Michael P. Brenner

Glover Professor of Applied Mathematics and Applied Physics

Harvard College Professor


School of Engineering and Applied Sciences

Kavli Insitute for Bionano Science and Technology

Harvard University

 
 

Our research is divided roughly equally into topics in the physical and biological sciences. Examples of current research projects are listed below.


Physical Sciences                                                                        Biological Sciences



Evolution and Physiology

I am interested in understanding in as much detail as possible how evolution operates, in the context of the setting up and tuning of specific physiological systems.  There has been much talk in recent years of a posteriori design principles but the real question is what evolution actually does, in specific systems. This is hard to figure out, but the best chance is to look at families of proteins where the physiology is well understood.


To this end, we have been working on two sets of proteins: voltage gated ion channels, and hemoglobin. Both of these have specific well studied physiological roles and the biology of the proteins is well studied (though not in all cases well understood).


Voltage gated sodium channels We are interested in studying the evolution of mammalian voltage gated sodium channels. The first question is to understand why there are 10 different sodium channels in mammals, most of which are more than 90% identical by sequence. However these small sequence differences are evolutionarily stable (in rat-mouse-human). We have undertaken a data collection effort to understand the variation in physiological response of these channels. The goal is to first understand what the constraints are for functional channels, and second to discover which properties of the different channels are tuned differently. The significant physiological database that we have constructed can be combined with sequence information to inform models of channel gating. Our work thus far has suggested that current models need to be modified, and we are in the process of trying to invent mathematical methods for predicting the most likely model consistent with the data.  What is nice about this class of problems is that like other problems in systems biology the goal is to infer a network from a data set:  but here the data set is much more detailed and precise, and there is fifty years of history of ion channel physiology to inform possible choices.  


Ultimately we aspire to use this type of information to start to understand how the differences in channels evolved--for example, invertebrates have only five voltage gated sodium channels. Calcium channels and Potassium channels are in the same superfamily of ion channels. The methods of analysis that we are developing should be applicable to this larger class of problems, at least if we can find ways of acquiring the needed measurements of channel function.


The evolution of hemoglobin. This work is in collaboration with Ron Milo, Marc Kirschner, Jennifer Hou and Walter Fontana.  Here we use hemoglobin to try to understand the effect of physiological adaptations on evolutionary adaptations. Hemoglobin is responsible for the high oxygen saturation of blood. We know from common experience that climbing a mountain leaves one initially short of breath, though eventually hemoglobin adjusts (by shifting its oxygen saturation curve) to allow our breathing to return to normal level. The question is: what is the relationship between such physiological adaptation and evolution? There is an old idea due to Baldwin that evolution fixes physiological adaptations.  Such an idea has been qualitatively argued for nearly a century but has not been tested quantitatively: the hemoglobin molecule is an ideal system for this, given both that extensive data exists,  and moreover the relationship between phenotype, molecular properties and fitness is relatively well understood. We studied experimental measurements in the literature of several dozen mammals and under various physiological conditions. We find a natural basis of parameters that characterize the changes observed in physiological and evolutionary adaptations. We observe an orthogonality relationship where the main parameter changing in physiology is relatively constant in evolution whereas the parameter changing in evolution is relatively constant in physiology. Thus adaptations at these different regimes are manifested by regulating different “knobs”. One possible explanation to this observation is that it is an indication of selection for adaptability.



Mechanics and Biology


Biofilms

Another completely different class of problems that we are working on involves the growth of biofilms, and mechanical mechanisms that biofilms use to regulate colony morphology. This is a collaboration with Roberto Kolter (HMS) and Marcus Roper. The principal idea here is that there is a substantial extant literature on genes that trigger morphological changes in colonies, which affect the fitness of the colony as a whole. On the other hand, from a physical perspective biofilms are physical gels, and changes in gel morphology must involve the exertion of physical forces. There are only so many ways that a gel can exert forces on itself to change its morphology. We are combining mechanical models with experiments in a few well chosen configurations. In the systems of current interest the morphology changes are correlated with the production of a surfactant from the bacteria in the biofilm (which is usually a gene under a quorum sensing control mechanism). Our current goal is to quantitatively compare models with experiments to reproduce the expeirmentally observed behaviors. Once this is done we plan on trying to use our understanding of the basic physics of morphology change to ask more interesting biological questions about biofilms and their evolution.


Elastic Instabilities in Yeast Colonies

The differential adhesion between cells is believed to be the major driving force behind the formation of tissues.  An aggregate of cells minimizes the overall adhesive energy between cell surfaces. We studied (both through calculations and experiments) a simple model system -- a growing yeast colony-- to determine the conditions under which a slowly growing tissue indeed minimizes surface energy.   The experiments considered three strains of yeast with different levels of stickiness.  Initially the colonies grew as spherical caps with fixed contact angle, just as expected for a substance minimizing surface energy. However, at a critical volume the morphology of the yeast colony underwent an instability. We demonstrated both through experiments and through  a mathematical model that the instability arose from the competition between elastic and surface energies. The predicted criterion from the model qualitatively agrees with the experiments.




The shapes of fungal spores

With Marcus Roper and Anne Pringle (OEB), we have been working on the shapes of ejected fungal spores. This is an example of a problem where there is a clear evolutionary pressure on the shape of the spore (on one hand), but on the other it should eventually be possible to study the development of the spore shape to understand something about how this shape is determined. For now we have been studying the spore shapes in ejected fungal spores and understanding whether the shapes are consistent with the hypothesis that they minimize drag. Fungi grown in dung must escape the dung for reproductive success since animals eat outside of a zone of repugnance around the dung. Reproductive success depends upon the ascospores germinating far from the parent fungus, and consequently ascomycota have evolved mechanisms for achieving very large launch velocities, applying initial accelerations that are unmatched in the plant or animal kingdoms. The drag experienced by the spore, rather than its weight, is known to be the primary determinant of its range. By comparing the shapes from wide numbers of fungi whose spores are ejected with minimal drag shapes we establish that drag minimization operates on the shape of the spores. In future work we will study how this works in more detail, both through selection experiments and hopefully studies of the development of the spore shape.


Other


Selectivity of the Nuclear Pore complex. The nuclear pore is a remarkable machine, providing both quantitative discrimination between different proteins and doing so without much sacrifice in the rate that things move across the pore. With Katharina Ribbeck and Lucy Colwell, we have developed a proposal for what controls the selectivity gating of the nuclear pore complex, the channels that regulate protein transfer between the nucleus and the cytoplasm . We used a physically based bioinformatic approach to compare the properties of proteins that translocate the pore successfully with those that do not. The selectivity filter appears to have an electrostatic component: particles that traverse the pore have the opposite charge to the interior of the pore itself. The model has many consequences, ranging from predictions for which proteins can traverse the pore to a proposed  role for post translational modifications of proteins in enabling nuclear transport.



Model Reduction

It has become fashionable to write down large numbers of differential equations , with large numbers of measurable (but unmeasured) parameters, and to fit these models to data. With Natalie Arkus, we have been carrying out studies to develop mathematical methods to reduce large complicated sets of ordinary differential equation that arise in biological models (e.g. recently published models of heat shock system, of cell cycles, or  the RAN GTP system) to simpler systems that quantitatively capture the same dynamics. The advantage of this is that one can then see explicitly what the role of various factors is in changing the system dynamics. The simplest example of the type of analysis we are learning to carry out is the Michaelis-Menton kinetics: in this classical example the separation of timescales between the enzyme -substrate interaction and the production of product leads to a simple and accurate description of the dependence of the rate of product formation on the enzyme-substrate interaction. This same type of analysis can be carried out on more complicated networks (where the responses involve many variables and the nonlinearities are more complicated than the Michaelis-menton type). The question is whether one can use this to expose the essential mechanisms underlying models currently under discussion.