Evidence for an upper limit to mitotic spindle length
Entry by Andrew Capulli, AP225 Fall 2011
Martin Wuehr, Yao Chen, Sophie Dumont, Aaron Groen, Daniel Needleman, Adrian Salic, Timothy J. Mitchison, Evidence for an Upper Limit to Mitotic Spindle Length. Current Biology, 2008, 18, 1256-1261
All living organisms have, at the very least, one thing in common: DNA. Although relative amounts of DNA and chromosomes vary among species (bacteria have a pair of chromosomes while humans have 23 pairs and monkeys have 24 pairs for example), DNA contains the coding for future life in any living organism (Note: DNA's role in transcription, translation, protein formation: see wikipedia entry on the "Central Dogma of Molecular Biology": http://en.wikipedia.org/wiki/Central_dogma_of_molecular_biology). It begs the question then, how, if all species are based upon their DNA (and species have DNA), do species scale? Perhaps more clearly: why are certain species large and others small? Does cell size have anything to do with scaling? As discussed in lecture, it is often the goal of physicists to find the length scale; in the world of log-log plots, the slope of those plots is scaling and the rationalization of that slope is the true science. What Needleman et. al. begin to do is address this scaling question in terms of the human body, mitosis spindle fibers, and DNA. The question of scaling the human body as a whole may seem extreme right now given our limited knowledge, but the authors of this experimental paper have begun to break the ice at the level of the fundamental unit of life: the cell.Needleman et. al. do most of their work in this study investigating the length of mitotic spindle fibers as they scale with cell size (a step toward the questions raised above). Using Xenopus Laevis cells (a type of frog with large cells easier to study than say, smaller human cells), the authors essentially measure spindle length as it varies with maximum cell length during different stages of mitosis. Further (and what I beleive to be more interesting and maybe more suggestive) studies varying DNA amounts in the cells and observing how spindle fiber length scales are done and will be discussed more below.
Summary of Main Experimentation
The purpose of this study was to identify how spindle fibers in mitosis scale with cell size in the Xenopus Laevis species. The Xenopus Laevis cells vary in cell size during mitosis ranging about 10um to about 1300um (cell size as defined in this study is the maximum distance across an elliptical cell- pole to pole of a mitotic cell). Using Xenopus Laevis cells was therefore advantageous, giving the research team a large variety of cell sizes to examine. Using standard methanol fixation and immunofluorescence, microscopy images like those below (Figure 1) were taken and spindle length calculated as a function of cell size. As can be seen, at different stages in the cell mitosis, spindle fiber length and cell size vary (graphical analysis shown and discussed below). (C) in Figure 1 shows Mitosis 2 where the image on top shows the cell size and the image below shows the spindle size. Notice that these two measures are drastically different in Xenopus Laevis cells; there appears to be some sort of limit to the spindle length (despite the far greater cell length/size). Its more usual for biologists and physiologists (especially of the human body) to visualize mitosis like the cartoon graphic in the thumb image above. The large cell size of Xenopus Laevis in Mitosis 2 gives some incite into a possible limit on spindle fiber length.
More revealing are the data graphically depicted (see second part of Figure 1 below). As the graph shows, each color represents a different stage of cell division and, for the purpose of discussion, each color represents an approximate cell length or size associated with that stage of mitosis. For the purpose of discussion, I will use cell size instead of stage of mitosis for making observations but, as can be seen by the data, the cell size and stage of mitosis can be roughly correlated. As the cell grows (when still relatively small with respect to the whole range of sizes), the spindle lengths grow somewhat linearly; my quick calculations from the graph say that the spindle is about 60% as long as the cell in this range of the data. However, as cells continue to grow, the spindle length appears to hit an asymptotic value of about 60um as seen in the graph and claimed by the authors. This is the interesting data: while the cells continue to grow, the spindles do not. Questions begin to arise, some even by the authors such as if the spindles do not scale with the cell size, how do they 'know' where to align (in the center of the cell for telophase and later complete cell division)? Cytokinesis (cell splitting at the end of mitosis) could not occur properly if the spindles did not align in the middle of the cell. What is the connection between cell size and spindle size then (ie, which governs which?). The authors suggest some incite into these question toward the end of the article; its possible that some intrinsic property of the microtubule based spindles is limited in length, meaning at a certain length (60um!?) the microtubule structure cannot physically be supported. Perhaps, as the authors continue, DNA may only code for microtubules of certain length which is plausible considering the finite amount of DNA and resources available to cell. In mathematics it is easy to argue many things could go to infinity but in reality the cell is limited in space and resources. Regardless of the mechanism by which spindle formation is limited, a rather bothersome asymptote is reached in this study, disrupting any claims of scaling to cell size over the whole range cell sizes in this species.
Further experimentation into the effects of DNA (amounts of DNA) on spindle length was conducted. Essentially, both diploid (full set of paired chromosomes) and haploid (set of chromosomes [unpaired]) cells of the same size were imaged and spindle lengths taken. As seen below in Figure 3 (D), there was a statistically significant decrease of 10% with a reduction of 50% DNA (ie, haploid cell spindle fibers were 10% shorter than diploid spindle fibers). While this simple graph is buried in part (D) of Figure 3 and only briefly discussed in the paper, I beleive the implications of this may be bigger than what, on the surface, doesn't seem to matter too much. This data suggests that spindle fiber length depends on amount of DNA... but that is just the tip of the iceberg. Here, two amounts of DNA are studied; between two data points there is always a line. But what if different amounts of DNA were also studied (such as cells with double the DNA... or triple even). Yes, this is far-fetched... but only in terms of the species itself. Like I suggest in the first few sentences written above, the amount of DNA species have varies tremendously. So, perhaps DNA exponentially shortens spindle fiber length as the amount of DNA in the cell increases: this is the next experiment that is begging to be done.
For completeness of my summary, the authors also extracted Xenopus Laevis spindle fiber and allowed for assembly in a test tube. By using a number of test tube sizes, the authors suggest that the spindles formed in vitro did not depend on container size which suggests that spindle fiber length is not necessarily dependent on cell size either. I'll return to this below (and why I'm not sure I can agree with these claims).
Connection to Soft Matter
This section of the course was dedicated to the scaling of polymer size with the size and number of the free moving unit of the polymer (not necessarily the monomer itself, but the smallest repeating unit of the polymer able to move freely relative to the previous unit). Here Needleman et. al. have begun to apply these questions of scaling to the human body: spindle fibers. Spindle fibers, or microtubules, are polymers made by the body. Our more basic physics derived in class (and it hurts to call it basic!) does not consider the limiting variables present in practice; in the case of this study, the cell. There are so many potential factors such as chemical and physical environment of the cell that will, in some way, contribute to the scaling of spindle fiber formation. As the authors have begun to discuss, even the relative amount of DNA on the spindles seems to effect spindle length. In class, we didn't experience an asymptote... but in vivo and in the case of spindle fibers, we do.
Numerous bioengineering laboratories here at Harvard invest much of their time and direct much of their funds investigating the mechanotransduction of cells. This is to say (and to simplify) how cells sense their mechanical environment and interpret mechanical ques. This is why the minimal attention the authors gave to the diploid/haploid study bothers me. There was a statistically significant decrease in spindle length as a result of less DNA on the spindle. Perhaps DNA doesn't effect spindle length too much, but it may (data between two amounts of DNA doesn't suffice in my opinion to make any claims). The fact that a difference was observed should have triggered further investigation. Perhaps it is the weight of the DNA or added pressure in the cell that can be sensed within the cell and the feedback is to shorten/lengthen the spindle fibers. Its possible that there is a maximum density of spindle fibers and more are needed for increased amounts of DNA and thus an increase in length? In class we saw how scaling of a polymer was affected when first no interactions where considered then when the more complex situation of self avoidance was considered: the scaling is significantly altered. Similarly, the model of the cell adds almost infinite complexity...