NSF Fellowship Application Tips

Around this time last year, I applied to the National Science Foundation Graduate Research Fellowship Program (NSF GRFP). It has a pretty low acceptance rate and is highly dependent on factors outside of our control, such as the review panelists we are randomly assigned and their moods on the day they read our statements. I knew it was a crapshoot, and I was mostly applying because, as a second year, it was my last chance to do so. Getting accepted for the fellowship was a very pleasant surprise. It has made me feel a lot more confident in my abilities and career goals and has made me somewhat more motivated to work through these very difficult times.

I was the only person in my department who applied last year, and most of the resources I used for my application came from online, and from the advice and examples of successful statements by my seniors in Queer organizations on campus I have been participating in. I am also very thankful for my advisor, who gave me thorough suggestions on my proposal. I know at least one person in my department is applying this month, and I would like to pay forward the support I’ve received in the ways I can. I have started a part-time position at my university campus Graduate Writing Center, where I will be reading other students’ statements and providing them with feedback and support. I will not be publishing my statements online, but I will provide some general suggestions and strategies that I have learned here. If you would like to see my statements, you can feel free to contact me, either through the contact form or through other means if we already know each other! If this is helpful for you, my application was in Mathematical Sciences – Mathematical Biology.

Tip # 1: Read the program solicitation. Read all of it. Make sure you understand exactly what they are looking for. The two main review criteria for this fellowship application are Intellectual Merit and Broader Impacts. Make sure you devote enough in your statements to the Broader Impacts portion, as this is a common shortcoming of many applications.

Tip # 2: This is not the time for modesty! If you were meeting a new friend for coffee or going on a date, it might be a good idea not to rattle off a laundry list of all your accomplishments. But you are not trying to get the review panel to like you as a person. You are trying to convince them that you are worth throwing government money at. Make sure to list everything you’ve ever done, especially when it comes to publications and presentations. I will say right now that I did not have any publications when applying, but I am currently working on a first author publication (fingers crossed that it’ll be submission-ready this month!). So I listed this tentative paper with the year 2020, and wrote In Preparation. I would highly recommend this, especially if you currently do not have any publications, or if you are in the process of preparing a first-author publication – which often carries more weight. Also, make sure to list every poster and/or oral presentation you’ve ever done, even if it was just a department-wide poster session or presentation and you don’t think it was a big deal. This is not the time to leave anything out.

Tip # 4: Create a narrative about your scientific journey. If you are applying for this fellowship, it is likely that you have a range of professional experiences before this point, whether it is working in a lab, industry, healthcare, or peer-led projects. There is probably something that you’ve gained from each of these experiences that have led you to the project you are proposing today. Make sure that everything you are listing somehow ties into skills or perspectives you’ve gained that have made you more able to conduct the project you are proposing. Make sure you don’t list anything without somehow tying it in to how it has shaped you as the researcher you are today.

Tip # 5: For Broader Impacts, while it might be helpful to mention your own personal adversities and minority status, what will be even more useful is to list the ways that you plan to uplift other marginalized groups on a broad level. If you are not a member of a marginalized group, talk about initiatives you’ve taken to support those in marginalized groups throughout your career, and how to plan to continue doing so as you progress. If you are a member of a marginalized group, a good way to mention it is to bring it up in the context of outreach organizations you’ve participated in, and how you plan to use representation to encourage others in STEM, such as recruiting people to your program and increasing retention by making workspaces safer for marginalized people. If you identify as LGBTQ+, but you have never participated in and do not plan to participate in identity-based orgs, I would suggest not including it. However, if you were inspired by a talk by an LGBTQ+ identifying faculty member and it has shaped your confidence and pursuit of your career in some way, that could be a powerful thing to include.

Tip # 8: If you don’t get the fellowship, DON’T BE DISCOURAGED. It does not mean anything about you as a scientist. There are so many faculty members I admire and respect who have been rejected by this fellowship, but they still went on to be amazing scientists. There are peers of mine who deserve it just as much as I did, if not more. It is a very random process! I also know someone whose labmate applied one year and got rejected, and applied the next year with nearly the same application and got accepted. That just goes to show that getting accepted and rejected has so much to do with factors that are out of your control. It is always a good idea to try, because you never know (for the same reasons), but just know that even if you don’t get it, you are incredibly awesome and you can still do amazing science!

I hope this was helpful, and feel free to contact me for any feedback! Also, know that these tips are just one person’s opinion, and there are many more resources for advice and support! I will include some that I have personally used:

NSF GRFP Website

Tips Websites:

https://www.alexhunterlang.com/nsf-fellowship

https://www.profellow.com/tips/8-tips-for-crafting-a-winning-nsf-grfp-application/

http://www.clairemckaybowen.com/fellowships.html

Network Dynamics, Biophysics, and Mental Illness

[latexpage] This past fall was my first quarter of graduate school, and one of our core courses was Deterministic Models in Biology. For our final project, we chose a quantitative biology paper on a topic of our interest and presented on it to the class. The paper I chose was a review paper, Psychiatric Illnesses as Disorders of Network Dynamics by Daniel Durstewitz, Quentin J.M. Huys, and Georgia Koppe. My undergraduate research focused on the dynamics of neurons at the molecular level, and this paper helped me connect it to specific characteristics of mental illnesses.

This paper proposes that since observable cognitive and emotional states rely on the underlying dynamics of neuronal networks, we should use Dynamical Systems Theory (DST) to characterize, diagnose, and develop therapeutic strategies for mental illness.

The central idea of DST is that there is a set of differential equations that evolve in time. A set of dynamical equations could look as follows:

$\frac{dx_1}{dt} = \dot{x_1} = f_1(x_1, … , x_M, t; \boldsymbol{\theta} )$
$\frac{dx_2}{dt} = \dot{x_2} = f_1(x_1, … , x_M, t; \boldsymbol{\theta})$
$\vdots$
$\frac{dx_M}{dt} = \dot{x_M} = f_M(x_1, … , x_M, t; \boldsymbol{\theta})$

The variables $x_1, x_2, … x_M$ represent the dynamical variables such as voltage or neural firing rate. These equations describe how each of these variables change over time. $\boldsymbol{\theta}$ represents parameters, fixed values that are properties of the system that do not change over time.

We define a fixed point as the point at which the derivatives of all of the variables are equal to 0. Fixed points are stable if activity converges towards them, and unstable if activity diverges from them. Stable fixed points are called attractors. We can define the basin of attraction as the set of points from which activity converges towards the attractor.

The figure below shows an example of a phase plane, a representation of a space spanned by the two variables of a system. Note that it is possible to use dimensionality reduction methods to obtain visual representations for higher dimensional systems. The arrows show the activity of the system. The blue and orange curves represent nullclines, and along each of these curves, the derivative of one of the variables is 0. The green line represents the barrier between the two basins of attractions. It is possible to cross over this barrier as a result of either external influences or random fluctuations.

I will discuss some basic neuroscience before going into the dynamics of mental illnesses. There are many ion currents that pass through a neuron membrane such as sodium, potassium, and calcium. The dynamics of these ions are driven by electrochemical gradients. Spiking activity occurs when there is a rapid influx of sodium ions, producing the spike followed by an efflux of potassium ions, returning the membrane potential to the threshold potential.

We can think of a neuron membrane as a capacitor, where positive and negative charges are accumulated on either side. The current is the rate of charge flowing per time, $I = \frac{dq}{dt}$, and the charge of a capacitor is defined as q = CV. The current through the membrane is this $I_m = C_m \frac{dV_m}{dt}$. We can think of this system as the circuit shown below:

Because of charge conservation, the sum of the currents across the capacitor and each of the resistors must be 0. In mathematical terms, this is $C_m \frac{dV_m}{dt} = -\sum_i I_i$.

If we approximate each of these currents as ohmic, they will satisfy Ohm’s law, V = IR, meaning that the current is proportional to the difference between the membrane voltage and the threshold voltage by a factor of 1/R, or in other words, the conductance.

If the conductance were constant over time, these would be linear. However, the conductance depends on the proportion of ion channels that are open and the proportion of channels that are closed, called the gating variables. For example, a sodium current can be described as

$I_{Na} = g_{max}m^3h(V_m – E_{Na})$

In this system, m and h are the gating variables, and they vary from 0 to 1, and $g_{max}$ is the maximal conductance.

We can think of the dynamical equations for the gating variables as the result of a mass equation. Consider the reaction

$Closed \rightleftharpoons Open$

Suppose $\alpha$ is the rate of opening of a channel, or the forward reaction above, and $\beta$ is the rate of closing, the reverse reaction above, and both of these rates depend on the voltage. If m represents the proportion of channels that are open, the derivative over time is equal to the  forward rate times the concentration of reactants minus the reverse rate times the concentration of products. In other words:

$\frac{dm}{dt} = \alpha(V_m)(1-m) – \beta (V_m)m$

Another form of this dynamical equation commonly seen in the literature is:

$\frac{dm}{dt} = \frac{m_{\infty}(V_m) – m}{\tau_{Na}(V_m)}$

$\tau_{Na}$ is the voltage-dependent time constant, and $m_{\infty}$ is the steady-state proportion of open channels as a function of voltage.

The dynamical equation for voltage for the simple NaKL model is as follows:

$\frac{dV}{dt} = g_{Na}m^3h(E_{Na}-V) + g_K n^4 (E_K -V) + g_L (E_L – V) + I_{inj}C^{-1}$

Neuronal networks are the result of multiple neurons connected to one another through synapses. Pre-synaptic neurons deliverer chemicals, called neurotransmitters, to post-synaptic neurons. Some neurotransmitters are excitatory, such as NMDA (N-Methyl-D-aspartic acid), meaning they increase the likelihood of spiking activity, and others are inhibitory, such as GABA (gamma-aminobutyric acid), meaning that they decrease the likelihood of spiking activity. To describe the networks of neuronal networks, each individual neuron has a voltage equation as illustrated above, with additional terms relating to its synaptic currents. These currents depend on the synaptic conductance, the difference between the membrane voltage and the threshold voltage, the strengths of the synaptic connections, and the fraction of open channels for each receptor. The dynamical equation for the fraction of open channels usually depends on properties of the presynaptic neuron.

So far, the variables we have been considering have been the voltage and the gating variables. In order to discuss the dynamics of mental illness, we must think about another important variable: firing rate. This simply describes the rate of voltage spikes over time. Below is an example of a phase plane, where the vertical axis is the average firing rate of inhibitory neurons, and the horizontal axis is the average firing rate of excitatory neurons.

In this system, the fixed points can be thought of as memories or goal-states, and we can use this system to consider the effects of the underlying dynamics on working memory or decision making. Increasing the depth of the basin of attraction can have the effect of increasing the stability of the state, while flattening the basin of attraction reduces the stability of the state.

This paper highlights the key role of dopamine in altering these attractor dynamics. Stimulating the D1 dopamine receptors has the effect of increasing firing activity of both excitatory (NMDA) and inhibitory (GABA) neurons. This alters the parameters of the system, in particular, the strengths of synaptic connections, over time. As a result, the basins of attraction are deepened, and the state is more stable and robust to external perturbations or noise fluctuations.

Stimulation of the D2 dopamine receptors has the opposite effect, flattening the basins of attractions. These flat attractor landscapes could lead to disorganized or spontaneous thoughts that can be experienced as hallucinations that are characteristic of schizophrenia. This can also explain the high distractibility in attention-deficit hyperactive disorder (ADHD). On the other hand, Obsessive Compulsive Disorder (OCD), a disorder characterized by rumination, invasive and recurrent obsessions and compulsions, can be linked to deep basins of attractions that are robust to potential distractors. Major Depressive Disorder characterized by a coexistence of rumination and a negative mood with lack of concentration and distractibility, and one can think of it as an imbalance between multiple attractor states.

The main point this review paper aims to illustrate is that in order to characterize and develop treatments for mental illnesses, one must consider the underlying network dynamics. The suggested role of dopamine in altering the depth of basins of attractions suggest that we might try to target the dynamics of schizophrenia patients, for example, through dopaminergic drugs.

I found the process of reading this review paper and the sources it cited extremely helpful for me in improving my understanding of neurons, neuronal networks, biophysics, and nonlinear dynamics, and linking my previous understanding of neurons to cognitive processes, something that I had not fully understood before. Because the review paper goes over the general information, I read many of the papers it cited to find the basis behind some of its claims. However, I still do not clearly understand the mechanism behind the changes in the attractor dynamics. I would like to learn more about how the parameters are changed, and how these changes, in turn, alter the attractor landscapes.

At this point, I believe that the connection between these dynamics and mental illnesses as presented in this paper seems rather speculative. However, I think that as more data is collected and analyzed, and further models are developed to understand the dynamics of neuronal networks, we can glean more insight towards understanding and developing treatments for mental illnesses.

References:

Durstewitz, D., Huys, Quentin J. M., Koppe, Georgia. (2018). Psychiatric Illnesses as Disorders of Network Dynamics. doi: https://arxiv.org/pdf/1809.06303.pdf

Durstewitz, D. (2009). Implications of synaptic biophysics for recurrent network dynamics and active memory. Neural Networks, 22(8), 1189-1200.

Durstewitz, D., Seamans, J. K. (2008). The dual-state theory of prefrontal cortex dopamine function with relevance to catechol-o-methyltransferase genotypes and schizophrenia. Biological Psychiatry, 64(9), 739-749.

Durstewitz, D. (2006). A few important points about dopamine’s role in neural network dynamics. Pharmacopsychiatry, 39(S 1), 72-75.

Izhikevich, E. M. (2007). Dynamical Systems in Neuroscience: MIT Press.

Johnston, Daniel, Wu, Samuel Miao-Sin . (2001) Foundations of Cellular Neurophysiology. MIT Press.

Rolls, E. T., Loh, M., Deco, G. (2008). An attractor hypothesis of obsessive-compulsive disorder. European Journal of Neuroscience, 28(4), 782-793. doi: 10.1111/j.1460-9568.2008.06379.x

Strogatz, S. H. (2018). Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering: CRC Press.

Introduction

I am a first-year grad student in California, and I decided to create this blog to document some of my experiences on this path working towards becoming a scientist. I would like to use this page as a record of some of my ideas in research, as well as some personal reflections about research, classes, teaching experiences, social experiences, and pursuing hobbies.

My department, Biomathematics, is a small basic science research department within the school of medicine. It focuses on theoretical, computational, and statistical modeling in biology and biomedicine. My research interests are in neuroscience, and the project I have been starting to work on this year focuses on applying tools from physics and applied mathematics to model neuronal networks.

I started college as a chemistry major, but after a while, I realized that while I loved the theoretical side of chemistry, experiments were very much not my strong suit. I changed my major to mathematics/applied science, which allowed me to take theoretical chemistry classes along with a set of courses in applied mathematics. I have always found myself interested in neuroscience, and in my last two years of undergrad, I worked in a research group that studied neurons and neuronal networks from the perspective of theoretical biophysics. There, I picked up a lot of skills in programming and applied mathematics. More than anything, I learned how to find the background information I need for a given task, which has been tremendously helpful transitioning into graduate school.

Aside from curiosity, my main motivation to study neuroscience comes from a desire to improve our understanding of the brain and mental health from a quantitative perspective. Mental health diagnoses are often based on self-reported qualitative data such as questionnaires, which are imprecise and very susceptible to bias. I believe that a greater understanding of the brain and cognitive processes from a theoretical perspective could not only better inform diagnosis and therapeutic intervention, but could reduce the stigma surrounding mental illness. Mental illnesses such as depression, anxiety, attention-deficit hyperactive disorder (ADHD), and obsessive-compulsive disorder (OCD) are often not taken as seriously as physical illness. As a result, many people suffer in silence and do not seek the treatment they need. A greater understanding of the mechanistic aspects of cognitive disorders is, I believe, a step towards recognizing the biological basis of mental illnesses and validating the health concerns of those affected. It motivates me to think about this as a long term goal, and that my studies in science are not only for my own benefit, but towards the benefit of society as a whole.

During my free time, I like finding content on the internet, in the form of blogs, art, and youtube videos. Since school is obviously a large part of my life, I like content about college and graduate school. I have found some content about life as a STEM student in graduate school, and I have felt a sense of inspiration and motivation from watching others working towards their research goals while simultaneously pursuing their hobbies. However, since my field, the interface between biology and mathematics, is relatively new, I rarely find content from students who are studying similar things that I can relate to. So I decided that if it doesn’t already exist, why not create it?

I believe it will be helpful for me to have a record of my progress in learning the material I need to know for my research, and writing things out in a pedagogical way would probably aid my own understanding of the things I’m learning. I also think that it will help me hold myself accountable, not only for my research progress, but also towards personal goals and hobbies, such as drawing and painting, swimming, dance, making new friends, and putting myself out there in the queer community.

It is likely that this blog will mostly be for my own record, and maybe some of my friends who might be interested in what I am doing. However, part of the reason I found it difficult to identify with other people in STEM is that I am often surrounded by peers who are very different from me. I have often benefitted from meeting other women, people of South Asian origin, and queer people in my field, and I know from my own experience how important representation is. I would love to know if anyone relates to any part of my experience, so please do not hesitate to contact me.

Here’s to a fruitful new year, and I am excited to begin this new journey.