Biological systems are staggeringly complex. To untangle this complexity and make predictions about biological systems is a continuous goal of biological research. One approach to achieve these goals is to emphasize the use of quantitative measures of biological processes. Advances in quantitative biology data collection and analysis across scales (molecular, cellular, organismal, ecological) has transformed how we understand, categorize, and predict complex biological systems. Simultaneously, thanks to increased computational power, mathematicians, engineers and physical scientists -- collectively termed theoreticians -- have developed sophisticated models of biological systems at different scales. But there is still a disconnect between the two fields. This surge of quantitative data creates an opportunity to apply, develop, and evaluate mathematical models of biological systems and explore novel methods of analysis. The novel modeling schemes can also offer deeper understanding of principles in biology. In the context of this paper, we use “models” to refer to mathematical representations of biological systems.
This data revolution puts scientists in a unique position to leverage information-rich datasets to improve descriptive modeling. Moreover, advances in technology allow inclusion of heterogeneity and variability within these datasets and mathematical models. This inclusion may lead to identifying previously undetermined variables driving or maintaining heterogeneity and diversity. Improved inclusion of variation may even improve biologically meaningful predictions about how systems will respond to perturbations. Although some of these practices are mainstream in specific sub-fields of biology, such practices are not widespread across all fields of biological sciences. With resources dedicated to better integrating biology and mathematical modeling, we envision a transformational improvement in the ability to describe and predict complex biological systems

Barbar, Elisar

Buan, Nicole R.

Ghosh, Kingshuk

McEntire, Kira

Robinson, Lecia

White, Katharine

English

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University of Nebraska - Lincoln 
DigitalCommons@University of Nebraska - Lincoln 
Biochemistry -- Faculty Publications Biochemistry, Department of 
2019 
Charting a new frontier of science by integrating mathematical 
modeling to understand and predict complex biological systems 
Katharine White 
Kira McEntire 
Nicole R. Buan 
Kingshuk Ghosh 
Lecia Robinson 
See next page for additional authors 
Follow this and additional works at: https://digitalcommons.unl.edu/biochemfacpub 
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Authors 
Katharine White, Kira McEntire, Nicole R. Buan, Kingshuk Ghosh, Lecia Robinson, and Elisar Barbar 
Charting a new frontier of science by integrating mathematical modeling to 
understand and predict complex biological systems 
 
Katharine White (University of Notre Dame, Department of Chemistry and Biochemistry, 
kwhite6@nd.edu), Kira McEntire (Trinity University, Department of Biology, 
kmcentir@trinity.edu), Nicole Buan (University of Nebraska-Lincoln, Department of 
Biochemistry, nbuan@unl.edu), Kingshuk Ghosh (University of Denver, Dept of Physics and 
Astronomy, Molecular and Cellular Biophysics, kingshuk.ghosh@du.edu), Lecia Robinson 
(Tuskegee University, Department of Biology, lrobinson@tuskegee.edu), Elisar Barbar (Oregon 
State University, Department of Biochemistry and Biophysics, barbare@oregonstate.edu). 
 
*Authorship determined by random order. 
 
Critical time for biological modeling  
Biological systems are staggeringly complex. To untangle this complexity and make predictions 
about biological systems is a continuous goal of biological research. One approach to achieve 
these goals is to emphasize the use of quantitative measures of biological processes. Advances 
in quantitative biology data collection and analysis across scales (molecular, cellular, 
organismal, ecological) has transformed how we understand, categorize, and predict complex 
biological systems. Simultaneously, thanks to increased computational power, mathematicians, 
engineers and physical scientists -- collectively termed theoreticians -- have developed 
sophisticated models of biological systems at different scales. But there is still a disconnect 
between the two fields. This surge of quantitative data creates an opportunity to apply, develop, 
and evaluate mathematical models of biological systems and explore novel methods of analysis. 
The novel modeling schemes can also offer deeper understanding of principles in biology. In the 
context of this paper, we use “models” to refer to mathematical representations of biological 
systems. 
  
This data revolution puts scientists in a unique position to leverage information-rich datasets to 
improve descriptive modeling. Moreover, advances in technology allow inclusion of 
heterogeneity and variability within these datasets and mathematical models. This inclusion may 
lead to identifying previously undetermined variables driving or maintaining heterogeneity and 
diversity. Improved inclusion of variation may even improve biologically meaningful predictions 
about how systems will respond to perturbations. Although some of these practices are 
mainstream in specific sub-fields of biology, such practices are not widespread across all fields 
of biological sciences. With resources dedicated to better integrating biology and mathematical 
modeling, we envision a transformational improvement in the ability to describe and predict 
complex biological systems.  
 
We envision a future where an integrated scientific community of biologists and mathematicians 
work toward common goals, including but not limited to:  
 
i) Fully harnessing information-rich biological datasets to improve models. Technological 
advances have resulted in an unprecedented access to volumes of biological data. 
Utilizing models that can handle and incorporate multivariable and complex datasets is 
critical for improving descriptive and predictive models.  
ii) Using model-directed collection of biological data. Not all biological data is collected in 
such a way that enables use in model development or validation. Collecting data with a 
mind on where and how it will be used in modeling is necessary to better integrate 
biology and mathematical modeling.  
iii) Determining how to better transfer and validate models developed at one biological 
system (or scale) to other systems or scales. Mathematical models that can translate 
and scale to other biological systems would be transformative in creating common 
language and nodes of understanding between fields. Identifying models and biological 
systems to develop in depth as “anchor” models/systems is a critical and complex goal.  
iv) Developing and applying better predictive models to streamline experimental 
hypothesis testing. Descriptive models are useful in explaining biological phenomena, 
revealing control points, and identifying regulators. Turning our focus towards building 
robust predictive models would enable us to design better biological validation 
experiments and improve scientific outcomes with limited time, money, and people. 
v) Applying predictive models to generate testable “dataset” space in fields where 
dataset collection is prohibitive (i.e. costly, low sample size, ethical constraints, latent 
processes, etc.). Developing predictive models in representative biological systems 
would enable us to create virtual datasets. This would reduce the need to collect large 
datasets for all similar systems and would enhance our ability to predict outcomes of 
successively more complex biological systems in a rapidly changing world.  
 
Achieving just a subset of these goals would be transformative for our ability to understand and 
predict complex biological systems. In order to reach these goals, we need to expand the use of 
existing mathematical models in biology, develop new models, overcome technological 
challenges, and nurture a cultural shift towards interdisciplinary and cross-field interactions. We 
will explore each of these approaches below. 
 
Expanding the use of existing models in biology 
A range of models can be applied to biological problems. While many of these models are well 
known in sub-fields, they are often unknown beyond their immediate sphere of application. For 
example, a biologist’s familiarity with the following models: agent based models (ABM), 
statistical physics models (including all-atom simulations), bioinformatics-based prediction 
algorithms, geometric and graph based algorithms for network analysis, image processing 
algorithms, software testing algorithms, and global climate models, is likely to be entirely 
dependent on their subfield or particular expertise. As a result, the vast majority of existing 
modeling tools remain underutilized in biology. For example, simple statistical physics and agent 
based models (ABMs) have been proven to be highly valuable to derive insights in widely 
varying fields: from aquatic plant ecosystems, to forest fires, to bacterial biofilms, to disease 
propagation. Thus, applying this modeling method to biology at different levels of organization 
has profoundly improved our understanding of disparate biological processes at varying scales. 
Better communication across different sub-disciplines will increase awareness and promote 
wide-spread usage of existing technology. Furthermore, broader dissemination and cross-talk 
between diverse communities may even generate new modeling platforms by creatively 
combining existing complementary methods.  
 
Developing new models to better describe and predict complex biology 
At present, most modeling schemes fall within two extremes: reductionist and systems-level. 
Reductionist models are built by incorporating the minimum number of variables to accurately 
describe or predict biology. While these models produce results that sometimes don’t scale to 
more complex systems, the results (and key variables) are usually readily identifiable. Systems-
level models are often combined with machine learning, and can give accurate classifications 
when trained on correct data, but rarely produce human-interpretable models and make 
hypothesis generation and testing more difficult. Models represent our understanding of the 
world we observe, and hence should be representative of the system in the simplest way 
possible to gain deeper understanding: “everything should be made as simple as possible but 
not simpler.”  
 
Existing mathematical models struggle with the challenge of balancing necessary simplification 
with accurately capturing biological complexity. Issues of applicability also invariably arise when 
considering how to adapt models to new systems. A fundamental conundrum facing biologists is 
whether to choose a model from the existing range of models or to develop a new model that 
better fits or explains the data. This dilemma can obscure the interpretation of biological results 
and appropriate resolution requires input and feedback from theoreticians, which can be difficult 
to obtain.  
 
Current models often do not fully harness available data, and have a particularly difficult time 
dealing with biological variances, or distributions, resulting from biological phenomena. From 
ecology to single-cell measurements to single-molecule imaging, we observe fluctuations in 
data that are intrinsic to the system, can hold key information, and may be biologically 
meaningful. Models that allow us to better decouple different sources of noise, experimental 
error, and intrinsic variability would be transformative for uncovering biological roles for 
stochasticity and heterogeneity.  
 
To address these challenges, we need to transform existing bio-math to better incorporate 
probabilistic tools for model building and borrow tools from data science. The probabilistic 
framework allows us to explore the importance of intrinsic noise while still allowing us to 
decouple “signal” from “noise”. When low-dimension models -- derived from physical laws and 
insights generated from reductionist approach -- are developed and benchmarked with data we 
can move from descriptive modeling to predictive modeling. Development and dissemination of 
emerging models that combine physical reasoning and machine learning would be paradigm 
shifting.  
 
Overcoming technical and cultural barriers  
To better integrate mathematical modeling in complex biological systems, we must overcome 
technical barriers. These technical barriers range from data collection to model validation. For 
data collection, we need to make sure to collect data that can be used in model development or 
validation. This may require collecting data in multiple ways for the same question. At the same 
time, we need to ensure the data generated is high quality and determine better ways to 
evaluate measurement error and meaningful biological variation. Technological advances such 
as probabilistic models make it possible to grapple with variation in data sets and the 
appropriate analysis of this variation is critical for understanding biology.  
 
Models often tend to become black-boxes and lose the power to generate insights/principles 
because of unresolved complexity. A challenge many biologists have faced how to select the 
best model when competing models fit the same data. Guided generation of new data combined 
with data science tools can transform model validation. In parallel, we should also advance 
theoretical models that try to unravel the black box of deep learning. A handful of such efforts 
are underway that need further studies and support. A deeper understanding of principles 
behind deep learning may enable us to provide models with more insights not only in biology but 
well outside biology. The final technical barrier are challenges to large dataset storage and 
curation. To help with data accumulation and dissemination, we propose the development of 
databases for storage of experimental results with standardized metadata to make it easily 
accessible for theoreticians. 
 Some of these technical barriers are being addressed in specific sub-fields. However, theorists 
and experimental biologists do not often cross paths, do not speak the same language, and do 
not always understand each-others’ tools. To break these cultural barriers, we suggest creating 
user-friendly and publicly-available modeling systems that are accessible to biologists not well 
versed in theory. One fine example of this is PhysiCell, which is computationally powerful yet 
user-friendly for novices (with easy-to-follow tutorials). In another approach, the Department of 
Energy KBase is an evolving bioinformatics and modeling platform where users can upload or 
use open-source tools with the help of exemplary narratives. Funds could support training 
workshops and hack-a-thons to use, disseminate, and develop novel user-friendly applications. 
In addition, we propose incorporation of funding mechanisms that support and accelerate 
interdisciplinary research at the interface of biology and physical sciences. These would include 
dedicated funding opportunities for pilot projects between multiple researchers as well as funds 
to organize regional conferences that bring together scientists from diverse biological 
backgrounds with mathematicians, physicists, and computational chemists. These meetings 
would facilitate crosstalk between experimental researchers and the theoreticians who create 
computational resources.  
 
The current culture of science encourages researchers who work in discipline-specific silos, 
often to the detriment of research advances. Mathematical model frameworks can serve as a 
unifying device connecting the fields of biology and mathematics. The most effective route to 
overcome cultural barriers includes training a new generation of scientists to work at the 
interdisciplinary interface between mathematics and biology. We propose a threefold systematic 
approach that incorporates training, curriculum, and outreach. 
 
Training the next generation of scientists to work at the interface between math and biology 
requires dedicated funding opportunities for pre-doctoral and post-doctoral fellowships to 
support trainees wanting to work at this interface. Curriculum expansion within math and biology 
degree programs at the undergraduate and graduate levels will serve to integrate these fields 
early on in a student’s post-secondary training. Creating a database of training modules that 
include datasets, code, and model tutorials would help faculty and teachers create integrated 
lessons for undergraduate and graduate education. Finally, outreach at middle and high schools 
is critical for building up a strong undergraduate cohort interested in the interface of 
mathematics and biology. The training modules described above could be easily simplified and 
adapted for use in middle and high schools to show students how math has improved our 
understanding of biological questions relevant to society (i.e. climate change, human health, 
etc.). 
 
Transdisciplinary research can be uncomfortable, difficult, and humbling. Critical to overcoming 
cultural issues is emphasizing the creation of a warm and welcoming environment of like-
minded researchers who are motivated to learn collectively from diverse perspectives. Special 
attention needs to be placed on setting a stage that lowers barriers to building a community of 
“learning teachers” rather than experts. At the same time, creating such an atmosphere would 
undoubtedly further encourage people from all backgrounds to continue at the interface 
between biology and math and enhance the creative potential of the field.  
  
Scientific Outcomes 
All biological sub-disciplines could benefit tremendously from better integrating theoretical 
modeling approaches as proposed here. The theoretical modeling approaches developed in 
physics and chemistry disciplines are powerful in their reductionist simplicity to elucidate 
principles and can be highly predictive under defined or constrained conditions. Conversely, the 
complexity of biological systems necessitates new ideas on how to express higher-order model 
behavior and how to scale reductionist models to higher levels of complexity. Unifying biology 
with physics, chemistry and mathematics/statistics through the use of common model 
methodologies has the potential to revolutionize our fundamental understanding of the rules 
of life. 
 
 
Furthermore, accurate and predictive models have the power to transform society by serving as 
a foundation for technological innovation. If biological models could approach the predictive 
accuracy of physical models, we would be able to predict and design biology with the ease that 
we can design a computer. Predictive biological models may eventually forecast the 
evolutionary trajectory of organisms similar to how we can predict the weather, design 
organisms to counteract the effects of climate or habitat change, reduce the time to harvest food 
crops to feed a growing world population, cure disease and prevent the spread of emerging 
threats, and design biological technologies to generate clean renewable energy. These 
outcomes cannot be achieved unless we foster transdisciplinary collaboration and train the next 
generation of scientists to explore a New Science frontier. 
 
 


Charting a new frontier of science by integrating mathematical modeling to understand and predict complex biological systems

https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1450&amp;context=biochemfacpub

Charting a new frontier of science by integrating mathematical modeling to understand and predict complex biological systems

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