Mathematical models for systems biology of infectious diseases

Mathematical models help make sense of complex biological systems. Models that are accurate enough can even predict how the system responds to perturbations. This can be used for example to devise a public health strategy to stop an infection from spreading across a population.

On March 15 we published a review on the mathematical modeling in infectious diseases. The review discusses many applications, not only tracking disease spread. Some of the examples we covered include the metabolism of a pathogen’s cells, transcriptomic networks, microbiome ecology, and understanding why antimicrobials that can kill a pathogen in vitro may fail to work in vivo.

The coauthors of this review span a wide array of modelers working on various systems. We came together through a Modeling Work Group of the NIAID Systems Biology for Infectious Diseases Research Program. It wasn’t easy to conceive a review to include all models because they were so different, but we found interesting parallels. Especially interesting was that many of the models use mass-action kinetics as their main assumption. The elements described by mass action range in scale, though. For example, metabolic network models describe the metabolites in a metabolic network, while epidemiology models describe individual people interacting socially in a population. We also discuss considerations for publishing a mathematical model. The suggestions come from our experiences in sharing models among the members of the Modeling Workgroup. Read the review at:

Mathematical models to study the biology of pathogens and the infectious diseases they cause. Joao B. Xavier, Jonathan M.Monk, Saugat Poudel, Charles J. Norsigian, Anand V. Sastry, Chen Liao, JoseBento, Marc A. Suchard, Mario L. Arrieta-Ortiz, Eliza J. R. Peterson, Nitin S. Baliga, ThomasStoeger, Felicia Ruffin, Reese A.K. Richardson, Catherine A. Gao, Thomas D. Horvath, Anthony M. Haag, Qinglong Wu, Tor Savidge, Michael R. Yeaman. iScience [online]

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Mathematical models to optimize the scheduling of cancer treatments

This review is on how mathematical models can be used to make the best of cancer drugs already available. The review precedes our research paper on pulsed treatment which is about to come out soon in the AACR journal Molecular Cancer Therapeutics.

Optimizing the future: how mathematical models inform treatment schedules for cancer.
Deepti Mathur, Ethan Barnett, Howard I. Scher & Joao B. Xavier. Trends in Cancer [online]

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“How to win against competitors and influence your neighbors”

Read the blog post by Hilary, Yanyan and Kevin on Nature’s eco and evo community. Here’s the link to the original paper:
Spatial-temporal dynamics of a microbial cooperative behavior resistant to cheating.
Hilary Monaco, Kevin S. Liu, Tiago Sereno, Maxime Deforet, Bradford P. Taylor, Yanyan Chen, Caleb C. Reagor & Joao B. Xavier. Nature Communications [open access]

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10+ years of swarming reviewed

I filmed my first swarm on February 29, 2008. I placed the inoculated Petri dish under a video camera, inside a temperature-controlled room set to 37C. The camera took a picture at every 10 minutes for 24 h, which I then stitched into a 14 seconds long time-lapsed video. I had grown swarms before, but had not seen them move yet. I wanted to see how the dilute culture of bacteria spotted at the center each time developed into the branched colony in less than 24 h.

This was the first movie, and my lab members and I have made dozens since then. We used swarming as a model to understand how billions of bacteria behave cooperatively, moving together across distances >10,000x their body length in a few hours. Today we have a review in Annual Reviews Microbiology called “The Ultimate Guide to Bacterial Swarming: An Experimental Model to Study the Evolution of Cooperative Behavior”. The review talks about how we used the swarming assay to address evolutionary questions. It also tries to explain the difference between proximate mechanism and ultimate mechanism–I hope we have succeeded at that. Here’s an example: Proximate mechanism is for example when we determined that mutations in the gene fleN cause bacteria to become multi-flagellated and swarm faster than the wild-type. Ultimate mechanism is when we say that fleN-mutated hyperswarmers can’t exist in the wild because they are bad at making biofilms and should be disfavored by natural selection.

Read our review here:
The Ultimate Guide to Bacterial Swarming: An Experimental Model to Study the Evolution of Cooperative Behavior.
Jinyuan Yan, Hilary T. Monaco, and Joao B. Xavier. Annual Reviews Microbiology [online early]

See also Maxime’s paper where we proposed a new rule for evolution of faster dispersal at the edge of expanding populations. The paper was inspired by the hyperswarmers, and has many cool experiments with hyperswarming to test the new rule. The paper is now peer-reviewed and published in the American Naturalist.

Evolution at the edge of expanding populations.
Maxime Deforet, Carlos Carmona Fontaine, Kirill S. Korolev, Joao B. Xavier. The American Naturalist [in press-preprint on bioRxiv|early view at Am Nat]

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The impact of the gut microbiota on circulating leukocyte levels

We posted our new study on bioRxiv were we compared the impact of the microbiota white blood cells dynamics in patients receiving hematopoietic cell transplantation.

We estimate that microbiota diversity can have a suppressive effect on circulating lymphocytes similar to that of immunosuppressive drugs administered to reduce graft vs host disease. This may help explain previous studies from our MSKCC collaborators that associated microbiota diversity to lower transplant-related mortality. There’s more work to be done for a mechanism linking the microbiota to systemic immunity, of course. But this study stands out because it addresses the problem directly in humans.

We are going to wait a few days before we submit the paper for peer review. We appreciate any comments to improve the paper.

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Antibiotics and weight gain

Martin Blaser’s lab showed a few years ago that exposing mice to low doses of antibiotics very early in their lives changes their gut microbiota and makes the mice gain more fat and gain more body weight later in life. Jonas Schluter and I started collaborating with Blaser’s group three years ago.  In a paper published today in the ISMEJ we analyzed one of their latest experiments–one with a large scale cohousing scheme that sought to determine whether exchanging gut microbes with untreated mice would lower the tendency that antibiotic-exposed mice to had to gain more weight.

We saw that mice exposed to antibiotics in early life mice got on a weight-gain trajectory, and they stayed on that trajectory despite exchanging microbes with mice who were never exposed to antibiotics.  We ran many statistical tests as part of our analysis. The paper shows that the effect of antibiotics is reproducible and robust.

Our paper has implication for obesity in people too. We are frequently exposed to low doses of antibiotics that could cause us to gain more weight. The impact of antibiotics is robust, and reversing the propensity to gain weight may not be solved simply by borrowing excrement from someone else to do a fecal microbiota transplant, appealing as that may sound.

Read the paper: The impact of early-life sub-therapeutic antibiotic treatment (STAT) on excessive weight is robust despite transfer of intestinal microbes.
Anjelique F. Schulfer, Jonas Schluter, Yilong Zhang, Quincy Brown, Wimal Pathmasiri, Susan McRitchie, Susan Sumner, Huilin Li, Joao B. Xavier & Martin J. Blaser. ISMEJ
[Open access]

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Results from auto-FMT pilot

Our team at Memorial Sloan Kettering has been investigating the intestinal microbiota of patients receiving bone marrow transplantations for more than eight years now. We have found through several studies that these patients lose important healthy bacteria from their microbiota and that these losses are mostly caused by the antibiotics given as prophylaxis or to treat infections. We also found that the drastic changes in the microbiota composition, especially the intestinal dominations by bacteria such as Enterococcus, increase the risk of transplant-related complications and lowered patient survival. Here we tested whether autologous microbiota transplant (auto-FMT) could reconstitute lost bacteria. In this randomized study led by Ying Taur and Eric Pamer we could see that auto-FMT indeed reconstituted important microbial groups to patients.

The success of auto-FMT varied from patient to patient, though. In the best case a patient recovered practically 100% but in the worst case, recovery was 50%. The effect of auto-FMT was statistically significantly overall, but understanding why its success can vary between patients (which could be due to factors like the actual composition of the transplant, the state of the microbiota before the transplant or even personal factors like host genetics or the underlying disease) is an important direction for future research, and for future microbiota therapies.

As the pilot study continues we should be able to determine whether auto-FMT also improves clinical outcomes for this patients. This is a question left unanswered in our report but which will be addressed in the near future.


Timeline for a study patient undergoing allo-HSCT and randomized to receive auto-FMT.  Allo-HSCT was initiated with pretransplant conditioning [chemotherapy and total body irradiation (TBI)], followed by allogeneic hematopoietic stem cell infusion (day 0). Various antibiotics were given throughout this period for prophylactic and treatment purposes. After stem cell engraftment, randomization assigned this patient to the treatment arm and the patient received an auto-FMT on day 49 using the patient’s initial pretreatment feces, which had been collected and stored before allo-HSCT (initial feces collected at day −21). The intestinal microbiota was restored to that before the transplant.

Read the paper: Reconstitution of the gut microbiota of antibiotic-treated patients by autologous fecal microbiota transplant. Taur et alScience Translational Medicine [PDF]

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Machine learning in simple biochemical networks

Our bow-tie paper is finally out. Here’s the teaser:


Bow-tie: never out of style

How does evolution shape living organisms that seem so well adapted that they could be intelligently designed? Here, we address this question by analyzing a simple biochemical network that directs social behavior in bacteria; we find that it works analogously to a machine learning algorithm that learns from data. Inspired by new experiments, we derive a model which shows that natural selection—by favoring biochemical networks that maximize fitness across a series of fluctuating environments—can be mathematically equivalent to training a machine learning model to solve a classification problem. Beyond bacteria, the formal link between evolution and learning opens new avenues for biology: machine learning is a fast-moving field and its many theoretical breakthroughs can answer long-standing questions in evolution.

Read the full paper:
Bow-tie signaling in c-di-GMP: machine learning in a simple biochemical network
Jinyuan Yan, Maxime Deforet, Kerry E. Boyle, Rayees Rahman, Raymond Liang, Chinweike Okegbe, Lars E. P. Dietrich, Weigang Qiu and Joao B. Xavier. PLOS Computational Biology
[Open access]

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Metabolism and the evolution of social behavior

Kerry Boyle’s PhD paper is out today. It’s still in the early-view, unformatted version but it is now officially published!

In this paper we addressed a fundamental question: Why do organisms of many species seem to change their behavior toward others depending on their internal metabolic state? To investigate this problem at an ultimate level we carried experiments with swarming Pseudomonas aeruginosa, a bacterial model of social behavior. Experiments with bacteria allowed us to alter the metabolic state genetically and to determine—with a level of detail that would be difficult in more complex model organisms—how those changes influenced the evolution of social social behavior.

Our paper uses a combination of experimental evolution, molecular microbiology, whole-genome sequencing and is—to the best of our knowledge—the first to use metabolomics to investigate the role of metabolism in the evolution of a social behavior. This was only possible thanks to our collaborators at Kyu Rhee‘s lab, experts in microbial metabolomics.


The implications go beyond P. aeruginosa: Natural selection favors organisms that can regulate their social behaviors and reduce their fitness cost-to-benefit ratio. Metabolism—currency of all physiological processes—is a very obvious away that social genes have to modulate the cost of a behavior; metabolism should influence social behavior in all organisms, including ourselves. For a review on genes and social behavior see Robinson et al, 2008, Science.

Metabolism and the evolution of social behavior
Kerry E. Boyle, Hilary T. Monaco, Maxime Deforet, Jinyuan Yan, Zhe Wang, Kyu Rhee and Joao Xavier. Molecular Biology and Evolution
[Open Access]

Watch a video abstract made by Natalie Anselmi:

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NYC BIG 2017

A conference that used to be a meeting for Bacillus researchers in the Northeastern United States and has broadened to other bacteria as well. This year the NYC/BIG is on June 8th. Hilary Monaco and Jinyuan Yan will talk about their work on Pseudomonas aeruginosa. See:


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