Michael Shapiro
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Michael Shapiro has a total of 90 co-authors. Here are the top co-authors by number of shared publications:
- David A. Thorley-Lawson
Department of Pathology, Tufts University School of Medicine, Boston, Massachusetts, United States of America
7 shared publications - Edgar Delgado-Eckert
Paediatric Research Centre, University Children’s Hospital Basel UKBB, University of Basel, Basel, Switzerland
6 shared publications - Anna Laddach
Nervous System Development and Homeostasis Laboratory, The Francis Crick Institute, London, UK
4 shared publications - Jared B. Hawkins
Boston Children's Hospital Harvard Medical School Boston MA USA
3 shared publications - Nicholas Polys
Advanced Research Computing, Virginia Tech, Blacksburg, USA
3 shared publications Vey Hadinoto
Department of Pathology, Tufts University School of Medicine, Boston, Massachusetts, United States of America
3 shared publications
Latest Publications
- Open Access
- 2 January 2026
- Published by Oxford University Press (OUP) in Bioinformatics
- Vol. 42 (1)
Capturing gene–cell duality in a cat’s cradle
Summary: CatsCradle is an R package for single-cell analysis that exploits the duality between cells and the genes they express. Our package provides tools to cluster genes, visualize relationships between them, and to explore relationships between gene clusters (programmes) and cell clusters (cell types). Availability and implementation: CatsCradle is available freely as an R Bioconductor package (https://bioconductor.org/packages/CatsCradle) and interfaces directly with Seurat (Hao et al. 2024) and SingleCellExperiment (Amezquita et al. 2020) data structures.
- 2 January 2026
- Published by Oxford University Press (OUP) in Bioinformatics
- Vol. 42 (1)
Open AccessCapturing gene–cell duality in a cat’s cradle
Summary: CatsCradle is an R package for single-cell analysis that exploits the duality between cells and the genes they express. Our package provides tools to cluster genes, visualize relationships between them, and to explore relationships between gene clusters (programmes) and cell clusters (cell types). Availability and implementation: CatsCradle is available freely as an R Bioconductor package (https://bioconductor.org/packages/CatsCradle) and interfaces directly with Seurat (Hao et al. 2024) and SingleCellExperiment (Amezquita et al. 2020) data structures.
- Open Access
- 28 September 2024
- Published by Oxford University Press (OUP) in NAR Genomics and Bioinformatics
- Vol. 6 (4) , lqae139
TrajectoryGeometry suggests cell fate decisions can involve branches rather than bifurcations
Differentiation of multipotential progenitor cells is a key process in the development of any multi-cellular organism and often continues throughout its life. It is often assumed that a bi-potential progenitor develops along a (relatively) straight trajectory until it reaches a decision point where the trajectory bifurcates. At this point one of two directions is chosen, each direction representing the unfolding of a new transcriptional programme. However, we have lacked quantitative means for testing this model. Accordingly, we have developed the R package TrajectoryGeometry. Applying this to published data we find several examples where, rather than bifurcate, developmental pathways branch. That is, the bipotential progenitor develops along a relatively straight trajectory leading to one of its potential fates. A second relatively straight trajectory branches off from this towards the other potential fate. In this sense only cells that branch off to follow the second trajectory make a ‘decision’. Our methods give precise descriptions of the genes and cellular pathways involved in these trajectories. We speculate that branching may be the more common behaviour and may have advantages from a control-theoretic viewpoint.
- 28 September 2024
- Published by Oxford University Press (OUP) in NAR Genomics and Bioinformatics
- Vol. 6 (4) , lqae139
Open AccessTrajectoryGeometry suggests cell fate decisions can involve branches rather than bifurcations
Differentiation of multipotential progenitor cells is a key process in the development of any multi-cellular organism and often continues throughout its life. It is often assumed that a bi-potential progenitor develops along a (relatively) straight trajectory until it reaches a decision point where the trajectory bifurcates. At this point one of two directions is chosen, each direction representing the unfolding of a new transcriptional programme. However, we have lacked quantitative means for testing this model. Accordingly, we have developed the R package TrajectoryGeometry. Applying this to published data we find several examples where, rather than bifurcate, developmental pathways branch. That is, the bipotential progenitor develops along a relatively straight trajectory leading to one of its potential fates. A second relatively straight trajectory branches off from this towards the other potential fate. In this sense only cells that branch off to follow the second trajectory make a ‘decision’. Our methods give precise descriptions of the genes and cellular pathways involved in these trajectories. We speculate that branching may be the more common behaviour and may have advantages from a control-theoretic viewpoint.
- Open Access
- 3 May 2024
- Published by Oxford University Press (OUP) in Journal of Leukocyte Biology
- Vol. 116 (2) , 369-378
The AHR repressor limits expression of antimicrobial genes but not AHR-dependent genes in intestinal eosinophils
Intestinal eosinophils express the aryl hydrocarbon receptor (AHR), an environmental sensor and ligand-activated transcription factor that responds to dietary or environmental ligands. AHR regulates tissue adaptation, survival, adhesion, and immune functions in intestinal eosinophils. The AHR repressor (AHRR) is itself induced by AHR and believed to limit AHR activity in a negative feedback loop. We analyzed gene expression in intestinal eosinophils from wild-type and AHRR knockout mice and found that AHRR did not suppress most AHR-dependent genes. Instead, AHRR limited the expression of a distinct small set of genes involved in the innate immune response. These included S100 proteins, antimicrobial proteins, and alpha-defensins. Using bone marrow–derived eosinophils, we found that AHRR knockout eosinophils released more reactive oxygen species upon stimulation. This work shows that the paradigm of AHRR as a repressor of AHR transcriptional activity does not apply to intestinal eosinophils. Rather, AHRR limits the expression of innate immune response and antimicrobial genes, possibly to maintain an anti-inflammatory phenotype in eosinophils when exposed to microbial signals in the intestinal environment.
- 3 May 2024
- Published by Oxford University Press (OUP) in Journal of Leukocyte Biology
- Vol. 116 (2) , 369-378
Open AccessThe AHR repressor limits expression of antimicrobial genes but not AHR-dependent genes in intestinal eosinophils
Intestinal eosinophils express the aryl hydrocarbon receptor (AHR), an environmental sensor and ligand-activated transcription factor that responds to dietary or environmental ligands. AHR regulates tissue adaptation, survival, adhesion, and immune functions in intestinal eosinophils. The AHR repressor (AHRR) is itself induced by AHR and believed to limit AHR activity in a negative feedback loop. We analyzed gene expression in intestinal eosinophils from wild-type and AHRR knockout mice and found that AHRR did not suppress most AHR-dependent genes. Instead, AHRR limited the expression of a distinct small set of genes involved in the innate immune response. These included S100 proteins, antimicrobial proteins, and alpha-defensins. Using bone marrow–derived eosinophils, we found that AHRR knockout eosinophils released more reactive oxygen species upon stimulation. This work shows that the paradigm of AHRR as a repressor of AHR transcriptional activity does not apply to intestinal eosinophils. Rather, AHRR limits the expression of innate immune response and antimicrobial genes, possibly to maintain an anti-inflammatory phenotype in eosinophils when exposed to microbial signals in the intestinal environment.
- Open Access
Trajectorygeometry suggests cell fate decisions involve branches rather than bifurcations
A bstract: Differentiation of multipotential progenitor cells is a key process in the development of any multi-cellular organism and often continues throughout its life. It is often assumed that a bi-potential progenitor develops along a (relatively) straight trajectory until it reaches a decision point where the trajectory bifurcates. At this point one of two directions is chosen, each direction representing the unfolding of a new transcriptomic programme. However, we have lacked quantitative means for testing this model. Accordingly, we have developed the R package TrajectoryGeometry. Applying this to published data we find several examples where, rather than bifurcate, developmental pathways branch . That is, the bipotential progenitor develops along a relatively straight trajectory leading to one of its potential fates. A second relatively straight trajectory branches off from this towards the other potential fate. In this sense only cells that branch off to follow the second trajectory make a “decision”. Our methods give precise descriptions of the genes and cellular pathways involved in these trajectories. We speculate that branching may be the more common behaviour and may have advantages from a control-theoretic viewpoint.
Open AccessTrajectorygeometry suggests cell fate decisions involve branches rather than bifurcations
A bstract: Differentiation of multipotential progenitor cells is a key process in the development of any multi-cellular organism and often continues throughout its life. It is often assumed that a bi-potential progenitor develops along a (relatively) straight trajectory until it reaches a decision point where the trajectory bifurcates. At this point one of two directions is chosen, each direction representing the unfolding of a new transcriptomic programme. However, we have lacked quantitative means for testing this model. Accordingly, we have developed the R package TrajectoryGeometry. Applying this to published data we find several examples where, rather than bifurcate, developmental pathways branch . That is, the bipotential progenitor develops along a relatively straight trajectory leading to one of its potential fates. A second relatively straight trajectory branches off from this towards the other potential fate. In this sense only cells that branch off to follow the second trajectory make a “decision”. Our methods give precise descriptions of the genes and cellular pathways involved in these trajectories. We speculate that branching may be the more common behaviour and may have advantages from a control-theoretic viewpoint.
- Open Access
A branching model of cell fate decisions in the enteric nervous system
How neurogenesis and gliogenesis are coordinated during development and why mature glial cells often share properties with neuroectodermal progenitors remains unclear. Here, we have used single cell RNA sequencing to map the regulatory landscape of neuronal and glial differentiation in the mammalian enteric nervous system (ENS). Our analysis indicates that neurogenic trajectories branch directly from a linear gliogenic axis defined by autonomic neural crest cells adopting sequential states as they progressively lose their strong neurogenic bias and acquire properties of adult enteric glia. We identify gene modules associated with transcriptional programs driving enteric neurogenesis and cell state transitions along the gliogenic axis. By comparing the chromatin accessibility profile of autonomic neural crest and adult enteric glia we provide evidence that the latter maintain an epigenetic memory of their neurogenic past. Finally, we demonstrate that adult enteric glia maintain neurogenic potential and are capable of generating enteric neurons in certain contexts by activating transcriptional programs employed by early ENS progenitors. Our studies uncover a novel configuration of enteric neurogenesis and gliogenesis that enables the coordinate development of ENS lineages and provides a mechanistic explanation for the ability of enteric glia to be functionally integrated into the adult intestine and simultaneously maintain attributes of early ENS progenitors.
Open AccessA branching model of cell fate decisions in the enteric nervous system
How neurogenesis and gliogenesis are coordinated during development and why mature glial cells often share properties with neuroectodermal progenitors remains unclear. Here, we have used single cell RNA sequencing to map the regulatory landscape of neuronal and glial differentiation in the mammalian enteric nervous system (ENS). Our analysis indicates that neurogenic trajectories branch directly from a linear gliogenic axis defined by autonomic neural crest cells adopting sequential states as they progressively lose their strong neurogenic bias and acquire properties of adult enteric glia. We identify gene modules associated with transcriptional programs driving enteric neurogenesis and cell state transitions along the gliogenic axis. By comparing the chromatin accessibility profile of autonomic neural crest and adult enteric glia we provide evidence that the latter maintain an epigenetic memory of their neurogenic past. Finally, we demonstrate that adult enteric glia maintain neurogenic potential and are capable of generating enteric neurons in certain contexts by activating transcriptional programs employed by early ENS progenitors. Our studies uncover a novel configuration of enteric neurogenesis and gliogenesis that enables the coordinate development of ENS lineages and provides a mechanistic explanation for the ability of enteric glia to be functionally integrated into the adult intestine and simultaneously maintain attributes of early ENS progenitors.
- Open Access
- 3 March 2022
- Published by Rockefeller University Press in Journal of Experimental Medicine
- Vol. 219 (4)
The aryl hydrocarbon receptor contributes to tissue adaptation of intestinal eosinophils in mice
Eosinophils are potent sources of inflammatory and toxic mediators, yet they reside in large numbers in the healthy intestine without causing tissue damage. We show here that intestinal eosinophils were specifically adapted to their environment and underwent substantial transcriptomic changes. Intestinal eosinophils upregulated genes relating to the immune response, cell–cell communication, extracellular matrix remodeling, and the aryl hydrocarbon receptor (AHR), a ligand-activated transcription factor with broad functions in intestinal homeostasis. Eosinophils from AHR-deficient mice failed to fully express the intestinal gene expression program, including extracellular matrix organization and cell junction pathways. AHR-deficient eosinophils were functionally impaired in the adhesion to and degradation of extracellular matrix, were more prone to degranulation, and had an extended life span. Lack of AHR in eosinophils had wider effects on the intestinal immune system, affecting the T cell compartment in nave and helminth-infected mice. Our study demonstrates that the response to environmental triggers via AHR partially shapes tissue adaptation of eosinophils in the small intestine.
- 3 March 2022
- Published by Rockefeller University Press in Journal of Experimental Medicine
- Vol. 219 (4)
Open AccessThe aryl hydrocarbon receptor contributes to tissue adaptation of intestinal eosinophils in mice
Eosinophils are potent sources of inflammatory and toxic mediators, yet they reside in large numbers in the healthy intestine without causing tissue damage. We show here that intestinal eosinophils were specifically adapted to their environment and underwent substantial transcriptomic changes. Intestinal eosinophils upregulated genes relating to the immune response, cell–cell communication, extracellular matrix remodeling, and the aryl hydrocarbon receptor (AHR), a ligand-activated transcription factor with broad functions in intestinal homeostasis. Eosinophils from AHR-deficient mice failed to fully express the intestinal gene expression program, including extracellular matrix organization and cell junction pathways. AHR-deficient eosinophils were functionally impaired in the adhesion to and degradation of extracellular matrix, were more prone to degranulation, and had an extended life span. Lack of AHR in eosinophils had wider effects on the intestinal immune system, affecting the T cell compartment in nave and helminth-infected mice. Our study demonstrates that the response to environmental triggers via AHR partially shapes tissue adaptation of eosinophils in the small intestine.
- Open Access
- 27 December 2019
- Published by Public Library of Science (PLoS) in PLOS Genetics
- Vol. 15 (12) , e1008501
The MITF-SOX10 regulated long non-coding RNA DIRC3 is a melanoma tumour suppressor
The MITF and SOX10 transcription factors regulate the expression of genes important for melanoma proliferation, invasion and metastasis. Despite growing evidence of the contribution of long noncoding RNAs (lncRNAs) in cancer, including melanoma, their functions within MITF-SOX10 transcriptional programmes remain poorly investigated. Here we identify 245 candidate melanoma associated lncRNAs whose loci are co-occupied by MITF-SOX10 and that are enriched at active enhancer-like regions. Our work suggests that one of these, Disrupted In Renal Carcinoma 3 (DIRC3), may be a clinically important MITF-SOX10 regulated tumour suppressor. DIRC3 depletion in human melanoma cells leads to increased anchorage-independent growth, a hallmark of malignant transformation, whilst melanoma patients classified by low DIRC3 expression have decreased survival. DIRC3 is a nuclear lncRNA that activates expression of its neighbouring IGFBP5 tumour suppressor through modulating chromatin structure and suppressing SOX10 binding to putative regulatory elements within the DIRC3 locus. In turn, DIRC3 dependent regulation of IGFBP5 impacts the expression of genes involved in cancer associated processes and is needed for DIRC3 control of anchorage-independent growth. Our work indicates that lncRNA components of MITF-SOX10 networks are an important new class of melanoma regulators and candidate therapeutic targets that can act not only as downstream mediators of MITF-SOX10 function but as feedback regulators of MITF-SOX10 activity. The human genome expresses thousands of long non-coding RNAs (lncRNAs), in addition to protein coding genes. Although the majority of these molecules are of unknown function, a subset of lncRNAs have been proposed to represent a new class of cancer causing genes. While lncRNAs in melanoma have great potential for the development of new treatments, it remains unclear how they integrate into the well-defined gene expression networks controlling the formation and progression of this disease. Here we have identified a new set of 245 candidate melanoma-associated lncRNAs that are targeted by the MITF and SOX10 melanoma transcription factors. We show that one of these, DIRC3, may be a clinically important MITF-SOX10 regulated melanoma tumour suppressor that acts to block the spread of the disease and that melanoma patients with low DIRC3 expression have decreased survival. We also discovered that DIRC3 functions as a new transcriptional regulator to activate its neighbouring IGFBP5 gene and control genome-wide expression programmes involved in cancer. Our results suggest that lncRNA components of MITF-SOX10 networks represent an important new class of melanoma regulators and predict that up-regulation of DIRC3 expression may represent an exciting new therapeutic strategy for melanoma.
- 27 December 2019
- Published by Public Library of Science (PLoS) in PLOS Genetics
- Vol. 15 (12) , e1008501
Open AccessThe MITF-SOX10 regulated long non-coding RNA DIRC3 is a melanoma tumour suppressor
The MITF and SOX10 transcription factors regulate the expression of genes important for melanoma proliferation, invasion and metastasis. Despite growing evidence of the contribution of long noncoding RNAs (lncRNAs) in cancer, including melanoma, their functions within MITF-SOX10 transcriptional programmes remain poorly investigated. Here we identify 245 candidate melanoma associated lncRNAs whose loci are co-occupied by MITF-SOX10 and that are enriched at active enhancer-like regions. Our work suggests that one of these, Disrupted In Renal Carcinoma 3 (DIRC3), may be a clinically important MITF-SOX10 regulated tumour suppressor. DIRC3 depletion in human melanoma cells leads to increased anchorage-independent growth, a hallmark of malignant transformation, whilst melanoma patients classified by low DIRC3 expression have decreased survival. DIRC3 is a nuclear lncRNA that activates expression of its neighbouring IGFBP5 tumour suppressor through modulating chromatin structure and suppressing SOX10 binding to putative regulatory elements within the DIRC3 locus. In turn, DIRC3 dependent regulation of IGFBP5 impacts the expression of genes involved in cancer associated processes and is needed for DIRC3 control of anchorage-independent growth. Our work indicates that lncRNA components of MITF-SOX10 networks are an important new class of melanoma regulators and candidate therapeutic targets that can act not only as downstream mediators of MITF-SOX10 function but as feedback regulators of MITF-SOX10 activity. The human genome expresses thousands of long non-coding RNAs (lncRNAs), in addition to protein coding genes. Although the majority of these molecules are of unknown function, a subset of lncRNAs have been proposed to represent a new class of cancer causing genes. While lncRNAs in melanoma have great potential for the development of new treatments, it remains unclear how they integrate into the well-defined gene expression networks controlling the formation and progression of this disease. Here we have identified a new set of 245 candidate melanoma-associated lncRNAs that are targeted by the MITF and SOX10 melanoma transcription factors. We show that one of these, DIRC3, may be a clinically important MITF-SOX10 regulated melanoma tumour suppressor that acts to block the spread of the disease and that melanoma patients with low DIRC3 expression have decreased survival. We also discovered that DIRC3 functions as a new transcriptional regulator to activate its neighbouring IGFBP5 gene and control genome-wide expression programmes involved in cancer. Our results suggest that lncRNA components of MITF-SOX10 networks represent an important new class of melanoma regulators and predict that up-regulation of DIRC3 expression may represent an exciting new therapeutic strategy for melanoma.
- 12 August 2017
- Published by Springer Nature in Geometriae Dedicata
- Vol. 195 (1) , 79-99
Growth in higher Baumslag–Solitar groups
- 12 August 2017
- Published by Springer Nature in Geometriae Dedicata
- Vol. 195 (1) , 79-99
Growth in higher Baumslag–Solitar groups
- 10 April 2015
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 143 (11) , 4723-4731
Equations in nilpotent groups
We show that there exists an algorithm to decide any single equation in the Heisenberg group in finite time. The method works for all two-step nilpotent groups with rank-one commutator, which includes the higher Heisenberg groups. We also prove that the decision problem for systems of equations is unsolvable in all non-abelian free nilpotent groups.
- 10 April 2015
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 143 (11) , 4723-4731
Equations in nilpotent groups
We show that there exists an algorithm to decide any single equation in the Heisenberg group in finite time. The method works for all two-step nilpotent groups with rank-one commutator, which includes the higher Heisenberg groups. We also prove that the decision problem for systems of equations is unsolvable in all non-abelian free nilpotent groups.
- Open Access
- 17 October 2013
- Published by Public Library of Science (PLoS) in PLOS Pathogens
- Vol. 9 (10) , e1003685
The Cycle of EBV Infection Explains Persistence, the Sizes of the Infected Cell Populations and Which Come under CTL Regulation
Previous analysis of Epstein-Barr virus (EBV) persistent infection has involved biological and immunological studies to identify and quantify infected cell populations and the immune response to them. This led to a biological model whereby EBV infects and activates naive B-cells, which then transit through the germinal center to become resting memory B-cells where the virus resides quiescently. Occasionally the virus reactivates from these memory cells to produce infectious virions. Some of this virus infects new naive B-cells, completing a cycle of infection. What has been lacking is an understanding of the dynamic interactions between these components and how their regulation by the immune response produces the observed pattern of viral persistence. We have recently provided a mathematical analysis of a pathogen which, like EBV, has a cycle of infected stages. In this paper we have developed biologically credible values for all of the parameters governing this model and show that with these values, it successfully recapitulates persistent EBV infection with remarkable accuracy. This includes correctly predicting the observed patterns of cytotoxic T-cell regulation (which and by how much each infected population is regulated by the immune response) and the size of the infected germinal center and memory populations. Furthermore, we find that viral quiescence in the memory compartment dictates the pattern of regulation but is not required for persistence; it is the cycle of infection that explains persistence and provides the stability that allows EBV to persist at extremely low levels. This shifts the focus away from a single infected stage, the memory B-cell, to the whole cycle of infection. We conclude that the mathematical description of the biological model of EBV persistence provides a sound basis for quantitative analysis of viral persistence and provides testable predictions about the nature of EBV-associated diseases and how to curb or prevent them. Epstein-Barr virus (EBV) is a herpesvirus that establishes a lifelong persistent infection in virtually all human beings. This infection is a risk factor for the subsequent development of certain tumors and possibly also autoimmune diseases. In order to understand the origin of these diseases, it is necessary to first understand how EBV maintains persistent infection. We have used mathematical analysis to study this question. We find that the characteristic cycle of infected stages that EBV establishes in vivo allows it to persist stably at extremely low levels. This represents a consistent mathematical description of EBV infection and allows us to describe what must change to convert benign infection into pathogenic infection, as well as what kind of efficacy drugs and vaccines must have in order to be useful.
- 17 October 2013
- Published by Public Library of Science (PLoS) in PLOS Pathogens
- Vol. 9 (10) , e1003685
Open AccessThe Cycle of EBV Infection Explains Persistence, the Sizes of the Infected Cell Populations and Which Come under CTL Regulation
Previous analysis of Epstein-Barr virus (EBV) persistent infection has involved biological and immunological studies to identify and quantify infected cell populations and the immune response to them. This led to a biological model whereby EBV infects and activates naive B-cells, which then transit through the germinal center to become resting memory B-cells where the virus resides quiescently. Occasionally the virus reactivates from these memory cells to produce infectious virions. Some of this virus infects new naive B-cells, completing a cycle of infection. What has been lacking is an understanding of the dynamic interactions between these components and how their regulation by the immune response produces the observed pattern of viral persistence. We have recently provided a mathematical analysis of a pathogen which, like EBV, has a cycle of infected stages. In this paper we have developed biologically credible values for all of the parameters governing this model and show that with these values, it successfully recapitulates persistent EBV infection with remarkable accuracy. This includes correctly predicting the observed patterns of cytotoxic T-cell regulation (which and by how much each infected population is regulated by the immune response) and the size of the infected germinal center and memory populations. Furthermore, we find that viral quiescence in the memory compartment dictates the pattern of regulation but is not required for persistence; it is the cycle of infection that explains persistence and provides the stability that allows EBV to persist at extremely low levels. This shifts the focus away from a single infected stage, the memory B-cell, to the whole cycle of infection. We conclude that the mathematical description of the biological model of EBV persistence provides a sound basis for quantitative analysis of viral persistence and provides testable predictions about the nature of EBV-associated diseases and how to curb or prevent them. Epstein-Barr virus (EBV) is a herpesvirus that establishes a lifelong persistent infection in virtually all human beings. This infection is a risk factor for the subsequent development of certain tumors and possibly also autoimmune diseases. In order to understand the origin of these diseases, it is necessary to first understand how EBV maintains persistent infection. We have used mathematical analysis to study this question. We find that the characteristic cycle of infected stages that EBV establishes in vivo allows it to persist stably at extremely low levels. This represents a consistent mathematical description of EBV infection and allows us to describe what must change to convert benign infection into pathogenic infection, as well as what kind of efficacy drugs and vaccines must have in order to be useful.