T H E many attempts which have been made to simulate curves of limited growth by mathematical formulations either aim at accounting for their form through certain fundamental postulates about the growth process, or else are severely practical in scope and inspired by the desire to obtain any relatively simple equation which contains the essence of the numerical data. In the empirical approach the magnitudes of the constants in the fitted equations may be used to assess the importance in growth of experimentally controllable factors, but the constants themselves are not regarded as having any absolute significance for the theory of growth. Obviously the usefulness of any empirical equation is enhanced if its constants yield easily information of direct biological interest. The three best-known 'growth functions' are as follows:

A Flexible Growth Function for Empirical Use

A newly described coronavirus named severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which is the causative agent of coronavirus disease 2019 (COVID-19), has infected over 2.3 million people, led to the death of more than 160,000 individuals and caused worldwide social and economic disruption1,2. There are no antiviral drugs with proven clinical efficacy for the treatment of COVID-19, nor are there any vaccines that prevent infection with SARS-CoV-2, and efforts to develop drugs and vaccines are hampered by the limited knowledge of the molecular details of how SARS-CoV-2 infects cells. Here we cloned, tagged and expressed 26 of the 29 SARS-CoV-2 proteins in human cells and identified the human proteins that physically associated with each of the SARS-CoV-2 proteins using affinity-purification mass spectrometry, identifying 332 high-confidence protein–protein interactions between SARS-CoV-2 and human proteins. Among these, we identify 66 druggable human proteins or host factors targeted by 69 compounds (of which, 29 drugs are approved by the US Food and Drug Administration, 12 are in clinical trials and 28 are preclinical compounds). We screened a subset of these in multiple viral assays and found two sets of pharmacological agents that displayed antiviral activity: inhibitors of mRNA translation and predicted regulators of the sigma-1 and sigma-2 receptors. Further studies of these host-factor-targeting agents, including their combination with drugs that directly target viral enzymes, could lead to a therapeutic regimen to treat COVID-19. A human–SARS-CoV-2 protein interaction map highlights cellular processes that are hijacked by the virus and that can be targeted by existing drugs, including inhibitors of mRNA translation and predicted regulators of the sigma receptors.

/pdf/a-sars-cov-2-protein-interaction-map-reveals-targets-for-5d1m2n6hc1.pdf

A SARS-CoV-2 protein interaction map reveals targets for drug repurposing.

A Manual of Methods for Baculovirus Vectors and Insect Cell Culture Procedures.

A streptomycete was isolated from an Easter Island soil sample and found to inhibit Candida albicans, Microsporum gypseum and Trichophyton granulosum. The antibiotic-producing microorganism was characterized and identified as Streptomyces hygroscopicus. The antifungal principle was extracted with organic solvent from the mycelium, isolated in crystalline form and named rapamycin. Rapamycin is mainly active against Candida albicans; minimum inhibitory concentration against ten strains ranged from 0.02 to 0.2 mug/ml. Its apparent activity against Microsporum gypseum and Trichophyton granulosum is lower because of its instability in culture media on prolonged incubation required by these fungi. No activity was observed against gram-positive and gram-negative bacteria. Acute toxicity in mice is low.

Rapamycin (ay-22, 989), a new antifungal antibiotic i. taxonomy of the producing streptomycete and isolation of the active principle

A real-time reverse transcriptase PCR (RRT-PCR) assay based on the avian influenza virus matrix gene was developed for the rapid detection of type A influenza virus. Additionally, H5 and H7 hemagglutinin subtype-specific probe sets were developed based on North American avian influenza virus sequences. The RRT-PCR assay utilizes a one-step RT-PCR protocol and fluorogenic hydrolysis type probes. The matrix gene RRT-PCR assay has a detection limit of 10 fg or approximately 1,000 copies of target RNA and can detect 0.1 50% egg infective dose of virus. The H5- and H7-specific probe sets each have a detection limit of 100 fg of target RNA or approximately 103 to 104 gene copies. The sensitivity and specificity of the real-time PCR assay were directly compared with those of the current standard for detection of influenza virus: virus isolation (VI) in embryonated chicken eggs and hemagglutinin subtyping by hemagglutination inhibition (HI) assay. The comparison was performed with 1,550 tracheal and cloacal swabs from various avian species and environmental swabs obtained from live-bird markets in New York and New Jersey. Influenza virus-specific RRT-PCR results correlated with VI results for 89% of the samples. The remaining samples were positive with only one detection method. Overall the sensitivity and specificity of the H7- and H5-specific RRT-PCR were similar to those of VI and HI.

Development of a Real-Time Reverse Transcriptase PCR Assay for Type A Influenza Virus and the Avian H5 and H7 Hemagglutinin Subtypes

A simple method of estimating fifty per cent endpoints

Pearl and Reed begin their paper with a discussion of exponential and parabolic growth formulas for past U S population growth, which we have omitted

https://www.pnas.org/content/pnas/6/6/275.full.pdf

On the Rate of Growth of the Population of the United States since 1790 and Its Mathematical Representation.

For infancy Reed and Merrell revise their q x formula to correct underenumeration, an approach that is not general. This has been omitted, as have their equations for L x and T x values by approximate integration. The article is followed by a note on other n q x formulas.

Lowell J. Reed

Papers

A simple method of estimating fifty per cent endpoints

On the Rate of Growth of the Population of the United States since 1790 and Its Mathematical Representation.

A short method for constructing an abridged life table

A Further Note on the Mathematical Theory of Population Growth

The logistic curve and the census count of 1940.