This talk will cover the convergence of two high profile themes in the scientific/medical literature (and even the lay press): personalized medicine and lack of reproducibility of scientific results. There have been many high profile examples of scientific findings related to genetic (or more generally) biomarker predictors of disease or drug effect that have not been confirmed with subsequent experimentation or investigation. Some recent literature suggests that inappropriate use of statistical analysis or inadequate use of statistical design principles play a major role in false positive findings. This talk will address the use of Bayesian statistical principles for how to assess the strength of evidence for a finding and how that can be applied generally to clinical trials and laboratory research.
* Likelihood of truth
** Any biological measurement to describe a patient
*** AKA personalized medicine, precision medicine, targeted medicine
Evolutionary relationships (i.e., homology) detected between proteins helps predict their properties such as spatial structures and functions. Homology is frequently obscured by sequence divergence, spatial structure changes and resemblance between unrelated 3D structures. Computational approaches to the analysis of distant homologs and their discrimination from proteins with fortuitous similarities will be discussed and examples of how this theoretical and bioinformatics work facilitates experimental discoveries will be given.
In this talk, I will report some recent results on the qualitative and numerical analysis of structure-preserving discretizations and robust preconditioners for several mathematical models that couple with the Navier-Stokes equations. I will study the Navier-Stokes equations coupled with elasticity equations, the Maxwell's equations, and the Poisson-Nernst-Planck system. These systems model fluid-structure interaction, magnetohydrodynamics, and electrokinetic phenomena, respectively, and are widely used in physics, biology, and engineering. I will also give some numerical examples to validate our analyses and models.
Experiments indicate that physical stress in the shoot apical meristem of Arabidopsis controls at least two aspects of cell biology – the cortical cytoskeleton, and the subcellular location of the PIN1 auxin transporter. Cortical microtubules align in shoot apical meristem epidermal cells such that they are parallel to the principal direction of maximal stress when the stress is highly anisotropic. PIN1 is asymmetrically distributed in the plasma membranes of the same cells, with the highest amount in the membrane adjacent to the most stressed side wall.
Cellulose synthase complexes ride the cortical microtubules, thereby reinforcing cells in the direction of maximal stress, which is a negative feedback on stress, and tends to cause cells to expand orthogonally to the maximal stress direction. Auxin, however, weakens walls, allowing cells to expand proportionally to their auxin concentration. As expanding cells (whose direction of expansion depends upon wall anisotropy) stress their neighbors, the neighbors transport auxin preferentially to expanding cells, further increasing their auxin concentration. This is a positive feedback – high auxin in a cell attracts more auxin, and creates more stress.
These sets of feedbacks create a supracellular, tissue-wide feedback system that creates plant shape, controls phyllotaxis, and regulates hormone flow. This system has been amenable to computational modeling. The present set of models successfully predicts phyllotactic pattern (as auxin induces new leaves and flowers, and models of auxin transport reproduce the pattern of the new organs), rates of cell expansion, and developing models also treat direction of expansion and planes of cell division (which are dictated by the microtubule array).
Therefore, including cellular responses to physical stress is as important as including cell-cell signaling in models of shoot meristem morphogenesis, and considering the effects of mechanical stress (and therefore of tissue shape and cell wall properties) leads to highly predictive models.
Recent evidence suggests that, like many normal tissues, many cancers are maintained by a small population of cancer stem cells that divide indefinitely to produce more differentiated cancerous cells. Tissues, however, contain many more differentiated cells than stem cells, and mutations may cause such cells to "dedifferentiate" into a stem-like state. We study the effects of dedifferentiation on the time to cancer onset and found that the effect of dedifferentiation depends critically on how stem cell numbers are controlled by the body. If homeostasis is very tight (due to all divisions being asymmetric), then dedifferentiation has little effect, but if homeostatic control is looser (allowing both symmetric and asymmetric divisions), then dedifferentiation can dramatically hasten cancer onset and lead to exponential growth of the cancer stem cell population. We consider both space-free and spatial versions of this process to look at effect that tissue architecture can play in this process. Our results suggest that dedifferentiation may be a very important factor in cancer and that more study of dedifferentiation and stem cell control is necessary to understand and prevent cancer onset.
In a Wall Street Journal article published in 2013, E. O. Wilson attempted to make the case that biologists don't really need to learn any mathematics -- whenever they run into difficulty with numerical issues they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilson's Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson mathematics is mere number crunching, but as Galileo said long ago, The laws of Nature are written in the language of mathematics... the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word. Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science. In this talk we will take this a step further and show how mathematics has been used to make new and experimentally-verified discoveries and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades -- that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. We will highlight a few instances where modeling has been used to push experiments forward and highlight problems in biology that cannot be adequately addressed without mathematical modeling.
We synthesize findings from neuroscience, psychology, and behavioral biology to show that some key features of cognition in the neuron-based brains of vertebrates are also present in the insect-based swarm of honey bees. We present our ideas in the context of the cognitive task of nest-site selection by honey bee swarms. After reviewing the mechanisms of distributed evidence gathering and processing that are the basis of decision-making in bee swarms, we point out numerous similarities in the functional organization of vertebrate brains and honey bee swarms. These include the existence of interconnected subunits, parallel processing of information, a spatially distributed memory, layered processing of information, lateral inhibition, and mechanisms of focusing attention on critical stimuli. We also review the performance of simulated swarms in standard psychological tests of decision making: tests of discrimination ability and assessments of distractor effects.
Motivated by data from multiple randomized trials of colon cancer, we model time-to-cancer-recurrence and time-to-death using a multi-state model. We incorporate a latent cured state into the model to allow for subjects who will never recur. Parametric models that assume Weibull hazards and include baseline covariates are used. Information from the multiple trials are included using a hierarchical model. Bayesian estimation methods are used. The model is used to assess whether there is improved efficiency in the analysis of the effect of treatment on time-to-death in each trial by using the information provided by earlier cancer recurrence. For subjects who are censored for death, multiple imputation is used to impute death times, where the imputation distribution is derived from the estimated model. Gains in efficiency are possible, although sometimes modest, using the extra information provided by the recurrence time.
Zebrafish is a small fish with distinctive black and yellow stripes that form during early development due to cell differentiation and movement. I will discuss an agent-based model for stripe formation in zebrafish that incorporates biological data. This model can reproduce ablation experiment and make predictions for the development of stripes from a larval pre-pattern and the effect of mutations. Among the conclusions are that fish growth shortens the necessary scale for long-range interactions and that iridophores, a third type of pigment cell, help maintain stripe boundary integrity.
Humans are unique both in their cognitive abilities and in the extent of cooperation in large groups of unrelated individuals. How our species evolved high intelligence in spite of various costs of having a large brain is perplexing. Equally puzzling is how our ancestors managed to overcome the collective action problem and evolve strong innate preferences for cooperative behaviour. Here, I theoretically study the evolution of social-cognitive competencies as driven by selection emerging from the need to produce public goods in games against nature or in direct competition with other groups. I use collaborative ability in collective actions as a proxy for social-cognitive competencies. My results suggest that collaborative ability is more likely to evolve first by between-group conflicts and then later be utilized and improved in games against nature. Evolution of collaborative ability creates conditions for the subsequent evolution of collaborative communication and cultural learning.
When the human visual system is subjected to diffuse flickering light in the range of 5-25 Hz, many subjects report beautiful swirling colorful geometric patterns. In the years since Jan Purkinje first described them, there have been many qualitative and quantitative analyses of the conditions in which they occur. Here, we use a simple excitatory-inhibitory neural network to explain the dynamics of these fascinating patterns. We employ a combination of computational and mathematical methods to show why these patterns arise. We demonstrate that the geometric forms of the patterns are intimately tied to the frequency of the flickering stimuli. We also show that the patters that arise are completely expected based on symmetric bifurcation arguments.
The three-dimensional (3D) configuration of chromosomes within the eukaryote nucleus is consequential for several cellular functions, including gene expression regulation, and is also associated with cancer-causing translocation events. While visualization of such architecture remains limited to low resolutions, the ability to infer structures at high resolution has been enabled by recently-devised chromosome conformation capture assays. In particular, when coupled with next generation sequencing, such methods yield a genome-wide inventory of chromatin interactions. Various algorithms have been advanced to operate on such data to produce reconstructed 3D configurations. Several studies have shown that such reconstructions provide added value over raw interaction data with respect to downstream biological analysis.
However, such added value has yet to be fully realized for higher eukaryotes since no high resolution genome-wide reconstructions have been inferred for these organisms because of computational bottlenecks and organismal complexity. After overviewing existing reconstruction approaches we propose a two-stage algorithm, deploying multi-dimensional scaling and Procrustes transformation, that overcomes these barriers. 3D architectures for mouse and human are presented and methods for evaluating these solutions discussed. Finally, reverting to yeast, we demonstrate the advantages bestowed by 3D structures with respect to identifying co-regulatory elements.
We have developed and combined several novel methods to improve protein structure prediction from the amino acid sequence, and modeling of protein dynamics. One of the most promising developments in protein structure prediction are many-body potentials that take into account dense packing, and cooperativity of interactions in protein cores. We developed a method that uses whole protein information filtered through machine learners to score protein models based on their likeness to native structures. These results were published by us , and tested successfully in CASP 9, where our prediction group 4_BODY_POTENTIALS was among top three predictors in the category of template-free modeling for the most difficult targets. Recently we have significantly improved our potentials by considering electrostatic interactions and residue depth and used them for the prediction of protein structure and blind tested them in CASP 10. Our prediction group Kloczkowski_Lab was ranked as the third one in prediction of structure (based on the single model) for all targets, and ranked also as the second one for template free-modeling (see: http://www.predictioncenter.org/casp10/groups_analysis.cgi ) . By combing statistical contact potentials with entropies from the elastic network models of proteins we can compute free energy and improve coarse-grained modeling of protein structure and dynamics . The consideration of protein flexibility and its fluctuational dynamics improves protein structure prediction, leads to a better refinement of computational models of proteins, and significantly improves protein docking [4,5]. We studied also the self-assembly of FVFLM peptide and its influence on the kinetics of Aβ16-20 oligomerization.
1. P. Gniewek, A. Kolinski, R.L. Jernigan, and A. Kloczkowski, Proteins 79, 1923 (2011)
2. E. Faraggi and A. Kloczkowski, Proteins 82, 3170-6, (2014)
3. M.T. Zimmermann, S.P. Leelananda, A. Kloczkowski, and R.L. Jernigan, JPC B116, 6725 (2012)
4. P. Gniewek, A. Kolinski, R.L. Jernigan, and A. Kloczkowski, JCP 136, 195101 (2012)
5. P. Gniewek, A. Kolinski, R.L. Jernigan, and A. Kloczkowski, Proteins 80, 335 (2012)