Machine Learning and Data Science Approaches in Mathematical Biology: Recent Advances and Emerging Topics

Tuesday, June 15 at 05:45pm (PDT)
Wednesday, June 16 at 01:45am (BST)
Wednesday, June 16 09:45am (KST)

SMB2021 SMB2021 Follow Tuesday (Wednesday) during the "MS09" time block.
Note: this minisymposia has multiple sessions. The second session is MS08-DDMB (click here).

Share this


Paul Atzberger (University of California Santa Barbara, USA), Smita Krishnaswamy (Yale University, USA), Kevin Lin (University of Arizona, USA)


Biological investigations have resulted historically in the development of many new methods for data analysis. This session aims to discuss recent advances both concerning new biological application areas and algorithms drawing on increasingly large datasets and availability of computational resources. Topic areas include but are not limited to, data-driven modeling, applications of deep learning to problems in biology (sequence analysis, protein folding, experimental design, control), physics-informed machine learning, kernel methods for biological systems, linear and non-linear system identification, hybrid data-driven simulation methods, and other areas. The session also aims to facilitate discussions on emerging methods and areas for the biological sciences where data analysis is playing increasingly central roles.

Zhuo-Cheng Xiao

(Courant Institute, NYU)
"A data-informed mean-field approach to mapping cortical landscapes"
Cortical circuits are characterized by a high degree of structural and dynamical complexity, and this biological reality is reflected in the large number of parameters in even highly idealized cortical models. A fundamental task of computational neuroscience is to understand how these parameters govern neuronal network dynamics. While some neuronal parameters can be measured in vivo, many remain poorly constrained due to limitations of available experimental techniques. Computational models can address this problem by relating difficult-to-measure parameters to observable quantities, but to do so one must overcome two challenges: (1) the computational expense of mapping a high dimensional parameter space, and (2) extracting biological insights from such a map. In this study, we address these challenges in the following ways: First, we propose a data-informed, parsimonious mean-field algorithm that efficiently predicts spontaneous cortical activity, thereby speeding up the mapping of parameter landscapes. Second, we show that lateral inhibition provides a basis for conceptualizing cortical parameter space, enabling us to begin to make sense of its geometric structure. We illustrate our approach on a biologically realistic model of the Macaque primary visual cortex.

Andrea Arnold

(Worcester Polytechnic Institute, USA)
"Data Assimilation for Time-Varying Parameter Estimation in Biological Systems"
Estimating and quantifying uncertainty in system parameters remains a big challenge in many biological applications. In particular, such problems may involve parameters that are known to vary with time but have unknown dynamics and/or cannot be measured. This talk will address the use of data assimilation in novel approaches to time-varying parameter estimation, with emphasis on how uncertainty in the parameter estimates affects the corresponding model predictions. Results will be demonstrated on several biological examples, including systems from computational neuroscience.

John Fricks

(Arizona State University, USA)
"A Bayesian Analysis of 2-D Motor-Cargo Complex Dynamics"
Molecular motors, such as kinesin and dynein, move along microtubules in cells while the tails of the motors are connected to cargos. The cargos can be tracked in fluorescence or dark field experiments yielding a stack of images. Processing allows for the localization of the cargos yielding a two-dimensional time series; typically, further processing projects the data on to one-dimension along the direction of the microtubule. However, curvature or misidentification of the microtubule may be relevant, but is generally not considered. In this talk, we will propose an analysis of the original two-dimensional time series, which can also extract additional information on the dynamics of these motor-cargo complexes.

Mengyang Gu

(University of California, Santa Barbara, USA)
"Uncertainty quantification and estimation in differential dynamic microscopy for biomaterials characterization"
Differential dynamic microscopy (DDM) is a form of video image analysis that combines the sensitivity of scattering and the direct visualization benefits of microscopy. DDM is broadly useful in determining dynamical properties including the intermediate scattering function for many spatiotemporally correlated systems. Despite its straightforward analysis, DDM has not been fully adopted as a routine characterization tool, largely due to computational cost and lack of algorithmic robustness. We present a comprehensive statistical framework that aims at quantifying error, reducing the computational order and enhancing the robustness of DDM analysis. We quantify the error, and propagate an independent noise term to derive a closed-form expression of the expected value and variance of the observed image structure function. Significantly, we propose an unbiased estimator of the mean of the noise in the observed image structure function, which can be determined experimentally and significantly improves the accuracy of applications of DDM. Furthermore, through use of Gaussian Process Regression (GPR), we find that predictive samples of the image structure function require only around 1% of the Fourier Transforms of the observed quantities. This vastly reduces computational cost, while preserving information of the quantities of interest, such as quantiles of the image scattering function, for subsequent analysis. The approach, which we call DDM with Uncertainty Quantification (DDM-UQ), is validated using both simulations and experiments with respect to accuracy and computational efficiency, as compared with conventional DDM and multiple particle tracking. Overall, we propose that DDM-UQ lays the foundation for important new applications of DDM, as well as to high-throughput characterization.

Hosted by SMB2021 Follow
Virtual conference of the Society for Mathematical Biology, 2021.