Questions tagged [theoretical-biology]
Questions relating to biological theory or theoretical developments that deals with biological processes.
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How is the Allee effect modeled in the presence of a highly variable carrying capacity?
Consider a rather standard model of population dynamics in the presence of a strong Allee effect:
$$ \frac{du}{dt}=u\left(1-\frac{u}{K}\right)\left(\frac{u}{A}-1\right),$$
where $u(t)$ is population, $...
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Why do V_Na and V_K stay unchanged in Hodgkin-Huxley model?
In the Hodgkin-Huxley model, ionic current $i_\mathrm{Na}$ and $i_\mathrm{K}$ are given by
$$
i_\mathrm{Na}=g_\mathrm{Na}(V_\mathrm{m}-V_\mathrm{Na})\\
i_\mathrm{K}=g_\mathrm{K}(V_\mathrm{m}-V_\mathrm{...
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Linking models of spreading of infection to type of network describing the relationships of animals of a habitat
I am studying networks describing the relationships between animals in a habitat.There are many types of networks studied which are useful and we can approximate a real network to one of the studied ...
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Why is there a negative sign before voltage in the gate variable functions of the Hodgkin-Huxley model?
In Hodgkin and Huxley's articles (1952, J. Physiol.; 1990, Bulletin of Mathematical Biology), the gate variables are formulated as
In particular, as $V$ increases, $\alpha_n$ decreases and $\beta_n$ ...
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Reproduction number in SAIQR model
$$ \dot S (t)=\Lambda-\beta_1 S(t)A(t)-\beta_2S(t)I(t)-\mu S(t)$$
$$ \dot A (t)= \beta_1 S(t)A(t)+\beta_2S(t)I(t)-(\mu+\alpha) A(t)$$
$$ \dot I (t)=\alpha A(t)-(\mu+\theta)I(t)$$
$$ \dot Q (t)=\theta ...
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Understanding infection rate of a complex network
Suppose we have a complex network of people and the spread of a disease is modelled as a branching process (Diekmann et al. 1998)
The rate of infection of the complex network is:
$r = \tau(n-2)-g$
...
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Calculation for underlying genetic value of a phenotype given parents genetic values
What is the most accurate way to calculate a child's genetic predisposition to a phenotype, given both parents' genotypic predispositions?
Assume trait X is 50% heritable and controlled by an ...
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Biological reason for correlation of CD36 with S100A4 , S100A6
We are analysing single cell RNA+proteom (CITE-seq) data.
One of the things we see - quite stable correlation between CD36 (protein) and S100A4 , S100A6 (rna).
Question: Any ideas/comments what might ...
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Can the concept of fisherian runaway be explained using simple models?
I want to understand the concept of fisherian runaway. Dawkins' book tells about this, but it's not clear enough. It can be seen that the essence of Fisher's idea is that when a male peacock with a ...
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How can combusted methane from landfill samples be quantified? [closed]
Background:
For my studies I'm wanting and attempting to make a landfill greenhouse gas emissions (GHG) model that predicts the amount of greenhouse gas equivalent emissions ($GHG_{eq}$ [tonnes/year]) ...
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Mathematical aspects of the study of dinosaur locomotion
I'm interested in getting a better understanding of dinosaur locomotion. Therefore, I am looking for a book that will cover various mathematical aspects and discuss various mathematical tools for ...
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Questions about ChIP-seq reads and MACS
I had a few questions raised by the below diagram in relation to how ChIP-seq reads look like (source). I would be very grateful for your insight on them!
From the below diagram, it seems that, in a ...
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Cross correlation metric in ChIP-seq experiments
I found this explanation of cross-correlation metric in ChIP-seq.
Now, the definition of Pearson's correlation coefficient between two random variables $X$ and $Y$ is $$\rho_x = \frac{Cov(X,Y)}{\...
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How do you calculate the time until the steady-state of a drug?
I encountered a mathematically intriguing conundrum, in that it's related to medicine but is centered around mathematics.
Suppose drug A has a half-life in the body of 30 hours. The patient takes 40mg ...
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PCR: From transgene/microgram to cell concentration
I am doing research on CAR T-cell kinetics. The measurement of CAR T-cell concentrations across time is normally carried out with qPCR (see here, Fig. 1). These concentrations are generally reported ...
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What is the latest estimated probability for the self assembly of a primitive cell? [closed]
Peusner (Concepts in Bioenergetics, 1974) estimated the probability of the self-assembly of a primitive cell as $10^{-254}$. Given how much more we now know about cell biology, what is the latest ...
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Resources for understanding the basics of cell signaling, gene expression and cell fate determination, for a physics student?
I'm a physics student who will join a theoretical biology/applied mathematics research group this September. I'll link some papers at the end for further context.
The main problem I have is that my ...
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Finding population dynamics models for multi-generational species evolution with delays
I am working on a problem from economics, to understand how populations evolve within business organizations. I have found that some of the population dynamics literature is very relevant to my own ...
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Examples of bifurcations in real-life systems
Does period-doubling bifurcation and Neimark-Sacker bifurcation happen in real-life systems? Are there some examples? I'm particularly interested in biological host-parasitoid and predator-prey models....
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What could be a refuge in host-parasitoid models
I was reading about refuge effect in host-parasitoid models and I found somewhere that refuge does not have to be only a place in habitat where hosts can hide, but also some "situation" ...
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Ecosystem Control Theory
I've used EcoNet online tool to analyze an ecosystem. You can run the default model by pressing "run model" in order to follow my question.
Among the extended results there are 2 'Control ...
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Why don't viruses reach broad concentration outdoors in a city like allergens?
Why don't airborne viruses reach concentrations that infect most people vulnerable outdoors in a city the way an allergen can cause inflammation to everyone sensitive to it. Both are (often) ...
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How does genetic feedback shape the evolution of whole ecosystems?
While looking into the organization of ecosystems and how evolution shapes it, I've been reading "Ecology" (1975) by Eugene Odum. In chapter 6, p. 167, Odum speaks about the mutualistic ...
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Price Equation in Evolution
I am trying to solve for $\text{cov}(w_i,z_i)+E(w_i\Delta z_i)$ as it apears in Price Equations in terms of the mean $\overline{w}$ and variance $\sigma_{w}^2$ of the fitness of a population where I ...
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Difference between IC50 and Michaelis-Menten constant
I am new to biology, and getting to know the term IC50, I found that there is a connection between IC50 and Michaelis-Menten constant by the Cheng-Prusoff equation
$K_{i}=\frac{\mathrm{IC}_{50}}{1+\...
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What did Masatoshi Nei 1972 mean by "However, evolution does not occur so as to assure this property at least at the nucleotide level."?
In Nei 1972 he describes what is now called Nei's standard genetic distance. This math.SE post provides an exerpt to the definition of Nei's standard genetic distance. In this paper he states
In the ...
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Calculation of drug efficacy- mathematical biology approach
I am participating in a mathematical biology project.
I would like to discuss the following problem:
Let A be a drug such that $x_{o}$ chemical units of it kills 12% of $y$ cells per 1 day, I would ...
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How many cells does a single blood cell generally visit in its lifespan?
Taking the point of view of a single RBC travelling through blood vessels, approximately how many cells will it affect throughout its lifetime? As blood tends to provide O2 as a whole, I am taking &...
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Method of determining base values of traits in isolated populations
Prelude: I came across a discussion about the correct formula for calculating the average IQ of offspring, which goes something like the following
$$ 100 + \frac35 \left( \left(\text{father's IQ} + \...
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Which approach is the common one in the literature for determining the bacterial growth rate?
I have the following data, which is OD600 (the second component) vs. time (the first component):
...
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Genetic evolution without crossover
Can someone please point me to the origin of the system of coupled differential equations (1) in Section 2 of Shahshahani's book$^\star$?
$$ \dot{x}_i = x_i \sum_{j=1}^n m_{ij} \frac{x_j}{|x|} $$
...
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Can deterministic and stochastic models be used to models different parts of the same phenomenon?
A biological phenomenon including two different causally dependent phenomenon occurs in the cell. (Phenomenon2 initiates as a result of phenomenon1). Phenomenon1 and phenomenon2 are linked with ...
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Is there such a science in which the knowledge of biological processes (e.g., evolution) would be mathematically axiomatized and inferred (deduced)? [duplicate]
There is the following Mathematical Challenge Twenty-three
Mathematical Challenge Twenty-three: What are the Fundamental Laws of Biology?
* This question will remain front and center for the next 100 ...
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Difference between heritability on the scale of liability versus the scale of observation
I was reading a paper on disease heritability ("Estimating Missing Heritability for Disease from Genome-wide Association Studies") and it struck me that I don't have a great understanding of ...
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Understanding expected mean number of breeding seasons
I've recently come across an equation for the expected mean number of breeding seasons after the first breeding season, as a function of the annual survival rate (S) and the probability of breeding,
$$...
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What does it mean to quantitatively describe a cell?
To begin this question, I will quote Molecular Biology of the Cell (page 38):
... Biological systems are, ..., full of feedback loops, and the behavior of even the simplest of systems with feedback ...
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Interpreting replicator dynamic for simplest population model
Suppose the simplest population model where we track the size $y$ of a population:
$$\frac{dy}{dt} = ry$$
for a positive constant $r$ and some $y$ such that $y(0) > 0$.
For this population model ...
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Remarkable attempts of studying biological systems axiomatically
I am reading Anti-Tech Revolution by Theodore Kaczynski, in the second chapter the author talks about how technology will cause problems in society and before he begins the discussion, he introduces ...
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Understanding the paper "Why war is a man's game"
I have read this article
https://royalsocietypublishing.org/doi/10.1098/rspb.2018.0975
but I don't understand the mathematics which tries to explain why war is male-exclusive. In which branch of ...
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Is there any reliable data about the correlation between the size of a species and number of individuals that belong to it?
I'm curious to know if such a collection of data exists, so I could visualize it with a graph, and see how humans compare to other spieces of similar size.
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higher-order evolutionary adaptations
Most adaptations are what I'd call first-order. Cats evolve better eyesight; redwoods evolve to grow taller; male cardinals evolve attractive bright feathers. All of these changes were selected for ...
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References for historical momentum in asexual species definitions
For sexually reproducing organisms, the scope of a species is somewhat fixed by reproductive compatibility.
However, this all collapses for organisms that exclusively reproduce asexually.
Here, my ...
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Co-culture models of bacterial invasion: where to find them?
I am interested in models showing how pathogenic bacteria (namely Escherichia coli O157) can overcome commensal species (thus, causing a disease). This is a basic concept in biology but I can't find a ...
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Nonlinear (Quadratic) selection gradients formula
Under scenarios of stabilizing or disruptive selection, we can add a quadratic component to our model of phenotype and fitness like so.
Specifically, I am not clear on where the 1/2 comes from nor do ...
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Conservation Law in Gene Regulatory Network modelling
I was going through the GRN modelling from Chemical and enzyme kinetics
by D. Gonze & M. Kaufman (PDF). The gene has 2 sites for activator/repressor. It say the DNA $D_0$ combines with activator/...
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Mathematical/statistical models for forecasting population distributions of age, sex, weight, and height [closed]
I come from a mathematical background but I have no experience with the topic of mathematical biology.
Are there well established mathematical/statistical models for forecasting the evolution of ...
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Does parental conflict lead to genes combining important functions with functions only advantageous for one of the parents?
In a sitation of a mother-father conflict of interests, the mother might use epigenetics to turn off some genes only advantageous for the father's genes and not her own. I thought a logical father's ...
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How does the Endoplasmic Reticulum scale with Cell Volume in Epithelial Cells?
I am working on a mathematical model of a biological tissue (drosophila pupal notum; an epithelial tissue) where the tissue is built up from cells all described by the same cellular-model. The tissue ...
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Examples for oscillatory behaviour in the human body
I'm looking for examples in the human body which show periodicity, more precisely, I'm looking for examples of oscillating reactions that occur in the human body which can be modelled using the ...
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Can the fungal form of Malassezia morph into the fungal form of Candidia when feeling threatened? Resistance Mechanisms
Malassezia feeds on oils in the carbon chain 11-24 and Candida feeds on sugars. I recall learning that when these types of fungus feel they are under attack, they can morph. Does this mean they can ...
