalizes RGS activity

G protein-coupled receptors (GPCRs) can interact with regulator of G protein signaling (RGS) proteins. However, the effects of such interactions on signal transduction and their physiological relevance have been largely undetermined. Ligand-bound GPCRs initiate by promoting exchange of GDP for GTP on the Gα subunit of heterotrimeric G proteins. Signaling is terminated by hydrolysis of GTP to GDP through intrinsic GTPase activity of the Gα subunit, a reaction catalyzed by RGS proteins. Using yeast as a tool to study GPCR signaling in isolation, we define an interaction between the cognate GPCR (Mam2) and RGS (Rgs1), mapping the interaction domains. This reaction tethers Rgs1 at the plasma membrane and is essential for physiological signaling response. In vivo quantitative data inform the development of a kinetic model of the GTPase cycle, which extends previous attempts by including GPCR-RGS interactions. In vivo and in silico data confirm that GPCR-RGS interactions can impose an additional layer of regulation through mediating RGS subcellular localization to compartmentalize RGS activity within a cell, thus highlighting their importance as potential targets to modulate GPCR signaling pathways.

Dissecting the catalytic mechanism of Trypanosoma brucei trypanothione synthetase by kinetic analysis and computational modeling

In pathogenic trypanosomes, trypanothione synthetase (TryS) catalyzes the synthesis of both glutathionylspermidine (Gsp) and trypanothione (bis(glutathionyl)spermidine (T(SH)₂)). Here we present a thorough kinetic analysis of Trypanosoma brucei TryS in a newly developed phosphate buffer system at pH 7.0 and 37 °C, mimicking the physiological environment of the enzyme in the cytosol of bloodstream parasites. Under these conditions, TryS displays K_m values for GSH, ATP, spermidine, and Gsp of 34, 18, 687, and 32 μm, respectively, as well as K_i values for GSH and T(SH)₂ of 1 mm and 360 μm, respectively. As Gsp hydrolysis has a K_m value of 5.6 mm, the in vivo amidase activity is probably negligible. To obtain deeper insight in the molecular mechanism of TryS, we have formulated alternative kinetic models, with elementary reaction steps represented by linear kinetic equations. The model parameters were fitted to the extensive matrix of steady-state data obtained for different substrate/product combinations under the in vivo-like conditions. The best model describes the full kinetic profile and is able to predict time course data that were not used for fitting. This system's biology approach to enzyme kinetics led us to conclude that (i) TryS follows a ter-reactant mechanism, (ii) the intermediate Gsp dissociates from the enzyme between the two catalytic steps, and (iii) T(SH)₂ inhibits the enzyme by remaining bound at its product site and, as does the inhibitory GSH, by binding to the activated enzyme complex. The newly detected concerted substrate and product inhibition suggests that TryS activity is tightly regulated.

Inducible tumor necrosis factor (TNF) receptor-associated factor-1 expression couples the canonical to the non-canonical NF-κB pathway in TNF stimulation

The NF-κB transcription factor mediates the inflammatory response through distinct (canonical and non-canonical) signaling pathways. The mechanisms controlling utilization of either of these pathways are largely unknown. Here we observe that TNF stimulation induces delayed NF-κB2/p100 processing and investigate the coupling mechanism. TNF stimulation induces TNF-associated factor-1 (TRAF-1) that directly binds NF-κB-inducing kinase (NIK) and stabilizes it from degradation by disrupting its interaction with TRAF2·cIAP2 ubiquitin ligase complex. We show that TRAF1 depletion prevents TNF-induced NIK stabilization and reduces p52 production. To further examine the interactions of TRAF1 and NIK with NF-κB2/p100 processing, we mathematically modeled TRAF1·NIK as a coupling signaling complex and validated computational inference by siRNA knockdown to show non-canonical pathway activation is dependent not only on TRAF1 induction but also NIK stabilization by forming TRAF1·NIK complex. Thus, these integrated computational-experimental studies of TNF-induced TRAF1 expression identified TRAF1·NIK as a central complex linking canonical and non-canonical pathways by disrupting the TRAF2-cIAP2 ubiquitin ligase complex. This feed-forward kinase pathway is essential for the activation of non-canonical pathway.

Mathematical modeling approaches in the study of glaucoma disparities among people of African and European descents

Open angle glaucoma (OAG) is a severe ocular disease characterized by progressive and irreversible vision loss. While elevated intraocular pressure (IOP) is a well-established risk factor for OAG, the progression of OAG in many cases, despite IOP treatment, suggests that other risk factors must play significant roles in the development of the disease. For example, various structural properties of the eye, ocular blood flow properties, and systemic conditions have been identified as risk factors for OAG. Ethnicity has also been indicated as a relevant factor that affects the incidence and prevalence of OAG; in fact, OAG is the leading cause of blindness among people of African descent. Numerous clinical studies have been designed to examine the possible correlation and causation between OAG and these factors; however, these studies are met with the challenge of isolating the individual role of multiple interconnected factors. Over the last decade, various mathematical modeling approaches have been implemented in combination with clinical studies in order to provide a mechanical and hemodynamical description of the eye in relation to the entire human body and to assess the contribution of single risk factors to the development of OAG. This review provides a summary of the clinical evidence of ocular structural differences, ocular vascular differences and systemic vascular differences among people of African and European descent, describes the mathematical approaches that have been proposed to study ocular mechanics and hemodynamics while discussing how they could be used to investigate the relevance to OAG of racial disparities, and outlines possible new directions of research.